Truth table

Truth table is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

A truth table is a display of the inputs to, and the output of a Boolean equation organised as a table where each row gives one combination of input values and the corresponding value of the equation.

Task

1. Input a Boolean equation from the user as a string then calculate and print a formatted truth table for the given equation.
   (One can assume that the user input is correct).
2. Print and show output for Boolean equations of two and three input variables, but any program should not be limited to that many variables in the equation.
3. Either reverse-polish or infix notation expressions are allowed.

Cf.

• Boolean values
• Ternary logic

Ref.

• Wolfram mathworld entry on truth tables.
• Some examples from Google.

Go

Variance from statement of task: Runtime evaluation or code generation is not directly supported in Go. The function tt here does however accept functions with any number of arguments and produce the corresponding truth table. <lang go>package main

import (

   "fmt"
   "reflect"

)

func xor(a, b bool) bool {

   return a != b

}

func stu(s, t, u bool) bool {

   return s || xor(t, u)

}

func abcd(a, b, c, d bool) bool {

   return xor(a, xor(b, xor(c, d)))

}

func main() {

   tt(xor,  "A     B        A ^ B")
   tt(stu,  "S     T     U        S | ( T ^ U )")
   tt(abcd, "A     B     C     D        A ^ (B ^ (C ^ D))")

}

func tt(f interface{}, label string) {

   fmt.Println()
   fmt.Println(label)
   tv := []bool{false, true}
   v := reflect.ValueOf(f)
   n := reflect.TypeOf(f).NumIn()
   a := make([]reflect.Value, n)
   lines := 1 << uint(n)
   for l := 0; l < lines; l++ {
       s := "  "
       lBits := l
       for i := range a {
           ba := tv[lBits & 1]
           s = fmt.Sprintf("%-5t %s", ba, s)
           a[n-1-i] = reflect.ValueOf(ba)
           lBits >>= 1
       }
       fmt.Println(s, v.Call(a)[0].Bool())
   }

}</lang> Output:

A     B        A ^ B
false false    false
false true     true
true  false    true
true  true     false

S     T     U        S | ( T ^ U )
false false false    false
false false true     true
false true  false    true
false true  true     false
true  false false    true
true  false true     true
true  true  false    true
true  true  true     true

A     B     C     D        A ^ (B ^ (C ^ D))
false false false false    false
false false false true     true
false false true  false    true
false false true  true     false
false true  false false    true
false true  false true     false
false true  true  false    false
false true  true  true     true
true  false false false    true
true  false false true     false
true  false true  false    false
true  false true  true     true
true  true  false false    false
true  true  false true     true
true  true  true  false    true
true  true  true  true     false

J

Implementation:

<lang j>truthTable=:3 :0

 assert. -. 1 e. 'data expr names table' e.&;: y
 names=. ~. (#~ _1 <: nc) ;:expr=. y
 data=. #:i.2^#names
 (names)=. |:data
 (' ',;:inv names,<expr),(1+#@>names,<expr)":data,.".expr

)</lang>

The argument is expected to be a valid boolean J sentence which, among other things, does not use any of the words used within the implementation (but any single-character name is valid).

Example use:

<lang j> truthTable '-.b'

b -.b
0   1
1   0
  truthTable 'a*b'
a b a*b
0 0   0
0 1   0
1 0   0
1 1   1
  truthTable 'a+.b'
a b a+.b
0 0    0
0 1    1
1 0    1
1 1    1
  truthTable 'a<:b'
a b a<:b
0 0    1
0 1    1
1 0    0
1 1    1
  truthTable '(a*bc)+.d'
a bc d (a*bc)+.d
0  0 0         0
0  0 1         1
0  1 0         0
0  1 1         1
1  0 0         0
1  0 1         1
1  1 0         1
1  1 1         1</lang>

Java

Works with: Java version 1.5+

This example would require a system of pages that would be moderately complicated to set up and follow (or a really huge page that would also be hard to follow) since there is no eval in Java, so you can find information about it here. There is a link to an executable jar file with the required source files there. The program shows the expression and the truth table in a window. The expression must use prefix notation, single characters for input names (numerals, lowercase letters, and uppercase letters are the easiest to read), and the outputs can be shown as 1/0 or T/F. There is also a "Check" button which will make sure that the operators have enough operands. The window looks something like this:

Liberty BASIC

This at first seems trivial, given our lovely 'eval' function. However it is complicated by LB's use of 'non-zero' for 'true', and by the requirements of accepting different numbers and names of variables. My program assumes all space-separated words in the expression$ are either a logic-operator, bracket delimiter, or variable name. Since a truth table for 8 or more variables is of silly length, I regard that as a practical limit. <lang lb> print

   print " TRUTH TABLES"
   print
   print " Input a valid Boolean expression for creating the truth table "
   print " Use lowercase 'and', 'or', 'xor', '(', 'not(' and ')'."
   print
   print " Take special care to precede closing bracket with a space."
   print
   print " You can use any alphanumeric variable names, but no spaces."
   print " You can refer again to a variable used already."
   print " Program assumes <8 variables will be used.."
   print
   print " eg 'A xor B and not( C or A )'"
   print " or 'Too_High xor not( Fuel_Out )'"

   print

[start]
   input "        "; expression$
   if expression$ ="" then [start]

   print

   'used$           =""
   numVariables    =0  '   count of detected variable names
   variableNames$  ="" '   filled with detected variable names
   i               =1  '   index to space-delimited word in the expression$

 [parse]
   m$ =word$( expression$, i, " ")
   if m$ ="" then [analyse]
   '   is it a reserved word, or a variable name already met?
   if m$ <>"and" and m$ <>"or" and m$ <>"not(" and m$ <>")" and m$ <>"xor"_
    and not( instr( variableNames$, m$)) then
       variableNames$ =variableNames$ +m$ +" ": numVariables =numVariables +1
   end if

   i =i +1
   goto [parse]

 [analyse]
   for i =1 to numVariables
       ex$          =FindReplace$( expression$, word$( variableNames$, i, " "), chr$( 64 +i), 1)
       expression$  =ex$
   next i

   'print " "; numVariables; " variables, simplifying to "; expression$

   print ,;
   for j =1 to numVariables
       print word$( variableNames$, j, " "),
   next j
   print "Result"
   print

   for i =0 to ( 2^numVariables) -1
       print ,;
       A                         =i mod 2:          print A,
       if numVariables >1 then B =int( i /2) mod 2: print B,
       if numVariables >2 then C =int( i /4) mod 2: print C,
       if numVariables >3 then D =int( i /4) mod 2: print D,
       if numVariables >4 then E =int( i /4) mod 2: print E,
       if numVariables >5 then F =int( i /4) mod 2: print F,
       if numVariables >6 then G =int( i /4) mod 2: print G,
       '   .......................... etc

       'e =eval( expression$)
       if eval( expression$) <>0 then e$ ="1" else e$ ="0"
       print "==>  "; e$
   next i

   print

   goto [start]

   end

function FindReplace$( FindReplace$, find$, replace$, replaceAll)

   if ( ( FindReplace$ <>"") and ( find$ <>"")) then
       fLen = len( find$)
       rLen = len( replace$)
       do
           fPos            = instr( FindReplace$, find$, fPos)
           if not( fPos) then exit function
           pre$            = left$( FindReplace$, fPos -1)
           post$           =  mid$( FindReplace$, fPos +fLen)
           FindReplace$    = pre$ +replace$ +post$
           fPos            = fPos +(rLen -fLen) +1
       loop while ( replaceAll)
   end if

end function </lang>

        Too_High and Fuel_Out
              Too_High      Fuel_Out      Result

              0             0             ==>  0
              1             0             ==>  0
              0             1             ==>  0
              1             1             ==>  1

        Fat or Ugly and not( Rich )
              Fat           Ugly          Rich          Result

              0             0             0             ==>  0
              1             0             0             ==>  1
              0             1             0             ==>  1
              1             1             0             ==>  1
              0             0             1             ==>  0
              1             0             1             ==>  0
              0             1             1             ==>  0
              1             1             1             ==>  0

Mathematica

<lang Mathematica>VariableNames[data_] := Module[ {TokenRemoved},

TokenRemoved = StringSplit[data,{"~And~","~Or~","~Xor~","!","(",")"}];
Union[Select[Map[StringTrim,TokenRemoved] , Not[StringMatchQ[#,""]]&]]

]

TruthTable[BooleanEquation_] := Module[ {TestDataSet},

 TestDataSet = MapThread[Rule,{ToExpression@VariableNames[BooleanEquation],#}]&/@
    Tuples[{False,True}, Length[VariableNames[BooleanEquation]]];

 Join[List[Flatten[{VariableNames[BooleanEquation],BooleanEquation}]],
   Flatten[{#/.Rule[x_,y_] -> y,ReplaceAll[ToExpression[BooleanEquation],#]}]&/@TestDataSet]//Grid

]</lang>

Example usage:

TruthTable["V ~Xor~ (B ~Xor~ (K ~Xor~ D ) )"]

B	D	K	V	V ~Xor~ (B ~Xor~ (K ~Xor~ D ) )
False	False	False	False	False
False	False	False	True	True
False	False	True	False	True
False	False	True	True	False
False	True	False	False	True
False	True	False	True	False
False	True	True	False	False
False	True	True	True	True
True	False	False	False	True
True	False	False	True	False
True	False	True	False	False
True	False	True	True	True
True	True	False	False	False
True	True	False	True	True
True	True	True	False	True
True	True	True	True	False

Perl

Note: can't process stuff like "X xor Y"; "xor" would be treated as a variable name here. <lang perl>#!/usr/bin/perl

sub truth_table { my $s = shift; my (%seen, @vars); for ($s =~ /([a-zA-Z_]\w*)/g) { $seen{$_} //= do { push @vars, $_; 1 }; }

print "\n", join("\t", @vars, $s), "\n", '-' x 40, "\n"; @vars = map("\$$_", @vars);

$s =~ s/([a-zA-Z_]\w*)/\$$1/g; $s = "print(".join(',"\t", ', map("($_?'T':'F')", @vars, $s)).",\"\\n\")"; $s = "for my $_ (0, 1) { $s }" for (reverse @vars); eval $s; }

truth_table 'A ^ A_1'; truth_table 'foo & bar | baz';

truth_table 'Jim & (Spock ^ Bones) | Scotty';</lang>

Output:

A       A_1     A ^ A_1
----------------------------------------
F       F       F
F       T       T
T       F       T
T       T       F
foo     bar     baz     foo & bar | baz
----------------------------------------
F       F       F       F
F       F       T       T
F       T       F       F
F       T       T       T
T       F       F       F
T       F       T       T
T       T       F       T
T       T       T       T
Jim     Spock   Bones   Scotty  Jim & (Spock ^ Bones) | Scotty
----------------------------------------
F       F       F       F       F
...<snip for space -- not like you're gonna verify it anyway>...
T       T       T       T       T

Perl 6

Works with: niecza version 2012-03-30

<lang perl6>sub MAIN ($x) {

   my @n = $x.comb(/<ident>/);
   my &fun = eval "-> {('\\' «~« @n).join(',')} \{ [{ (@n,"so $x").join(',') }] \}";

   say (@n,$x).join("\t");
   .join("\t").say for map &fun, map { .fmt("\%0{+@n}b").comb».so }, 0 ..^ 2**@n;

}</lang>

Output:

$ truthtable 'A ^ B'
A	B	A ^ B
False	False	False
False	True	True
True	False	True
True	True	False

$ truthtable 'foo & bar | baz'
foo	bar	baz	foo & bar | baz
False	False	False	False
False	False	True	True
False	True	False	False
False	True	True	True
True	False	False	False
True	False	True	True
True	True	False	True
True	True	True	True

$ truthtable 'Jim & (Spock ^ Bones) | Scotty'
Jim	Spock	Bones	Scotty	Jim & (Spock ^ Bones) | Scotty
False	False	False	False	False
False	False	False	True	True
False	False	True	False	False
False	False	True	True	True
False	True	False	False	False
False	True	False	True	True
False	True	True	False	False
False	True	True	True	True
True	False	False	False	False
True	False	False	True	True
True	False	True	False	True
True	False	True	True	True
True	True	False	False	True
True	True	False	True	True
True	True	True	False	False
True	True	True	True	True

PicoLisp

<lang PicoLisp>(de truthTable (Expr)

  (let Vars
     (uniq
        (make
           (setq Expr
              (recur (Expr)  # Convert infix to prefix notation
                 (cond
                    ((atom Expr) (link Expr))
                    ((== 'not (car Expr))
                       (list 'not (recurse (cadr Expr))) )
                    (T
                       (list
                          (cadr Expr)
                          (recurse (car Expr))
                          (recurse (caddr Expr)) ) ) ) ) ) ) )
     (for V Vars
        (prin (align -7 V)) )
     (prinl)
     (bind (mapcar cons Vars)
        (do (** 2 (length Vars))
           (for "V" Vars
              (space (if (print (val "V")) 6 4)) )
           (println (eval Expr))
           (find '(("V") (set "V" (not (val "V")))) Vars) ) ) ) )</lang>

Test:

<lang PicoLisp>: (truthTable (str "A and (B or C)")) A B C NIL NIL NIL NIL T NIL NIL NIL NIL T NIL NIL T T NIL T NIL NIL T NIL T NIL T T NIL T T NIL T T T T

(truthTable (str "not (Foo and (Bar or Mumble))"))

Foo Bar Mumble NIL NIL NIL T T NIL NIL T NIL T NIL T T T NIL NIL NIL NIL T T T NIL T NIL NIL T T T T T T NIL

(truthTable (str "(A xor B) and (B or C)"))

A B C NIL NIL NIL NIL T NIL NIL NIL NIL T NIL T T T NIL NIL NIL NIL T NIL T NIL T T NIL T T T T T T NIL

(truthTable (str "(A xor B) and ((not B) or C)"))

A B C NIL NIL NIL NIL T NIL NIL T NIL T NIL NIL T T NIL NIL NIL NIL T NIL T NIL T T NIL T T T T T T NIL</lang>

Python

This accepts correctly formatted Python boolean expressions. <lang python>from itertools import product

while True:

   bexp = input('\nBoolean expression: ')
   bexp = bexp.strip()
   if not bexp:
       print("\nThank you")
       break
   code = compile(bexp, '<string>', 'eval')
   names = code.co_names
   print('\n' + ' '.join(names), ':', bexp)
   for values in product(range(2), repeat=len(names)):
       env = dict(zip(names, values))
       print(' '.join(str(v) for v in values), ':', eval(code, env))

</lang>

Sample output

Boolean expression: A ^ B

A B : A ^ B
0 0 : 0
0 1 : 1
1 0 : 1
1 1 : 0

Boolean expression: S | ( T ^ U )

S T U : S | ( T ^ U )
0 0 0 : 0
0 0 1 : 1
0 1 0 : 1
0 1 1 : 0
1 0 0 : 1
1 0 1 : 1
1 1 0 : 1
1 1 1 : 1

Boolean expression: A ^ (B ^ (C ^ D))

A B C D : A ^ (B ^ (C ^ D))
0 0 0 0 : 0
0 0 0 1 : 1
0 0 1 0 : 1
0 0 1 1 : 0
0 1 0 0 : 1
0 1 0 1 : 0
0 1 1 0 : 0
0 1 1 1 : 1
1 0 0 0 : 1
1 0 0 1 : 0
1 0 1 0 : 0
1 0 1 1 : 1
1 1 0 0 : 0
1 1 0 1 : 1
1 1 1 0 : 1
1 1 1 1 : 0

Boolean expression: 

Thank you

REXX

I had the thought that this program would just transform the boolean expression into what REXX approves of, and just step
through the 26 possible propositional constants (which makes a deeply nested DO construct, if nothing else, it looks pretty).
I later added support for all 16 boolean functions --- REXX natively supports three infix operators:

• & (and)
• | (or)
• && (xor)

and one prefix operator:

• ¬ (not or negation).

Some REXX intepreters also (or instead) support:

• backslash (\)
• forward slash (/)
• tidle (~)
• carot (^)

Also included is support for two boolean values: TRUE and FALSE which are part of boolean expressions.

Some older REXXes don't have a changestr bif, so one is included here. <lang rexx>/*REXX program displays a truth table the variables and an expression. */ /*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 expression /*get expression from command line.*/ if expression\= then do /*got one? Then show user's stuff.*/

                      call truthTable expression   /*show and tell time*/
                      exit             /*we're all done with truth table. */
                      end

call truthTable "G ^ H ; XOR" /*txt after ; is shown in output*/ call truthTable "i | j ; OR" call truthTable "G nxor H ; NXOR" call truthTable "k ! t ; NOR" call truthTable "p & q ; AND" call truthTable "e ¡ f ; NAND" call truthTable "S | (T ^ U )" call truthTable "(p=>q) v (q=>r)" call truthTable "A ^ (B ^ (C ^ D))"

exit /*quit while we're ahead, by gum.*/

                                      /*shows a 32,768 line truth table*/

call truthTable "A^(B^(C^(D^(E^(F^(G^(H^(I^(J^(L^(N^(N^(O^P)))))))))))))" exit /*stick a fork in it, we're done.*/

/*─────────────────────────────────────truthTable subroutine────────────*/ truthTable: procedure; parse arg $ ';' comm 1 $o; $o=strip($o) $=translate(strip($),'|',"v"); $u=$; upper $u $u=translate($u,'()()()',"[]{}«»"); $$.=0; PCs=; hdrPCs= @abc='abcdefghijklmnopqrstuvwxyz'; @abcU=@abc; upper @abcU

/* The boxed table below was constructed from an old IBM publication:

  "PL/I Language Specifications"     ───  March 1968.
      ┌────────────────────────────────────────────────────────────┐
      │                  bool(bitsA, bitsB, BF)                    │
      ├────────────────────────────────────────────────────────────┤
      │ performs the boolean function  BF    ┌──────┬─────────┐    │
      │      on the   A   bitstring          │  BF  │ common  │    │
      │    with the   B   bitstring.         │ value│  name   │    │
      │                                      ├──────┼─────────┤    │
      │ BF  must be a  one to four bit       │ 0000 │boolfalse│    │
      │ value  (from  0000 ──► 1111),        │ 0001 │ and     │    │
      │ leading zeroes can be omitted.       │ 0010 │ NaIMPb  │    │
      │                                      │ 0011 │ boolB   │    │
      │ BF  may have multiple values (one    │ 0100 │ NbIMPa  │    │
      │ for each pair of bitstrings):        │ 0101 │ boolA   │    │
      │                                      │ 0110 │ xor     │    │
      │  ┌──────┬──────┬───────────────┐     │ 0111 │ or      │    │
      │  │ Abit │ Bbit │   returns     │     │ 1000 │ nor     │    │
      │  ├──────┼──────┼───────────────┤     │ 1001 │ nxor    │    │
      │  │   0  │   0  │ 1st bit in BF │     │ 1010 │ notB    │    │
      │  │   0  │   1  │ 2nd bit in BF │     │ 1011 │ bIMPa   │    │
      │  │   1  │   0  │ 3rd bit in BF │     │ 1100 │ notA    │    │
      │  │   1  │   1  │ 4th bit in BF │     │ 1101 │ aIMPb   │    │
      │  └──────┴──────┴───────────────┘     │ 1110 │ nand    │    │
      │                                      │ 1111 │booltrue │    │
      │                                   ┌──┴──────┴─────────┤    │
      │                                   │ A  0101           │    │
      │                                   │ B  0011           │    │
      │                                   └───────────────────┘    │
      └────────────────────────────────────────────────────────────┘   */

?='ff'x /*─────────infix operators───────*/ op.= /*a single quote (') wan't */

                                      /*  implemented for negation.    */

op.0 ='false boolFALSE' /*unconditionally false */ op.1 ='& 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, exclusive OR */ op.7 ='| 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 */ op.18='>= GE ─> => ──> ==>' "1a"x /*conditional */ op.19='< LT' /*conditional */ op.20='<= LE <─ <= <── <==' /*conditional */ op.21='\= NE ~= ─= .= ¬=' /*conditional */ op.22='= EQ EQUAL EQUALS =' "1b"x /*biconditional */ op.23='0 boolTRUE' /*trueness */ op.24='1 boolFALSE' /*falseness */

 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 new!=?  /*expresion needs transcribing.  */
                         else new!=new
   $u=changestr(_,$u,new!)            /*transcribe the function (maybe)*/
   if new!==?  then $u=changeFunc($u,?,new)   /*use internal bool 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=1                          /*found:  set upper bound for it.*/
     PCs=PCs _                        /*also, add to propositional cons*/
     hdrPCs=hdrPCS center(_,length('false'))       /*build a PC header.*/
     end

$u=PCs '('$u")" /*separate PCs from expression. */ ptr='_────►+_' /*a pointer for the truth table. */ hdrPCs=substr(hdrPCs,2) /*create a header for the PCs. */ say hdrPCs left(,length(ptr)-1) $o /*display PC header + expression.*/ say copies('───── ',words(PCs)) left(,length(ptr)-2) copies('─',length($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(1,_,'_true')   /*convert 1──►_true*/
                         _=changestr(0,_,'false')   /*convert 0──►false*/
                         _=insert(ptr,_,wordindex(_,words(_))-1)  /*──►*/
                         say translate(_,,'_')      /*display truth tab*/
                         end
                        end
                       end
                      end
                     end
                    end
                   end
                  end
                 end
                end
               end
              end
             end
            end
           end
          end
         end
        end
       end
      end
     end
    end
   end
  end
 end
end

say return /*─────────────────────────────────────SCAN subroutine──────────────────*/ 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

return min(j,L) /*─────────────────────────────────────changeFunc subroutine────────────*/ 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('bool{',  z,  where)
            end

/*─────────────────────────────────────BOOL subroutine──────────────────*/ bool: procedure; arg a,$,b

        select

/*0*/ when $=='FALSE' then return 0 /*1*/ when $=='AND' then return a & b /*2*/ when $=='NAIMPB' then return \ (\a & \b) /*3*/ when $=='BOOLB' then return b /*4*/ when $=='NBIMPA' then return \ (\b & \a) /*5*/ when $=='BOOLA' then return a /*6*/ when $=='XOR' then return a && b /*7*/ when $=='OR' then return a | b /*8*/ when $=='NOR' then return \ (a | b) /*9*/ when $=='XNOR' then return \ (a && b) /*a*/ when $=='NOTB' then return \ b /*c*/ when $=='NOTA' then return \ a /*d*/ when $=='AIMPB' then return \ (a & \b) /*e*/ when $=='NAND' then return \ (a & b) /*f*/ when $=='TRUE' then return 1

        otherwise        return -13   /*error.*/
        end   /*select*/</lang>

output when using the default input

  G     H          G ^ H ; XOR
───── ─────        ───────────
false false  ────► false
false  true  ────►  true
 true false  ────►  true
 true  true  ────► false

  I     J          i | j ; OR
───── ─────        ──────────
false false  ────► false
false  true  ────►  true
 true false  ────►  true
 true  true  ────►  true

  G     H          G nxor H ; NXOR
───── ─────        ───────────────
false false  ────►  true
false  true  ────► false
 true false  ────► false
 true  true  ────►  true

  K     T          k ! t ; NOR
───── ─────        ───────────
false false  ────►  true
false  true  ────► false
 true false  ────► false
 true  true  ────► false

  P     Q          p & q ; AND
───── ─────        ───────────
false false  ────► false
false  true  ────► false
 true false  ────► false
 true  true  ────►  true

  E     F          e ¡ f ; NAND
───── ─────        ────────────
false false  ────►  true
false  true  ────►  true
 true false  ────►  true
 true  true  ────► false

  S     T     U          S | (T ^ U )
───── ───── ─────        ────────────
false false false  ────► false
false false  true  ────►  true
false  true false  ────►  true
false  true  true  ────► false
 true false false  ────►  true
 true false  true  ────►  true
 true  true false  ────►  true
 true  true  true  ────►  true

  P     Q     R          (p=>q) v (q=>r)
───── ───── ─────        ───────────────
false false false  ────►  true
false false  true  ────►  true
false  true false  ────►  true
false  true  true  ────►  true
 true false false  ────►  true
 true false  true  ────►  true
 true  true false  ────►  true
 true  true  true  ────►  true

  A     B     C     D          A ^ (B ^ (C ^ D))
───── ───── ───── ─────        ─────────────────
false false false false  ────► false
false false false  true  ────►  true
false false  true false  ────►  true
false false  true  true  ────► false
false  true false false  ────►  true
false  true false  true  ────► false
false  true  true false  ────► false
false  true  true  true  ────►  true
 true false false false  ────►  true
 true false false  true  ────► false
 true false  true false  ────► false
 true false  true  true  ────►  true
 true  true false false  ────► false
 true  true false  true  ────►  true
 true  true  true false  ────►  true
 true  true  true  true  ────► false

Ruby

Uses eval, so blindly trusts the user's input. The core true and false objects understand the methods & (and), | (or), ! (not) and ^ (xor) -- [1] <lang ruby>loop do

 print "\ninput a boolean expression (e.g. 'a & b'): "
 expr = gets.strip.downcase 
 break if expr.empty?

 vars = expr.scan(/\p{Alpha}+/)
 if vars.empty?
   puts "no variables detected in your boolean expression"
   next
 end

 vars.each {|v| print "#{v}\t"}
 puts "| #{expr}"

 prefix = []
 suffix = []
 vars.each do |v|
   prefix << "[false, true].each do |#{v}|"
   suffix << "end"
 end

 body = vars.inject("puts ") {|str, v| str + "#{v}.to_s + '\t' + "} 
 body += '"| " + eval(expr).to_s'

 eval (prefix + [body] + suffix).join("\n")

end</lang>

Example

input a boolean expression (e.g. 'a & b'): !a
a       | !a
false   | true
true    | false

input a boolean expression (e.g. 'a & b'): a|!b
a       b       | a|!b
false   false   | true
false   true    | false
true    false   | true
true    true    | true

input a boolean expression (e.g. 'a & b'): ((a^b)^c)^d
a       b       c       d       | ((a^b)^c)^d
false   false   false   false   | false
false   false   false   true    | true
false   false   true    false   | true
false   false   true    true    | false
false   true    false   false   | true
false   true    false   true    | false
false   true    true    false   | false
false   true    true    true    | true
true    false   false   false   | true
true    false   false   true    | false
true    false   true    false   | false
true    false   true    true    | true
true    true    false   false   | false
true    true    false   true    | true
true    true    true    false   | true
true    true    true    true    | false

Tcl

<lang tcl>package require Tcl 8.5

puts -nonewline "Enter a boolean expression: " flush stdout set exp [gets stdin]

1. Generate the nested loops as the body of a lambda term.

set vars [lsort -unique [regexp -inline -all {\$\w+} $exp]] set cmd [list format [string repeat "%s\t" [llength $vars]]%s] append cmd " {*}\[[list subst $vars]\] \[[list expr $exp]\]" set cmd "puts \[$cmd\]" foreach v [lreverse $vars] {

   set cmd [list foreach [string range $v 1 end] {0 1} $cmd]

}

puts [join $vars \t]\tResult apply [list {} $cmd]</lang> Sample run:

Enter a boolean expression: ($a&&$b)||$c
$a	$b	$c	Result
0	0	0	0
0	0	1	1
0	1	0	0
0	1	1	1
1	0	0	0
1	0	1	1
1	1	0	1
1	1	1	1