# Ternary logic

Ternary logic
You are encouraged to solve this task according to the task description, using any language you may know.
 This page uses content from Wikipedia. The original article was at Ternary logic. The list of authors can be seen in the page history. As with Rosetta Code, the text of Wikipedia is available under the GNU FDL. (See links for details on variance)

In logic, a three-valued logic (also trivalent, ternary, or trinary logic, sometimes abbreviated 3VL) is any of several many-valued logic systems in which there are three truth values indicating true, false and some indeterminate third value.

This is contrasted with the more commonly known bivalent logics (such as classical sentential or boolean logic) which provide only for true and false.

Conceptual form and basic ideas were initially created by Łukasiewicz, Lewis and Sulski.

These were then re-formulated by Grigore Moisil in an axiomatic algebraic form, and also extended to n-valued logics in 1945.

Example Ternary Logic Operators in Truth Tables:
not a
¬
True False
Maybe Maybe
False True
 ∧ True Maybe False True True Maybe False Maybe Maybe Maybe False False False False False
 ∨ True Maybe False True True True True Maybe True Maybe Maybe False True Maybe False
 ⊃ True Maybe False True True Maybe False Maybe True Maybe Maybe False True True True
 ≡ True Maybe False True True Maybe False Maybe Maybe Maybe Maybe False False Maybe True

Task
• Define a new type that emulates ternary logic by storing data trits.
• Given all the binary logic operators of the original programming language, reimplement these operators for the new Ternary logic type trit.
• Generate a sampling of results using trit variables.
• Kudos for actually thinking up a test case algorithm where ternary logic is intrinsically useful, optimises the test case algorithm and is preferable to binary logic.

Note:   Setun   (Сетунь) was a   balanced ternary   computer developed in 1958 at   Moscow State University.   The device was built under the lead of   Sergei Sobolev   and   Nikolay Brusentsov.   It was the only modern   ternary computer,   using three-valued ternary logic

## Ada

We first specify a package "Logic" for three-valued logic. Observe that predefined Boolean functions, "and" "or" and "not" are overloaded:

`package Logic is   type Ternary is (True, Unknown, False);     -- logic functions   function "and"(Left, Right: Ternary) return Ternary;   function "or"(Left, Right: Ternary) return Ternary;   function "not"(T: Ternary) return Ternary;   function Equivalent(Left, Right: Ternary) return Ternary;   function Implies(Condition, Conclusion: Ternary) return Ternary;    -- conversion functions   function To_Bool(X: Ternary) return Boolean;   function To_Ternary(B: Boolean) return Ternary;   function Image(Value: Ternary) return Character;end Logic;`

Next, the implementation of the package:

`package body Logic is   -- type Ternary is (True, Unknown, False);    function Image(Value: Ternary) return Character is   begin      case Value is         when True    => return 'T';         when False   => return 'F';         when Unknown => return '?';      end case;   end Image;    function "and"(Left, Right: Ternary) return Ternary is   begin      return Ternary'max(Left, Right);   end "and";    function "or"(Left, Right: Ternary) return Ternary is   begin      return Ternary'min(Left, Right);   end "or";    function "not"(T: Ternary) return Ternary is   begin      case T is         when False   => return True;         when Unknown => return Unknown;         when True    => return False;      end case;   end "not";    function To_Bool(X: Ternary) return Boolean is   begin      case X is         when True  => return True;         when False => return False;         when Unknown => raise Constraint_Error;      end case;   end To_Bool;    function To_Ternary(B: Boolean) return Ternary is   begin      if B then         return True;      else         return False;      end if;   end To_Ternary;    function Equivalent(Left, Right: Ternary) return Ternary is   begin      return To_Ternary(To_Bool(Left) = To_Bool(Right));   exception      when Constraint_Error => return Unknown;   end Equivalent;    function Implies(Condition, Conclusion: Ternary) return Ternary is   begin      return (not Condition) or Conclusion;   end Implies; end Logic;`

Finally, a sample program:

`with Ada.Text_IO, Logic; procedure Test_Tri_Logic is    use Logic;    type F2 is access function(Left, Right: Ternary) return Ternary;   type F1 is access function(Trit: Ternary) return Ternary;    procedure Truth_Table(F: F1; Name: String) is   begin      Ada.Text_IO.Put_Line("X | " & Name & "(X)");      for T in Ternary loop         Ada.Text_IO.Put_Line(Image(T) & " |  " & Image(F(T)));      end loop;   end Truth_Table;    procedure Truth_Table(F: F2; Name: String) is   begin      Ada.Text_IO.New_Line;      Ada.Text_IO.Put_Line("X | Y | " & Name & "(X,Y)");      for X in Ternary loop         for Y in Ternary loop            Ada.Text_IO.Put_Line(Image(X) & " | " & Image(Y) & " |  " & Image(F(X,Y)));         end loop;      end loop;   end Truth_Table; begin   Truth_Table(F => "not"'Access, Name => "Not");   Truth_Table(F => "and"'Access, Name => "And");   Truth_Table(F => "or"'Access, Name => "Or");   Truth_Table(F => Equivalent'Access, Name => "Eq");   Truth_Table(F => Implies'Access, Name => "Implies");end Test_Tri_Logic;`
Output:
```X | Not(X)
T |  F
? |  ?
F |  T

X | Y | And(X,Y)
T | T |  T
T | ? |  ?
T | F |  F
? | T |  ?
? | ? |  ?
? | F |  F
F | T |  F
F | ? |  F
F | F |  F

... (and so on)```

## ALGOL 68

Works with: ALGOL 68 version Revision 1 - one minor extension to language used - PRAGMA READ, like C's #include directive.
Works with: ALGOL 68G version Any - tested with release 1.18.0-9h.tiny.

File: Ternary_logic.a68

`# -*- coding: utf-8 -*- # INT trit width = 1, trit base = 3;MODE TRIT = STRUCT(BITS trit);CO FORMAT trit fmt = \$c("?","⌈","⌊",#|"~"#)\$; CO # These values treated are as per "Balanced ternary" ## eg true=1, maybe=0, false=-1 #TRIT true =INITTRIT 4r1, maybe=INITTRIT 4r0,     false=INITTRIT 4r2; # Warning: redefines standard builtins flip & flop #LONGCHAR flap="?", flip="⌈", flop="⌊"; OP REPR = (TRIT t)LONGCHAR:  []LONGCHAR(flap, flip, flop)[1+ABS trit OF t]; ############################################# Define some OPerators for coercing MODES #############################################OP INITTRIT = (BOOL in)TRIT:  (in|true|false); OP INITBOOL = (TRIT in)BOOL:  (trit OF in=trit OF true|TRUE|:trit OF in=trit OF false|FALSE|    raise value error(("vague TRIT to BOOL coercion: """, REPR in,""""));~  );OP B = (TRIT in)BOOL: INITBOOL in; # These values treated are as per "Balanced ternary" ## n.b true=1, maybe=0, false=-1 ## Warning: BOOL ABS FALSE (0) is not the same as TRIT ABS false (-1) # OP INITINT = (TRIT t)INT:  CASE 1+ABS trit OF t  IN #maybe# 0, #true # 1, #false#-1  OUT raise value error(("invalid TRIT value",REPR t)); ~  ESAC; OP INITTRIT = (INT in)TRIT: (  TRIT out;  trit OF out:= trit OF    CASE 2+in    IN false, maybe, true    OUT raise value error(("invalid TRIT value",in)); ~    ESAC;  out); OP INITTRIT = (BITS b)TRIT:  (TRIT out; trit OF out:=b; out); ################################################### Define the LOGICAL OPerators for the TRIT MODE ###################################################MODE LOGICAL = TRIT;PR READ "Template_operators_logical_mixin.a68" PR COMMENT  Kleene logic truth tables:END COMMENT OP AND = (TRIT a,b)TRIT: (  [,]TRIT(    # ∧  ##  false, maybe, true  #    #false# (false, false, false),    #maybe# (false, maybe, maybe),    #true # (false, maybe, true )  )[@-1,@-1][INITINT a, INITINT b]); OP OR = (TRIT a,b)TRIT: (  [,]TRIT(    # ∨  ##  false, maybe, true #    #false# (false, maybe, true),    #maybe# (maybe, maybe, true),    #true # (true,  true,  true)  )[@-1,@-1][INITINT a, INITINT b]); PRIO IMPLIES = 1; # PRIO = 1.9 #OP IMPLIES = (TRIT a,b)TRIT: (  [,]TRIT(    # ⊃   ## false, maybe, true #    #false# (true,  true,  true),    #maybe# (maybe, maybe, true),    #true # (false, maybe, true)  )[@-1,@-1][INITINT a, INITINT b]); PRIO EQV = 1; # PRIO = 1.8 #OP EQV = (TRIT a,b)TRIT: (  [,]TRIT(    # ≡   ## false, maybe, true #    #false# (true,  maybe, false),    #maybe# (maybe, maybe, maybe),    #true # (false, maybe, true )  )[@-1,@-1][INITINT a, INITINT b]);`
File: Template_operators_logical_mixin.a68
`# -*- coding: utf-8 -*- # OP & = (LOGICAL a,b)LOGICAL: a AND b;CO # not included as they are treated as SCALAR #OP EQ = (LOGICAL a,b)LOGICAL: a = b,   NE = (LOGICAL a,b)LOGICAL: a /= b,   ≠ = (TRIT a,b)TRIT: a /= b,   ¬= = (TRIT a,b)TRIT: a /= b;END CO #IF html entities possible THEN¢ "parked" operators for completeness ¢OP ¬ = (LOGICAL a)LOGICAL: NOT a,   ∧  = (LOGICAL a,b)LOGICAL: a AND b,   /\ = (LOGICAL a,b)LOGICAL: a AND b,   ∨  = (LOGICAL a,b)LOGICAL: a OR b,   \/ = (LOGICAL a,b)LOGICAL: a OR b,   ⊃ = (TRIT a,b)TRIT: a IMPLIES b,   ≡ = (TRIT a,b)TRIT: a EQV b;FI# #IF algol68c THENOP ~ = (LOGICAL a)LOGICAL: NOT a,   ~= = (LOGICAL a,b)LOGICAL: a /= b; SCALAR!FI#`
File: test_Ternary_logic.a68
`#!/usr/local/bin/a68g --script ## -*- coding: utf-8 -*- # PR READ "prelude/general.a68" PRPR READ "Ternary_logic.a68" PR []TRIT trits = (false, maybe, true); FORMAT   col fmt = \$" "g" "\$,  row fmt = \$l3(f(col fmt)"|")f(col fmt)\$,  row sep fmt = \$l3("---+")"---"l\$; PROC row sep = VOID:  printf(row sep fmt); PROC title = (STRING op name, LONGCHAR op char)VOID:(  print(("Operator: ",op name));  printf((row fmt,op char,REPR false, REPR maybe, REPR true))); PROC print trit op table = (LONGCHAR op char, STRING op name, PROC(TRIT,TRIT)TRIT op)VOID: (  printf(\$l\$);  title(op name, op char);  FOR i FROM LWB trits TO UPB trits DO    row sep;    TRIT ti = trits[i];    printf((col fmt, REPR ti));    FOR j FROM LWB trits TO UPB trits DO      TRIT tj = trits[j];      printf((\$"|"\$, col fmt, REPR op(ti,tj)))    OD  OD;  printf(\$l\$)); printf((  \$"Comparitive table of coercions:"l\$,  \$"  TRIT BOOL         INT"l\$)); FOR it FROM LWB trits TO UPB trits DO  TRIT t = trits[it];  printf(( \$"  "g"  "\$, REPR t,     IF trit OF t = trit OF maybe THEN " " ELSE B t FI,    INITINT t, \$l\$))OD; printf((  \$l"Specific test of the IMPLIES operator:"l\$,  \$"  "g" implies "g" is "b("not ","")"a contradiction!"l\$,    B false,    B false,    B(false IMPLIES false),    B false,    B true,     B(false IMPLIES true),    B false,    REPR maybe, B(false IMPLIES maybe),    B true,     B false,    B(true  IMPLIES false),    B true,     B true,     B(true  IMPLIES true),    REPR maybe, Btrue,      B(maybe IMPLIES true),  \$"  "g" implies "g" is "g" a contradiction!"l\$,    B true,     REPR maybe, REPR (true  IMPLIES maybe),    REPR maybe, B false,    REPR (maybe IMPLIES false),    REPR maybe, REPR maybe, REPR (maybe IMPLIES maybe),  \$l\$)); printf(\$"Kleene logic truth table samples:"l\$); print trit op table("≡","EQV",     (TRIT a,b)TRIT: a EQV b);print trit op table("⊃","IMPLIES", (TRIT a,b)TRIT: a IMPLIES b);print trit op table("∧","AND",     (TRIT a,b)TRIT: a AND b);print trit op table("∨","OR",      (TRIT a,b)TRIT: a OR b)`
Output:
```Comparitive table of coercions:
TRIT BOOL         INT
⌊    F             -1
?                  +0
⌈    T             +1

Specific test of the IMPLIES operator:
F implies F is not a contradiction!
F implies T is not a contradiction!
F implies ? is not a contradiction!
T implies F is a contradiction!
T implies T is not a contradiction!
? implies T is not a contradiction!
T implies ? is ? a contradiction!
? implies F is ? a contradiction!
? implies ? is ? a contradiction!

Kleene logic truth table samples:

Operator: EQV
≡ | ⌊ | ? | ⌈
---+---+---+---
⌊ | ⌈ | ? | ⌊
---+---+---+---
? | ? | ? | ?
---+---+---+---
⌈ | ⌊ | ? | ⌈

Operator: IMPLIES
⊃ | ⌊ | ? | ⌈
---+---+---+---
⌊ | ⌈ | ⌈ | ⌈
---+---+---+---
? | ? | ? | ⌈
---+---+---+---
⌈ | ⌊ | ? | ⌈

Operator: AND
∧ | ⌊ | ? | ⌈
---+---+---+---
⌊ | ⌊ | ⌊ | ⌊
---+---+---+---
? | ⌊ | ? | ?
---+---+---+---
⌈ | ⌊ | ? | ⌈

Operator: OR
∨ | ⌊ | ? | ⌈
---+---+---+---
⌊ | ⌊ | ? | ⌈
---+---+---+---
? | ? | ? | ⌈
---+---+---+---
⌈ | ⌈ | ⌈ | ⌈
```

## AutoHotkey

`Ternary_Not(a){	SetFormat, Float, 2.1	return Abs(a-1)} Ternary_And(a,b){	return a<b?a:b} Ternary_Or(a,b){	return a>b?a:b} Ternary_IfThen(a,b){	return a=1?b:a=0?1:a+b>1?1:0.5} Ternary_Equiv(a,b){	return a=b?1:a=1?b:b=1?a:0.5}`
Examples:
`aa:=[1,0.5,0]bb:=[1,0.5,0] for index, a in aa	Res .= "`tTernary_Not`t" a "`t=`t" Ternary_Not(a) "`n"Res .= "-------------`n" for index, a in aa	for index, b in bb		Res .= a "`tTernary_And`t" b "`t=`t" Ternary_And(a,b) "`n"Res .= "-------------`n" for index, a in aa	for index, b in bb		Res .= a "`tTernary_or`t" b "`t=`t" Ternary_Or(a,b) "`n"Res .= "-------------`n" for index, a in aa	for index, b in bb		Res .= a "`tTernary_then`t" b "`t=`t" Ternary_IfThen(a,b) "`n"Res .= "-------------`n" for index, a in aa	for index, b in bb		Res .= a "`tTernary_equiv`t" b "`t=`t" Ternary_Equiv(a,b) "`n" StringReplace, Res, Res, 1, true, allStringReplace, Res, Res, 0.5, maybe, allStringReplace, Res, Res, 0, false, allMsgBox % Resreturn`
Output:
```	Ternary_Not	true	=	false
Ternary_Not	maybe	=	maybe
Ternary_Not	false	=	true
-------------
true	Ternary_And	true	=	true
true	Ternary_And	maybe	=	maybe
true	Ternary_And	false	=	false
maybe	Ternary_And	true	=	maybe
maybe	Ternary_And	maybe	=	maybe
maybe	Ternary_And	false	=	false
false	Ternary_And	true	=	false
false	Ternary_And	maybe	=	false
false	Ternary_And	false	=	false
-------------
true	Ternary_or	true	=	true
true	Ternary_or	maybe	=	true
true	Ternary_or	false	=	true
maybe	Ternary_or	true	=	true
maybe	Ternary_or	maybe	=	maybe
maybe	Ternary_or	false	=	maybe
false	Ternary_or	true	=	true
false	Ternary_or	maybe	=	maybe
false	Ternary_or	false	=	false
-------------
true	Ternary_then	true	=	true
true	Ternary_then	maybe	=	maybe
true	Ternary_then	false	=	false
maybe	Ternary_then	true	=	true
maybe	Ternary_then	maybe	=	maybe
maybe	Ternary_then	false	=	maybe
false	Ternary_then	true	=	true
false	Ternary_then	maybe	=	true
false	Ternary_then	false	=	true
-------------
true	Ternary_equiv	true	=	true
true	Ternary_equiv	maybe	=	maybe
true	Ternary_equiv	false	=	false
maybe	Ternary_equiv	true	=	maybe
maybe	Ternary_equiv	maybe	=	true
maybe	Ternary_equiv	false	=	maybe
false	Ternary_equiv	true	=	false
false	Ternary_equiv	maybe	=	maybe
false	Ternary_equiv	false	=	true```

## BBC BASIC

`      INSTALL @lib\$ + "CLASSLIB"       REM Create a ternary class:      DIM trit{tor, tand, teqv, tnot, tnor, s, v}      DEF PRIVATE trit.s (t&) LOCAL t\$():DIM t\$(2):t\$()="FALSE","MAYBE","TRUE":=t\$(t&)      DEF PRIVATE trit.v (t\$) = INSTR("FALSE MAYBE TRUE", t\$) DIV 6      DEF trit.tnot (t\$) = FN(trit.s)(2 - FN(trit.v)(t\$))      DEF trit.tor (a\$,b\$) LOCAL t:t=FN(trit.v)(a\$)ORFN(trit.v)(b\$):=FN(trit.s)(t+(t>2))      DEF trit.tnor (a\$,b\$) = FN(trit.tnot)(FN(trit.tor)(a\$,b\$))      DEF trit.tand (a\$,b\$) = FN(trit.tnor)(FN(trit.tnot)(a\$),FN(trit.tnot)(b\$))      DEF trit.teqv (a\$,b\$) = FN(trit.tor)(FN(trit.tand)(a\$,b\$),FN(trit.tnor)(a\$,b\$))      PROC_class(trit{})       PROC_new(mytrit{}, trit{})       REM Test it:      PRINT "Testing NOT:"      PRINT "NOT FALSE = " FN(mytrit.tnot)("FALSE")      PRINT "NOT MAYBE = " FN(mytrit.tnot)("MAYBE")      PRINT "NOT TRUE  = " FN(mytrit.tnot)("TRUE")       PRINT '"Testing OR:"      PRINT "FALSE OR FALSE = " FN(mytrit.tor)("FALSE","FALSE")      PRINT "FALSE OR MAYBE = " FN(mytrit.tor)("FALSE","MAYBE")      PRINT "FALSE OR TRUE  = " FN(mytrit.tor)("FALSE","TRUE")      PRINT "MAYBE OR MAYBE = " FN(mytrit.tor)("MAYBE","MAYBE")      PRINT "MAYBE OR TRUE  = " FN(mytrit.tor)("MAYBE","TRUE")      PRINT "TRUE  OR TRUE  = " FN(mytrit.tor)("TRUE","TRUE")       PRINT '"Testing AND:"      PRINT "FALSE AND FALSE = " FN(mytrit.tand)("FALSE","FALSE")      PRINT "FALSE AND MAYBE = " FN(mytrit.tand)("FALSE","MAYBE")      PRINT "FALSE AND TRUE  = " FN(mytrit.tand)("FALSE","TRUE")      PRINT "MAYBE AND MAYBE = " FN(mytrit.tand)("MAYBE","MAYBE")      PRINT "MAYBE AND TRUE  = " FN(mytrit.tand)("MAYBE","TRUE")      PRINT "TRUE  AND TRUE  = " FN(mytrit.tand)("TRUE","TRUE")       PRINT '"Testing EQV (similar to EOR):"      PRINT "FALSE EQV FALSE = " FN(mytrit.teqv)("FALSE","FALSE")      PRINT "FALSE EQV MAYBE = " FN(mytrit.teqv)("FALSE","MAYBE")      PRINT "FALSE EQV TRUE  = " FN(mytrit.teqv)("FALSE","TRUE")      PRINT "MAYBE EQV MAYBE = " FN(mytrit.teqv)("MAYBE","MAYBE")      PRINT "MAYBE EQV TRUE  = " FN(mytrit.teqv)("MAYBE","TRUE")      PRINT "TRUE  EQV TRUE  = " FN(mytrit.teqv)("TRUE","TRUE")       PROC_discard(mytrit{})`
Output:
```Testing NOT:
NOT FALSE = TRUE
NOT MAYBE = MAYBE
NOT TRUE  = FALSE

Testing OR:
FALSE OR FALSE = FALSE
FALSE OR MAYBE = MAYBE
FALSE OR TRUE  = TRUE
MAYBE OR MAYBE = MAYBE
MAYBE OR TRUE  = TRUE
TRUE  OR TRUE  = TRUE

Testing AND:
FALSE AND FALSE = FALSE
FALSE AND MAYBE = FALSE
FALSE AND TRUE  = FALSE
MAYBE AND MAYBE = MAYBE
MAYBE AND TRUE  = MAYBE
TRUE  AND TRUE  = TRUE

Testing EQV (similar to EOR):
FALSE EQV FALSE = TRUE
FALSE EQV MAYBE = MAYBE
FALSE EQV TRUE  = FALSE
MAYBE EQV MAYBE = MAYBE
MAYBE EQV TRUE  = MAYBE
TRUE  EQV TRUE  = TRUE
```

## C

### Implementing logic using lookup tables

`#include <stdio.h> typedef enum {  TRITTRUE,  /* In this enum, equivalent to integer value 0 */  TRITMAYBE, /* In this enum, equivalent to integer value 1 */  TRITFALSE  /* In this enum, equivalent to integer value 2 */} trit; /* We can trivially find the result of the operation by passing   the trinary values as indeces into the lookup tables' arrays. */trit tritNot = {TRITFALSE , TRITMAYBE, TRITTRUE};trit tritAnd = { {TRITTRUE, TRITMAYBE, TRITFALSE},                       {TRITMAYBE, TRITMAYBE, TRITFALSE},                       {TRITFALSE, TRITFALSE, TRITFALSE} }; trit tritOr = { {TRITTRUE, TRITTRUE, TRITTRUE},                      {TRITTRUE, TRITMAYBE, TRITMAYBE},                      {TRITTRUE, TRITMAYBE, TRITFALSE} }; trit tritThen = { { TRITTRUE, TRITMAYBE, TRITFALSE},                        { TRITTRUE, TRITMAYBE, TRITMAYBE},                        { TRITTRUE, TRITTRUE, TRITTRUE } }; trit tritEquiv = { { TRITTRUE, TRITMAYBE, TRITFALSE},                         { TRITMAYBE, TRITMAYBE, TRITMAYBE},                         { TRITFALSE, TRITMAYBE, TRITTRUE } }; /* Everything beyond here is just demonstration */ const char* tritString = {"T", "?", "F"}; void demo_binary_op(trit operator, const char* name){  trit operand1 = TRITTRUE; /* Declare. Initialize for CYA */  trit operand2 = TRITTRUE; /* Declare. Initialize for CYA */   /* Blank line */  printf("\n");   /* Demo this operator */  for( operand1 = TRITTRUE; operand1 <= TRITFALSE; ++operand1 )  {    for( operand2 = TRITTRUE; operand2 <= TRITFALSE; ++operand2 )    {      printf("%s %s %s: %s\n", tritString[operand1],                               name,                               tritString[operand2],                               tritString[operator[operand1][operand2]]);    }  } } int main(){  trit op1 = TRITTRUE; /* Declare. Initialize for CYA */  trit op2 = TRITTRUE; /* Declare. Initialize for CYA */   /* Demo 'not' */  for( op1 = TRITTRUE; op1 <= TRITFALSE; ++op1 )  {    printf("Not %s: %s\n", tritString[op1], tritString[tritNot[op1]]);  }  demo_binary_op(tritAnd, "And");  demo_binary_op(tritOr, "Or");  demo_binary_op(tritThen, "Then");  demo_binary_op(tritEquiv, "Equiv");    return 0;}`
Output:
```Not T: F
Not ?: ?
Not F: T

T And T: T
T And ?: ?
T And F: F
? And T: ?
? And ?: ?
? And F: F
F And T: F
F And ?: F
F And F: F

T Or T: T
T Or ?: T
T Or F: T
? Or T: T
? Or ?: ?
? Or F: ?
F Or T: T
F Or ?: ?
F Or F: F

T Then T: T
T Then ?: ?
T Then F: F
? Then T: T
? Then ?: ?
? Then F: ?
F Then T: T
F Then ?: T
F Then F: T

T Equiv T: T
T Equiv ?: ?
T Equiv F: F
? Equiv T: ?
? Equiv ?: ?
? Equiv F: ?
F Equiv T: F
F Equiv ?: ?
F Equiv F: T```

### Using functions

`#include <stdio.h> typedef enum { t_F = -1, t_M, t_T } trit; trit t_not  (trit a) { return -a; }trit t_and  (trit a, trit b) { return a < b ? a : b; }trit t_or   (trit a, trit b) { return a > b ? a : b; }trit t_eq   (trit a, trit b) { return a * b; }trit t_imply(trit a, trit b) { return -a > b ? -a : b; }char t_s(trit a) { return "F?T"[a + 1]; } #define forall(a) for(a = t_F; a <= t_T; a++)void show_op(trit (*f)(trit, trit), const char *name) {	trit a, b;	printf("\n[%s]\n    F ? T\n  -------", name);	forall(a) {		printf("\n%c |", t_s(a));		forall(b) printf(" %c", t_s(f(a, b)));	}	puts("");} int main(void){	trit a; 	puts("[Not]");	forall(a) printf("%c | %c\n", t_s(a), t_s(t_not(a))); 	show_op(t_and,   "And");	show_op(t_or,    "Or");	show_op(t_eq,    "Equiv");	show_op(t_imply, "Imply"); 	return 0;}`
Output:
```[Not]
F | T
? | ?
T | F

[And]
F ? T
-------
F | F F F
? | F ? ?
T | F ? T

[Or]
F ? T
-------
F | F ? T
? | ? ? T
T | T T T

[Equiv]
F ? T
-------
F | T ? F
? | ? ? ?
T | F ? T

[Imply]
F ? T
-------
F | T T T
? | ? ? T
T | F ? T```

### Variable truthfulness

Represent each possible truth value as a floating point value x, where the var has x chance of being true and 1 - x chance of being false. When using `if3` conditional on a potential truth varible, the result is randomly sampled to true or false according to the chance. (This description is definitely very confusing perhaps).

`#include <stdio.h>#include <stdlib.h> typedef double half_truth, maybe; inline maybe not3(maybe a) { return 1 - a; } inline maybeand3(maybe a, maybe b) { return a * b; } inline maybeor3(maybe a, maybe b) { return a + b - a * b; } inline maybeeq3(maybe a, maybe b) { return 1 - a - b + 2 * a * b; } inline maybeimply3(maybe a, maybe b) { return or3(not3(a), b); } #define true3(x) ((x) * RAND_MAX > rand())#define if3(x) if (true3(x)) int main(){	maybe roses_are_red = 0.25; /* they can be white or black, too */	maybe violets_are_blue = 1; /* aren't they just */	int i; 	puts("Verifying flowery truth for 40 times:\n"); 	puts("Rose is NOT red:"); /* chance: .75 */	for (i = 0; i < 40 || !puts("\n"); i++)		printf( true3( not3(roses_are_red) ) ? "T" : "_"); 	/* pick a rose and a violet; */	puts("Rose is red AND violet is blue:");	/* chance of rose being red AND violet being blue is .25 */	for (i = 0; i < 40 || !puts("\n"); i++)		printf( true3( and3(roses_are_red, violets_are_blue) )			? "T" : "_"); 	/* chance of rose being red OR violet being blue is 1 */	puts("Rose is red OR violet is blue:");	for (i = 0; i < 40 || !puts("\n"); i++)		printf( true3( or3(roses_are_red, violets_are_blue) )			? "T" : "_"); 	/* pick two roses; chance of em being both red or both not red is .625 */	puts("This rose is as red as that rose:");	for (i = 0; i < 40 || !puts("\n"); i++)		if3(eq3(roses_are_red, roses_are_red)) putchar('T');		else putchar('_'); 	return 0;}`

## C++

Essentially the same logic as the Using functions implementation above, but using class-based encapsulation and overridden operators.

`#include <iostream>#include <stdlib.h> class trit {public:    static const trit False, Maybe, True;     trit operator !() const {        return static_cast<Value>(-value);    }     trit operator &&(const trit &b) const {        return (value < b.value) ? value : b.value;    }     trit operator ||(const trit &b) const {        return (value > b.value) ? value : b.value;    }     trit operator >>(const trit &b) const {        return -value > b.value ? static_cast<Value>(-value) : b.value;    }     trit operator ==(const trit &b) const {        return static_cast<Value>(value * b.value);    }     char chr() const {        return "F?T"[value + 1];    } protected:    typedef enum { FALSE=-1, MAYBE, TRUE } Value;     Value value;     trit(const Value value) : value(value) { }}; std::ostream& operator<<(std::ostream &os, const trit &t){    os << t.chr();    return os;} const trit trit::False = trit(trit::FALSE);const trit trit::Maybe = trit(trit::MAYBE);const trit trit::True = trit(trit::TRUE); int main(int, char**) {    const trit trits = { trit::True, trit::Maybe, trit::False }; #define for_each(name) \    for (size_t name=0; name<3; ++name) #define show_op(op) \    std::cout << std::endl << #op << " "; \    for_each(a) std::cout << ' ' << trits[a]; \    std::cout << std::endl << "  -------"; \    for_each(a) { \        std::cout << std::endl << trits[a] << " |"; \        for_each(b) std::cout << ' ' << (trits[a] op trits[b]); \    } \    std::cout << std::endl;     std::cout << "! ----" << std::endl;    for_each(a) std::cout << trits[a] << " | " << !trits[a] << std::endl;     show_op(&&);    show_op(||);    show_op(>>);    show_op(==);    return EXIT_SUCCESS;}`
Output:
```! ----
T | F
? | ?
F | T

&&  T ? F
-------
T | T ? F
? | ? ? F
F | F F F

||  T ? F
-------
T | T T T
? | T ? ?
F | T ? F

>>  T ? F
-------
T | T ? F
? | T ? ?
F | T T T

==  T ? F
-------
T | T ? F
? | ? ? ?
F | F ? T```

## C#

`using System; /// <summary>/// Extension methods on nullable bool./// </summary>/// <remarks>/// The operators !, & and | are predefined./// </remarks>public static class NullableBoolExtension{    public static bool? Implies(this bool? left, bool? right)    {        return !left | right;    }     public static bool? IsEquivalentTo(this bool? left, bool? right)    {        return left.HasValue && right.HasValue ? left == right : default(bool?);    }     public static string Format(this bool? value)    {        return value.HasValue ? value.Value.ToString() : "Maybe";    }} public class Program{    private static void Main()    {        var values = new[] { true, default(bool?), false };         foreach (var left in values)        {            Console.WriteLine("¬{0} = {1}", left.Format(), (!left).Format());            foreach (var right in values)            {                Console.WriteLine("{0} & {1} = {2}", left.Format(), right.Format(), (left & right).Format());                Console.WriteLine("{0} | {1} = {2}", left.Format(), right.Format(), (left | right).Format());                Console.WriteLine("{0} → {1} = {2}", left.Format(), right.Format(), left.Implies(right).Format());                Console.WriteLine("{0} ≡ {1} = {2}", left.Format(), right.Format(), left.IsEquivalentTo(right).Format());            }        }    }}`
Output:
```¬True = False
True & True = True
True | True = True
True → True = True
True ≡ True = True
True & Maybe = Maybe
True | Maybe = True
True → Maybe = Maybe
True ≡ Maybe = Maybe
True & False = False
True | False = True
True → False = False
True ≡ False = False
¬Maybe = Maybe
Maybe & True = Maybe
Maybe | True = True
Maybe → True = True
Maybe ≡ True = Maybe
Maybe & Maybe = Maybe
Maybe | Maybe = Maybe
Maybe → Maybe = Maybe
Maybe ≡ Maybe = Maybe
Maybe & False = False
Maybe | False = Maybe
Maybe → False = Maybe
Maybe ≡ False = Maybe
¬False = True
False & True = False
False | True = True
False → True = True
False ≡ True = False
False & Maybe = False
False | Maybe = Maybe
False → Maybe = True
False ≡ Maybe = Maybe
False & False = False
False | False = False
False → False = True
False ≡ False = True```

## Common Lisp

`(defun tri-not (x) (- 1 x))(defun tri-and (&rest x) (apply #'* x))(defun tri-or (&rest x) (tri-not (apply #'* (mapcar #'tri-not x))))(defun tri-eq (x y) (+ (tri-and x y) (tri-and (- 1 x) (- 1 y))))(defun tri-imply (x y) (tri-or (tri-not x) y)) (defun tri-test (x) (< (random 1e0) x))(defun tri-string (x) (if (= x 1) "T" (if (= x 0) "F" "?"))) ;; to say (tri-if (condition) (yes) (no))(defmacro tri-if (tri ifcase &optional elsecase)  `(if (tri-test ,tri) ,ifcase ,elsecase)) (defun print-table (func header)  (let ((vals '(1 .5 0)))    (format t "~%~a:~%" header)    (format t "    ~{~a ~^~}~%---------~%" (mapcar #'tri-string vals))    (loop for row in vals do	  (format t "~a | " (tri-string row))	  (loop for col in vals do		(format t "~a " (tri-string (funcall func row col))))	  (write-line "")))) (write-line "NOT:")(loop for row in '(1 .5 0) do      (format t "~a | ~a~%" (tri-string row) (tri-string (tri-not row)))) (print-table #'tri-and   "AND")(print-table #'tri-or    "OR")(print-table #'tri-imply "IMPLY")(print-table #'tri-eq    "EQUAL")`
Output:
```NOT:
T | F
? | ?
F | T

AND:
T ? F
---------
T | T ? F
? | ? ? F
F | F F F

OR:
T ? F
---------
T | T T T
? | T ? ?
F | T ? F

IMPLY:
T ? F
---------
T | T ? F
? | T ? ?
F | T T T

EQUAL:
T ? F
---------
T | T ? F
? | ? ? ?
F | F ? T```

## D

Partial translation of a C entry:

`import std.stdio; struct Trit {    private enum Val : byte { F = -1, M, T }    private Val t;    alias t this;    static immutable Trit vals = [{Val.F}, {Val.M}, {Val.T}];    static immutable F = Trit(Val.F); // Not necessary but handy.    static immutable M = Trit(Val.M);    static immutable T = Trit(Val.T);     string toString() const pure nothrow {        return "F?T"[t + 1  .. t + 2];    }     Trit opUnary(string op)() const pure nothrow    if (op == "~") {        return Trit(-t);    }     Trit opBinary(string op)(in Trit b) const pure nothrow    if (op == "&") {        return t < b ? this : b;    }     Trit opBinary(string op)(in Trit b) const pure nothrow    if (op == "|") {        return t > b ? this : b;    }     Trit opBinary(string op)(in Trit b) const pure nothrow    if (op == "^") {        return ~(this == b);    }     Trit opEquals(in Trit b) const pure nothrow {        return Trit(cast(Val)(t * b));    }     Trit imply(in Trit b) const pure nothrow {        return -t > b ? ~this : b;    }} void showOperation(string op)(in string opName) {    writef("\n[%s]\n    F ? T\n  -------", opName);    foreach (immutable a; Trit.vals) {        writef("\n%s |", a);        foreach (immutable b; Trit.vals)            static if (op == "==>")                writef(" %s", a.imply(b));            else                writef(" %s", mixin("a " ~ op ~ " b"));    }    writeln();} void main() {    writeln("[Not]");    foreach (const a; Trit.vals)        writefln("%s | %s", a, ~a);     showOperation!"&"("And");    showOperation!"|"("Or");    showOperation!"^"("Xor");    showOperation!"=="("Equiv");    showOperation!"==>"("Imply");}`
Output:
```[Not]
F | T
? | ?
T | F

[And]
F ? T
-------
F | F F F
? | F ? ?
T | F ? T

[Or]
F ? T
-------
F | F ? T
? | ? ? T
T | T T T

[Xor]
F ? T
-------
F | F ? T
? | ? ? ?
T | T ? F

[Equiv]
F ? T
-------
F | T ? F
? | ? ? ?
T | F ? T

[Imply]
F ? T
-------
F | T T T
? | ? ? T
T | F ? T```

## Delphi

`unit TrinaryLogic; interface //Define our own type for ternary logic.//This is actually still a Boolean, but the compiler will use distinct RTTI information.type    TriBool = type Boolean; const    TTrue:TriBool = True;    TFalse:TriBool = False;    TMaybe:TriBool = TriBool(2); function TVL_not(Value: TriBool): TriBool;function TVL_and(A, B: TriBool): TriBool;function TVL_or(A, B: TriBool): TriBool;function TVL_xor(A, B: TriBool): TriBool;function TVL_eq(A, B: TriBool): TriBool; implementation Uses    SysUtils; function TVL_not(Value: TriBool): TriBool;begin    if Value = True Then        Result := TFalse    else If Value = False Then        Result := TTrue    else        Result := Value;end; function TVL_and(A, B: TriBool): TriBool;begin    Result := TriBool(Iff(Integer(A * B) > 1, Integer(TMaybe), A * B));end; function TVL_or(A, B: TriBool): TriBool;begin    Result := TVL_not(TVL_and(TVL_not(A), TVL_not(B)));end; function TVL_xor(A, B: TriBool): TriBool;begin    Result := TVL_and(TVL_or(A, B), TVL_not(TVL_or(A, B)));end; function TVL_eq(A, B: TriBool): TriBool;begin    Result := TVL_not(TVL_xor(A, B));end; end.`

And that's the reason why you never on no account ever should compare against the values of True or False unless you intent ternary logic!

An alternative version would be using an enum type

`type TriBool = (tbFalse, tbMaybe, tbTrue);`

and defining a set of constants implementing the above tables:

`const    tvl_not: array[TriBool] = (tbTrue, tbMaybe, tbFalse);    tvl_and: array[TriBool, TriBool] = (        (tbFalse, tbFalse, tbFalse),        (tbFalse, tbMaybe, tbMaybe),        (tbFalse, tbMaybe, tbTrue),        );    tvl_or: array[TriBool, TriBool] = (        (tbFalse, tbMaybe, tbTrue),        (tbMaybe, tbMaybe, tbTrue),        (tbTrue, tbTrue, tbTrue),        );    tvl_xor: array[TriBool, TriBool] = (        (tbFalse, tbMaybe, tbTrue),        (tbMaybe, tbMaybe, tbMaybe),        (tbTrue, tbMaybe, tbFalse),        );    tvl_eq: array[TriBool, TriBool] = (        (tbTrue, tbMaybe, tbFalse),        (tbMaybe, tbMaybe, tbMaybe),        (tbFalse, tbMaybe, tbTrue),        ); `

That's no real fun, but lookup can then be done with

`Result := tvl_and[A, B];`

## Elena

ELENA 4.x :

`import extensions;import system'routines;import system'collections; sealed class Trit{    bool _value;     bool cast() = _value;     constructor(v)    {        if (v != nil)        {            _value := cast bool(v);        }            }     Trit equivalent(b)        = _value.equal(cast bool(b)) \ back:nilValue;     Trit Inverted        = _value.Inverted \ back:nilValue;     Trit and(b)    {        if (nil == _value)        {            ^ b.and:nil \ back:nilValue        }        else        {            ^ _value.and(lazy::(cast bool(b))) \ back:nilValue        }    }     Trit or(b)    {        if (nil == _value)        {            ^ b.or:nilValue \ back:nilValue        }        else        {            ^ _value.or(lazy::(cast bool(b))) \ back:nilValue        }    }     Trit implies(b)        = self.Inverted.or(b);     string Printable = _value.Printable \ back:"maybe";} public program(){    List<Trit> values := new Trit[]{true, nilValue, false};    values.forEach:(left)    {        console.printLine("¬",left," = ", left.Inverted);        values.forEach:(right)        {            console.printLine(left, " & ", right, " = ", left && right);            console.printLine(left, " | ", right, " = ", left || right);            console.printLine(left, " → ", right, " = ", left.implies:right);            console.printLine(left, " ≡ ", right, " = ", left.equivalent:right)        }    }}`
Output:
```¬ true = false
true & true = true
true | true = true
true →  true = true
true ≡  true = true
true & maybe = maybe
true | maybe = true
true →  maybe = maybe
true ≡  maybe = maybe
true & false = false
true | false = true
true →  false = false
true ≡  false = false
¬ maybe = maybe
maybe & true = maybe
maybe | true = true
maybe →  true = true
maybe ≡  true = maybe
maybe & maybe = maybe
maybe | maybe = maybe
maybe →  maybe = maybe
maybe ≡  maybe = maybe
maybe & false = false
maybe | false = maybe
maybe →  false = maybe
maybe ≡  false = maybe
¬ false = true
false & true = false
false | true = true
false →  true = true
false ≡  true = false
false & maybe = false
false | maybe = maybe
false →  maybe = true
false ≡  maybe = maybe
false & false = false
false | false = false
false →  false = true
false ≡  false = true
```

## Erlang

`% Implemented by Arjun Sunel-module(ternary).-export([main/0, nott/1, andd/2,orr/2, then/2, equiv/2]). main() ->	{ok, [A]} = io:fread("Enter A: ","~s"),	{ok, [B]} = io:fread("Enter B: ","~s"),	andd(A,B). nott(S) ->	if 		S=="T" ->			io : format("F\n"); 	 	S=="F" ->			io : format("T\n"); 		true ->			io: format("?\n")	end.	  andd(A, B) ->	if 		A=="T", B=="T" ->			io : format("T\n"); 		A=="F"; B=="F" ->			io : format("F\n");	 		true ->			io: format("?\n")	end.	  orr(A, B) ->	if 		A=="T"; B=="T" ->			io : format("T\n"); 		A=="?"; B=="?" ->			io : format("?\n");	 		true ->			io: format("F\n")	end.  then(A, B) ->	if 		B=="T" ->			io : format("T\n"); 		A=="?" ->			io : format("?\n");	 		A=="F" ->			io :format("T\n");		B=="F" ->			io:format("F\n");			true ->			io: format("?\n")	end.	 equiv(A, B) ->	if 		A=="?" ->			io : format("?\n"); 		A=="F" ->			io : format("~s\n", [nott(B)]);	 		true ->			io: format("~s\n", [B])	end.			 `

## Factor

For boolean logic, Factor uses t and f with the words >boolean, not, and, or, xor. For ternary logic, we add m and define the words >trit, tnot, tand, tor, txor and t=. Our new class, trit, is the union class of t, m and f.

`! rosettacode/ternary/ternary.factor! http://rosettacode.org/wiki/Ternary_logicUSING: combinators kernel ;IN: rosettacode.ternary SINGLETON: mUNION: trit t m POSTPONE: f ; GENERIC: >trit ( object -- trit )M: trit >trit ; : tnot ( trit1 -- trit )    >trit { { t [ f ] } { m [ m ] } { f [ t ] } } case ; : tand ( trit1 trit2 -- trit )    >trit {        { t [ >trit ] }        { m [ >trit { { t [ m ] } { m [ m ] } { f [ f ] } } case ] }        { f [ >trit drop f ] }    } case ; : tor ( trit1 trit2 -- trit )    >trit {        { t [ >trit drop t ] }        { m [ >trit { { t [ t ] } { m [ m ] } { f [ m ] } } case ] }        { f [ >trit ] }    } case ; : txor ( trit1 trit2 -- trit )    >trit {        { t [ tnot ] }        { m [ >trit drop m ] }        { f [ >trit ] }    } case ; : t= ( trit1 trit2 -- trit )    {        { t [ >trit ] }        { m [ >trit drop m ] }        { f [ tnot ] }    } case ;`

Example use:

`( scratchpad ) CONSTANT: trits { t m f }( scratchpad ) trits [ tnot ] map .{ f m t }( scratchpad ) trits [ trits swap [ tand ] curry map ] map .{ { t m f } { m m f } { f f f } }( scratchpad ) trits [ trits swap [ tor ] curry map ] map .{ { t t t } { t m m } { t m f } }( scratchpad ) trits [ trits swap [ txor ] curry map ] map .{ { f m t } { m m m } { t m f } }( scratchpad ) trits [ trits swap [ t= ] curry map ] map .{ { t m f } { m m m } { f m t } }`

## Fōrmulæ

In this page you can see the solution of this task.

Fōrmulæ programs are not textual, visualization/edition of programs is done showing/manipulating structures but not text (more info). Moreover, there can be multiple visual representations of the same program. Even though it is possible to have textual representation —i.e. XML, JSON— they are intended for transportation effects more than visualization and edition.

The option to show Fōrmulæ programs and their results is showing images. Unfortunately images cannot be uploaded in Rosetta Code.

The solution shown uses finite-valued logic, where the n-valued logic can be represented as n equally spaced values between 0 (pure false) and 1 (pure true). As an example, the traditional logic values are represented as 0 and 1, and ternary logic is represented with the values 0 (false), 1/2 (maybe) and 1 (true), and so on.

The solution also shows how to redefine the logic operations, and how to show the values and the operations using colors.

## Fortran

Please find the demonstration and compilation with gfortran at the start of the code. A module contains the ternary logic for easy reuse. Consider input redirection from unixdict.txt as vestigial. Or I could delete it.

` !-*- mode: compilation; default-directory: "/tmp/" -*-!Compilation started at Mon May 20 23:05:46!!a=./f && make \$a && \$a < unixdict.txt!gfortran -std=f2003 -Wall -ffree-form f.f03 -o f!!ternary not! 1.0 0.5 0.0!!!ternary and! 0.0 0.0 0.0! 0.0 0.5 0.5! 0.0 0.5 1.0!!!ternary or! 0.0 0.5 1.0! 0.5 0.5 1.0! 1.0 1.0 1.0!!!ternary if! 1.0 1.0 1.0! 0.5 0.5 1.0! 0.0 0.5 1.0!!!ternary eq! 1.0 0.5 0.0! 0.5 0.5 0.5! 0.0 0.5 1.0!!!Compilation finished at Mon May 20 23:05:46  !This program is based on the j implementation!not=: -.!and=: <.!or =: >.!if =: (>. -.)"0~!eq =: (<.&-. >. <.)"0 module trit   real, parameter :: true = 1,  false = 0, maybe = 0.5 contains   real function tnot(y)    real, intent(in) :: y    tnot = 1 - y  end function tnot   real function tand(x, y)    real, intent(in) :: x, y    tand = min(x, y)  end function tand   real function tor(x, y)    real, intent(in) :: x, y    tor = max(x, y)  end function tor   real function tif(x, y)    real, intent(in) :: x, y    tif = tor(y, tnot(x))  end function tif   real function teq(x, y)    real, intent(in) :: x, y    teq = tor(tand(tnot(x), tnot(y)), tand(x, y))  end function teq end module trit program ternaryLogic  use trit  integer :: i  real, dimension(3) :: a = [false, maybe, true] ! (/ ... /)  write(6,'(/a)')'ternary not' ; write(6, '(3f4.1/)') (tnot(a(i)), i = 1 , 3)  write(6,'(/a)')'ternary and' ; call table(tand, a, a)  write(6,'(/a)')'ternary or' ; call table(tor, a, a)  write(6,'(/a)')'ternary if' ; call table(tif, a, a)  write(6,'(/a)')'ternary eq' ; call table(teq, a, a) contains   subroutine table(u, x, y) ! for now, show the table.    real, external :: u    real, dimension(3), intent(in) :: x, y    integer :: i, j    write(6, '(3(3f4.1/))') ((u(x(i), y(j)), j=1,3), i=1,3)  end subroutine table end program ternaryLogic `

## Free Pascal

Free Pascal version with lookup. Note that for implication and equivalence there are two versions, one lookup and one applied logic as proof.

`program ternarytests;{\$mode objfpc}type  { ternary type }  trit = (F, U, T);   operator and (const a,b:trit):trit;inline;    const lookupAnd:array[trit,trit] of trit =                     ((F,F,F),(F,U,U),(F,U,T));  begin    Result:= LookupAnd[a,b];  end;    operator or (const a,b:trit):trit;inline;    const lookupOr:array[trit,trit] of trit =                    ((F,U,T),(U,U,T),(T,T,T));  begin    Result := LookUpOr[a,b];  end;    operator not (const a:trit):trit;inline;    const LookupNot:array[trit] of trit =(T,U,F);  begin     Result:= LookUpNot[a];  end;    operator xor (const a,b:trit):trit;inline;    const LookupXor:array[trit,trit] of trit =     ((F,U,T),(U,U,U),(T,U,F));  begin    Result := LookupXor[a,b];  end;   { using one of the free set operators  for EQU }  operator >< (const a,b:trit):trit;inline;    const LookupXor:array[trit,trit] of trit =     ((T,U,F),(U,U,U),(F,U,T));  begin    Result := LookupXor[a,b];  end;   { using the free power operator for IMP }  operator ** (const a,b:trit):trit;inline;    const LookupXor:array[trit,trit] of trit =     ((T,T,T),(U,U,T),(F,U,T));  begin    Result := LookupXor[a,b];  end;   { or if you don't like the two above, use functions }  function EQU(const a,b:trit):trit;inline;  begin    Result := NOT (a XOR b) ;  end;   function IMP(const a,b:trit):trit;inline;  begin    Result := NOT(a) OR b;  end; begin  writeln(' a AND b');  writeln('__FUT');  writeln('F|',F and F,F and U,F and T);  writeln('U|',U and F,U and U,U and T);  writeln('T|',T and F,T and U,T and T);  writeln;   writeln(' a OR b');  writeln('__FUT');  writeln('F|',F or F,F or U,F or T);  writeln('U|',U or F,U or U,U or T);  writeln('T|',T or F,T or U,T or T);  writeln;   writeln(' NOT a');  writeln('__FUT');  writeln('F|',not F);  writeln('U|',not U);  writeln('T|',not T);  writeln;   writeln(' a XOR b');  writeln('__FUT');  writeln('F|',F xor F,F xor U,F xor T);  writeln('U|',U xor F,U xor U,U xor T);  writeln('T|',T xor F,T xor U,T xor T);  writeln;   writeln(' NOT (a XOR b)  -> equivalent');  writeln('__FUT');  writeln('F|',not(F xor F),not(F xor U),not(F xor T));  writeln('U|',not(U xor F),not(U xor U),not(U xor T));  writeln('T|',not(T xor F),not(T xor U),not(T xor T));  writeln;   writeln(' using >< as EQU  -> equivalence');  writeln('__FUT');  writeln('F|',F >< F,F >< U,F >< T);  writeln('U|',U >< F,U >< U,U >< T);  writeln('T|',T >< F,T >< U,T >< T);  writeln;   writeln(' NOT(a) OR b  -> IMP. a.k.a. IfThen');   writeln('T|',(not T) or T,(not T) or U,(not T) or F);  writeln('U|',(not U) or T,(not U) or U,(not U) or F);  writeln('F|',(not F) or T,(not F) or U,(not F) or F);  writeln;   writeln(' using ** as IMP a.k.a. IfThen');   writeln('T|',T ** T,T ** U,T ** F);  writeln('U|',U ** T,U ** U,U ** F);  writeln('F|',F ** T,F ** U,F ** F); end.`
```Output:
a AND b
__FUT
F|FFF
U|FUU
T|FUT

a OR b
__FUT
F|FUT
U|UUT
T|TTT

NOT a
__FUT
F|T
U|U
T|F

a XOR b
__FUT
F|FUT
U|UUU
T|TUF

NOT (a XOR b)  -> equivalent
__FUT
F|TUF
U|UUU
T|FUT

using >< as EQU  -> equivalence
__FUT
F|TUF
U|UUU
T|FUT

NOT(a) OR b  -> IMP. a.k.a. IfThen
T|TUF
U|TUU
F|TTT

using ** as IMP a.k.a. IfThen
T|TUF
U|TUU
F|TTT```

## Go

Go has four operators for the bool type: ==, &&, ||, and !.

`package main import "fmt" type trit int8 const (    trFalse trit = iota - 1    trMaybe    trTrue) func (t trit) String() string {    switch t {    case trFalse:        return "False"    case trMaybe:        return "Maybe"    case trTrue:        return "True "    }    panic("Invalid trit")} func trNot(t trit) trit {    return -t} func trAnd(s, t trit) trit {    if s < t {        return s    }    return t} func trOr(s, t trit) trit {    if s > t {        return s    }    return t} func trEq(s, t trit) trit {    return s * t} func main() {    trSet := []trit{trFalse, trMaybe, trTrue}     fmt.Println("t     not t")    for _, t := range trSet {        fmt.Println(t, trNot(t))    }     fmt.Println("\ns     t     s and t")    for _, s := range trSet {        for _, t := range trSet {            fmt.Println(s, t, trAnd(s, t))        }    }     fmt.Println("\ns     t     s or t")    for _, s := range trSet {        for _, t := range trSet {            fmt.Println(s, t, trOr(s, t))        }    }     fmt.Println("\ns     t     s eq t")    for _, s := range trSet {        for _, t := range trSet {            fmt.Println(s, t, trEq(s, t))        }    }}`
Output:
```t     not t
False True
Maybe Maybe
True  False

s     t     s and t
False False False
False Maybe False
False True  False
Maybe False False
Maybe Maybe Maybe
Maybe True  Maybe
True  False False
True  Maybe Maybe
True  True  True

s     t     s or t
False False False
False Maybe Maybe
False True  True
Maybe False Maybe
Maybe Maybe Maybe
Maybe True  True
True  False True
True  Maybe True
True  True  True

s     t     s eq t
False False True
False Maybe Maybe
False True  False
Maybe False Maybe
Maybe Maybe Maybe
Maybe True  Maybe
True  False False
True  Maybe Maybe
True  True  True
```

## Groovy

Solution:

`enum Trit {    TRUE, MAYBE, FALSE     private Trit nand(Trit that) {        switch ([this,that]) {            case { FALSE in it }: return TRUE            case { MAYBE in it }: return MAYBE            default             : return FALSE        }    }    private Trit nor(Trit that) { this.or(that).not() }     Trit and(Trit that)   { this.nand(that).not() }    Trit or(Trit that)    { this.not().nand(that.not()) }    Trit not()            { this.nand(this) }    Trit imply(Trit that) { this.nand(that.not()) }    Trit equiv(Trit that) { this.and(that).or(this.nor(that)) }}`

Test:

`printf 'AND\n         'Trit.values().each { b -> printf ('%6s', b) }println '\n          ----- ----- -----'Trit.values().each { a ->    printf ('%6s | ', a)    Trit.values().each { b -> printf ('%6s', a.and(b)) }    println()} printf '\nOR\n         'Trit.values().each { b -> printf ('%6s', b) }println '\n          ----- ----- -----'Trit.values().each { a ->    printf ('%6s | ', a)    Trit.values().each { b -> printf ('%6s', a.or(b)) }    println()} println '\nNOT'Trit.values().each {    printf ('%6s | %6s\n', it, it.not())} printf '\nIMPLY\n         'Trit.values().each { b -> printf ('%6s', b) }println '\n          ----- ----- -----'Trit.values().each { a ->    printf ('%6s | ', a)    Trit.values().each { b -> printf ('%6s', a.imply(b)) }    println()} printf '\nEQUIV\n         'Trit.values().each { b -> printf ('%6s', b) }println '\n          ----- ----- -----'Trit.values().each { a ->    printf ('%6s | ', a)    Trit.values().each { b -> printf ('%6s', a.equiv(b)) }    println()}`
Output:
```AND
TRUE MAYBE FALSE
----- ----- -----
TRUE |   TRUE MAYBE FALSE
MAYBE |  MAYBE MAYBE FALSE
FALSE |  FALSE FALSE FALSE

OR
TRUE MAYBE FALSE
----- ----- -----
TRUE |   TRUE  TRUE  TRUE
MAYBE |   TRUE MAYBE MAYBE
FALSE |   TRUE MAYBE FALSE

NOT
TRUE |  FALSE
MAYBE |  MAYBE
FALSE |   TRUE

IMPLY
TRUE MAYBE FALSE
----- ----- -----
TRUE |   TRUE MAYBE FALSE
MAYBE |   TRUE MAYBE MAYBE
FALSE |   TRUE  TRUE  TRUE

EQUIV
TRUE MAYBE FALSE
----- ----- -----
TRUE |   TRUE MAYBE FALSE
MAYBE |  MAYBE MAYBE MAYBE
FALSE |  FALSE MAYBE  TRUE```

## Haskell

All operations given in terms of NAND, the functionally-complete operation.

`import Prelude hiding (Bool(..), not, (&&), (||), (==)) main = mapM_ (putStrLn . unlines . map unwords)    [ table "not"     \$ unary not    , table "and"     \$ binary (&&)    , table "or"      \$ binary (||)    , table "implies" \$ binary (=->)    , table "equals"  \$ binary (==)    ] data Trit = False | Maybe | True deriving (Show) False `nand` _     = True_     `nand` False = TrueTrue  `nand` True  = False_     `nand` _     = Maybe not a = nand a a a && b = not \$ a `nand` b a || b = not a `nand` not b a =-> b = a `nand` not b a == b = (a && b) || (not a && not b) inputs1 = [True, Maybe, False]inputs2 = [(a,b) | a <- inputs1, b <- inputs1] unary f = map (\a -> [a, f a]) inputs1binary f = map (\(a,b) -> [a, b, f a b]) inputs2 table name xs = map (map pad) . (header :) \$ map (map show) xs    where header = map (:[]) (take ((length \$ head xs) - 1) ['A'..]) ++ [name] pad s = s ++ replicate (5 - length s) ' '`
Output:
```A     not
True  False
Maybe Maybe
False True

A     B     and
True  True  True
True  Maybe Maybe
True  False False
Maybe True  Maybe
Maybe Maybe Maybe
Maybe False False
False True  False
False Maybe False
False False False

A     B     or
True  True  True
True  Maybe True
True  False True
Maybe True  True
Maybe Maybe Maybe
Maybe False Maybe
False True  True
False Maybe Maybe
False False False

A     B     implies
True  True  True
True  Maybe Maybe
True  False False
Maybe True  True
Maybe Maybe Maybe
Maybe False Maybe
False True  True
False Maybe True
False False True

A     B     equals
True  True  True
True  Maybe Maybe
True  False False
Maybe True  Maybe
Maybe Maybe Maybe
Maybe False Maybe
False True  False
False Maybe Maybe
False False True```

## Icon and Unicon

The following example works in both Icon and Unicon. There are a couple of comments on the code that pertain to the task requirements:

• Strictly speaking there are no binary values in Icon and Unicon. There are a number of flow control operations that result in expression success (and a result) or failure which affects flow. As a result there really isn't a set of binary operators to map into ternary. The example provides the minimum required by the task plus xor.
• The code below does not define a data type as it doesn't really make sense in this case. Icon and Unicon can create records which would be overkill and clumsy in this case. Unicon can create objects which would also be overkill. The only remaining option is to reinterpret one of the existing types as ternary values. The code below implements balanced ternary values as integers in order to simplify several of the functions.
• The use of integers doesn't really support strings of trits well. While there is a function showtrit to ease display a converse function to decode character trits in a string is not included.

`\$define TRUE    1\$define FALSE  -1\$define UNKNOWN 0  invocable alllink printf procedure main()  # demonstrate ternary logic ufunc := ["not3"]bfunc := ["and3", "or3", "xor3", "eq3", "ifthen3"] every f := !ufunc  do {   # display unary functions   printf("\nunary function=%s:\n",f)   every t1 := (TRUE | FALSE | UNKNOWN) do      printf(" %s : %s\n",showtrit(t1),showtrit(not3(t1)))   }  every f :=  !bfunc do {   # display binary functions   printf("\nbinary function=%s:\n     ",f)   every t1 := (&null | TRUE | FALSE | UNKNOWN) do {       printf(" %s : ",showtrit(\t1))      every t2 := (TRUE | FALSE | UNKNOWN | &null) do {         if /t1 then printf("  %s",showtrit(\t2)|"\n")         else printf("  %s",showtrit(f(t1,\t2))|"\n")         }      }   }end procedure showtrit(a)   #: return printable trit of error if invalidreturn case a of {TRUE:"T";FALSE:"F";UNKNOWN:"?";default:runerr(205,a)}end procedure istrit(a)     #: return value of trit or error if invalidreturn (TRUE|FALSE|UNKNOWN|runerr(205,a)) = a end procedure not3(a)       #: not of trit or error if invalidreturn FALSE * istrit(a)end procedure and3(a,b)     #: and of two trits or error if invalidreturn min(istrit(a),istrit(b))end procedure or3(a,b)      #: or of two trits or error if invalidreturn max(istrit(a),istrit(b))end procedure eq3(a,b)      #: equals of two trits or error if invalidreturn istrit(a) * istrit(b)end procedure ifthen3(a,b)  #: if trit then trit or error if invalidreturn case istrit(a) of { TRUE: istrit(b) ; UNKNOWN: or3(a,b); FALSE: TRUE }end procedure xor3(a,b)     #: xor of two trits or error if invalidreturn not3(eq3(a,b))end`
Output:
```unary function=not3:
T : F
F : T
? : ?

binary function=and3:
T  F  ?
T :   T  F  ?
F :   F  F  F
? :   ?  F  ?

binary function=or3:
T  F  ?
T :   T  T  T
F :   T  F  ?
? :   T  ?  ?

binary function=xor3:
T  F  ?
T :   F  T  ?
F :   T  F  ?
? :   ?  ?  ?

binary function=eq3:
T  F  ?
T :   T  F  ?
F :   F  T  ?
? :   ?  ?  ?

binary function=ifthen3:
T  F  ?
T :   T  F  ?
F :   T  T  T
? :   T  ?  ?```

## J

The designers of J felt that user defined types were harmful, so that part of the task will not be supported here.

Instead:

true: 1 false: 0 maybe: 0.5

`not=: -.and=: <.or =: >.if =: (>. -.)"0~eq =: (<.&-. >. <.)"0`

Example use:

`   not 0 0.5 11 0.5 0    0 0.5 1 and/ 0 0.5 10   0   00 0.5 0.50 0.5   1    0 0.5 1 or/ 0 0.5 1  0 0.5 10.5 0.5 1  1   1 1    0 0.5 1 if/ 0 0.5 1  1   1 10.5 0.5 1  0 0.5 1    0 0.5 1 eq/ 0 0.5 1  1 0.5   00.5 0.5 0.5  0 0.5   1`

Note that this implementation is a special case of "fuzzy logic" (using a limited set of values).

Note that while `>.` and `<.` could be used for boolean operations instead of J's `+.` and `*.`, the identity elements for >. and <. are not boolean values, but are negative and positive infinity. See also: Boolean ring

Note that we might instead define values between 0 and 1 to represent independent probabilities:

`not=: -.and=: *or=: *&.-.if =: (or -.)"0~eq =: (*&-. or *)"0`

However, while this might be a more intellectually satisfying approach, this gives us some different results from the task requirement, for the combination of two "maybe" values (we could "fix" this by adding some "logic" which replaced any non-integer value with "0.5" - this would satisfy literal compliance with the task specification and might even be a valid engineering choice if we are implementing in hardware, for example):

`   not 0 0.5 11 0.5 0    0 0.5 1 and/ 0 0.5 10    0   00 0.25 0.50  0.5   1    0 0.5 1 or/ 0 0.5 1  0  0.5 10.5 0.75 1  1    1 1    0 0.5 1 if/ 0 0.5 1  1    1 10.5 0.75 1  0  0.5 1    0 0.5 1 eq/ 0 0.5 1  1    0.5   00.5 0.4375 0.5  0    0.5   1`

Another interesting possibility would involve using George Boole's original operations. This leaves us without any "not", (if we include the definition of logical negation which was later added to the definition of Boolean algebra, then the only numbers which can be used with Boolean algebra are 1 and 0). So, it's not clear how we would implement "if" or "eq". However, "and" and "or" would look like this:

`and=: *.or=: +.`

And, the boolean result tables would look like this:

`   0 0.5 1 and/ 0 0.5 10   0 00 0.5 10   1 1    0 0.5 1 or/ 0 0.5 1  0 0.5   10.5 0.5 0.5  1 0.5   1`

## Java

Works with: Java version 1.5+
`public class Logic{	public static enum Trit{		TRUE, MAYBE, FALSE; 		public Trit and(Trit other){			if(this == TRUE){				return other;			}else if(this == MAYBE){				return (other == FALSE) ? FALSE : MAYBE;			}else{				return FALSE;			}		} 		public Trit or(Trit other){			if(this == TRUE){				return TRUE;			}else if(this == MAYBE){				return (other == TRUE) ? TRUE : MAYBE;			}else{				return other;			}		} 		public Trit tIf(Trit other){			if(this == TRUE){				return other;			}else if(this == MAYBE){				return (other == TRUE) ? TRUE : MAYBE;			}else{				return TRUE;			}		} 		public Trit not(){			if(this == TRUE){				return FALSE;			}else if(this == MAYBE){				return MAYBE;			}else{				return TRUE;			}		} 		public Trit equals(Trit other){			if(this == TRUE){				return other;			}else if(this == MAYBE){				return MAYBE;			}else{				return other.not();			}		}	}	public static void main(String[] args){		for(Trit a:Trit.values()){			System.out.println("not " + a + ": " + a.not());		}		for(Trit a:Trit.values()){			for(Trit b:Trit.values()){				System.out.println(a+" and "+b+": "+a.and(b)+						"\t "+a+" or "+b+": "+a.or(b)+						"\t "+a+" implies "+b+": "+a.tIf(b)+						"\t "+a+" = "+b+": "+a.equals(b));			}		}	}}`
Output:
```not TRUE: FALSE
not MAYBE: MAYBE
not FALSE: TRUE
TRUE and TRUE: TRUE	 TRUE or TRUE: TRUE	 TRUE implies TRUE: TRUE	 TRUE = TRUE: TRUE
TRUE and MAYBE: MAYBE	 TRUE or MAYBE: TRUE	 TRUE implies MAYBE: MAYBE	 TRUE = MAYBE: MAYBE
TRUE and FALSE: FALSE	 TRUE or FALSE: TRUE	 TRUE implies FALSE: FALSE	 TRUE = FALSE: FALSE
MAYBE and TRUE: MAYBE	 MAYBE or TRUE: TRUE	 MAYBE implies TRUE: TRUE	 MAYBE = TRUE: MAYBE
MAYBE and MAYBE: MAYBE	 MAYBE or MAYBE: MAYBE	 MAYBE implies MAYBE: MAYBE	 MAYBE = MAYBE: MAYBE
MAYBE and FALSE: FALSE	 MAYBE or FALSE: MAYBE	 MAYBE implies FALSE: MAYBE	 MAYBE = FALSE: MAYBE
FALSE and TRUE: FALSE	 FALSE or TRUE: TRUE	 FALSE implies TRUE: TRUE	 FALSE = TRUE: FALSE
FALSE and MAYBE: FALSE	 FALSE or MAYBE: MAYBE	 FALSE implies MAYBE: TRUE	 FALSE = MAYBE: MAYBE
FALSE and FALSE: FALSE	 FALSE or FALSE: FALSE	 FALSE implies FALSE: TRUE	 FALSE = FALSE: TRUE```

## JavaScript

Let's use the trit already available in JavaScript: true, false (both boolean) and undefined…

`var L3 = new Object(); L3.not = function(a) {  if (typeof a == "boolean") return !a;  if (a == undefined) return undefined;  throw("Invalid Ternary Expression.");} L3.and = function(a, b) {  if (typeof a == "boolean" && typeof b == "boolean") return a && b;  if ((a == true && b == undefined) || (a == undefined && b == true)) return undefined;  if ((a == false && b == undefined) || (a == undefined && b == false)) return false;  if (a == undefined && b == undefined) return undefined;  throw("Invalid Ternary Expression.");} L3.or = function(a, b) {  if (typeof a == "boolean" && typeof b == "boolean") return a || b;  if ((a == true && b == undefined) || (a == undefined && b == true)) return true;  if ((a == false && b == undefined) || (a == undefined && b == false)) return undefined;  if (a == undefined && b == undefined) return undefined;  throw("Invalid Ternary Expression.");} // A -> B is equivalent to -A or BL3.ifThen = function(a, b) {  return L3.or(L3.not(a), b);} // A <=> B is equivalent to (A -> B) and (B -> A)L3.iff = function(a, b) {  return L3.and(L3.ifThen(a, b), L3.ifThen(b, a));} `

… and try these:

` L3.not(true)         // falseL3.not(var a)        // undefined L3.and(true, a)      // undefined L3.or(a, 2 == 3)     // false L3.ifThen(true, a)   // undefined L3.iff(a, 2 == 2)    // undefined      `

## jq

jq itself does not have an extensible type system, so we'll use false, "maybe", and true as the three values since ternary logic agrees with Boolean logic for true and false, and because jq prints these three values consistently.

For consistency, all the ternary logic operators are defined here with the prefix "ternary_", but such a prefix is only needed for "not", "and", and "or", as these are jq keywords.
`def ternary_nand(a; b):  if a == false or b == false then true  elif a == "maybe" or b == "maybe" then "maybe"  else false  end ; def ternary_not(a):    ternary_nand(a; a); def ternary_or(a; b):  ternary_nand( ternary_not(a); ternary_not(b) ); def ternary_nor(a; b): ternary_not( ternary_or(a;b) ); def ternary_and(a; b): ternary_not( ternary_nand(a; b) ); def ternary_imply(this; that):  ternary_nand(this, ternary_not(that)); def ternary_equiv(this; that):   ternary_or( ternary_and(this; that); ternary_nor(this; that) ); def display_and(a; b):  a as \$a | b as \$b   | "\(\$a) and \(\$b) is \( ternary_and(\$a; \$b) )";def display_equiv(a; b):  a as \$a | b as \$b  | "\(\$a) equiv \(\$b) is \( ternary_equiv(\$a; \$b) )";# etc etc # Invoke the display functions:display_and( (false, "maybe", true );  (false, "maybe", true) ),display_equiv( (false, "maybe", true );  (false, "maybe", true) ),"etc etc" `
Output:
```"false and false is false"
"false and maybe is false"
"false and true is false"
"maybe and false is false"
"maybe and maybe is maybe"
"maybe and true is maybe"
"true and false is false"
"true and maybe is maybe"
"true and true is true"
"false equiv false is true"
"false equiv maybe is maybe"
"false equiv true is false"
"maybe equiv false is maybe"
"maybe equiv maybe is maybe"
"maybe equiv true is maybe"
"true equiv false is false"
"true equiv maybe is maybe"
"true equiv true is true"
"etc etc"
```

## Julia

Works with: Julia version 0.6
`@enum Trit False Maybe Trueconst trits = (False, Maybe, True) Base.:!(a::Trit) = a == False ? True : a == Maybe ? Maybe : False∧(a::Trit, b::Trit) = a == b == True ? True : (a, b) ∋ False ? False : Maybe∨(a::Trit, b::Trit) = a == b == False ? False : (a, b) ∋ True ? True : Maybe⊃(a::Trit, b::Trit) = a == False || b == True ? True : (a, b) ∋ Maybe ? Maybe : False≡(a::Trit, b::Trit) = (a, b) ∋ Maybe ? Maybe : a == b ? True : False println("Not (!):")println(join(@sprintf("%10s%s is %5s", "!", t, !t) for t in trits))println("And (∧):")for a in trits    println(join(@sprintf("%10s ∧ %5s is %5s", a, b, a ∧ b) for b in trits))endprintln("Or (∨):")for a in trits    println(join(@sprintf("%10s ∨ %5s is %5s", a, b, a ∨ b) for b in trits))endprintln("If Then (⊃):")for a in trits    println(join(@sprintf("%10s ⊃ %5s is %5s", a, b, a ⊃ b) for b in trits))endprintln("Equivalent (≡):")for a in trits    println(join(@sprintf("%10s ≡ %5s is %5s", a, b, a ≡ b) for b in trits))end`
Output:
```Not (!):
!False is  True         !Maybe is Maybe         !True is False
And (∧):
False ∧ False is False     False ∧ Maybe is False     False ∧  True is False
Maybe ∧ False is False     Maybe ∧ Maybe is Maybe     Maybe ∧  True is Maybe
True ∧ False is False      True ∧ Maybe is Maybe      True ∧  True is  True
Or (∨):
False ∨ False is False     False ∨ Maybe is Maybe     False ∨  True is  True
Maybe ∨ False is Maybe     Maybe ∨ Maybe is Maybe     Maybe ∨  True is  True
True ∨ False is  True      True ∨ Maybe is  True      True ∨  True is  True
If Then (⊃):
False ⊃ False is  True     False ⊃ Maybe is  True     False ⊃  True is  True
Maybe ⊃ False is Maybe     Maybe ⊃ Maybe is Maybe     Maybe ⊃  True is  True
True ⊃ False is False      True ⊃ Maybe is Maybe      True ⊃  True is  True
Equivalent (≡):
False ≡ False is  True     False ≡ Maybe is Maybe     False ≡  True is False
Maybe ≡ False is Maybe     Maybe ≡ Maybe is Maybe     Maybe ≡  True is Maybe
True ≡ False is False      True ≡ Maybe is Maybe      True ≡  True is  True```

## Alternative version

Works with: Julia version 0.7

With Julia 1.0 and the new type missing, three-value logic is implemented by default

`# built-in: true, false and missing using Printf const tril = (true, missing, false) @printf("\n%8s | %8s\n", "A", "¬A")for A in tril    @printf("%8s | %8s\n", A, !A)end @printf("\n%8s | %8s | %8s\n", "A", "B", "A ∧ B")for (A, B) in Iterators.product(tril, tril)    @printf("%8s | %8s | %8s\n", A, B, A & B)end @printf("\n%8s | %8s | %8s\n", "A", "B", "A ∨ B")for (A, B) in Iterators.product(tril, tril)    @printf("%8s | %8s | %8s\n", A, B, A | B)end @printf("\n%8s | %8s | %8s\n", "A", "B", "A ≡ B")for (A, B) in Iterators.product(tril, tril)    @printf("%8s | %8s | %8s\n", A, B, A == B)end ⊃(A, B) = B | !A @printf("\n%8s | %8s | %8s\n", "A", "B", "A ⊃ B")for (A, B) in Iterators.product(tril, tril)    @printf("%8s | %8s | %8s\n", A, B, A ⊃ B)end`
Output:
```       A |       ¬A
true |    false
missing |  missing
false |     true

A |        B |    A ∧ B
true |     true |     true
missing |     true |  missing
false |     true |    false
true |  missing |  missing
missing |  missing |  missing
false |  missing |    false
true |    false |    false
missing |    false |    false
false |    false |    false

A |        B |    A ∨ B
true |     true |     true
missing |     true |     true
false |     true |     true
true |  missing |     true
missing |  missing |  missing
false |  missing |  missing
true |    false |     true
missing |    false |  missing
false |    false |    false

A |        B |    A ≡ B
true |     true |     true
missing |     true |  missing
false |     true |    false
true |  missing |  missing
missing |  missing |  missing
false |  missing |  missing
true |    false |    false
missing |    false |  missing
false |    false |     true

A |        B |    A ⊃ B
true |     true |     true
missing |     true |     true
false |     true |     true
true |  missing |  missing
missing |  missing |  missing
false |  missing |     true
true |    false |    false
missing |    false |  missing```

## Kotlin

`// version 1.1.2 enum class Trit {    TRUE, MAYBE, FALSE;     operator fun not() = when (this) {        TRUE  -> FALSE        MAYBE -> MAYBE        FALSE -> TRUE    }     infix fun and(other: Trit) = when (this) {        TRUE  -> other        MAYBE -> if (other == FALSE) FALSE else MAYBE        FALSE -> FALSE    }     infix fun or(other: Trit) = when (this) {        TRUE  -> TRUE        MAYBE -> if (other == TRUE) TRUE else MAYBE        FALSE -> other    }     infix fun imp(other: Trit) = when (this) {        TRUE  -> other        MAYBE -> if (other == TRUE) TRUE else MAYBE        FALSE -> TRUE    }     infix fun eqv(other: Trit) = when (this) {        TRUE  -> other        MAYBE -> MAYBE        FALSE -> !other    }     override fun toString() = this.name.toString()} fun main(args: Array<String>) {    val ta = arrayOf(Trit.TRUE, Trit.MAYBE, Trit.FALSE)     // not    println("not")    println("-------")    for (t in ta) println(" \$t  | \${!t}")    println()     // and    println("and | T  M  F")    println("-------------")    for (t in ta) {        print(" \$t  | ")        for (tt in ta) print("\${t and tt}  ")        println()    }    println()     // or    println("or  | T  M  F")    println("-------------")    for (t in ta) {        print(" \$t  | ")        for (tt in ta) print("\${t or tt}  ")        println()    }    println()     // imp    println("imp | T  M  F")    println("-------------")    for (t in ta) {        print(" \$t  | ")        for (tt in ta) print("\${t imp tt}  ")        println()    }    println()     // eqv    println("eqv | T  M  F")    println("-------------")    for (t in ta) {        print(" \$t  | ")        for (tt in ta) print("\${t eqv tt}  ")        println()    }}`
Output:
```not
-------
T  | F
M  | M
F  | T

and | T  M  F
-------------
T  | T  M  F
M  | M  M  F
F  | F  F  F

or  | T  M  F
-------------
T  | T  T  T
M  | T  M  M
F  | T  M  F

imp | T  M  F
-------------
T  | T  M  F
M  | T  M  M
F  | T  T  T

eqv | T  M  F
-------------
T  | T  M  F
M  | M  M  M
F  | F  M  T
```

## Liberty BASIC

` 'ternary logic'0 1 2'F ? T'False Don't know True'LB has NOT AND OR XOR, so we implement them.'LB has no EQ, but XOR could be expressed via EQ. In 'normal' boolean at least. global tFalse, tDontKnow, tTruetFalse = 0tDontKnow = 1tTrue = 2 print "Short and long names for ternary logic values"for i = tFalse to tTrue    print shortName3\$(i);" ";longName3\$(i)nextprint print "Single parameter functions"print "x";" ";"=x";"  ";"not(x)"for i = tFalse to tTrue    print shortName3\$(i);"  ";shortName3\$(i);"    ";shortName3\$(not3(i))nextprint print "Double  parameter fuctions"print "x";" ";"y";"  ";"x AND y";"  ";"x OR y";"  ";"x EQ y";"  ";"x XOR y"for a = tFalse to tTrue    for b = tFalse to tTrue        print shortName3\$(a);" ";shortName3\$(b);"     "; _            shortName3\$(and3(a,b));"       "; shortName3\$(or3(a,b));"       "; _            shortName3\$(eq3(a,b));"        "; shortName3\$(xor3(a,b))    nextnext function and3(a,b)    and3 = min(a,b)end function function or3(a,b)    or3 = max(a,b)end function function eq3(a,b)    select case    case a=tDontKnow or b=tDontKnow        eq3 = tDontKnow    case a=b        eq3 = tTrue    case else        eq3 = tFalse    end selectend function function xor3(a,b)    xor3 = not3(eq3(a,b))end function function not3(b)    not3 = 2-bend function '------------------------------------------------function shortName3\$(i)   shortName3\$ = word\$("F ? T", i+1)end function function longName3\$(i)    longName3\$ = word\$("False,Don't know,True", i+1, ",")end function `
Output:
```Short and long names for ternary logic values
F False
? Don't know
T True

Single parameter functions
x =x  not(x)
F  F    T
?  ?    ?
T  T    F

Double  parameter fuctions
x y  x AND y  x OR y  x EQ y  x XOR y
F F     F       F       T        F
F ?     F       ?       ?        ?
F T     F       T       F        T
? F     F       ?       ?        ?
? ?     ?       ?       ?        ?
? T     ?       T       ?        ?
T F     F       T       F        T
T ?     ?       T       ?        ?
T T     T       T       T        F
```

## Maple

The logic system in Maple is implicitly ternary with truth values true, false, and FAIL.

The following script generates all truth tables for Maple logical operations. Note that in addition to the usual built-in logical operators for not, or, and, and xor, Maple also has implies.

`tv := [true, false, FAIL];NotTable     := Array(1..3, i->not tv[i] );AndTable     := Array(1..3, 1..3, (i,j)->tv[i] and tv[j] );OrTable      := Array(1..3, 1..3, (i,j)->tv[i] or tv[j] );XorTable     := Array(1..3, 1..3, (i,j)->tv[i] xor tv[j] );ImpliesTable := Array(1..3, 1..3, (i,j)->tv[i] implies tv[j] );`
Output:
`> tv := [true, false, FAIL];                                     tv := [true, false, FAIL] > NotTable := Array(1..3, i->not tv[i] );                                  NotTable := [false, true, FAIL] > AndTable := Array(1..3, 1..3, (i,j)->tv[i] and tv[j] );                                           [true     false    FAIL ]                                           [                       ]                               AndTable := [false    false    false]                                           [                       ]                                           [FAIL     false    FAIL ] > OrTable := Array(1..3, 1..3, (i,j)->tv[i] or tv[j] );                                           [true    true     true]                                           [                     ]                                OrTable := [true    false    FAIL]                                           [                     ]                                           [true    FAIL     FAIL] > XorTable := Array(1..3, 1..3, (i,j)->tv[i] xor tv[j] );                                           [false    true     FAIL]                                           [                      ]                               XorTable := [true     false    FAIL]                                           [                      ]                                           [FAIL     FAIL     FAIL] > ImpliesTable := Array(1..3, 1..3, (i,j)->tv[i] implies tv[j] );                                              [true    false    FAIL]                                              [                     ]                              ImpliesTable := [true    true     true]                                              [                     ]                                              [true    FAIL     FAIL]`

## Mathematica

Type definition is not allowed in Mathematica. We can just use the build-in symbols "True" and "False", and add a new symbol "Maybe".

`Maybe /: ! Maybe = Maybe;Maybe /: (And | Or | Nand | Nor | Xor | Xnor | Implies | Equivalent)[Maybe, Maybe] = Maybe;`

Example:

`trits = {True, Maybe, False};[email protected][   ArrayFlatten[{{{{Not}}, {{Null}}}, {List /@ trits,       List /@ Not /@ trits}}]];Do[[email protected][   ArrayFlatten[{{{{operator}}, {{Null, Null,         Null}}}, {{{Null}}, {trits}}, {List /@ trits,       Outer[operator, trits, trits]}}]], {operator, {And, Or, Nand,    Nor, Xor, Xnor, Implies, Equivalent}}]`
Output:
```Not
True	False
Maybe	Maybe
False	True

And
True	Maybe	False
True	True	Maybe	False
Maybe	Maybe	Maybe	False
False	False	False	False

Or
True	Maybe	False
True	True	True	True
Maybe	True	Maybe	Maybe
False	True	Maybe	False

Nand
True	Maybe	False
True	False	Maybe	True
Maybe	Maybe	Maybe	True
False	True	True	True

Nor
True	Maybe	False
True	False	False	False
Maybe	False	Maybe	Maybe
False	False	Maybe	True

Xor
True	Maybe	False
True	False	Maybe	True
Maybe	Maybe	Maybe	Maybe
False	True	Maybe	False

Xnor
True	Maybe	False
True	True	Maybe	False
Maybe	Maybe	Maybe	Maybe
False	False	Maybe	True

Implies
True	Maybe	False
True	True	Maybe	False
Maybe	True	Maybe	Maybe
False	True	True	True

Equivalent
True	Maybe	False
True	True	Maybe	False
Maybe	Maybe	Maybe	Maybe
False	False	Maybe	True

```

## МК-61/52

`П0	Сx	С/П	^	1	+	3	*	+	1+	3	x^y	ИП0	<->	/	[x]	^	^	3/	[x]	3	*	-	1	-	С/П	1	56	3	3	БП	00	1	9	5	6	9БП	00	1	5	9	2	9	БП	00	15	6	6	5	БП	00	/-/	ЗН	С/П`

Instruction:

БП XX С/П a ^ b С/П,

where XX = 28 for AND; 35 for OR; 42 for implies; 49 for equivalent; 56 for NOT;

a, b ∈ {-1, 0, 1}.

## Nim

`type Trit* = enum ttrue, tmaybe, tfalse proc `\$`*(a: Trit): string =  case a  of ttrue: "T"  of tmaybe: "?"  of tfalse: "F" proc `not`*(a: Trit): Trit =  case a  of ttrue: tfalse  of tmaybe: tmaybe  of tfalse: ttrue proc `and`*(a, b: Trit): Trit =  const t: array[Trit, array[Trit, Trit]] =    [ [ttrue,  tmaybe, tfalse]    , [tmaybe, tmaybe, tfalse]    , [tfalse, tfalse, tfalse] ]  t[a][b] proc `or`*(a, b: Trit): Trit =  const t: array[Trit, array[Trit, Trit]] =    [ [ttrue, ttrue,  ttrue]    , [ttrue, tmaybe, tmaybe]    , [ttrue, tmaybe, tfalse] ]  t[a][b] proc then*(a, b: Trit): Trit =  const t: array[Trit, array[Trit, Trit]] =    [ [ttrue, tmaybe, tfalse]    , [ttrue, tmaybe, tmaybe]    , [ttrue, ttrue,  ttrue] ]  t[a][b] proc equiv*(a, b: Trit): Trit =  const t: array[Trit, array[Trit, Trit]] =    [ [ttrue,  tmaybe, tfalse]    , [tmaybe, tmaybe, tmaybe]    , [tfalse, tmaybe, ttrue] ]  t[a][b] import strutils var  op1 = ttrue  op2 = ttrue for t in Trit:  echo "Not ", t , ": ", not t for op1 in Trit:  for op2 in Trit:    echo "\$# and   \$#: \$#".format(op1, op2, op1 and op2)    echo "\$# or    \$#: \$#".format(op1, op2, op1 or op2)    echo "\$# then  \$#: \$#".format(op1, op2, op1.then op2)    echo "\$# equiv \$#: \$#".format(op1, op2, op1.equiv op2)`
Output:
```Not T: F
Not ?: ?
Not F: T
T and   T: T
T or    T: T
T then  T: T
T equiv T: T
T and   ?: ?
T or    ?: T
T then  ?: ?
T equiv ?: ?
T and   F: F
T or    F: T
T then  F: F
T equiv F: F
? and   T: ?
? or    T: T
? then  T: T
? equiv T: ?
? and   ?: ?
? or    ?: ?
? then  ?: ?
? equiv ?: ?
? and   F: F
? or    F: ?
? then  F: ?
? equiv F: ?
F and   T: F
F or    T: T
F then  T: T
F equiv T: F
F and   ?: F
F or    ?: ?
F then  ?: T
F equiv ?: ?
F and   F: F
F or    F: F
F then  F: T
F equiv F: T```

## OCaml

`type trit = True | False | Maybe let t_not = function  | True -> False  | False -> True  | Maybe -> Maybe let t_and a b = match (a,b) with   | (True,True) -> True   | (False,_)  | (_,False) -> False   | _ -> Maybe let t_or a b = t_not (t_and (t_not a) (t_not b)) let t_eq a b = match (a,b) with   | (True,True) | (False,False) -> True   | (False,True) | (True,False) -> False   | _ -> Maybe let t_imply a b = t_or (t_not a) b let string_of_trit = function  | True -> "True"  | False -> "False"  | Maybe -> "Maybe" let () =  let values = [| True; Maybe; False |] in  let f = string_of_trit in  Array.iter (fun v -> Printf.printf "Not %s: %s\n" (f v) (f (t_not v))) values;  print_newline ();  let print op str =    Array.iter (fun a ->      Array.iter (fun b ->        Printf.printf "%s %s %s: %s\n" (f a) str (f b) (f (op a b))      ) values    ) values;    print_newline ()  in  print t_and "And";  print t_or "Or";  print t_imply "Then";  print t_eq "Equiv";;;`
Output:
```Not True: False
Not Maybe: Maybe
Not False: True

True And True: True
True And Maybe: Maybe
True And False: False
Maybe And True: Maybe
Maybe And Maybe: Maybe
Maybe And False: False
False And True: False
False And Maybe: False
False And False: False

True Or True: True
True Or Maybe: True
True Or False: True
Maybe Or True: True
Maybe Or Maybe: Maybe
Maybe Or False: Maybe
False Or True: True
False Or Maybe: Maybe
False Or False: False

True Then True: True
True Then Maybe: Maybe
True Then False: False
Maybe Then True: True
Maybe Then Maybe: Maybe
Maybe Then False: Maybe
False Then True: True
False Then Maybe: True
False Then False: True

True Equiv True: True
True Equiv Maybe: Maybe
True Equiv False: False
Maybe Equiv True: Maybe
Maybe Equiv Maybe: Maybe
Maybe Equiv False: Maybe
False Equiv True: False
False Equiv Maybe: Maybe
False Equiv False: True
```

### Using a general binary -> ternary transform

Instead of writing all of the truth-tables by hand, we can construct a general binary -> ternary transform and apply it to any logical function we want:

`type trit = True | False | Maybe let to_bin = function True -> [true] | False -> [false] | Maybe -> [true;false] let eval f x =   List.fold_left (fun l c -> List.fold_left (fun m d -> ((d c) :: m)) l f) [] x let rec from_bin =   function [true] -> True | [false] -> False   | h :: t -> (match (h, from_bin t) with      (true,True) -> True | (false,False) -> False | _ -> Maybe)   | _ -> Maybe let to_ternary1 uop = fun x -> from_bin (eval [uop] (to_bin x))let to_ternary2 bop = fun x y -> from_bin (eval (eval [bop] (to_bin x)) (to_bin y)) let t_not   = to_ternary1 (not)let t_and   = to_ternary2 (&&)let t_or    = to_ternary2 (||)let t_equiv = to_ternary2 (=)let t_imply = to_ternary2 (fun p q -> (not p) || q) let str = function True -> "True " | False -> "False" | Maybe -> "Maybe"let iterv f = List.iter f [True; False; Maybe] let table1 s u =   print_endline ("\n"^s^":");   iterv (fun v -> print_endline ("  "^(str v)^" -> "^(str (u v))));; let table2 s b =   print_endline ("\n"^s^":");   iterv (fun u ->      iterv (fun v ->         print_endline ("  "^(str u)^" "^(str v)^" -> "^(str (b u v)))));; table1 "not" t_not;;table2 "and" t_and;;table2 "or" t_or;;table2 "equiv" t_equiv;;table2 "implies" t_imply;;`
Output:
```not:
True  -> False
False -> True
Maybe -> Maybe

and:
True  True  -> True
True  False -> False
True  Maybe -> Maybe
False True  -> False
False False -> False
False Maybe -> False
Maybe True  -> Maybe
Maybe False -> False
Maybe Maybe -> Maybe

or:
True  True  -> True
True  False -> True
True  Maybe -> True
False True  -> True
False False -> False
False Maybe -> Maybe
Maybe True  -> True
Maybe False -> Maybe
Maybe Maybe -> Maybe

equiv:
True  True  -> True
True  False -> False
True  Maybe -> Maybe
False True  -> False
False False -> True
False Maybe -> Maybe
Maybe True  -> Maybe
Maybe False -> Maybe
Maybe Maybe -> Maybe

implies:
True  True  -> True
True  False -> False
True  Maybe -> Maybe
False True  -> True
False False -> True
False Maybe -> True
Maybe True  -> True
Maybe False -> Maybe
Maybe Maybe -> Maybe```

## ooRexx

` tritValues = .array~of(.trit~true, .trit~false, .trit~maybe)tab = '09'x say "not operation (\)"loop a over tritValues    say "\"a":" (\a)end saysay "and operation (&)"loop aa over tritValues    loop bb over tritValues        say (aa" & "bb":" (aa&bb))    endend saysay "or operation (|)"loop aa over tritValues    loop bb over tritValues        say (aa" | "bb":" (aa|bb))    endend saysay "implies operation (&&)"loop aa over tritValues    loop bb over tritValues        say (aa" && "bb":" (aa&&bb))    endend saysay "equals operation (=)"loop aa over tritValues    loop bb over tritValues        say (aa" = "bb":" (aa=bb))    endend ::class trit-- making this a private method so we can control the creation-- of these.  We only allow 3 instances to exist::method new class private  forward class(super) ::method init class  expose true false maybe  -- delayed creation  true = .nil  false = .nil  maybe = .nil -- read only attribute access to the instances.-- these methods create the appropriate singleton on the first call::attribute true class get  expose true  if true == .nil then true = self~new("True")  return true ::attribute false class get  expose false  if false == .nil then false = self~new("False")  return false ::attribute maybe class get  expose maybe  if maybe == .nil then maybe = self~new("Maybe")  return maybe -- create an instance::method init  expose value  use arg value -- string method to return the value of the instance::method string  expose value  return value -- "and" method using the operator overload::method "&"  use strict arg other  if self == .trit~true then return other  else if self == .trit~maybe then do      if other == .trit~false then return .trit~false      else return .trit~maybe  end  else return .trit~false -- "or" method using the operator overload::method "|"  use strict arg other  if self == .trit~true then return .trit~true  else if self == .trit~maybe then do      if other == .trit~true then return .trit~true      else return .trit~maybe  end  else return other -- implies method...using the XOR operator for this::method "&&"  use strict arg other  if self == .trit~true then return other  else if self == .trit~maybe then do      if other == .trit~true then return .trit~true      else return .trit~maybe  end  else return .trit~true -- "not" method using the operator overload::method "\"  if self == .trit~true then return .trit~false  else if self == .trit~maybe then return .trit~maybe  else return .trit~true -- "equals" using the "=" override.  This makes a distinction between-- the "==" operator, which is real equality and the "=" operator, which-- is trinary equality.::method "="  use strict arg other  if self == .trit~true then return other  else if self == .trit~maybe then return .trit~maybe  else return \other `
```not operation (\)
\True: False
\False: True
\Maybe: Maybe

and operation (&)
True & True: True
True & False: False
True & Maybe: Maybe
False & True: False
False & False: False
False & Maybe: False
Maybe & True: Maybe
Maybe & False: False
Maybe & Maybe: Maybe

or operation (|)
True | True: True
True | False: True
True | Maybe: True
False | True: True
False | False: False
False | Maybe: Maybe
Maybe | True: True
Maybe | False: Maybe
Maybe | Maybe: Maybe

implies operation (&&)
True && True: True
True && False: False
True && Maybe: Maybe
False && True: True
False && False: True
False && Maybe: True
Maybe && True: True
Maybe && False: Maybe
Maybe && Maybe: Maybe

equals operation (=)
True = True: True
True = False: False
True = Maybe: Maybe
False = True: False
False = False: True
False = Maybe: Maybe
Maybe = True: Maybe
Maybe = False: Maybe
Maybe = Maybe: Maybe
```

## Pascal

`Program TernaryLogic (output); type  trit = (terTrue, terMayBe, terFalse); function terNot (a: trit): trit;  begin    case a of      terTrue:  terNot := terFalse;      terMayBe: terNot := terMayBe;      terFalse: terNot := terTrue;    end;  end; function terAnd (a, b: trit): trit;  begin    terAnd := terMayBe;    if (a = terFalse) or (b = terFalse) then      terAnd := terFalse    else      if (a = terTrue) and (b = terTrue) then        terAnd := terTrue;  end; function terOr (a, b: trit): trit;  begin    terOr := terMayBe;    if (a = terTrue) or (b = terTrue) then      terOr := terTrue    else      if (a = terFalse) and (b = terFalse) then        terOr := terFalse;  end; function terEquals (a, b: trit): trit;  begin    if a = b then      terEquals := terTrue    else      if a <> b then        terEquals := terFalse;    if (a = terMayBe) or (b = terMayBe) then      terEquals := terMayBe;  end; function terIfThen (a, b: trit): trit;  begin    terIfThen := terMayBe;    if (a = terTrue) or (b = terFalse)  then      terIfThen := terTrue    else      if (a = terFalse) and (b = terTrue) then        terIfThen := terFalse;  end; function terToStr(a: trit): string;  begin    case a of      terTrue:  terToStr := 'True ';      terMayBe: terToStr := 'Maybe';      terFalse: terToStr := 'False';    end;  end; begin  writeln('Ternary logic test:');  writeln;  writeln('NOT ', ' True ', ' Maybe', ' False');  writeln('     ', terToStr(terNot(terTrue)), ' ', terToStr(terNot(terMayBe)), ' ', terToStr(terNot(terFalse)));  writeln;  writeln('AND   ', ' True ', ' Maybe', ' False');  writeln('True   ', terToStr(terAnd(terTrue,terTrue)),  ' ', terToStr(terAnd(terMayBe,terTrue)),  ' ', terToStr(terAnd(terFalse,terTrue)));  writeln('Maybe  ', terToStr(terAnd(terTrue,terMayBe)), ' ', terToStr(terAnd(terMayBe,terMayBe)), ' ', terToStr(terAnd(terFalse,terMayBe)));  writeln('False  ', terToStr(terAnd(terTrue,terFalse)), ' ', terToStr(terAnd(terMayBe,terFalse)), ' ', terToStr(terAnd(terFalse,terFalse)));  writeln;  writeln('OR    ', ' True ', ' Maybe', ' False');  writeln('True   ', terToStr(terOR(terTrue,terTrue)),  ' ', terToStr(terOR(terMayBe,terTrue)),  ' ', terToStr(terOR(terFalse,terTrue)));  writeln('Maybe  ', terToStr(terOR(terTrue,terMayBe)), ' ', terToStr(terOR(terMayBe,terMayBe)), ' ', terToStr(terOR(terFalse,terMayBe)));  writeln('False  ', terToStr(terOR(terTrue,terFalse)), ' ', terToStr(terOR(terMayBe,terFalse)), ' ', terToStr(terOR(terFalse,terFalse)));  writeln;  writeln('IFTHEN', ' True ', ' Maybe', ' False');  writeln('True   ', terToStr(terIfThen(terTrue,terTrue)),  ' ', terToStr(terIfThen(terMayBe,terTrue)),  ' ', terToStr(terIfThen(terFalse,terTrue)));  writeln('Maybe  ', terToStr(terIfThen(terTrue,terMayBe)), ' ', terToStr(terIfThen(terMayBe,terMayBe)), ' ', terToStr(terIfThen(terFalse,terMayBe)));  writeln('False  ', terToStr(terIfThen(terTrue,terFalse)), ' ', terToStr(terIfThen(terMayBe,terFalse)), ' ', terToStr(terIfThen(terFalse,terFalse)));  writeln;  writeln('EQUAL ', ' True ', ' Maybe', ' False');  writeln('True   ', terToStr(terEquals(terTrue,terTrue)),  ' ', terToStr(terEquals(terMayBe,terTrue)),  ' ', terToStr(terEquals(terFalse,terTrue)));  writeln('Maybe  ', terToStr(terEquals(terTrue,terMayBe)), ' ', terToStr(terEquals(terMayBe,terMayBe)), ' ', terToStr(terEquals(terFalse,terMayBe)));  writeln('False  ', terToStr(terEquals(terTrue,terFalse)), ' ', terToStr(terEquals(terMayBe,terFalse)), ' ', terToStr(terEquals(terFalse,terFalse)));  writeln;end.`
Output:
```:> ./TernaryLogic
Ternary logic test:

NOT  True  Maybe False
False Maybe True

AND    True  Maybe False
True   True  Maybe False
Maybe  Maybe Maybe False
False  False False False

OR     True  Maybe False
True   True  True  True
Maybe  True  Maybe Maybe
False  True  Maybe False

IFTHEN True  Maybe False
True   True  Maybe False
Maybe  True  Maybe Maybe
False  True  True  True

EQUAL  True  Maybe False
True   True  Maybe False
Maybe  Maybe Maybe Maybe
False  False Maybe True

```

## Perl

File Trit.pm:

`package Trit; # -1 = false ; 0 = maybe ; 1 = true use Exporter 'import'; our @EXPORT_OK = qw(TRUE FALSE MAYBE is_true is_false is_maybe);our %EXPORT_TAGS = (	all => \@EXPORT_OK,	const => [qw(TRUE FALSE MAYBE)],	bool => [qw(is_true is_false is_maybe)],); use List::Util qw(min max); use overload'='  => sub { \$_->clone() },'<=>'=> sub { \$_->cmp(\$_) },'cmp'=> sub { \$_->cmp(\$_) },'==' => sub { \${\$_} == \${\$_} },'eq' => sub { \$_->equiv(\$_) },'>'  => sub { \${\$_} > \${\$_} },'<'  => sub { \${\$_} < \${\$_} },'>=' => sub { \${\$_} >= \${\$_} },'<=' => sub { \${\$_} <= \${\$_} },'|'  => sub { \$_->or(\$_) },'&'  => sub { \$_->and(\$_) },'!'  => sub { \$_->not() },'~'  => sub { \$_->not() },'""' => sub { \$_->tostr() },'0+' => sub { \$_->tonum() },; sub new{	my (\$class, \$v) = @_;	my \$ret =		!defined(\$v) ? 0 :		\$v eq 'true' ? 1 :		\$v eq 'false'? -1 :		\$v eq 'maybe'? 0 :		\$v > 0 ? 1 :		\$v < 0 ? -1 :		0;	return bless \\$ret, \$class;} sub TRUE()  { new Trit( 1) }sub FALSE() { new Trit(-1) }sub MAYBE() { new Trit( 0) } sub clone{	my \$ret = \${\$_};	return bless \\$ret, ref(\$_);} sub tostr { \${\$_} > 0 ? "true" : \${\$_} < 0 ? "false" : "maybe" }sub tonum { \${\$_} } sub is_true { \${\$_} > 0 }sub is_false { \${\$_} < 0 }sub is_maybe { \${\$_} == 0 } sub cmp { \${\$_} <=> \${\$_} }sub not { new Trit(-\${\$_}) }sub and { new Trit(min(\${\$_}, \${\$_}) ) }sub or  { new Trit(max(\${\$_}, \${\$_}) ) } sub equiv { new Trit( \${\$_} * \${\$_} ) }`

File test.pl:

`use Trit ':all'; my @a = (TRUE(), MAYBE(), FALSE()); print "\na\tNOT a\n";print "\$_\t".(!\$_)."\n" for @a;	# Example of use of prefix operator NOT. Tilde ~ also can be used.  print "\nAND\t".join("\t",@a)."\n";for my \$a (@a) {	print \$a;	for my \$b (@a) {		print "\t".(\$a & \$b);	# Example of use of infix & (and)	}	print "\n";} print "\nOR\t".join("\t",@a)."\n";for my \$a (@a) {	print \$a;	for my \$b (@a) {		print "\t".(\$a | \$b);	# Example of use of infix | (or)	}	print "\n";} print "\nEQV\t".join("\t",@a)."\n";for my \$a (@a) {	print \$a;	for my \$b (@a) {		print "\t".(\$a eq \$b);	# Example of use of infix eq (equivalence)	}	print "\n";} print "\n==\t".join("\t",@a)."\n";for my \$a (@a) {	print \$a;	for my \$b (@a) {		print "\t".(\$a == \$b);	# Example of use of infix == (equality)	}	print "\n";}`
Output:
```a	NOT a
true	false
maybe	maybe
false	true

AND	true	maybe	false
true	true	maybe	false
maybe	maybe	maybe	false
false	false	false	false

OR	true	maybe	false
true	true	true	true
maybe	true	maybe	maybe
false	true	maybe	false

EQV	true	maybe	false
true	true	maybe	false
maybe	maybe	maybe	maybe
false	false	maybe	true

==	true	maybe	false
true	1
maybe		1
false			1```

## Perl 6

Works with: rakudo version 2018.03

The precedence of each operator is specified as equivalent to an existing operator. We've taken the liberty of using a double arrow for implication, to avoid confusing it with , (U+2283 SUPERSET OF).

`# Implementation:enum Trit <Foo Moo Too>; sub prefix:<¬> (Trit \$a) { Trit(1-(\$a-1)) } sub infix:<∧> (Trit \$a, Trit \$b) is equiv(&infix:<*>) { \$a min \$b }sub infix:<∨> (Trit \$a, Trit \$b) is equiv(&infix:<+>) { \$a max \$b } sub infix:<⇒> (Trit \$a, Trit \$b) is equiv(&infix:<..>) { ¬\$a max \$b }sub infix:<≡> (Trit \$a, Trit \$b) is equiv(&infix:<eq>) { Trit(1 + (\$a-1) * (\$b-1)) } # Testing:say '¬';say "Too {¬Too}";say "Moo {¬Moo}";say "Foo {¬Foo}"; sub tbl (&op,\$name) {    say '';    say "\$name   Too Moo Foo";    say "   ╔═══════════";    say "Too║{op Too,Too} {op Too,Moo} {op Too,Foo}";    say "Moo║{op Moo,Too} {op Moo,Moo} {op Moo,Foo}";    say "Foo║{op Foo,Too} {op Foo,Moo} {op Foo,Foo}";} tbl(&infix:<∧>, '∧');tbl(&infix:<∨>, '∨');tbl(&infix:<⇒>, '⇒');tbl(&infix:<≡>, '≡'); say '';say 'Precedence tests should all print "Too":';say ~(    Foo ∧ Too ∨ Too ≡ Too,    Foo ∧ (Too ∨ Too) ≡ Foo,    Too ∨ Too ∧ Foo ≡ Too,    (Too ∨ Too) ∧ Foo ≡ Foo,     ¬Too ∧ Too ∨ Too ≡ Too,    ¬Too ∧ (Too ∨ Too) ≡ ¬Too,    Too ∨ Too ∧ ¬Too ≡ Too,    (Too ∨ Too) ∧ ¬Too ≡ ¬Too,     Foo ∧ Too ∨ Foo ⇒ Foo ≡ Too,    Foo ∧ Too ∨ Too ⇒ Foo ≡ Foo,);`
Output:
```¬
Too Foo
Moo Moo
Foo Too

∧   Too Moo Foo
╔═══════════
Too║Too Moo Foo
Moo║Moo Moo Foo
Foo║Foo Foo Foo

∨   Too Moo Foo
╔═══════════
Too║Too Too Too
Moo║Too Moo Moo
Foo║Too Moo Foo

⇒   Too Moo Foo
╔═══════════
Too║Too Moo Foo
Moo║Too Moo Moo
Foo║Too Too Too

≡   Too Moo Foo
╔═══════════
Too║Too Moo Foo
Moo║Moo Moo Moo
Foo║Foo Moo Too

Precedence tests should all print "Too":
Too Too Too Too Too Too Too Too Too Too```

## Phix

`enum type ternary T, M, F end type function t_not(ternary a)    return F+1-aend function function t_and(ternary a, ternary b)    return iff(a=T and b=T?T:iff(a=F or b=F?F:M))   end function function t_or(ternary a, ternary b)    return iff(a=T or b=T?T:iff(a=F and b=F?F:M))   end function function t_xor(ternary a, ternary b)    return iff(a=M or b=M?M:iff(a=b?F:T))end function function t_implies(ternary a, ternary b)    return iff(a=F or b=T?T:iff(a=T and b=F?F:M))   end function function t_equal(ternary a, ternary b)    return iff(a=M or b=M?M:iff(a=b?T:F))end function function t_string(ternary a)    return iff(a=T?"T":iff(a=M?"?":"F"))end function procedure show_truth_table(integer rid, integer unary, string name)    printf(1,"%-3s |%s\n",{name,iff(unary?"":" T | ? | F")})    printf(1,"----+---%s\n",{iff(unary?"":"+---+---")})    for x=T to F do        printf(1," %s ",{t_string(x)})        if unary then            printf(1," | %s",{t_string(call_func(rid,{x}))})        else            for y=T to F do                printf(1," | %s",{t_string(call_func(rid,{x,y}))})            end for        end if        printf(1,"\n")    end for    printf(1,"\n")end procedure show_truth_table(routine_id("t_not"),1,"not")show_truth_table(routine_id("t_and"),0,"and")show_truth_table(routine_id("t_or"),0,"or")show_truth_table(routine_id("t_xor"),0,"xor")show_truth_table(routine_id("t_implies"),0,"imp")show_truth_table(routine_id("t_equal"),0,"eq")`
Output:
```not |
----+---
T  | F
?  | ?
F  | T

and | T | ? | F
----+---+---+---
T  | T | ? | F
?  | ? | ? | F
F  | F | F | F

or  | T | ? | F
----+---+---+---
T  | T | T | T
?  | T | ? | ?
F  | T | ? | F

xor | T | ? | F
----+---+---+---
T  | F | ? | T
?  | ? | ? | ?
F  | T | ? | F

imp | T | ? | F
----+---+---+---
T  | T | ? | F
?  | T | ? | ?
F  | T | T | T

eq  | T | ? | F
----+---+---+---
T  | T | ? | F
?  | ? | ? | ?
F  | F | ? | T
```

## PHP

Save the sample code as executable shell script on your *nix system:

`#!/usr/bin/php<?php # defined as numbers, so I can use max() and min() on itif (! define('triFalse',0))  trigger_error('Unknown error defining!', E_USER_ERROR);if (! define('triMaybe',1))  trigger_error('Unknown error defining!', E_USER_ERROR);if (! define('triTrue', 2))  trigger_error('Unknown error defining!', E_USER_ERROR); \$triNotarray = array(triFalse=>triTrue, triMaybe=>triMaybe, triTrue=>triFalse); # output helperfunction triString (\$tri) {    if (\$tri===triFalse) return 'false  ';    if (\$tri===triMaybe) return 'unknown';    if (\$tri===triTrue)  return 'true   ';    trigger_error('triString: parameter not a tri value', E_USER_ERROR);} function triAnd() {    if (func_num_args() < 2)        trigger_error('triAnd needs 2 or more parameters', E_USER_ERROR);    return min(func_get_args());} function triOr() {    if (func_num_args() < 2)        trigger_error('triOr needs 2 or more parameters', E_USER_ERROR);    return max(func_get_args());} function triNot(\$t) {    global \$triNotarray; # using result table    if (in_array(\$t, \$triNotarray)) return \$triNotarray[\$t];    trigger_error('triNot: Parameter is not a tri value', E_USER_ERROR);} function triImplies(\$a, \$b) {    if (\$a===triFalse || \$b===triTrue)  return triTrue;    if (\$a===triMaybe || \$b===triMaybe) return triMaybe;    # without parameter type check I just would return triFalse here    if (\$a===triTrue &&  \$b===triFalse) return triFalse;    trigger_error('triImplies: parameter type error', E_USER_ERROR);} function triEquiv(\$a, \$b) {    if (\$a===triTrue)  return \$b;    if (\$a===triMaybe) return \$a;    if (\$a===triFalse) return triNot(\$b);    trigger_error('triEquiv: parameter type error', E_USER_ERROR);} # data samplingprintf("--- Sample output for a equivalent b ---\n\n"); foreach ([triTrue,triMaybe,triFalse] as \$a) {    foreach ([triTrue,triMaybe,triFalse] as \$b) {        printf("for a=%s and b=%s a equivalent b is %s\n",               triString(\$a), triString(\$b), triString(triEquiv(\$a, \$b)));    }}  `

Sample output:

```--- Sample output for a equivalent b ---

for a=true    and b=true    a equivalent b is true
for a=true    and b=unknown a equivalent b is unknown
for a=true    and b=false   a equivalent b is false
for a=unknown and b=true    a equivalent b is unknown
for a=unknown and b=unknown a equivalent b is unknown
for a=unknown and b=false   a equivalent b is unknown
for a=false   and b=true    a equivalent b is false
for a=false   and b=unknown a equivalent b is unknown
for a=false   and b=false   a equivalent b is true
```

## PicoLisp

In addition for the standard T (for "true") and NIL (for "false") we define 0 (zero, for "maybe").

`(de 3not (A)   (or (=0 A) (not A)) ) (de 3and (A B)   (cond      ((=T A) B)      ((=0 A) (and B 0)) ) ) (de 3or (A B)   (cond      ((=T A) T)      ((=0 A) (or (=T B) 0))      (T B) ) ) (de 3impl (A B)   (cond      ((=T A) B)      ((=0 A) (or (=T B) 0))      (T T) ) ) (de 3equiv (A B)   (cond      ((=T A) B)      ((=0 A) 0)      (T (3not B)) ) )`

Test:

`(for X '(T 0 NIL)   (println 'not X '-> (3not X)) ) (for Fun '((and . 3and) (or . 3or) (implies . 3impl) (equivalent . 3equiv))   (for X '(T 0 NIL)      (for Y '(T 0 NIL)         (println X (car Fun) Y '-> ((cdr Fun) X Y)) ) ) )`
Output:
```not T -> NIL
not 0 -> 0
not NIL -> T
T and T -> T
T and 0 -> 0
T and NIL -> NIL
0 and T -> 0
0 and 0 -> 0
0 and NIL -> NIL
NIL and T -> NIL
NIL and 0 -> NIL
NIL and NIL -> NIL
T or T -> T
T or 0 -> T
T or NIL -> T
0 or T -> T
0 or 0 -> 0
0 or NIL -> 0
NIL or T -> T
NIL or 0 -> 0
NIL or NIL -> NIL
T implies T -> T
T implies 0 -> 0
T implies NIL -> NIL
0 implies T -> T
0 implies 0 -> 0
0 implies NIL -> 0
NIL implies T -> T
NIL implies 0 -> T
NIL implies NIL -> T
T equivalent T -> T
T equivalent 0 -> 0
T equivalent NIL -> NIL
0 equivalent T -> 0
0 equivalent 0 -> 0
0 equivalent NIL -> 0
NIL equivalent T -> NIL
NIL equivalent 0 -> 0
NIL equivalent NIL -> T```

## Python

In Python, the keywords 'and', 'not', and 'or' are coerced to always work as boolean operators. I have therefore overloaded the boolean bitwise operators &, |, ^ to provide the required functionality.

`class Trit(int):    def __new__(cls, value):        if value == 'TRUE':            value = 1        elif value == 'FALSE':            value = 0        elif value == 'MAYBE':            value = -1        return super(Trit, cls).__new__(cls, value // (abs(value) or 1))      def __repr__(self):        if self > 0:            return 'TRUE'        elif self == 0:            return 'FALSE'        return 'MAYBE'     def __str__(self):        return repr(self)     def __bool__(self):        if self > 0:            return True        elif self == 0:            return False        else:            raise ValueError("invalid literal for bool(): '%s'" % self)     def __or__(self, other):        if isinstance(other, Trit):            return _ttable[(self, other)]        else:            try:                return _ttable[(self, Trit(bool(other)))]            except:                return NotImplemented     def __ror__(self, other):        if isinstance(other, Trit):            return _ttable[(self, other)]        else:            try:                return _ttable[(self, Trit(bool(other)))]            except:                return NotImplemented     def __and__(self, other):        if isinstance(other, Trit):            return _ttable[(self, other)]        else:            try:                return _ttable[(self, Trit(bool(other)))]            except:                return NotImplemented     def __rand__(self, other):        if isinstance(other, Trit):            return _ttable[(self, other)]        else:            try:                return _ttable[(self, Trit(bool(other)))]            except:                return NotImplemented     def __xor__(self, other):        if isinstance(other, Trit):            return _ttable[(self, other)]        else:            try:                return _ttable[(self, Trit(bool(other)))]            except:                return NotImplemented     def __rxor__(self, other):        if isinstance(other, Trit):            return _ttable[(self, other)]        else:            try:                return _ttable[(self, Trit(bool(other)))]            except:                return NotImplemented     def __invert__(self):        return _ttable[self]     def __getattr__(self, name):        if name in ('_n', 'flip'):            # So you can do x._n == x.flip; the inverse of x            # In Python 'not' is strictly boolean so we can't write `not x`            # Same applies to keywords 'and' and 'or'.            return _ttable[self]        else:            raise AttributeError    TRUE, FALSE, MAYBE = Trit(1), Trit(0), Trit(-1) _ttable = {    #    A: -> flip_A         TRUE: FALSE,        FALSE:  TRUE,        MAYBE: MAYBE,    #     (A, B): -> (A_and_B, A_or_B, A_xor_B)        (MAYBE, MAYBE): (MAYBE, MAYBE, MAYBE),        (MAYBE, FALSE): (FALSE, MAYBE, MAYBE),        (MAYBE,  TRUE): (MAYBE,  TRUE, MAYBE),        (FALSE, MAYBE): (FALSE, MAYBE, MAYBE),        (FALSE, FALSE): (FALSE, FALSE, FALSE),        (FALSE,  TRUE): (FALSE,  TRUE,  TRUE),        ( TRUE, MAYBE): (MAYBE,  TRUE, MAYBE),        ( TRUE, FALSE): (FALSE,  TRUE,  TRUE),        ( TRUE,  TRUE): ( TRUE,  TRUE, FALSE),    }  values = ('FALSE', 'TRUE ', 'MAYBE') print("\nTrit logical inverse, '~'")for a in values:    expr = '~%s' % a    print('  %s = %s' % (expr, eval(expr))) for op, ophelp in (('&', 'and'), ('|', 'or'), ('^', 'exclusive-or')):    print("\nTrit logical %s, '%s'" % (ophelp, op))    for a in values:        for b in values:            expr = '%s %s %s' % (a, op, b)            print('  %s = %s' % (expr, eval(expr)))`
Output:
```Trit logical inverse, '~'
~FALSE = TRUE
~TRUE  = FALSE
~MAYBE = MAYBE

Trit logical and, '&'
FALSE & FALSE = FALSE
FALSE & TRUE  = FALSE
FALSE & MAYBE = FALSE
TRUE  & FALSE = FALSE
TRUE  & TRUE  = TRUE
TRUE  & MAYBE = MAYBE
MAYBE & FALSE = FALSE
MAYBE & TRUE  = MAYBE
MAYBE & MAYBE = MAYBE

Trit logical or, '|'
FALSE | FALSE = FALSE
FALSE | TRUE  = TRUE
FALSE | MAYBE = MAYBE
TRUE  | FALSE = TRUE
TRUE  | TRUE  = TRUE
TRUE  | MAYBE = TRUE
MAYBE | FALSE = MAYBE
MAYBE | TRUE  = TRUE
MAYBE | MAYBE = MAYBE

Trit logical exclusive-or, '^'
FALSE ^ FALSE = FALSE
FALSE ^ TRUE  = TRUE
FALSE ^ MAYBE = MAYBE
TRUE  ^ FALSE = TRUE
TRUE  ^ TRUE  = FALSE
TRUE  ^ MAYBE = MAYBE
MAYBE ^ FALSE = MAYBE
MAYBE ^ TRUE  = MAYBE
MAYBE ^ MAYBE = MAYBE```
Extra doodling in the Python shell
```>>> values = (TRUE, FALSE, MAYBE)
>>> for a in values:
for b in values:
assert (a & ~b) | (b & ~a) == a ^ b

>>> ```

## Racket

`#lang typed/racket ; to avoid the hassle of adding a maybe value that is as special as; the two standard booleans, we'll use symbols to make our own(define-type trit (U 'true 'false 'maybe)) (: not (trit -> trit))(define (not a)  (case a    [(true) 'false]    [(maybe) 'maybe]    [(false) 'true])) (: and (trit trit -> trit))(define (and a b)  (case a    [(false) 'false]    [(maybe) (case b               [(false) 'false]               [else 'maybe])]    [(true) (case b              [(true) 'true]              [(maybe) 'maybe]              [(false) 'false])])) (: or (trit trit -> trit))(define (or a b)  (case a    [(true) 'true]    [(maybe) (case b               [(true) 'true]               [else 'maybe])]    [(false) (case b               [(true) 'true]               [(maybe) 'maybe]               [(false) 'false])])) (: ifthen (trit trit -> trit))(define (ifthen a b)  (case b    [(true) 'true]    [(maybe) (case a               [(false) 'true]               [else 'maybe])]    [(false) (case a               [(true) 'false]               [(maybe) 'maybe]               [(false) 'true])])) (: iff (trit trit -> trit))(define (iff a b)  (case a    [(maybe) 'maybe]    [(true) b]    [(false) (not b)])) (for: : Void ([a (in-list '(true maybe false))])      (printf "~a ~a = ~a~n" (object-name not) a (not a)))(for: : Void ([proc (in-list (list and or ifthen iff))])  (for*: : Void ([a (in-list '(true maybe false))]                 [b (in-list '(true maybe false))])         (printf "~a ~a ~a = ~a~n" a (object-name proc) b (proc a b))))`
Output:
```not true = false
not maybe = maybe
not false = true
true and true = true
true and maybe = maybe
true and false = false
maybe and true = maybe
maybe and maybe = maybe
maybe and false = false
false and true = false
false and maybe = false
false and false = false
true or true = true
true or maybe = true
true or false = true
maybe or true = true
maybe or maybe = maybe
maybe or false = maybe
false or true = true
false or maybe = maybe
false or false = false
true ifthen true = true
true ifthen maybe = maybe
true ifthen false = false
maybe ifthen true = true
maybe ifthen maybe = maybe
maybe ifthen false = maybe
false ifthen true = true
false ifthen maybe = true
false ifthen false = true
true iff true = true
true iff maybe = maybe
true iff false = false
maybe iff true = maybe
maybe iff maybe = maybe
maybe iff false = maybe
false iff true = false
false iff maybe = maybe
false iff false = true
```

## REXX

This REXX program is a re-worked version of the REXX program used for the Rosetta Code task:   truth table.

`/*REXX program displays a ternary truth table  [true, false, maybe]   for the variables *//*──── and one or more expressions.                                                     *//*──── Infix notation is supported with one character propositional constants.          *//*──── Variables (propositional constants) allowed:    A ──► Z,     a ──► z   except  u.*//*──── All propositional constants are case insensative  (except lowercase  v).         */parse arg \$express                               /*obtain optional argument from the CL.*/if \$express\=''  then do                         /*Got one?  Then show user's expression*/                      call truthTable \$express   /*display the user's truth table──►term*/                      exit                       /*we're all done with the truth table. */                      end call truthTable  "a & b ; AND"call truthTable  "a | b ; OR"call truthTable  "a ^ b ; XOR"call truthTable  "a ! b ; NOR"call truthTable  "a ¡ b ; NAND"call truthTable  "a xnor b ; XNOR"               /*XNOR  is the same as  NXOR.          */exit                                             /*stick a fork in it,  we're all done. *//*──────────────────────────────────────────────────────────────────────────────────────*/truthTable: procedure; parse arg \$ ';' comm 1 \$o;        \$o=strip(\$o)      \$=translate(strip(\$), '|', "v");                   \$u=\$;        upper \$u      \$u=translate(\$u, '()()()', "[]{}«»");              \$\$.=0;       PCs=;        hdrPCs=      @abc= 'abcdefghijklmnopqrstuvwxyz';                @[email protected];  upper @abcU      @= 'ff'x                                         /*─────────infix operators───────*/      op.=                                             /*a single quote (') wasn't      */                                                       /*     implemented for negation. */      op.0  = 'false  boolFALSE'                       /*unconditionally  FALSE         */      op.1  = 'and    and & *'                         /* AND, conjunction              */      op.2  = 'naimpb NaIMPb'                          /*not A implies B                */      op.3  = 'boolb  boolB'                           /*B  (value of)                  */      op.4  = 'nbimpa NbIMPa'                          /*not B implies A                */      op.5  = 'boola  boolA'                           /*A  (value of)                  */      op.6  = 'xor    xor && % ^'                      /* XOR, exclusive OR             */      op.7  = 'or     or | + v'                        /*  OR, disjunction              */      op.8  = 'nor    nor ! ↓'                         /* NOR, not OR, Pierce operator  */      op.9  = 'xnor   xnor nxor'                       /*NXOR, not exclusive OR, not XOR*/      op.10 = 'notb   notB'                            /*not B (value of)               */      op.11 = 'bimpa  bIMPa'                           /*    B implies A                */      op.12 = 'nota   notA'                            /*not A (value of)               */      op.13 = 'aimpb  aIMPb'                           /*    A implies B                */      op.14 = 'nand   nand ¡ ↑'                        /*NAND, not AND, Sheffer operator*/      op.15 = 'true   boolTRUE'                        /*unconditionally   TRUE         */                                                       /*alphabetic names need changing.*/      op.16 = '\   NOT ~ ─ . ¬'                        /* NOT, negation                 */      op.17 = '>   GT'                                 /*conditional greater than       */      op.18 = '>=  GE ─> => ──> ==>' "1a"x             /*conditional greater than or eq.*/      op.19 = '<   LT'                                 /*conditional less than          */      op.20 = '<=  LE <─ <= <── <=='                   /*conditional less then or equal */      op.21 = '\=  NE ~= ─= .= ¬='                     /*conditional not equal to       */      op.22 = '=   EQ EQUAL EQUALS =' "1b"x            /*biconditional  (equals)        */      op.23 = '0   boolTRUE'                           /*TRUEness                       */      op.24 = '1   boolFALSE'                          /*FALSEness                      */       op.25 = 'NOT NOT NEG'                            /*not, neg  (negative)           */         do jj=0  while  op.jj\=='' | jj<16             /*change opers──►what REXX likes.*/        new=word(op.jj,1)          do kk=2  to words(op.jj)                     /*handle each token separately.  */          _=word(op.jj, kk);     upper _          if wordpos(_, \$u)==0   then iterate          /*no such animal in this string. */          if datatype(new, 'm')  then [email protected]           /*expresion needs transcribing.  */                                 else new!=new          \$u=changestr(_, \$u, new!)                    /*transcribe the function (maybe)*/          if [email protected]  then \$u=changeFunc(\$u, @, new)   /*use the internal boolean name. */          end   /*kk*/        end     /*jj*/       \$u=translate(\$u, '()', "{}")                     /*finish cleaning up transcribing*/            do jj=1  for length(@abcU)                 /*see what variables are used.   */            _=substr(@abcU, jj, 1)                     /*use available upercase alphabet*/            if pos(_,\$u)==0  then iterate              /*found one?   No, keep looking. */            \$\$.jj=2                                    /*found:  set upper bound for it.*/            PCs=PCs _                                  /*also, add to propositional cons*/            hdrPCs=hdrPCS  center(_, length('false'))  /*build a propositional cons hdr.*/            end   /*jj*/      \$u=PCs  '('\$u")"                                 /*sep prop. cons. from expression*/      ptr='_────►_'                                    /*a pointer for the truth table. */      hdrPCs=substr(hdrPCs,2)                          /*create a header for prop. cons.*/      say hdrPCs left('', length(ptr) -1)   \$o         /*show prop cons hdr +expression.*/      say copies('───── ', words(PCs))   left('', length(ptr)-2)   copies('─', length(\$o))                                                       /*Note: "true"s:  right─justified*/              do a=0  to \$\$.1               do b=0  to \$\$.2                do c=0  to \$\$.3                 do d=0  to \$\$.4                  do e=0  to \$\$.5                   do f=0  to \$\$.6                    do g=0  to \$\$.7                     do h=0  to \$\$.8                      do i=0  to \$\$.9                       do j=0  to \$\$.10                        do k=0  to \$\$.11                         do l=0  to \$\$.12                          do m=0  to \$\$.13                           do n=0  to \$\$.14                            do o=0  to \$\$.15                             do p=0  to \$\$.16                              do q=0  to \$\$.17                               do r=0  to \$\$.18                                do s=0  to \$\$.19                                 do t=0  to \$\$.20                                  do u=0  to \$\$.21                                   do !=0  to \$\$.22                                    do w=0  to \$\$.23                                     do x=0  to \$\$.24                                      do y=0  to \$\$.25                                       do z=0  to \$\$.26                                       interpret '_=' \$u             /*evaluate truth T.*/                                       _=changestr(0, _, 'false')    /*convert 0──►false*/                                       _=changestr(1, _, '_true')    /*convert 1──►_true*/                                       _=changestr(2, _, 'maybe')    /*convert 2──►maybe*/                                       _=insert(ptr, _, wordindex(_, words(_)) -1) /*──►*/                                       say translate(_, , '_')       /*display truth tab*/                                       end   /*z*/                                      end    /*y*/                                     end     /*x*/                                    end      /*w*/                                   end       /*v*/                                  end        /*u*/                                 end         /*t*/                                end          /*s*/                               end           /*r*/                              end            /*q*/                             end             /*p*/                            end              /*o*/                           end               /*n*/                          end                /*m*/                         end                 /*l*/                        end                  /*k*/                       end                   /*j*/                      end                    /*i*/                     end                     /*h*/                    end                      /*g*/                   end                       /*f*/                  end                        /*e*/                 end                         /*d*/                end                          /*c*/               end                           /*b*/              end                            /*a*/      say      return/*──────────────────────────────────────────────────────────────────────────────────────*/scan: procedure; parse arg x,at;    L=length(x);    t=L;     lp=0;     apost=0;    quote=0      if at<0  then do;   t=1;   x= translate(x, '()', ")(");    end                       do j=abs(at)  to t  by sign(at);  _=substr(x,j,1);  __=substr(x,j,2)                      if quote           then do; if _\=='"'  then iterate                                              if __=='""'     then do; j=j+1; iterate; end                                              quote=0;  iterate                                              end                      if apost           then do; if _\=="'"  then iterate                                              if __=="''"     then do; j=j+1; iterate; end                                              apost=0;  iterate                                              end                      if _=='"'          then do;  quote=1;                   iterate; end                      if _=="'"          then do;  apost=1;                   iterate; end                      if _==' '          then iterate                      if _=='('          then do;  lp=lp+1;                   iterate; end                      if lp\==0          then do;  if _==')'  then lp=lp-1;   iterate; end                      if datatype(_,'U') then return j - (at<0)                      if at<0            then return j + 1                      end   /*j*/      return min(j,L)/*──────────────────────────────────────────────────────────────────────────────────────*/changeFunc: procedure;  parse arg z,fC,newF;       funcPos= 0            do forever            funcPos= pos(fC, z, funcPos + 1);      if funcPos==0  then return z            origPos= funcPos                  z= changestr(fC, z, ",'"newF"',")            funcPos= funcPos + length(newF) + 4              where= scan(z, funcPos)     ;        z= insert(    '}',  z,  where)              where= scan(z, 1 - origPos) ;        z= insert('trit{',  z,  where)            end   /*forever*//*──────────────────────────────────────────────────────────────────────────────────────*/trit: procedure; arg a,\$,b;   v= \(a==2 | b==2);    o= (a==1 | b==1);     z= (a==0 | b==0)            select            when \$=='FALSE'   then            return 0            when \$=='AND'     then if v  then return a & b;      else return 2            when \$=='NAIMPB'  then if v  then return \(\a & \b); else return 2            when \$=='BOOLB'   then            return b            when \$=='NBIMPA'  then if v  then return \(\b & \a); else return 2            when \$=='BOOLA'   then            return a            when \$=='XOR'     then if v  then return a && b    ; else return 2            when \$=='OR'      then if v  then return a | b     ; else  if o  then return 1                                                                             else return 2            when \$=='NOR'     then if v  then return \(a | b)  ; else return 2            when \$=='XNOR'    then if v  then return \(a && b) ; else return 2            when \$=='NOTB'    then if v  then return \b        ; else return 2            when \$=='NOTA'    then if v  then return \a        ; else return 2            when \$=='AIMPB'   then if v  then return \(a & \b) ; else return 2            when \$=='NAND'    then if v  then return \(a &  b) ; else  if z  then return 1                                                                             else return 2            when \$=='TRUE'    then           return   1            otherwise                        return -13       /*error, unknown function.*/            end   /*select*/ `

Some older REXXes don't have a   changestr   BIF, so one is included here   ──►   CHANGESTR.REX.

output

```  A     B          a & b ; AND
───── ─────        ───────────
false false  ────► false
false  true  ────► false
false maybe  ────► maybe
true false  ────► false
true  true  ────►  true
true maybe  ────► maybe
maybe false  ────► maybe
maybe  true  ────► maybe
maybe maybe  ────► maybe

A     B          a | b ; OR
───── ─────        ──────────
false false  ────► false
false  true  ────►  true
false maybe  ────► maybe
true false  ────►  true
true  true  ────►  true
true maybe  ────►  true
maybe false  ────► maybe
maybe  true  ────►  true
maybe maybe  ────► maybe

A     B          a ^ b ; XOR
───── ─────        ───────────
false false  ────► false
false  true  ────►  true
false maybe  ────► maybe
true false  ────►  true
true  true  ────► false
true maybe  ────► maybe
maybe false  ────► maybe
maybe  true  ────► maybe
maybe maybe  ────► maybe

A     B          a ! b ; NOR
───── ─────        ───────────
false false  ────►  true
false  true  ────► false
false maybe  ────► maybe
true false  ────► false
true  true  ────► false
true maybe  ────► maybe
maybe false  ────► maybe
maybe  true  ────► maybe
maybe maybe  ────► maybe

A     B          a ¡ b ; NAND
───── ─────        ────────────
false false  ────►  true
false  true  ────►  true
false maybe  ────►  true
true false  ────►  true
true  true  ────► false
true maybe  ────► maybe
maybe false  ────►  true
maybe  true  ────► maybe
maybe maybe  ────► maybe

A     B          a xnor b ; XNOR
───── ─────        ───────────────
false false  ────►  true
false  true  ────► false
false maybe  ────► maybe
true false  ────► false
true  true  ────►  true
true maybe  ────► maybe
maybe false  ────► maybe
maybe  true  ────► maybe
maybe maybe  ────► maybe
```

## Ruby

Ruby, like Smalltalk, has two boolean classes: TrueClass for `true` and FalseClass for `false`. We add a third class, MaybeClass for `MAYBE`, and define ternary logic for all three classes.

We keep `!a`, `a & b` and so on for binary logic. We add `!a.trit`, `a.trit & b` and so on for ternary logic. The code for `!a.trit` uses `def !`, which works with Ruby 1.9, but fails as a syntax error with Ruby 1.8.

Works with: Ruby version 1.9
`# trit.rb - ternary logic# http://rosettacode.org/wiki/Ternary_logic require 'singleton' # MAYBE, the only instance of MaybeClass, enables a system of ternary# logic using TrueClass#trit, MaybeClass#trit and FalseClass#trit.##  !a.trit      # ternary not#  a.trit & b   # ternary and#  a.trit | b   # ternary or#  a.trit ^ b   # ternary exclusive or#  a.trit == b  # ternary equal## Though +true+ and +false+ are internal Ruby values, +MAYBE+ is not.# Programs may want to assign +maybe = MAYBE+ in scopes that use# ternary logic. Then programs can use +true+, +maybe+ and +false+.class MaybeClass  include Singleton   #  maybe.to_s  # => "maybe"  def to_s; "maybe"; endend MAYBE = MaybeClass.instance class TrueClass  TritMagic = Object.new  class << TritMagic    def index; 0; end    def !; false; end    def & other; other; end    def | other; true; end    def ^ other; [false, MAYBE, true][other.trit.index]; end    def == other; other; end  end   # Performs ternary logic. See MaybeClass.  #  !true.trit        # => false  #  true.trit & obj   # => obj  #  true.trit | obj   # => true  #  true.trit ^ obj   # => false, maybe or true  #  true.trit == obj  # => obj  def trit; TritMagic; endend class MaybeClass  TritMagic = Object.new  class << TritMagic    def index; 1; end    def !; MAYBE; end    def & other; [MAYBE, MAYBE, false][other.trit.index]; end    def | other; [true, MAYBE, MAYBE][other.trit.index]; end    def ^ other; MAYBE; end    def == other; MAYBE; end  end   # Performs ternary logic. See MaybeClass.  #  !maybe.trit        # => maybe  #  maybe.trit & obj   # => maybe or false  #  maybe.trit | obj   # => true or maybe  #  maybe.trit ^ obj   # => maybe  #  maybe.trit == obj  # => maybe  def trit; TritMagic; endend class FalseClass  TritMagic = Object.new  class << TritMagic    def index; 2; end    def !; true; end    def & other; false; end    def | other; other; end    def ^ other; other; end    def == other; [false, MAYBE, true][other.trit.index]; end  end   # Performs ternary logic. See MaybeClass.  #  !false.trit        # => true  #  false.trit & obj   # => false  #  false.trit | obj   # => obj  #  false.trit ^ obj   # => obj  #  false.trit == obj  # => false, maybe or true  def trit; TritMagic; endend`

This IRB session shows ternary not, and, or, equal.

`\$ irbirb(main):001:0> require './trit'=> trueirb(main):002:0> maybe = MAYBE=> maybeirb(main):003:0> !true.trit       => falseirb(main):004:0> !maybe.trit=> maybeirb(main):005:0> maybe.trit & false=> falseirb(main):006:0> maybe.trit | true=> trueirb(main):007:0> false.trit == true       => falseirb(main):008:0> false.trit == maybe=> maybe`

This program shows all 9 outcomes from `a.trit ^ b`.

`require 'trit'maybe = MAYBE [true, maybe, false].each do |a|  [true, maybe, false].each do |b|    printf "%5s ^ %5s => %5s\n", a, b, a.trit ^ b  endend`
```\$ ruby -I. trit-xor.rb
true ^  true => false
true ^ maybe => maybe
true ^ false =>  true
maybe ^  true => maybe
maybe ^ maybe => maybe
maybe ^ false => maybe
false ^  true =>  true
false ^ maybe => maybe
false ^ false => false```

## Run BASIC

`testFalse	= 0  ' FtestDoNotKnow	= 1  ' ?testTrue	= 2  ' T print "Short and long names for ternary logic values"for i = testFalse to testTrue    print shortName3\$(i);" ";longName3\$(i)next iprint print "Single parameter functions"print "x";" ";"=x";"  ";"not(x)"for i = testFalse to testTrue    print shortName3\$(i);"  ";shortName3\$(i);"    ";shortName3\$(not3(i))nextprint print "Double  parameter fuctions"html "<table border=1><TR align=center bgcolor=wheat><TD>x</td><td>y</td><td>x AND y</td><td>x OR y</td><td>x EQ y</td><td>x XOR y</td></tr>"for a	= testFalse to testTrue    for b	= testFalse to testTrue      html "<TR align=center><td>"      html shortName3\$(a);        "</td><td>";shortName3\$(b);        "</td><td>"      html shortName3\$(and3(a,b));"</td><td>";shortName3\$(or3(a,b)); "</td><td>"      html shortName3\$(eq3(a,b)); "</td><td>";shortName3\$(xor3(a,b));"</td></tr>"    nextnexthtml "</table>"function and3(a,b)    and3	= min(a,b)end function function or3(a,b)    or3	= max(a,b)end function function eq3(a,b)    eq3 	= testFalse    if a	= tDontKnow or b	= tDontKnow then eq3	= tDontKnow    if a	= b then eq3	= testTrueend function function xor3(a,b)    xor3	= not3(eq3(a,b))end function function not3(b)    not3	= 2-bend function '------------------------------------------------function shortName3\$(i)   shortName3\$	= word\$("F ? T", i+1)end function function longName3\$(i)    longName3\$	= word\$("False,Don't know,True", i+1, ",")end function`
```Short and long names for ternary logic values
F False
? Don't know
T True
Single parameter functions
x =x  not(x)
F  F  T
?  ?  ?
T  T  F

Double  parameter fuctions```
 x y x AND y x OR y x EQ y x XOR y F F F F T F F ? F ? F T F T F T F T ? F F ? F T ? ? ? ? T F ? T ? T F T T F F T F T T ? ? T F T T T T T T F

## Rust

Translation of: Kotlin
`use std::{ops, fmt}; #[derive(Copy, Clone, Debug)]enum Trit {    True,    Maybe,    False,} impl ops::Not for Trit {    type Output = Self;    fn not(self) -> Self {        match self {            Trit::True => Trit::False,            Trit::Maybe => Trit::Maybe,            Trit::False => Trit::True,        }    }} impl ops::BitAnd for Trit {    type Output = Self;    fn bitand(self, other: Self) -> Self {        match (self, other) {            (Trit::True, Trit::True) => Trit::True,            (Trit::False, _) | (_, Trit::False) => Trit::False,            _ => Trit::Maybe,        }    }} impl ops::BitOr for Trit {    type Output = Self;    fn bitor(self, other: Self) -> Self {        match (self, other) {            (Trit::True, _) | (_, Trit::True) => Trit::True,            (Trit::False, Trit::False) => Trit::False,            _ => Trit::Maybe,        }    }} impl Trit {    fn imp(self, other: Self) -> Self {        match self {            Trit::True => other,            Trit::Maybe => {                if let Trit::True = other {                    Trit::True                } else {                    Trit::Maybe                }            }            Trit::False => Trit::True,        }    }     fn eqv(self, other: Self) -> Self {        match self {            Trit::True => other,            Trit::Maybe => Trit::Maybe,            Trit::False => !other,        }    }} impl fmt::Display for Trit {    fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {        write!(            f,            "{}",            match self {                Trit::True => 'T',                Trit::Maybe => 'M',                Trit::False => 'F',            }        )    }} static TRITS: [Trit; 3] = [Trit::True, Trit::Maybe, Trit::False]; fn main() {    println!("not");    println!("-------");    for &t in &TRITS {        println!(" {}  | {}", t, !t);    }     table("and", |a, b| a & b);    table("or", |a, b| a | b);    table("imp", |a, b| a.imp(b));    table("eqv", |a, b| a.eqv(b));} fn table(title: &str, f: impl Fn(Trit, Trit) -> Trit) {    println!();    println!("{:3} | T  M  F", title);    println!("-------------");    for &t1 in &TRITS {        print!(" {}  | ", t1);        for &t2 in &TRITS {            print!("{}  ", f(t1, t2));        }        println!();    }}`
Output:
```not
-------
T  | F
M  | M
F  | T

and | T  M  F
-------------
T  | T  M  F
M  | M  M  F
F  | F  F  F

or  | T  M  F
-------------
T  | T  T  T
M  | T  M  M
F  | T  M  F

imp | T  M  F
-------------
T  | T  M  F
M  | T  M  M
F  | T  T  T

eqv | T  M  F
-------------
T  | T  M  F
M  | M  M  M
F  | F  M  T  ```

## Scala

`sealed trait Trit { self =>  def nand(that:Trit):Trit=(this,that) match {    case (TFalse, _) => TTrue    case (_, TFalse) => TTrue    case (TMaybe, _) => TMaybe    case (_, TMaybe) => TMaybe    case _ => TFalse  }   def nor(that:Trit):Trit = this.or(that).not()  def and(that:Trit):Trit = this.nand(that).not()  def or(that:Trit):Trit = this.not().nand(that.not())  def not():Trit = this.nand(this)  def imply(that:Trit):Trit = this.nand(that.not())  def equiv(that:Trit):Trit = this.and(that).or(this.nor(that))}case object TTrue extends Tritcase object TMaybe extends Tritcase object TFalse extends Trit object TernaryLogic extends App {  val v=List(TTrue, TMaybe, TFalse)  println("- NOT -")  for(a<-v) println("%6s => %6s".format(a, a.not))  println("\n- AND -")  for(a<-v; b<-v) println("%6s : %6s => %6s".format(a, b, a and b))  println("\n- OR -")  for(a<-v; b<-v) println("%6s : %6s => %6s".format(a, b, a or b))  println("\n- Imply -")  for(a<-v; b<-v) println("%6s : %6s => %6s".format(a, b, a imply b))  println("\n- Equiv -")  for(a<-v; b<-v) println("%6s : %6s => %6s".format(a, b, a equiv b))		}`
Output:
```- NOT -
TTrue => TFalse
TMaybe => TMaybe
TFalse =>  TTrue

- AND -
TTrue :  TTrue =>  TTrue
TTrue : TMaybe => TMaybe
TTrue : TFalse => TFalse
TMaybe :  TTrue => TMaybe
TMaybe : TMaybe => TMaybe
TMaybe : TFalse => TFalse
TFalse :  TTrue => TFalse
TFalse : TMaybe => TFalse
TFalse : TFalse => TFalse

- OR -
TTrue :  TTrue =>  TTrue
TTrue : TMaybe =>  TTrue
TTrue : TFalse =>  TTrue
TMaybe :  TTrue =>  TTrue
TMaybe : TMaybe => TMaybe
TMaybe : TFalse => TMaybe
TFalse :  TTrue =>  TTrue
TFalse : TMaybe => TMaybe
TFalse : TFalse => TFalse

- Imply -
TTrue :  TTrue =>  TTrue
TTrue : TMaybe => TMaybe
TTrue : TFalse => TFalse
TMaybe :  TTrue =>  TTrue
TMaybe : TMaybe => TMaybe
TMaybe : TFalse => TMaybe
TFalse :  TTrue =>  TTrue
TFalse : TMaybe =>  TTrue
TFalse : TFalse =>  TTrue

- Equiv -
TTrue :  TTrue =>  TTrue
TTrue : TMaybe => TMaybe
TTrue : TFalse => TFalse
TMaybe :  TTrue => TMaybe
TMaybe : TMaybe => TMaybe
TMaybe : TFalse => TMaybe
TFalse :  TTrue => TFalse
TFalse : TMaybe => TMaybe
TFalse : TFalse =>  TTrue```

## Seed7

The type boolean does not define separate xor, implies and equiv operators. But there are replacements for them:

Instead of Use
p xor q p <> q
p implies q p <= q
p equiv q p = q

Since ternary logic needs xor, implies and equiv with a trit result they are introduced as the operators xor, -> and ==. The trit operators and and or are defined as short circuit operators. A short circuit operator evaluates the second parameter only when necessary. This is analogous to the boolean operators and and or, which use also short circuit evaluation.

`\$ include "seed7_05.s7i"; const type: trit is new enum    False, Maybe, True  end enum; # Enum types define comparisons (=, <, >, <=, >=, <>) and# the conversions ord and conv. const func string: str (in trit: aTrit) is  return [] ("False", "Maybe", "True")[succ(ord(aTrit))]; enable_output(trit);  # Allow writing trit values const array trit: tritNot is [] (True, Maybe, False);const array array trit: tritAnd is [] (    [] (False, False, False),    [] (False, Maybe, Maybe),    [] (False, Maybe, True ));const array array trit: tritOr is [] (    [] (False, Maybe, True ),    [] (Maybe, Maybe, True ),    [] (True,  True,  True ));const array array trit: tritXor is [] (    [] (False, Maybe, True ),    [] (Maybe, Maybe, Maybe),    [] (True,  Maybe, False));const array array trit: tritImplies is [] (    [] (True,  True,  True ),    [] (Maybe, Maybe, True ),    [] (False, Maybe, True ));const array array trit: tritEquiv is [] (    [] (True,  Maybe, False),    [] (Maybe, Maybe, Maybe),    [] (False, Maybe, True )); const func trit: not (in trit: aTrit) is  return tritNot[succ(ord(aTrit))]; const func trit: (in trit: aTrit1) and (in trit: aTrit2) is  return tritAnd[succ(ord(aTrit1))][succ(ord(aTrit2))]; const func trit: (in trit: aTrit1) and (ref func trit: aTrit2) is func  result    var trit: res is False;  begin    if aTrit1 = True then      res := aTrit2;    elsif aTrit1 = Maybe and aTrit2 <> False then      res := Maybe;    end if;  end func; const func trit: (in trit: aTrit1) or (in trit: aTrit2) is  return tritOr[succ(ord(aTrit1))][succ(ord(aTrit2))]; const func trit: (in trit: aTrit1) or (ref func trit: aTrit2) is func  result    var trit: res is True;  begin    if aTrit1 = False then      res := aTrit2;    elsif aTrit1 = Maybe and aTrit2 <> True then      res := Maybe;    end if;  end func; \$ syntax expr: .().xor.() is -> 15;const func trit: (in trit: aTrit1) xor (in trit: aTrit2) is  return tritImplies[succ(ord(aTrit1))][succ(ord(aTrit2))]; const func trit: (in trit: aTrit1) -> (in trit: aTrit2) is  return tritImplies[succ(ord(aTrit1))][succ(ord(aTrit2))]; const func trit: (in trit: aTrit1) == (in trit: aTrit2) is  return tritEquiv[succ(ord(aTrit1))][succ(ord(aTrit2))]; const func trit: rand (in trit: low, in trit: high) is  return trit conv (rand(ord(low), ord(high))); # Begin of test code var trit: operand1 is False;var trit: operand2 is False; const proc: writeTable (ref func trit: tritExpr, in string: name) is func  begin    writeln;    writeln(" " <& name rpad 7 <& " | False  Maybe  True");    writeln("---------+---------------------");    for operand1 range False to True do      write(" " <& operand1 rpad 7 <& " | ");      for operand2 range False to True do        write(tritExpr rpad 7);      end for;      writeln;    end for;  end func; const proc: main is func  begin    writeln(" not" rpad 8 <& " | False  Maybe  True");    writeln("---------+---------------------");    write("         | ");    for operand1 range False to True do      write(not operand1 rpad 7);    end for;    writeln;    writeTable(operand1 and operand2, "and");    writeTable(operand1 or operand2,  "or");    writeTable(operand1 xor operand2, "xor");    writeTable(operand1 -> operand2,  "->");    writeTable(operand1 == operand2,  "==");  end func;`
Output:
``` not     | False  Maybe  True
---------+---------------------
| True   Maybe  False

and     | False  Maybe  True
---------+---------------------
False   | False  False  False
Maybe   | False  Maybe  Maybe
True    | False  Maybe  True

or      | False  Maybe  True
---------+---------------------
False   | False  Maybe  True
Maybe   | Maybe  Maybe  True
True    | True   True   True

xor     | False  Maybe  True
---------+---------------------
False   | True   True   True
Maybe   | Maybe  Maybe  True
True    | False  Maybe  True

->      | False  Maybe  True
---------+---------------------
False   | True   True   True
Maybe   | Maybe  Maybe  True
True    | False  Maybe  True

==      | False  Maybe  True
---------+---------------------
False   | True   Maybe  False
Maybe   | Maybe  Maybe  Maybe
True    | False  Maybe  True
```

## Tcl

The simplest way of doing this is by constructing the operations as truth tables. The code below uses an abbreviated form of truth table.

`package require Tcl 8.5namespace eval ternary {    # Code generator    proc maketable {name count values} {	set sep ""	for {set i 0; set c 97} {\$i<\$count} {incr i;incr c} {	    set v [format "%c" \$c]	    lappend args \$v; append key \$sep "\$" \$v	    set sep ","	}	foreach row [split \$values \n] {	    if {[llength \$row]>1} {		lassign \$row from to		lappend table \$from [list return \$to]	    }	}	proc \$name \$args \	    [list ckargs \$args]\;[concat [list switch -glob --] \$key [list \$table]]	namespace export \$name    }    # Helper command to check argument syntax    proc ckargs argList {	foreach var \$argList {	    upvar 1 \$var v	    switch -exact -- \$v {		true - maybe - false {		    continue		}		default {		    return -level 2 -code error "bad ternary value \"\$v\""		}	    }	}    }     # The "truth" tables; “*” means “anything”    maketable not 1 {	true false	maybe maybe	false true    }    maketable and 2 {	true,true true	false,* false	*,false false	* maybe    }    maketable or 2 {	true,* true	*,true true	false,false false	* maybe    }    maketable implies 2 {	false,* true	*,true true	true,false false	* maybe    }    maketable equiv 2 {	*,maybe maybe	maybe,* maybe	true,true true	false,false true	* false    }}`

Demonstrating:

`namespace import ternary::*puts "x /\\ y == x \\/ y"puts " x     | y     || result"puts "-------+-------++--------"foreach x {true maybe false} {    foreach y {true maybe false} {	set z [equiv [and \$x \$y] [or \$x \$y]]	puts [format " %-5s | %-5s || %-5s" \$x \$y \$z]    }}`
Output:
```x /\ y == x \/ y
x     | y     || result
-------+-------++--------
true  | true  || true
true  | maybe || maybe
true  | false || false
maybe | true  || maybe
maybe | maybe || maybe
maybe | false || maybe
false | true  || false
false | maybe || maybe
false | false || true
```