# Truth table

Truth table
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 equation organised as a table where each row gives one combination of input values and the corresponding value of the equation.

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.

## ALGOL 68

Works with: ALGOL 68G version Any - tested with release 2.8.3.win32

Uses the Algol 68G specific evaluate procedure to evaluate the Boolean expressions. The expressions must therefore be infix and valid Algol 68 boolean expressions.

`# 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`
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

Translation of: D
`#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);    }} 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;    s.top = -1;    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 (s.top != 0) {        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++;            }        }        if (vars_len == 0) {            printf("\nNo variables were entered.\n");            continue;        }        printf("\n");        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;}`
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#

Works with: C sharp version 7

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.

`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();        }    }}`
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

Translation of: JavaScript
`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; optionallyseperated 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);}`
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

 This example is incorrect. Please fix the code and remove this message.Details: User input is not arbitrary but fixed to the three examples shown
`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)" @stuprint-truth-table [ "A" "B" "C" "D" ] "A ^ (B ^ (C ^ D))" @abcd`
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.

`USING: arrays combinators eval formatting io kernel listenermath.combinatorics prettyprint qw sequences splittingvocabs.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`
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

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.

`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 tablefunc (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 astfunc 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))} `

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
```

### Reverse Polish Notation

Accepts expressions given in RPN, tokenized by whitespace. Uses operators "&", "|", "!", "^" (xor), "=>" (implication); all other words are interpreted as variable names.

`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 printingshowTable 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`
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:

`{-# 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`
Output:
`λ> putStr \$ truthTable \$ toRPN "(Human => Mortal) & (Socratus => Human) => (Socratus => Mortal)" Human  Mortal Socratus resultTrue   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 `

## J

Implementation:

`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)`

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:

`   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`

## Java

Works with: Java version 1.8+

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).

`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>() {{        // Can't use && or || because shortcut evaluation may mean the stack is not popped enough        put( "&", stack -> Boolean.logicalAnd( stack.pop(), stack.pop() ) );        put( "|", stack -> Boolean.logicalOr( stack.pop(), stack.pop() ) );        put( "!", stack -> ! stack.pop() );        put( "^", stack -> ! stack.pop().equals ( stack.pop() ) );    }};     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>() {{ add(false); }} );                add( new ArrayList<Boolean>() {{ add(true);  }} );            }};         return new ArrayList<List<Boolean>>() {{            for ( final List<Boolean> head : enumerate( size - 1 ) ) {                add( new ArrayList<Boolean>( head ) {{ add(false); }} );                add( new ArrayList<Boolean>( head ) {{ 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();    }}`
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.

`<!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="<b>"+str+expr+"</b>\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]?"<b>T</b>":"F")+" ";		elem.innerHTML+=str+(parsebool()?"<b>T</b>":"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>`
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:

`module TruthTable using Printfusing MacroTools isvariablename(::Any) = falseisvariablename(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`

Main:

`[email protected] !a[email protected] a | b[email protected] (a ⊻ b) | (c & a)[email protected] (a & b) | (c ⊻ d) `
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

Translation of: D
`// Version 1.2.31 import java.util.Stack class Variable(val name: Char, var value: Boolean = false) lateinit var expr: Stringvar 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)    }}`
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.

` 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 ifend function `
```        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

`VariableNames[data_] := Module[ {TokenRemoved}, TokenRemoved = StringSplit[data,{"~And~","~Or~","~Xor~","!","(",")"}]; Union[Select[Map[StringTrim,TokenRemoved] , Not[StringMatchQ[#,""]]&]]] TruthTable[BooleanEquation_] := Module[ {TestDataSet},  TestDataSet = MapThread[Rule,{[email protected][BooleanEquation],#}]&/@     Tuples[{False,True}, Length[VariableNames[BooleanEquation]]];   Join[List[Flatten[{VariableNames[BooleanEquation],BooleanEquation}]],    Flatten[{#/.Rule[x_,y_] -> y,ReplaceAll[ToExpression[BooleanEquation],#]}]&/@TestDataSet]//Grid]`

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

`/* Maxima already has the following logical operators          =, # (not equal), not, and, ordefine some more and set 'binding power' (operatorprecedence) 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 alist of the valueslsubst( '(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 ) )));`

OUtput of the last example:

`             [   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          ] `

## 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.

`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") \\ ORtruthTable("x*y") \\ AND`
Output:
```000
101
011
111

000
100
010
111```

## Pascal

Translation of: C
Works with: Free 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 functionsfunction 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;  endend; 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;  endend; 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);  endend; // removes space and converts to upper caseprocedure 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 := exprTmpend; 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. `
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.

`#!/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';`
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: Rakudo version 2016.01
`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{[email protected]}b").comb».Int».so }, 0 ..^ 2**@n;    say '';}`
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.

`sequence opstack = {}object tokenobject op = 0   -- 0 = nonestring s        -- the expression being parsedinteger 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 whileend 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 ifend 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 = 0end 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 = tend 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 ifend 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<p then exit end if        get_token()        Expr(thisp)        PushOp(operators[k])    end whileend procedure function eval(object s)    if atom(s) then        if s>=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 ifend 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 trueend function function fmt(bool b)    return {"0","1"}[b+1]   -- for 0/1--  return {"F","T"}[b+1]   -- for F/Tend 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`
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

`(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) ) ) ) )`

Test:

`: (truthTable (str "A and (B or C)"))A      B      CNIL    NIL    NIL    NILT      NIL    NIL    NILNIL    T      NIL    NILT      T      NIL    TNIL    NIL    T      NILT      NIL    T      TNIL    T      T      NILT      T      T      T : (truthTable (str "not (Foo and (Bar or Mumble))"))Foo    Bar    MumbleNIL    NIL    NIL    TT      NIL    NIL    TNIL    T      NIL    TT      T      NIL    NILNIL    NIL    T      TT      NIL    T      NILNIL    T      T      TT      T      T      NIL : (truthTable (str "(A xor B) and (B or C)"))A      B      CNIL    NIL    NIL    NILT      NIL    NIL    NILNIL    T      NIL    TT      T      NIL    NILNIL    NIL    T      NILT      NIL    T      TNIL    T      T      TT      T      T      NIL : (truthTable (str "(A xor B) and ((not B) or C)"))A      B      CNIL    NIL    NIL    NILT      NIL    NIL    TNIL    T      NIL    NILT      T      NIL    NILNIL    NIL    T      NILT      NIL    T      TNIL    T      T      TT      T      T      NIL`

## Prolog

Works with: SWI-Prolog version Any - tested with release 7.6.4
`/*	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 atomstok([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 termexpr(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 expressioneval_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).`
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.

`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)) `
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```

## 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 (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)) `

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.

`/*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 [email protected]  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.*/`

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]

`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`

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

Translation of: Ruby

A simple solution which accepts arbitrary user-input:

`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"))}`
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

`package require Tcl 8.5 puts -nonewline "Enter a boolean expression: "flush stdoutset 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]\tResultapply [list {} \$cmd]`

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
```