Truth table: Difference between revisions
(→{{header|C}}: Added two functions in order allow the application to use the field "top" only through the operations on the stack.) |
(→{{header|C}}: More structured loop) |
||
| Line 325: | Line 325: | ||
} |
} |
||
} |
} |
||
| ⚫ | |||
if (vars_len == 0) { |
if (vars_len == 0) { |
||
printf(" |
printf("No variables were entered.\n"); |
||
} |
|||
| ⚫ | |||
| ⚫ | |||
| ⚫ | |||
| ⚫ | |||
| ⚫ | |||
| ⚫ | |||
| ⚫ | |||
| ⚫ | |||
} |
} |
||
| ⚫ | |||
| ⚫ | |||
| ⚫ | |||
| ⚫ | |||
| ⚫ | |||
| ⚫ | |||
| ⚫ | |||
| ⚫ | |||
| ⚫ | |||
} |
} |
||
return 0; |
return 0; |
||
Revision as of 22:23, 6 March 2020
You are encouraged to solve this task according to the task description, using any language you may know.
A truth table is a display of the inputs to, and the output of a Boolean function organized as a table where each row gives one combination of input values and the corresponding value of the function.
- Task
- Input a Boolean function from the user as a string then calculate and print a formatted truth table for the given function.
(One can assume that the user input is correct). - Print and show output for Boolean functions of two and three input variables, but any program should not be limited to that many variables in the function.
- Either reverse-polish or infix notation expressions are allowed.
- Related tasks
- See also
ALGOL 68
Uses the Algol 68G specific evaluate procedure to evaluate the Boolean expressions. The expressions must therefore be infix and valid Algol 68 boolean expressions. <lang algol68># prints the truth table of a boolean expression composed of the 26 lowercase variables a..z, #
- the boolean operators AND, OR, XOR and NOT and the literal values TRUE and FALSE #
- The evaluation is done with the Algol 68G evaluate function which is an extension #
PROC print truth table = ( STRING expr )VOID:
BEGIN
# recursively prints the truth table #
PROC print line = ( INT v )VOID:
IF v > UPB bv
THEN
# at the end of the variables - print the line #
FOR e TO UPB bv DO
IF used[ e ] THEN print( ( " ", bv[ e ], " " ) ) FI
OD;
print( ( " ", evaluate( expr ), newline ) )
ELIF used[ v ]
THEN
# have another variable #
bv[ v ] := TRUE;
print line( v + 1 );
bv[ v ] := FALSE;
print line( v + 1 )
ELSE
# this variable is not used #
print line( v + 1 )
FI # print line # ;
# returns the name of the variable number #
PROC variable name = ( INT number )CHAR: REPR ( number + ( ABS "a" - 1 ) );
# the 26 boolean variables #
BOOL a := FALSE, b := FALSE, c := FALSE, d := FALSE, e := FALSE, f := FALSE;
BOOL g := FALSE, h := FALSE, i := FALSE, j := FALSE, k := FALSE, l := FALSE;
BOOL m := FALSE, n := FALSE, o := FALSE, p := FALSE, q := FALSE, r := FALSE;
BOOL s := FALSE, t := FALSE, u := FALSE, v := FALSE, w := FALSE, x := FALSE;
BOOL y := FALSE, z := FALSE;
# table of the variables allowng access by number #
[]REF BOOL bv = ( a, b, c, d, e, f, g, h, i, j, k, l, m
, n, o, p, q, r, s, t, u, v, w, x, y, z
);
[ 26 ]BOOL used;
BOOL at least one variable := FALSE;
# determine which variables are used in the expression #
FOR v TO UPB bv DO
used[ v ] := char in string( variable name( v ), NIL, expr );
IF used[ v ]THEN at least one variable := TRUE FI
OD;
# print truth table headings #
print( ( expr, ":", newline ) );
FOR v TO UPB bv DO
IF used[ v ] THEN print( ( " ", variable name( v ), " " ) ) FI
OD;
print( ( " value", newline ) );
FOR v TO UPB bv DO
IF used[ v ] THEN print( ( " - " ) ) FI
OD;
print( ( " -----", newline ) );
# evaluate the expression for each cobination of variables #
IF at least one variable
THEN
# the expression does not consist of literals only #
FOR v TO UPB bv DO bv[ v ] := FALSE OD;
print line( LWB bv )
ELSE
# the expression is constant #
print( ( " ", evaluate( expr ), newline ) )
FI
END # print truth table # ;
- print truth tables from the user's expressions #
print( ( "Please enter Boolean expressions using variables a, b, c, ..., z,", newline ) ); print( ( "operators AND, OR, NOT and XOR and literals TRUE and FALSE", newline ) ); print( ( "(Note operators and TRUE/FALSE must be uppercase and variables must be lower case)", newline ) ); print( ( "Enter a blank line to quit", newline ) ); WHILE
STRING expr; print( ( "expression> " ) ); read( ( expr, newline ) ); expr /= ""
DO
print truth table( expr )
OD</lang>
- Output:
Please enter Boolean expressions using variables a, b, c, ..., z, operators AND, OR, NOT and XOR and literals TRUE and FALSE (Note operators and TRUE/FALSE must be uppercase and variables must be lower case) Enter a blank line to quit expression> a OR b a OR b: a b value - - ----- T T T T F T F T T F F F expression> a AND ( b OR f ) a AND ( b OR f ): a b f value - - - ----- T T T T T T F T T F T T T F F F F T T F F T F F F F T F F F F F expression> ( NOT a ) OR ( b AND c ) ( NOT a ) OR ( b AND c ): a b c value - - - ----- T T T T T T F F T F T F T F F F F T T T F T F T F F T T F F F T expression>
C
<lang c>#include <stdio.h>
- include <string.h>
- include <stdlib.h>
- define TRUE 1
- define FALSE 0
- define STACK_SIZE 80
- define BUFFER_SIZE 100
typedef int bool;
typedef struct {
char name; bool val;
} var;
typedef struct {
int top; bool els[STACK_SIZE];
} stack_of_bool;
char expr[BUFFER_SIZE]; int expr_len; var vars[24]; int vars_len;
/* stack manipulation functions */
bool is_full(stack_of_bool *sp) {
return sp->top == STACK_SIZE - 1;
}
bool is_empty(stack_of_bool *sp) {
return sp->top == -1;
}
bool peek(stack_of_bool *sp) {
if (!is_empty(sp))
return sp->els[sp->top];
else {
printf("Stack is empty.\n");
exit(1);
}
}
void push(stack_of_bool *sp, bool val) {
if (!is_full(sp)) {
sp->els[++(sp->top)] = val;
}
else {
printf("Stack is full.\n");
exit(1);
}
}
bool pop(stack_of_bool *sp) {
if (!is_empty(sp))
return sp->els[(sp->top)--];
else {
printf("\nStack is empty.\n");
exit(1);
}
}
void make_empty(stack_of_bool *sp) {
sp->top = -1;
}
int elems_count(stack_of_bool *sp) {
return (sp->top) + 1;
}
bool is_operator(const char c) {
return c == '&' || c == '|' || c == '!' || c == '^';
}
int vars_index(const char c) {
int i;
for (i = 0; i < vars_len; ++i) {
if (vars[i].name == c) return i;
}
return -1;
}
bool eval_expr() {
int i, vi;
char e;
stack_of_bool s;
stack_of_bool *sp = &s;
make_empty(sp);
for (i = 0; i < expr_len; ++i) {
e = expr[i];
if (e == 'T')
push(sp, TRUE);
else if (e == 'F')
push(sp, FALSE);
else if((vi = vars_index(e)) >= 0) {
push(sp, vars[vi].val);
}
else switch(e) {
case '&':
push(sp, pop(sp) & pop(sp));
break;
case '|':
push(sp, pop(sp) | pop(sp));
break;
case '!':
push(sp, !pop(sp));
break;
case '^':
push(sp, pop(sp) ^ pop(sp));
break;
default:
printf("\nNon-conformant character '%c' in expression.\n", e);
exit(1);
}
}
if (elems_count(sp) != 1) {
printf("\nStack should contain exactly one element.\n");
exit(1);
}
return peek(sp);
}
void set_vars(int pos) {
int i;
if (pos > vars_len) {
printf("\nArgument to set_vars can't be greater than the number of variables.\n");
exit(1);
}
else if (pos == vars_len) {
for (i = 0; i < vars_len; ++i) {
printf((vars[i].val) ? "T " : "F ");
}
printf("%c\n", (eval_expr()) ? 'T' : 'F');
}
else {
vars[pos].val = FALSE;
set_vars(pos + 1);
vars[pos].val = TRUE;
set_vars(pos + 1);
}
}
/* removes whitespace and converts to upper case */ void process_expr() {
int i, count = 0;
for (i = 0; expr[i]; ++i) {
if (!isspace(expr[i])) expr[count++] = toupper(expr[i]);
}
expr[count] = '\0';
}
int main() {
int i, h;
char e;
printf("Accepts single-character variables (except for 'T' and 'F',\n");
printf("which specify explicit true or false values), postfix, with\n");
printf("&|!^ for and, or, not, xor, respectively; optionally\n");
printf("seperated by whitespace. Just enter nothing to quit.\n");
while (TRUE) {
printf("\nBoolean expression: ");
fgets(expr, BUFFER_SIZE, stdin);
fflush(stdin);
process_expr();
expr_len = strlen(expr);
if (expr_len == 0) break;
vars_len = 0;
for (i = 0; i < expr_len; ++i) {
e = expr[i];
if (!is_operator(e) && e != 'T' && e != 'F' && vars_index(e) == -1) {
vars[vars_len].name = e;
vars[vars_len].val = FALSE;
vars_len++;
}
}
printf("\n");
if (vars_len == 0) {
printf("No variables were entered.\n");
}
else {
for (i = 0; i < vars_len; ++i)
printf("%c ", vars[i].name);
printf("%s\n", expr);
h = vars_len * 3 + expr_len;
for (i = 0; i < h; ++i) printf("=");
printf("\n");
set_vars(0);
}
}
return 0;
}</lang>
- Output:
Accepts single-character variables (except for 'T' and 'F', which specify explicit true or false values), postfix, with &|!^ for and, or, not, xor, respectively; optionally seperated by whitespace. Just enter nothing to quit. Boolean expression: A B ^ A B AB^ ========= F F F F T T T F T T T F Boolean expression: A B C ^ | A B C ABC^| ============== F F F F F F T T F T F T F T T F T F F T T F T T T T F T T T T T Boolean expression: A B C D ^ ^ ^ A B C D ABCD^^^ =================== F F F F F F F F T T F F T F T F F T T F F T F F T F T F T F F T T F F F T T T T T F F F T T F F T F T F T F F T F T T T T T F F F T T F T T T T T F T T T T T F Boolean expression:
C#
This implementation allows the user to define the characters for true/false and the operators.
To not make it too complicated, operators are limited to a single character.
Either postfix or infix expressions are allowed. Infix expressions are converted to postfix.
<lang csharp>using System;
using System.Collections;
using System.Collections.Generic;
using System.Linq;
using System.Text;
public class TruthTable {
enum TokenType { Unknown, WhiteSpace, Constant, Operand, Operator, LeftParenthesis, RightParenthesis }
readonly char trueConstant, falseConstant; readonly IDictionary<char, Operator> operators = new Dictionary<char, Operator>();
public TruthTable(char falseConstant, char trueConstant)
{
this.trueConstant = trueConstant;
this.falseConstant = falseConstant;
Operators = new OperatorCollection(operators);
}
public OperatorCollection Operators { get; }
public void PrintTruthTable(string expression, bool isPostfix = false)
{
try {
foreach (string line in GetTruthTable(expression, isPostfix)) {
Console.WriteLine(line);
}
} catch (ArgumentException ex) {
Console.WriteLine(expression + " " + ex.Message);
}
}
public IEnumerable<string> GetTruthTable(string expression, bool isPostfix = false)
{
if (string.IsNullOrWhiteSpace(expression)) throw new ArgumentException("Invalid expression.");
//Maps parameters to an index in BitSet
//Makes sure they appear in the truth table in the order they first appear in the expression
var parameters = expression
.Where(c => TypeOf(c) == TokenType.Operand)
.Distinct()
.Reverse()
.Select((c, i) => (symbol: c, index: i))
.ToDictionary(p => p.symbol, p => p.index);
int count = parameters.Count;
if (count > 32) throw new ArgumentException("Cannot have more than 32 parameters.");
string header = count == 0 ? expression : string.Join(" ",
parameters.OrderByDescending(p => p.Value).Select(p => p.Key)) + " " + expression;
if (!isPostfix) expression = ConvertToPostfix(expression);
var values = default(BitSet);
var stack = new Stack<char>(expression.Length);
for (int loop = 1 << count; loop > 0; loop--) {
foreach (char token in expression) stack.Push(token);
bool result = Evaluate(stack, values, parameters);
if (header != null) {
if (stack.Count > 0) throw new ArgumentException("Invalid expression.");
yield return header;
header = null;
}
string line = (count == 0 ? "" : " ") + (result ? trueConstant : falseConstant);
line = string.Join(" ", Enumerable.Range(0, count)
.Select(i => values[count - i - 1] ? trueConstant : falseConstant)) + line;
yield return line;
values++;
}
}
public string ConvertToPostfix(string infix)
{
var stack = new Stack<char>();
var postfix = new StringBuilder();
foreach (char c in infix) {
switch (TypeOf(c)) {
case TokenType.WhiteSpace:
continue;
case TokenType.Constant:
case TokenType.Operand:
postfix.Append(c);
break;
case TokenType.Operator:
int precedence = Precedence(c);
while (stack.Count > 0 && Precedence(stack.Peek()) > precedence) {
postfix.Append(stack.Pop());
}
stack.Push(c);
break;
case TokenType.LeftParenthesis:
stack.Push(c);
break;
case TokenType.RightParenthesis:
char top = default(char);
while (stack.Count > 0) {
top = stack.Pop();
if (top == '(') break;
else postfix.Append(top);
}
if (top != '(') throw new ArgumentException("No matching left parenthesis.");
break;
default:
throw new ArgumentException("Invalid character: " + c);
}
}
while (stack.Count > 0) {
char top = stack.Pop();
if (top == '(') throw new ArgumentException("No matching right parenthesis.");
postfix.Append(top);
}
return postfix.ToString();
}
private bool Evaluate(Stack<char> expression, BitSet values, IDictionary<char, int> parameters)
{
if (expression.Count == 0) throw new ArgumentException("Invalid expression.");
char c = expression.Pop();
TokenType type = TypeOf(c);
while (type == TokenType.WhiteSpace) type = TypeOf(c = expression.Pop());
switch (type) {
case TokenType.Constant:
return c == trueConstant;
case TokenType.Operand:
return values[parameters[c]];
case TokenType.Operator:
bool right = Evaluate(expression, values, parameters);
Operator op = operators[c];
if (op.Arity == 1) return op.Function(right, right);
bool left = Evaluate(expression, values, parameters);
return op.Function(left, right);
default:
throw new ArgumentException("Invalid character: " + c);
}
}
private TokenType TypeOf(char c)
{
if (char.IsWhiteSpace(c)) return TokenType.WhiteSpace;
if (c == '(') return TokenType.LeftParenthesis;
if (c == ')') return TokenType.RightParenthesis;
if (c == trueConstant || c == falseConstant) return TokenType.Constant;
if (operators.ContainsKey(c)) return TokenType.Operator;
if (char.IsLetter(c)) return TokenType.Operand;
return TokenType.Unknown;
}
private int Precedence(char op) => operators.TryGetValue(op, out var o) ? o.Precedence : int.MinValue;
}
struct Operator {
public Operator(char symbol, int precedence, Func<bool, bool> function) : this(symbol, precedence, 1, (l, r) => function(r)) { }
public Operator(char symbol, int precedence, Func<bool, bool, bool> function) : this(symbol, precedence, 2, function) { }
private Operator(char symbol, int precedence, int arity, Func<bool, bool, bool> function) : this()
{
Symbol = symbol;
Precedence = precedence;
Arity = arity;
Function = function;
}
public char Symbol { get; }
public int Precedence { get; }
public int Arity { get; }
public Func<bool, bool, bool> Function { get; }
}
public class OperatorCollection : IEnumerable {
readonly IDictionary<char, Operator> operators;
internal OperatorCollection(IDictionary<char, Operator> operators) {
this.operators = operators;
}
public void Add(char symbol, int precedence, Func<bool, bool> function)
=> operators[symbol] = new Operator(symbol, precedence, function);
public void Add(char symbol, int precedence, Func<bool, bool, bool> function)
=> operators[symbol] = new Operator(symbol, precedence, function);
public void Remove(char symbol) => operators.Remove(symbol);
IEnumerator IEnumerable.GetEnumerator() => operators.Values.GetEnumerator();
}
struct BitSet {
private int bits;
private BitSet(int bits) { this.bits = bits; }
public static BitSet operator ++(BitSet bitSet) => new BitSet(bitSet.bits + 1);
public bool this[int index] => (bits & (1 << index)) != 0;
}
class Program {
public static void Main() {
TruthTable tt = new TruthTable('F', 'T') {
Operators = {
{ '!', 6, r => !r },
{ '&', 5, (l, r) => l && r },
{ '^', 4, (l, r) => l ^ r },
{ '|', 3, (l, r) => l || r }
}
};
//Add a crazy operator:
var rng = new Random();
tt.Operators.Add('?', 6, r => rng.NextDouble() < 0.5);
string[] expressions = {
"!!!T",
"?T",
"F & x | T",
"F & (x | T",
"F & x | T)",
"a ! (a & a)",
"a | (a * a)",
"a ^ T & (b & !c)",
};
foreach (string expression in expressions) {
tt.PrintTruthTable(expression);
Console.WriteLine();
}
//Define a different language
tt = new TruthTable('0', '1') {
Operators = {
{ '-', 6, r => !r },
{ '^', 5, (l, r) => l && r },
{ 'v', 3, (l, r) => l || r },
{ '>', 2, (l, r) => !l || r },
{ '=', 1, (l, r) => l == r },
}
};
expressions = new[] {
"-X v 0 = X ^ 1",
"(H > M) ^ (S > H) > (S > M)"
};
foreach (string expression in expressions) {
tt.PrintTruthTable(expression);
Console.WriteLine();
}
}
}</lang>
- Output:
!!!T F ?T F //Could be T or F x F & x | T F T T T F & (x | T No matching right parenthesis. F & x | T) No matching left parenthesis. a ! (a & a) Invalid expression. a | (a * a) Invalid character: * a b c a ^ T & (b & !c) F F F F F F T F F T F T F T T F T F F T T F T T T T F F T T T T X -X v 0 = -(X ^ 1) 0 1 1 1 H M S (H > M) ^ (S > H) > (S > M) 0 0 0 1 0 0 1 1 0 1 0 1 0 1 1 1 1 0 0 1 1 0 1 1 1 1 0 1 1 1 1 1
D
<lang d>import std.stdio, std.string, std.array, std.algorithm, std.typecons;
struct Var {
const char name; bool val;
} const string expr; Var[] vars;
bool pop(ref bool[] arr) pure nothrow {
const last = arr.back; arr.popBack; return last;
}
enum isOperator = (in char c) pure => "&|!^".canFind(c);
enum varsCountUntil = (in char c) nothrow =>
.vars.map!(v => v.name).countUntil(c).Nullable!(int, -1);
bool evalExp() {
bool[] stack;
foreach (immutable e; .expr) {
if (e == 'T')
stack ~= true;
else if (e == 'F')
stack ~= false;
else if (!e.varsCountUntil.isNull)
stack ~= .vars[e.varsCountUntil.get].val;
else switch (e) {
case '&':
stack ~= stack.pop & stack.pop;
break;
case '|':
stack ~= stack.pop | stack.pop;
break;
case '!':
stack ~= !stack.pop;
break;
case '^':
stack ~= stack.pop ^ stack.pop;
break;
default:
throw new Exception("Non-conformant character '" ~
e ~ "' in expression.");
}
}
assert(stack.length == 1); return stack.back;
}
void setVariables(in size_t pos) in {
assert(pos <= .vars.length);
} body {
if (pos == .vars.length)
return writefln("%-(%s %) %s",
.vars.map!(v => v.val ? "T" : "F"),
evalExp ? "T" : "F");
.vars[pos].val = false; setVariables(pos + 1); .vars[pos].val = true; setVariables(pos + 1);
}
static this() { "Accepts single-character variables (except for 'T' and 'F', which specify explicit true or false values), postfix, with &|!^ for and, or, not, xor, respectively; optionally seperated by whitespace.".writeln;
"Boolean expression: ".write; .expr = readln.split.join;
}
void main() {
foreach (immutable e; expr)
if (!e.isOperator && !"TF".canFind(e) &&
e.varsCountUntil.isNull)
.vars ~= Var(e);
if (.vars.empty)
return;
writefln("%-(%s %) %s", .vars.map!(v => v.name), .expr);
setVariables(0);
}</lang>
- Output:
Accepts single-character variables (except for 'T' and 'F', which specify explicit true or false values), postfix, with &|!^ for and, or, not, xor, respectively; optionally seperated by whitespace. Boolean expression: A B ^ A B AB^ F F F F T T T F T T T F ... Boolean expression: A B C ^ | A B C ABC^| F F F F F F T T F T F T F T T F T F F T T F T T T T F T T T T T ... Boolean expression: A B C D ^ ^ ^ A B C D ABCD^^^ F F F F F F F F T T F F T F T F F T T F F T F F T F T F T F F T T F F F T T T T T F F F T T F F T F T F T F F T F T T T T T F F F T T F T T T T T F T T T T T F
Déjà Vu
<lang dejavu>print-line lst end: for v in reversed copy lst: print\( v chr 9 ) print end
(print-truth-table) t n func: if n: (print-truth-table) push-through copy t 0 -- n @func (print-truth-table) push-through copy t 1 -- n @func else: print-line t func for in copy t
print-truth-table vars name func: print-line vars name (print-truth-table) [] len vars @func print "" # extra new line
stu s t u: or s /= t u
abcd a b c d: /= a /= b /= c d
print-truth-table [ "A" "B" ] "A ^ B" @/= print-truth-table [ "S" "T" "U" ] "S | (T ^ U)" @stu print-truth-table [ "A" "B" "C" "D" ] "A ^ (B ^ (C ^ D))" @abcd</lang>
- Output:
A B A ^ B 0 0 0 0 1 1 1 0 1 1 1 0 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 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
Factor
Postfix is a natural choice. That way, we can use (eval) to to evaluate the expressions without much fuss.
<lang factor>USING: arrays combinators eval formatting io kernel listener
math.combinatorics prettyprint qw sequences splitting
vocabs.parser ;
IN: rosetta-code.truth-table
- prompt ( -- str )
"Please enter a boolean expression using 1-long" print "variable names and postfix notation. Available" print "operators are and, or, not, and xor. Example:" print "> a b and" print nl "> " write readln nl ;
- replace-var ( str -- str' )
dup length 1 = [ drop "%s" ] when ;
- replace-vars ( str -- str' )
" " split [ replace-var ] map " " join ;
- extract-vars ( str -- seq )
" " split [ length 1 = ] filter ;
- count-vars ( str -- n )
" " split [ "%s" = ] count ;
- truth-table ( n -- seq )
qw{ t f } swap selections ;
- print-row ( seq -- )
[ write bl ] each ;
- print-table ( seq -- )
[ print-row nl ] each ;
! Adds a column to the end of a two-dimensional array.
- add-col ( seq col -- seq' )
[ flip ] dip 1array append flip ;
- header ( str -- )
[ extract-vars ] [ ] bi [ print-row "| " write ] [ print ] bi* "=================" print ;
- solve-expr ( seq str -- ? )
vsprintf [ "kernel" use-vocab ( -- x ) (eval) ] with-interactive-vocabs ;
- results ( str -- seq )
replace-vars dup count-vars truth-table [ swap solve-expr unparse ] with map ;
- main ( -- )
prompt [ header t ] [ replace-vars count-vars truth-table ] [ results [ "| " prepend ] map ] tri add-col print-table drop ;
MAIN: main</lang>
- Output:
Please enter a boolean expression using 1-long variable names and postfix notation. Available operators are and, or, not, and xor. Example: > a b and > a b or a b | a b or ================= t t | t t f | t f t | t f f | f Please enter a boolean expression using 1-long variable names and postfix notation. Available operators are and, or, not, and xor. Example: > a b and > x y and z xor not x y z | x y and z xor not ================= t t t | t t t f | f t f t | f t f f | t f t t | f f t f | t f f t | f f f f | 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.
Go
Expression parsing and evaluation taken from the Arithmetic evaluation task. Operator precedence and association are that of the Go language, and are determined by the library parser. The unary ^ is first, then &, then | and ^ associating left to right. Note also that the symbols &, |, and ^ operate bitwise on integer types in Go, but here since we implement our own evaluator we can apply them to the type of bool. <lang go>package main
import (
"bufio" "errors" "fmt" "go/ast" "go/parser" "go/token" "os" "reflect"
)
func main() {
in := bufio.NewScanner(os.Stdin)
for {
fmt.Print("Expr: ")
in.Scan()
if err := in.Err(); err != nil {
fmt.Println(err)
return
}
if !tt(in.Text()) {
return
}
}
}
func tt(expr string) bool {
// call library parser
tree, err := parser.ParseExpr(expr)
if err != nil {
fmt.Println(err)
return false
}
// create handy object to pass around
e := &evaluator{nil, map[string]bool{}, tree}
// library tree traversal function calls e.Visit for each node.
// use this to collect variables of the expression.
ast.Walk(e, tree)
// print headings for truth table
for _, n := range e.names {
fmt.Printf("%-6s", n)
}
fmt.Println(" ", expr)
// start recursive table generation function on first variable
e.evalVar(0)
return true
}
type evaluator struct {
names []string // variables, in order of appearance val map[string]bool // map variables to boolean values tree ast.Expr // parsed expression as ast
}
// visitor function called by library Walk function. // builds a list of unique variable names. func (e *evaluator) Visit(n ast.Node) ast.Visitor {
if id, ok := n.(*ast.Ident); ok {
if !e.val[id.Name] {
e.names = append(e.names, id.Name)
e.val[id.Name] = true
}
}
return e
}
// method recurses for each variable of the truth table, assigning it to // false, then true. At bottom of recursion, when all variables are // assigned, it evaluates the expression and outputs one line of the // truth table func (e *evaluator) evalVar(nx int) bool {
if nx == len(e.names) {
// base case
v, err := evalNode(e.tree, e.val)
if err != nil {
fmt.Println(" ", err)
return false
}
// print variable values
for _, n := range e.names {
fmt.Printf("%-6t", e.val[n])
}
// print expression value
fmt.Println(" ", v)
return true
}
// recursive case
for _, v := range []bool{false, true} {
e.val[e.names[nx]] = v
if !e.evalVar(nx + 1) {
return false
}
}
return true
}
// recursively evaluate ast func evalNode(nd ast.Node, val map[string]bool) (bool, error) {
switch n := nd.(type) {
case *ast.Ident:
return val[n.Name], nil
case *ast.BinaryExpr:
x, err := evalNode(n.X, val)
if err != nil {
return false, err
}
y, err := evalNode(n.Y, val)
if err != nil {
return false, err
}
switch n.Op {
case token.AND:
return x && y, nil
case token.OR:
return x || y, nil
case token.XOR:
return x != y, nil
default:
return unsup(n.Op)
}
case *ast.UnaryExpr:
x, err := evalNode(n.X, val)
if err != nil {
return false, err
}
switch n.Op {
case token.XOR:
return !x, nil
default:
return unsup(n.Op)
}
case *ast.ParenExpr:
return evalNode(n.X, val)
}
return unsup(reflect.TypeOf(nd))
}
func unsup(i interface{}) (bool, error) {
return false, errors.New(fmt.Sprintf("%v unsupported", i))
} </lang> Output:
Expr: A ^ B A B A ^ B false false false false true true true false true true true false Expr: S | ( T ^ U ) 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 Expr: d^b&(c^d) d b c d^b&(c^d) false false false false false false true false false true false false false true true true true false false true true false true true true true false false true true true true
Haskell
Reverse Polish Notation
Accepts expressions given in RPN, tokenized by whitespace. Uses operators "&", "|", "!", "^" (xor), "=>" (implication); all other words are interpreted as variable names.
<lang haskell>import Control.Monad (mapM, foldM, forever) import Data.List (unwords, unlines, nub) import Data.Maybe (fromJust)
truthTable expr = let
tokens = words expr
operators = ["&", "|", "!", "^", "=>"]
variables = nub $ filter (not . (`elem` operators)) tokens
table = zip variables <$> mapM (const [True,False]) variables
results = map (\r -> (map snd r) ++ (calculate tokens) r) table
header = variables ++ ["result"]
in
showTable $ header : map (map show) results
-- Performs evaluation of token sequence in a given context. -- The context is an assoc-list, which binds variable and it's value. -- Here the monad is simple ((->) r). calculate :: [String] -> [(String, Bool)] -> [Bool] calculate = foldM interprete []
where interprete (x:y:s) "&" = (: s) <$> pure (x && y) interprete (x:y:s) "|" = (: s) <$> pure (x || y) interprete (x:y:s) "^" = (: s) <$> pure (x /= y) interprete (x:y:s) "=>" = (: s) <$> pure (not y || x) interprete (x:s) "!" = (: s) <$> pure (not x) interprete s var = (: s) <$> fromJust . lookup var
-- pretty printing showTable tbl = unlines $ map (unwords . map align) tbl
where align txt = take colWidth $ txt ++ repeat ' ' colWidth = max 6 $ maximum $ map length (head tbl)
main = forever $ getLine >>= putStrLn . truthTable</lang>
- Output:
λ> main x ! x result True False False True A B & A B result True True True True False False False True False False False False x1 x2 ! ^ x2 & x1 x2 result True True True True False False False True False False False False
Infix Notation
Translation from infix notation to RPN using Parsec: <lang haskell>{-# LANGUAGE FlexibleContexts #-} import Text.Parsec
toRPN = parse impl "expression" . filter (/= ' ')
where
impl = chainl1 disj (op2 "=>")
disj = chainl1 conj (op2 "|" <|> op2 "^")
conj = chainl1 term (op2 "&")
term = string "(" *> impl <* string ")" <|>
op1 "!" <*> term <|>
many1 alphaNum
op1 s = (\x -> unwords [x, s]) <$ string s
op2 s = (\x y -> unwords [x, y, s]) <$ string s</lang>
- Output:
<lang haskell>λ> putStr $ truthTable $ toRPN "(Human => Mortal) & (Socratus => Human) => (Socratus => Mortal)"
Human Mortal Socratus result True True True True True True False True True False True True True False False True False True True True False True False True False False True True False False False True </lang>
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 this 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
This takes an expression from the command line in reverse Polish notation. The supported operators are & | ^ ! and you probably need to escape them so that your shell doesn't interpret them. As an exercise for the reader, you could make it prompt the user for input (which would avoid the escaping issue), or accept infix expressions (see other examples here for how to turn infix into RPN). <lang java>import java.util.ArrayList; import java.util.HashMap; import java.util.Iterator; import java.util.LinkedHashSet; import java.util.List; import java.util.Map; import java.util.Set; import java.util.Stack;
public class TruthTable {
public static void main( final String... args ) {
System.out.println( new TruthTable( args ) );
}
private interface Operator {
boolean evaluate( Stack<Boolean> s );
}
/**
* Supported operators and what they do. For more ops, add entries here.
*/
private static final Map<String,Operator> operators = new HashMap<String,Operator>() Truth table// Can't use && or;
private final List<String> variables; private final String[] symbols;
/**
* Constructs a truth table for the symbols in an expression.
*/
public TruthTable( final String... symbols ) {
final Set<String> variables = new LinkedHashSet<>();
for ( final String symbol : symbols ) {
if ( ! operators.containsKey( symbol ) ) {
variables.add( symbol );
}
}
this.variables = new ArrayList<>( variables );
this.symbols = symbols;
}
@Override
public String toString () {
final StringBuilder result = new StringBuilder();
for ( final String variable : variables ) {
result.append( variable ).append( ' ' );
}
result.append( ' ' );
for ( final String symbol : symbols ) {
result.append( symbol ).append ( ' ' );
}
result.append( '\n' );
for ( final List<Boolean> values : enumerate( variables.size () ) ) {
final Iterator<String> i = variables.iterator();
for ( final Boolean value : values ) {
result.append(
String.format(
"%-" + i.next().length() + "c ",
value ? 'T' : 'F'
)
);
}
result.append( ' ' )
.append( evaluate( values ) ? 'T' : 'F' )
.append( '\n' );
}
return result.toString (); }
/**
* Recursively generates T/F values
*/
private static List<List<Boolean>> enumerate( final int size ) {
if ( 1 == size )
return new ArrayList<List<Boolean>>() {{
add( new ArrayList<Boolean>() Template:Add(false); );
add( new ArrayList<Boolean>() Template:Add(true); );
}};
return new ArrayList<List<Boolean>>() {{
for ( final List<Boolean> head : enumerate( size - 1 ) ) {
add( new ArrayList<Boolean>( head ) Template:Add(false); );
add( new ArrayList<Boolean>( head ) Template:Add(true); );
}
}};
}
/**
* Evaluates the expression for a set of values.
*/
private boolean evaluate( final List<Boolean> enumeration ) {
final Iterator<Boolean> i = enumeration.iterator();
final Map<String,Boolean> values = new HashMap<>();
final Stack<Boolean> stack = new Stack<>();
variables.forEach ( v -> values.put( v, i.next() ) );
for ( final String symbol : symbols ) {
final Operator op = operators.get ( symbol );
// Reverse Polish notation makes this bit easy
stack.push(
null == op
? values.get ( symbol )
: op.evaluate ( stack )
);
}
return stack.pop();
}
}</lang>
- Output:
Note that the escape character is ^ for Windows
C:\rosettacode> java TruthTable a b c ^^ ^| a b c a b c ^ | F F F F F F T T F T F T F T T F T F F T T F T T T T F T T T T T C:\rosettacode> java TruthTable Jim Spock Bones ^^ ^& Scotty ^| Jim Spock Bones Scotty Jim Spock Bones ^ & Scotty | F F F F F F F F T T F F T F F F F T T T F T F F F F T F T T F T T F F F T T T T T F F F F T F F T T T F T F T T F T T T T T F F T T T F T T T T T F F T T T T T
JavaScript
Actually a HTML document. Save as a .html document and double-click it. You should be fine. <lang javascript><!DOCTYPE html><html><head><title>Truth table</title><script> var elem,expr,vars; function isboolop(chr){return "&|!^".indexOf(chr)!=-1;} function varsindexof(chr){ var i; for(i=0;i<vars.length;i++){if(vars[i][0]==chr)return i;} return -1; } function printtruthtable(){ var i,str; elem=document.createElement("pre"); expr=prompt("Boolean expression:\nAccepts single-character variables (except for \"T\" and \"F\", which specify explicit true or false values), postfix, with \"&|!^\" for and, or, not, xor, respectively; optionally seperated by whitespace.").replace(/\s/g,""); vars=[]; for(i=0;i<expr.length;i++)if(!isboolop(expr[i])&&expr[i]!="T"&&expr[i]!="F"&&varsindexof(expr[i])==-1)vars.push([expr[i],-1]); if(vars.length==0)return; str=""; for(i=0;i<vars.length;i++)str+=vars[i][0]+" "; elem.innerHTML=""+str+expr+"\n"; vars[0][1]=false; truthpartfor(1); vars[0][1]=true; truthpartfor(1); vars[0][1]=-1; document.body.appendChild(elem); } function truthpartfor(index){ if(index==vars.length){ var str,i; str=""; for(i=0;i<index;i++)str+=(vars[i][1]?"T":"F")+" "; elem.innerHTML+=str+(parsebool()?"T":"F")+"\n"; return; } vars[index][1]=false; truthpartfor(index+1); vars[index][1]=true; truthpartfor(index+1); vars[index][1]=-1; } function parsebool(){ var stack,i,idx; console.log(vars); stack=[]; for(i=0;i<expr.length;i++){ if(expr[i]=="T")stack.push(true); else if(expr[i]=="F")stack.push(false); else if((idx=varsindexof(expr[i]))!=-1)stack.push(vars[idx][1]); else if(isboolop(expr[i])){ switch(expr[i]){ case "&":stack.push(stack.pop()&stack.pop());break; case "|":stack.push(stack.pop()|stack.pop());break; case "!":stack.push(!stack.pop());break; case "^":stack.push(stack.pop()^stack.pop());break; } } else alert("Non-conformant character "+expr[i]+" in expression. Should not be possible."); console.log(stack); } return stack[0]; } </script></head><body onload="printtruthtable()"></body></html></lang>
- Output in browser window after entering "AB^":
A B AB^ F F F F T T T F T T T F
- Output in browser window after entering "ABC^|":
A B C ABC^| F F F F F F T T F T F T F T T F T F F T T F T T T T F T T T T T
Julia
Module: <lang julia>module TruthTable
using Printf using MacroTools
isvariablename(::Any) = false isvariablename(s::Symbol) = all(x -> isletter(x) || x == '_', string(s))
function table(expr)
if !isvariablename(expr) && !Meta.isexpr(expr, :call)
throw(ArgumentError("expr must be a boolean expression"))
end
exprstr = string(expr)
# Collect variable names
symset = Set{Symbol}()
MacroTools.prewalk(expr) do node
isvariablename(node) && push!(symset, node)
return node
end
symlist = collect(symset)
# Create assignment assertions + evaluate
blocks = Vector{Expr}(undef, 2 ^ length(symlist) + 1)
blocks[1] = quote
println(join(lpad.($(symlist), 6), " | "), " || ", $exprstr)
end
for (i, tup) in enumerate(Iterators.product(Iterators.repeated((false, true), length(symlist))...))
blocks[i + 1] = quote
let $(Expr(:(=), Expr(:tuple, symlist...), Expr(:tuple, tup...)))
println(join(lpad.($(Expr(:tuple, symlist...)), 6), " | "), " || ", lpad($expr, $(length(exprstr))))
end
end
end
return esc(Expr(:block, blocks...))
end
macro table(expr)
return table(expr)
end
end # module TruthTable</lang>
Main: <lang julia>TruthTable.@table !a TruthTable.@table a | b TruthTable.@table (a ⊻ b) | (c & a) TruthTable.@table (a & b) | (c ⊻ d) </lang>
- Output:
a || !a
false || true
true || false
a | b || a | b
false | false || false
true | false || true
false | true || true
true | true || true
a | b | c || (a ⊻ b) | c & a
false | false | false || false
true | false | false || true
false | true | false || true
true | true | false || false
false | false | true || false
true | false | true || true
false | true | true || true
true | true | true || true
a | b | d | c || a & b | (c ⊻ d)
false | false | false | false || false
true | false | false | false || false
false | true | false | false || false
true | true | false | false || true
false | false | true | false || true
true | false | true | false || true
false | true | true | false || true
true | true | true | false || true
false | false | false | true || true
true | false | false | true || true
false | true | false | true || true
true | true | false | true || true
false | false | true | true || false
true | false | true | true || false
false | true | true | true || false
true | true | true | true || true
Kotlin
<lang scala>// Version 1.2.31
import java.util.Stack
class Variable(val name: Char, var value: Boolean = false)
lateinit var expr: String var variables = mutableListOf<Variable>()
fun Char.isOperator() = this in "&|!^"
fun Char.isVariable() = this in variables.map { it.name }
fun evalExpression(): Boolean {
val stack = Stack<Boolean>()
for (e in expr) {
stack.push(
if (e == 'T')
true
else if (e == 'F')
false
else if (e.isVariable())
variables.single { it.name == e }.value
else when (e) {
'&' -> stack.pop() and stack.pop()
'|' -> stack.pop() or stack.pop()
'!' -> !stack.pop()
'^' -> stack.pop() xor stack.pop()
else -> throw RuntimeException("Non-conformant character '$e' in expression")
}
)
}
require(stack.size == 1) return stack.peek()
}
fun setVariables(pos: Int) {
require(pos <= variables.size)
if (pos == variables.size) {
val vs = variables.map { if (it.value) "T" else "F" }.joinToString(" ")
val es = if (evalExpression()) "T" else "F"
return println("$vs $es")
}
variables[pos].value = false
setVariables(pos + 1)
variables[pos].value = true
setVariables(pos + 1)
}
fun main(args: Array<String>) {
println("Accepts single-character variables (except for 'T' and 'F',")
println("which specify explicit true or false values), postfix, with")
println("&|!^ for and, or, not, xor, respectively; optionally")
println("seperated by spaces or tabs. Just enter nothing to quit.")
while (true) {
print("\nBoolean expression: ")
expr = readLine()!!.toUpperCase().replace(" ", "").replace("\t", "")
if (expr == "") return
variables.clear()
for (e in expr) {
if (!e.isOperator() && e !in "TF" && !e.isVariable()) variables.add(Variable(e))
}
if (variables.isEmpty()) return
val vs = variables.map { it.name }.joinToString(" ")
println("\n$vs $expr")
val h = vs.length + expr.length + 2
repeat(h) { print("=") }
println("\n")
setVariables(0)
}
}</lang>
- Output:
Sample session:
Accepts single-character variables (except for 'T' and 'F', which specify explicit true or false values), postfix, with &|!^ for and, or, not, xor, respectively; optionally seperated by spaces or tabs. Just enter nothing to quit. Boolean expression: A B ^ A B AB^ ========= F F F F T T T F T T T F Boolean expression: A B C ^ | A B C ABC^| ============== F F F F F F T T F T F T F T T F T F F T T F T T T T F T T T T T Boolean expression: A B C D ^ ^ ^ A B C D ABCD^^^ =================== F F F F F F F F T T F F T F T F F T T F F T F F T F T F T F F T T F F F T T T T T F F F T T F F T F T F T F F T F T T T T T F F F T T F T T T T T F T T T T T F Boolean expression:
Liberty BASIC
This at first seems trivial, given our lovely 'eval' function. However it is complicated by LB's use of 'non-zero' for 'true', and by the requirements of accepting different numbers and names of variables. My program assumes all space-separated words in the expression$ 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 )'"
[start] input " "; expression$ if expression$ ="" then [start]
'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
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
Maxima
<lang Maxima>/* Maxima already has the following logical operators
=, # (not equal), not, and, or
define some more and set 'binding power' (operator precedence) for them
- /
infix("xor", 60)$ "xor"(A,B):= (A or B) and not(A and B)$
infix("=>", 59)$ "=>"(A,B):= not A or B$
/* Substitute variables `r' in `e' with values taken from list `l' where `e' is expression, `r' is a list of independent variables, `l' is a list of the values lsubst( '(A + B), ['A, 'B], [1, 2]); 1 + 2;
- /
lsubst(e, r, l):= ev(e, maplist( lambda([x, y], x=y), r, l), 'simp)$
/* "Cartesian power" `n' of list `b'. Returns a list of lists of the form [<x_1>, ..., <x_n>], were <x_1>, .. <x_n> are elements of list `b' cartesian_power([true, false], 2); [[true, true], [true, false], [false, true], [false, false]]; cartesian_power([true, false], 3); [[true, true, true], [true, true, false], [true, false, true], [true, false, false], [false, true, true], [false, true, false], [false, false, true], [false, false, false]];
- /
cartesian_power(b, n) := block(
[aux_lst: makelist(setify(b), n)], listify(apply(cartesian_product, aux_lst)) )$
gen_table(expr):= block(
[var_lst: listofvars(expr), st_lst, res_lst, m],
st_lst: cartesian_power([true, false], length(var_lst)),
res_lst: create_list(lsubst(expr, var_lst, val_lst), val_lst, st_lst),
m : apply('matrix, cons(var_lst, st_lst)),
addcol(m, cons(expr, res_lst))
);
/* examples */ gen_table('(not A)); gen_table('(A xor B)); gen_table('(Jim and (Spock xor Bones) or Scotty)); gen_table('(A => (B and A))); gen_table('(V xor (B xor (K xor D ) )));</lang>
OUtput of the last example: <lang>
[ V B K D V xor (B xor (K xor D)) ]
[ ]
[ true true true true false ]
[ ]
[ true true true false true ]
[ ]
[ true true false true true ]
[ ]
[ true true false false false ]
[ ]
[ true false true true true ]
[ ]
[ true false true false false ]
[ ]
[ true false false true false ]
[ ]
[ true false false false true ]
[ ]
[ false true true true true ]
[ ]
[ false true true false false ]
[ ]
[ false true false true false ]
[ ]
[ false true false false true ]
[ ]
[ false false true true false ]
[ ]
[ false false true false true ]
[ ]
[ false false false true true ]
[ ]
[ false false false false false ]
</lang>
PARI/GP
Uses infix Boolean expressions with + for OR, * for AND, and the constants 0 and 1 for FALSE and TRUE.
It would be easy to modify the program to take + for XOR instead.
<lang parigp>vars(P)={
my(v=List(),x);
while(type(P)=="t_POL",
x=variable(P);
listput(v,x);
P=subst(P,x,1)
);
Vec(v)
};
truthTable(P)={
my(var=vars(P),t,b);
for(i=0,2^#var-1,
t=eval(P);
for(j=1,#var,
b=bittest(i,j-1);
t=subst(t,var[j],b);
print1(b)
);
print(!!t)
);
};
truthTable("x+y") \\ OR
truthTable("x*y") \\ AND</lang>
- Output:
000 101 011 111 000 100 010 111
Pascal
<lang Pascal> program TruthTables; const
StackSize = 80;
type
TVariable = record Name: Char; Value: Boolean; end;
TStackOfBool = record Top: Integer; Elements: array [0 .. StackSize - 1] of Boolean; end;
var
Expression: string; Variables: array [0 .. 23] of TVariable; VariablesLength: Integer; i, h: Integer; e: Char;
// Stack manipulation functions function IsFull(var s: TStackOfBool): Boolean; begin
IsFull := s.Top = StackSize - 1;
end;
function IsEmpty(var s: TStackOfBool): Boolean; begin
IsEmpty := s.Top = -1;
end;
function Peek(var s: TStackOfBool): Boolean; begin
if not IsEmpty(s) then
Peek := s.Elements[s.Top]
else
begin
Writeln('Stack is empty.');
Halt;
end;
end;
procedure Push(var s: TStackOfBool; val: Boolean); begin
if not IsFull(s) then
begin
Inc(s.Top);
s.Elements[s.Top] := val;
end
else
begin
Writeln('Stack is full.');
Halt;
end
end;
function Pop(var s: TStackOfBool): Boolean; begin
if not IsEmpty(s) then
begin
Pop := s.Elements[s.Top];
Dec(s.Top);
end
else
begin
Writeln;
Writeln('Stack is empty.');
Halt;
end
end;
function IsOperator(const c: Char): Boolean; begin
IsOperator := (c = '&') or (c = '|') or (c = '!') or (c = '^');
end;
function VariableIndex(const c: Char): Integer; var
i: Integer;
begin
for i := 0 to VariablesLength - 1 do
if Variables[i].Name = c then
begin
VariableIndex := i;
Exit;
end;
VariableIndex := -1;
end;
function EvaluateExpression: Boolean; var
i, vi: Integer; e: Char; s: TStackOfBool;
begin
s.Top := -1;
for i := 1 to Length(Expression) do
begin
e := Expression[i];
vi := VariableIndex(e);
if e = 'T' then
Push(s, True)
else if e = 'F' then
Push(s, False)
else if vi >= 0 then
Push(s, Variables[vi].Value)
else
begin
case e of
'&':
Push(s, Pop(s) and Pop(s));
'|':
Push(s, Pop(s) or Pop(s));
'!':
Push(s, not Pop(s));
'^':
Push(s, Pop(s) xor Pop(s));
else
Writeln;
Writeln('Non-conformant character ', e, ' in expression.', e);
Halt;
end;
end;
end;
if s.Top < 0 then
begin
Writeln;
Writeln('Stack should contain exactly one element.');
Halt;
end;
EvaluateExpression := Peek(s);
end;
procedure SetVariables(pos: Integer); var
i: Integer;
begin
if pos > VariablesLength then
begin
Writeln;
Writeln('Argument to SetVariables cannot be greater than the number of variables.');
Halt;
end
else if pos = VariablesLength then
begin
for i := 0 to VariablesLength - 1 do
begin
if Variables[i].Value then
Write('T ')
else
Write('F ');
end;
if EvaluateExpression then
Writeln('T')
else
Writeln('F');
end
else
begin
Variables[pos].Value := False;
SetVariables(pos + 1);
Variables[pos].Value := True;
SetVariables(pos + 1);
end
end;
// removes space and converts to upper case procedure ProcessExpression; var
i: Integer; exprTmp: string;
begin
exprTmp := ;
for i := 1 to Length(Expression) do
begin
if Expression[i] <> ' ' then
exprTmp := Concat(exprTmp, Expression[i]);
end;
Expression := exprTmp
end;
begin
Writeln('Accepts single-character variables (except for T and F,');
Writeln('which specify explicit true or false values), postfix, with');
Writeln('&|!^ for and, or, not, xor, respectively; optionally');
Writeln('seperated by space. Just enter nothing to quit.');
while (True) do
begin
Writeln;
Write('Boolean expression: ');
ReadLn(Expression);
ProcessExpression;
if Length(Expression) = 0 then
Break;
VariablesLength := 0;
for i := 1 to Length(Expression) do
begin
e := Expression[i];
if (not IsOperator(e)) and (e <> 'T') and (e <> 'F') and
(VariableIndex(e) = -1) then
begin
Variables[VariablesLength].Name := e;
Variables[VariablesLength].Value := False;
Inc(VariablesLength);
end;
end;
if VariablesLength = 0 then
begin
Writeln;
Writeln('No variables were entered.');
Continue;
end;
Writeln;
for i := 0 to VariablesLength - 1 do
begin
Write(Variables[i].Name, ' ');
end;
Writeln(Expression);
h := VariablesLength * 3 + Length(Expression);
for i := 0 to h - 1 do
Write('=');
Writeln;
SetVariables(0);
end;
end. </lang>
- Output:
Accepts single-character variables (except for 'T' and 'F', which specify explicit true or false values), postfix, with &|!^ for and, or, not, xor, respectively; optionally seperated by space. Just enter nothing to quit. Boolean expression: A B ^ A B AB^ ========= F F F F T T T F T T T F Boolean expression: A B C ^ | A B C ABC^| ============== F F F F F F T T F T F T F T T F T F F T T F T T T T F T T T T T Boolean expression: A B C D ^ ^ ^ A B C D ABCD^^^ =================== F F F F F F F F T T F F T F T F F T T F F T F F T F T F T F F T T F F F T T T T T F F F T T F F T F T F T F F T F T T T T T F F F T T F T T T T T F T T T T T F Boolean expression:
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 $s; }
truth_table 'A ^ A_1'; truth_table 'foo & bar | baz';
truth_table 'Jim & (Spock ^ Bones) | Scotty';</lang>
- Output:
A A_1 A ^ A_1 ---------------------------------------- F F F F T T T F T T T F
foo bar baz foo & bar | baz ---------------------------------------- F F F F F F T T F T F F F T T T T F F F T F T T T T F T T T T T
Jim Spock Bones Scotty Jim & (Spock ^ Bones) | Scotty ---------------------------------------- F F F F F ...<snip for space -- not like you're gonna verify it anyway>... T T T T T
Perl 6
<lang perl6>use MONKEY-SEE-NO-EVAL;
sub MAIN ($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, flat map { .fmt("\%0{+@n}b").comb».Int».so }, 0 ..^ 2**@n;
say ;
}</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
Phix
Expression parsing and evaluation similar to that in the Arithmetic evaluation task. <lang Phix>sequence opstack = {} object token object op = 0 -- 0 = none string s -- the expression being parsed integer sidx -- idx to "" integer ch -- s[sidx]
procedure err(string msg)
printf(1,"%s\n%s^ %s\n\nPressEnter...",{s,repeat(' ',sidx-1),msg})
{} = wait_key()
abort(0)
end procedure
procedure nxtch()
sidx += 1 ch = iff(sidx>length(s)?-1:s[sidx])
end procedure
procedure skipspaces()
while find(ch," \t\r\n")!=0 do nxtch() end while
end procedure
procedure get_token()
skipspaces()
if find(ch,"()!") then
token = s[sidx..sidx]
nxtch()
else
integer tokstart = sidx
if ch=-1 then token = "eof" return end if
while 1 do
nxtch()
if ch<'A' then exit end if
end while
token = s[tokstart..sidx-1]
end if
end procedure
procedure Match(string t)
if token!=t then err(t&" expected") end if get_token()
end procedure
procedure PopFactor() object p2 = opstack[$]
if op="not" then
opstack[$] = {0,op,p2}
else
opstack = opstack[1..$-1]
opstack[$] = {opstack[$],op,p2}
end if
op = 0
end procedure
sequence names -- {"false","true",...} sequence flags -- { 0, 1, ,...}
procedure PushFactor(string t)
if op!=0 then PopFactor() end if
integer k = find(t,names)
if k=0 then
names = append(names,t)
k = length(names)
end if
opstack = append(opstack,k)
end procedure
procedure PushOp(string t)
if op!=0 then PopFactor() end if op = t
end procedure
procedure Factor()
if token="not"
or token="!" then
get_token()
Factor()
if op!=0 then PopFactor() end if
PushOp("not")
elsif token="(" then
get_token()
Expr(0)
Match(")")
elsif not find(token,{"and","or","xor"}) then
PushFactor(token)
if ch!=-1 then
get_token()
end if
else
err("syntax error")
end if
end procedure
constant {operators,
precedence} = columnize({{"not",6},
{"and",5},
{"xor",4},
{"or",3}})
procedure Expr(integer p)
Factor()
while 1 do
integer k = find(token,operators)
if k=0 then exit end if
integer thisp = precedence[k]
if thisp
=1 then s = flags[s] end if return s end if object {lhs,op,rhs} = s lhs = eval(lhs) rhs = eval(rhs) if op="and" then return lhs and rhs elsif op="or" then return lhs or rhs elsif op="xor" then return lhs xor rhs elsif op="not" then return not rhs else ?9/0 end if end function function next_comb() integer fdx = length(flags) while flags[fdx]=1 do flags[fdx] = 0 fdx -= 1 end while if fdx<=2 then return false end if -- all done flags[fdx] = 1 return true end function function fmt(bool b) return {"0","1"}[b+1] -- for 0/1 -- return {"F","T"}[b+1] -- for F/T end function procedure test(string expr) opstack = {} op = 0 names = {"false","true"} s = expr sidx = 0 nxtch() get_token() Expr(0) if op!=0 then PopFactor() end if if length(opstack)!=1 then err("some error") end if flags = repeat(0,length(names)) flags[2] = 1 -- set "true" true printf(1,"%s %s\n",{join(names[3..$]),s}) while 1 do for i=3 to length(flags) do -- (skipping true&false) printf(1,"%s%s",{fmt(flags[i]),repeat(' ',length(names[i]))}) end for printf(1," %s\n",{fmt(eval(opstack[1]))}) if not next_comb() then exit end if end while puts(1,"\n") end procedure test("young and not (ugly or poor)") while 1 do puts(1,"input expression:") string t = trim(gets(0)) puts(1,"\n") if t="" then exit end if test(t) end while</lang>
- Output:
young ugly poor young and not (ugly or poor) 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 0 1 0 0 1 1 0 1 0 1 1 0 0 1 1 1 0 input expression:
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>
Prolog
<lang prolog>/* To evaluate the truth table a line of text is inputted and then there are three steps Let's say the expression is: 'not a and (b or c)'
Step 1: tokenize into atoms and brackets eg: Tokenized = [ not, a, and, '(', b, or, c, ')' ].
Step 2: convert to a term that can be evaluated, and get out the variables eg: Expression = op(and, op(not, a), op(or, b, c)), Variables = [ a, b, c ]
Step 3: permeate over the variables, substituting the values for each var, and evaluate the expression for each permutation eg: [ 0, 0, 0] op(and, op(not, 0), op(or, 0, 0)) op(and, 1, op(or, 0, 0)) op(and, 1, 0) 0
[ 0, 0, 1] op(and, op(not, 0), op(or, 0, 1)) op(and, 1, op(or, 0, 0)) op(and, 1, 1) 1
- /
truth_table :- current_input(In), read_line_to_codes(In, Line), atom_codes(A, Line), atom_chars(A, Chars),
% parse everything into the form we want phrase(tok(Tok), Chars, _), phrase(expr(Expr,Vars), Tok, _), list_to_set(Vars,VarSet),
% evaluate print_expr(Expr, VarSet), !.
print_expr(Expr, Vars) :- % write the header (once) maplist(format('~p '), Vars), format('~n'),
% write the results for as many times as there are rows eval_expr(Expr, Vars, Tvals, R), maplist(format('~p '), Tvals), format('~p~n', R), fail. print_expr(_, _).
% Step 1 - tokenize the input into spaces, brackets and atoms
tok([A|As]) --> spaces(_), chars([X|Xs]), {atom_codes(A, [X|Xs])}, spaces(_), tok(As).
tok([A|As]) --> spaces(_), bracket(A), spaces(_), tok(As).
tok([]) --> [].
chars([X|Xs]) --> char(X), { dif(X, ')'), dif(X, '(') }, !, chars(Xs).
chars([]) --> [].
spaces([X|Xs]) --> space(X), !, spaces(Xs).
spaces([]) --> [].
bracket('(') --> ['('].
bracket(')') --> [')'].
% Step 2 - Parse the expression into an evaluable term
expr(op(I, E, E2), V) --> starter(E, V1), infix(I), expr(E2, V2), { append(V1, V2, V) }.
expr(E, V) --> starter(E, V).
starter(op(not, E),V) --> [not], expr(E, V). starter(E,V) --> ['('], expr(E,V), [')']. starter(V,[V]) --> variable(V).
infix(or) --> [or]. infix(and) --> [and]. infix(xor) --> [xor]. infix(nand) --> [nand].
variable(V) --> [V], \+ infix(V), \+ bracket(V). space(' ') --> [' ']. char(X) --> [X], { dif(X, ' ') }.
% Step 3 - evaluate the parsed expression
eval_expr(Expr, Vars, Tvals, R) :-
length(Vars,Len),
length(Tvals, Len),
maplist(truth_val, Tvals),
eval(Expr, [Tvals,Vars],R).
eval(X, [Vals,Vars], R) :- nth1(N,Vars,X), nth1(N,Vals,R). eval(op(Op,A,B), V, R) :- eval(A,V,Ae), eval(B,V,Be), e(Op,Ae,Be,R). eval(op(not,A), V, R) :- eval(A,V,Ae), e(not,Ae,R).
truth_val(0). truth_val(1).
e(or,0,0,0). e(or,0,1,1). e(or,1,0,1). e(or,1,1,1). e(and,0,0,0). e(and,0,1,0). e(and,1,0,0). e(and,1,1,1). e(xor,0,0,0). e(xor,0,1,1). e(xor,1,0,1). e(xor,1,1,0). e(nand,0,0,1). e(nand,0,1,1). e(nand,1,0,1). e(nand,1,1,0). e(not, 1, 0). e(not, 0, 1).</lang>
- Output:
?- truth_table. |: not a and (b or c) a b c 0 0 0 0 0 0 1 1 0 1 0 1 0 1 1 1 1 0 0 0 1 0 1 0 1 1 0 0 1 1 1 0 true. ?-
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
R
<lang r> truth_table <- function(x) {
vars <- unique(unlist(strsplit(x, "[^a-zA-Z]+"))) vars <- vars[vars != ""] perm <- expand.grid(rep(list(c(FALSE, TRUE)), length(vars))) names(perm) <- vars perm[ , x] <- with(perm, eval(parse(text = x))) perm
}
"%^%" <- xor # define unary xor operator
truth_table("!A") # not
- A !A
- 1 FALSE TRUE
- 2 TRUE FALSE
truth_table("A | B") # or
- A B A | B
- 1 FALSE FALSE FALSE
- 2 TRUE FALSE TRUE
- 3 FALSE TRUE TRUE
- 4 TRUE TRUE TRUE
truth_table("A & B") # and
- A B A & B
- 1 FALSE FALSE FALSE
- 2 TRUE FALSE FALSE
- 3 FALSE TRUE FALSE
- 4 TRUE TRUE TRUE
truth_table("A %^% B") # xor
- A B A %^% B
- 1 FALSE FALSE FALSE
- 2 TRUE FALSE TRUE
- 3 FALSE TRUE TRUE
- 4 TRUE TRUE FALSE
truth_table("S | (T %^% U)") # 3 variables with brackets
- S T U S | (T %^% U)
- 1 FALSE FALSE FALSE FALSE
- 2 TRUE FALSE FALSE TRUE
- 3 FALSE TRUE FALSE TRUE
- 4 TRUE TRUE FALSE TRUE
- 5 FALSE FALSE TRUE TRUE
- 6 TRUE FALSE TRUE TRUE
- 7 FALSE TRUE TRUE FALSE
- 8 TRUE TRUE TRUE TRUE
truth_table("A %^% (B %^% (C %^% D))") # 4 variables with nested brackets
- A B C D A %^% (B %^% (C %^% D))
- 1 FALSE FALSE FALSE FALSE FALSE
- 2 TRUE FALSE FALSE FALSE TRUE
- 3 FALSE TRUE FALSE FALSE TRUE
- 4 TRUE TRUE FALSE FALSE FALSE
- 5 FALSE FALSE TRUE FALSE TRUE
- 6 TRUE FALSE TRUE FALSE FALSE
- 7 FALSE TRUE TRUE FALSE FALSE
- 8 TRUE TRUE TRUE FALSE TRUE
- 9 FALSE FALSE FALSE TRUE TRUE
- 10 TRUE FALSE FALSE TRUE FALSE
- 11 FALSE TRUE FALSE TRUE FALSE
- 12 TRUE TRUE FALSE TRUE TRUE
- 13 FALSE FALSE TRUE TRUE FALSE
- 14 TRUE FALSE TRUE TRUE TRUE
- 15 FALSE TRUE TRUE TRUE TRUE
- 16 TRUE TRUE TRUE TRUE FALSE
</lang>
Racket
Since the requirement is to read an expression dynamically, eval is a natural choice. The following isn't trying to protect against bad inputs when doing that.
<lang Racket>
- lang racket
(define (collect-vars sexpr)
(sort
(remove-duplicates
(let loop ([x sexpr])
(cond [(boolean? x) '()]
[(symbol? x) (list x)]
[(list? x) (append-map loop (cdr x))]
[else (error 'truth-table "Bad expression: ~e" x)])))
string<? #:key symbol->string))
(define ns (make-base-namespace))
(define (truth-table sexpr)
(define vars (collect-vars sexpr))
(printf "~a => ~s\n" (string-join (map symbol->string vars)) sexpr)
(for ([i (expt 2 (length vars))])
(define vals
(map (λ(x) (eq? #\1 x))
(reverse (string->list (~r i #:min-width (length vars)
#:pad-string "0"
#:base 2)))))
(printf "~a => ~a\n" (string-join (map (λ(b) (if b "T" "F")) vals))
(if (eval `(let (,@(map list vars vals)) ,sexpr) ns) "T" "F"))))
(printf "Enter an expression: ") (truth-table (read)) </lang>
Sample run:
Enter an expression: (and (or z x) (or y (not z))) x y z => (and (or z x) (or y (not z))) F F F => F T F F => T F T F => F T T F => T F F T => F T F T => F F T T => T T T T => T
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, negation).
Some REXX interpreters also (or instead) support:
- \ (backslash)
- / (forward slash, solidus)
- ~ (tilde)
- ^ (caret, circumflex, hat)
Also included is support for two boolean values: TRUE and FALSE which are part of boolean expressions. <lang rexx>/*REXX program displays a truth table of variables and an expression. Infix notation */ /*─────────────── is supported with one character propositional constants; variables */ /*─────────────── (propositional constants) that are allowed: A──►Z, a──►z except u.*/ /*─────────────── All propositional constants are case insensitive (except lowercase u).*/
parse arg userText /*get optional expression from the CL. */ if userText\= then do /*Got one? Then show user's stuff. */
call truthTable userText /*display truth table for the userText.*/
exit /*we're finished with the user's text. */
end
call truthTable "G ^ H ; XOR" /*text after ; is echoed to the 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 golly. */
/* ↓↓↓ no way, Jose. ↓↓↓ */ /* [↓] shows a 32,768 line truth table*/
call truthTable "A^ (B^ (C^ (D^ (E^ (F^ (G^ (H^ (I^ (J^ (L^ (L^ (M^ (N^O) ))))))))))))" exit /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ truthTable: procedure; parse arg $ ';' comm 1 $o; $o= strip($o); hdrPCs=
$= translate(strip($), '|', "v"); $u= $; upper $u
$u= translate($u, '()()()', "[]{}«»"); $$.= 0; PCs=
@abc= 'abcdefghijklmnopqrstuvwxyz'; @abcU= @abc; upper @abcU
/* ╔═════════════════════╦════════════════════════════════════════════════════════════╗
║ ║ 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 │ ║ ║ This boxed table ║ leading zeroes can be omitted. │ 0010 │ NaIMPb │ ║ ║ was re─constructed ║ │ 0011 │ boolB │ ║ ║ from an old IBM ║ BF may have multiple values (one │ 0100 │ NbIMPa │ ║ ║ publicastion: ║ for each pair of bitstrings): │ 0101 │ boolA │ ║ ║ ║ │ 0110 │ xor │ ║ ║ "PL/I Language ║ ┌──────┬──────┬───────────────┐ │ 0111 │ or │ ║ ║ Specifications" ║ │ Abit │ Bbit │ returns │ │ 1000 │ nor │ ║ ║ ║ ├──────┼──────┼───────────────┤ │ 1001 │ nxor │ ║ ║ ║ │ 0 │ 0 │ 1st bit in BF │ │ 1010 │ notB │ ║ ║ ║ │ 0 │ 1 │ 2nd bit in BF │ │ 1011 │ bIMPa │ ║ ║ ─── March 1969. ║ │ 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 (0──►15) */
op.= /*Note: a single quote (') wasn'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 that need changing. */
op.16= '\ NOT ~ ─ . ¬' /* NOT, negation */
op.17= '> GT' /*conditional */
op.18= '>= GE ─> => ──> ==>' "1a"x /*conditional; (see note below.)──┐*/
op.19= '< LT' /*conditional │*/
op.20= '<= LE <─ <= <── <==' /*conditional │*/
op.21= '\= NE ~= ─= .= ¬=' /*conditional │*/
op.22= '= EQ EQUAL EQUALS =' "1b"x /*bi─conditional; (see note below.)┐ │*/
op.23= '0 boolTRUE' /*TRUEness │ │*/
op.24= '1 boolFALSE' /*FALSEness ↓ ↓*/
/* [↑] glphys '1a'x and "1b"x can't*/
/* displayed under most DOS' & such*/
do jj=0 while op.jj\== | jj<16 /*change opers ──► into what REXX likes*/
new= word(op.jj, 1) /*obtain the 1st token of infex table.*/
/* [↓] process the rest of the tokens.*/
do kk=2 to words(op.jj) /*handle each of the tokens separately.*/
_=word(op.jj, kk); upper _ /*obtain another token from infix table*/
if wordpos(_, $u)==0 then iterate /*no such animal in this string. */
if datatype(new, 'm') then new!= @ /*it needs to be transcribed*/
else new!= new /*it doesn't need " " " */
$u= changestr(_, $u, new!) /*transcribe the function (maybe). */
if new!==@ then $u= changeFunc($u,@,new) /*use the internal boolean name. */
end /*kk*/
end /*jj*/
$u=translate($u, '()', "{}") /*finish cleaning up the transcribing. */
do jj=1 for length(@abcU) /*see what variables are being used. */
_= substr(@abcU, jj, 1) /*use the available upercase aLphabet. */
if pos(_,$u) == 0 then iterate /*Found one? No, then keep looking. */
$$.jj= 1 /*found: set upper bound for it. */
PCs= PCs _ /*also, add to propositional constants.*/
hdrPCs=hdrPCS center(_,length('false')) /*build a PC header for transcribing. */
end /*jj*/
ptr= '_────►_' /*a (text) pointer for the truth table.*/
$u= PCs '('$u")" /*separate the PCs from expression. */
hdrPCs= substr(hdrPCs, 2) /*create a header for the PCs. */
say hdrPCs left(, length(ptr) - 1) $o /*display PC header and expression. */
say copies('───── ', words(PCs)) left(, length(ptr) -2) copies('─', length($o))
/*Note: "true"s: are 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 /*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; 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 /* [↓] get 1 or 2 chars at location J*/
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 /*is _ uppercase ? */
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"',") /*arg 3 ≡ ",'" || 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 /*forever*/
/*──────────────────────────────────────────────────────────────────────────────────────*/ bool: procedure; arg a,?,b /* ◄─── ARG uppercases all args.*/
select /*SELECT chooses which function.*/
/*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
/*b*/ when ? == 'BIMPA' then return \ (b & \a)
/*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
end /*select*/ /* [↑] error, unknown function.*/</lang>
Some older REXXes don't have a changestr BIF, so one is included here ──► CHANGESTR.REX.
- output when using the default inputs:
(Output is shown at three-quarter size.)
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
Sidef
A simple solution which accepts arbitrary user-input: <lang ruby>loop {
var expr = Sys.readln("\nBoolean expression (e.g. 'a & b'): ").strip.lc
break if expr.is_empty;
var vars = expr.scan(/alpha:+/) if (vars.is_empty) { say "no variables detected in your boolean expression" next }
var prefix = []; var suffix = [];
vars.each { |v|
print "#{v}\t"
prefix << "[false, true].each { |#{v}|"
suffix << "}"
}
say "| #{expr}"
var body = ("say (" + vars.map{|v| v+",'\t'," }.join + " '| ', #{expr})")
eval(prefix + [body] + suffix -> join("\n"))
}</lang>
- Output:
Boolean expression (e.g. 'a & b'): (a & b) | c a b c | (a & b) | c 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
Tcl
<lang tcl>package require Tcl 8.5
puts -nonewline "Enter a boolean expression: " flush stdout set exp [gets stdin]
- 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