⚠️ Warning: This is a draft ⚠️
This means it might contain formatting issues, incorrect code, conceptual problems, or other severe issues.
If you want to help to improve and eventually enable this page, please fork RosettaGit's repository and open a merge request on GitHub.
{{task|Logic}} {{wikipedia|Ternary logic}}
In [[wp:logic|logic]], a '''three-valued logic''' (also '''trivalent''', '''ternary''', or '''trinary logic''', sometimes abbreviated '''3VL''') is any of several [[wp:many-valued logic|many-valued logic]] systems in which there are three [[wp:truth value|truth value]]s indicating ''true'', ''false'' and some indeterminate third value.
This is contrasted with the more commonly known [[wp:Principle of bivalence|bivalent]] logics (such as classical sentential or [[wp:boolean logic|boolean logic]]) which provide only for ''true'' and ''false''.
Conceptual form and basic ideas were initially created by [[wp:Jan Łukasiewicz|Łukasiewicz]], [[wp:C. I. Lewis|Lewis]] and [[wp:Sulski|Sulski]].
These were then re-formulated by [[wp:Grigore Moisil|Grigore Moisil]] in an axiomatic algebraic form, and also extended to ''n''-valued logics in 1945. {|
| +'''Example ''Ternary Logic Operators'' in ''Truth Tables'':''' |
|---|
| {| class=wikitable
| +''not'' a |
|---|
| ! colspan=2 |
| - |
| True |
| - |
| Maybe |
| - |
| False |
| } |
| { |
| +a ''and'' b |
| - |
| ! ∧ |
| True |
| - |
| True |
| - |
| Maybe |
| - |
| False |
| } |
| { |
| - |
| +a ''or'' b |
| - |
| ! ∨ |
| True |
| - |
| True |
| - |
| Maybe |
| - |
| False |
| } |
| - |
| { |
| - |
| +''if'' a ''then'' b |
| - |
| ! ⊃ |
| True |
| - |
| True |
| - |
| Maybe |
| - |
| False |
| } |
| { |
| - |
| +a ''is equivalent to'' b |
| - |
| ! ≡ |
| True |
| - |
| True |
| - |
| Maybe |
| - |
| False |
| } |
| } |
;Task:
- Define a new type that emulates ''ternary logic'' by storing data '''trits'''.
- Given all the binary logic operators of the original programming language, reimplement these operators for the new ''Ternary logic'' type '''trit'''.
- Generate a sampling of results using '''trit''' variables.
- [[wp:Kudos|Kudos]] for actually thinking up a test case algorithm where ''ternary logic'' is intrinsically useful, optimises the test case algorithm and is preferable to binary logic.
Note: '''[[wp:Setun|Setun]]''' (Сетунь) was a [[wp:balanced ternary|balanced ternary]] computer developed in 1958 at [[wp:Moscow State University|Moscow State University]]. The device was built under the lead of [[wp:Sergei Sobolev|Sergei Sobolev]] and [[wp:Nikolay Brusentsov|Nikolay Brusentsov]]. It was the only modern [[wp:ternary computer|ternary computer]], using three-valued [[wp:ternary logic|ternary logic]]
Ada
We first specify a package "Logic" for three-valued logic. Observe that predefined Boolean functions, "and" "or" and "not" are overloaded:
package Logic is
type Ternary is (True, Unknown, False);
-- logic functions
function "and"(Left, Right: Ternary) return Ternary;
function "or"(Left, Right: Ternary) return Ternary;
function "not"(T: Ternary) return Ternary;
function Equivalent(Left, Right: Ternary) return Ternary;
function Implies(Condition, Conclusion: Ternary) return Ternary;
-- conversion functions
function To_Bool(X: Ternary) return Boolean;
function To_Ternary(B: Boolean) return Ternary;
function Image(Value: Ternary) return Character;
end Logic;
Next, the implementation of the package:
package body Logic is
-- type Ternary is (True, Unknown, False);
function Image(Value: Ternary) return Character is
begin
case Value is
when True => return 'T';
when False => return 'F';
when Unknown => return '?';
end case;
end Image;
function "and"(Left, Right: Ternary) return Ternary is
begin
return Ternary'max(Left, Right);
end "and";
function "or"(Left, Right: Ternary) return Ternary is
begin
return Ternary'min(Left, Right);
end "or";
function "not"(T: Ternary) return Ternary is
begin
case T is
when False => return True;
when Unknown => return Unknown;
when True => return False;
end case;
end "not";
function To_Bool(X: Ternary) return Boolean is
begin
case X is
when True => return True;
when False => return False;
when Unknown => raise Constraint_Error;
end case;
end To_Bool;
function To_Ternary(B: Boolean) return Ternary is
begin
if B then
return True;
else
return False;
end if;
end To_Ternary;
function Equivalent(Left, Right: Ternary) return Ternary is
begin
return To_Ternary(To_Bool(Left) = To_Bool(Right));
exception
when Constraint_Error => return Unknown;
end Equivalent;
function Implies(Condition, Conclusion: Ternary) return Ternary is
begin
return (not Condition) or Conclusion;
end Implies;
end Logic;
Finally, a sample program:
with Ada.Text_IO, Logic;
procedure Test_Tri_Logic is
use Logic;
type F2 is access function(Left, Right: Ternary) return Ternary;
type F1 is access function(Trit: Ternary) return Ternary;
procedure Truth_Table(F: F1; Name: String) is
begin
Ada.Text_IO.Put_Line("X | " & Name & "(X)");
for T in Ternary loop
Ada.Text_IO.Put_Line(Image(T) & " | " & Image(F(T)));
end loop;
end Truth_Table;
procedure Truth_Table(F: F2; Name: String) is
begin
Ada.Text_IO.New_Line;
Ada.Text_IO.Put_Line("X | Y | " & Name & "(X,Y)");
for X in Ternary loop
for Y in Ternary loop
Ada.Text_IO.Put_Line(Image(X) & " | " & Image(Y) & " | " & Image(F(X,Y)));
end loop;
end loop;
end Truth_Table;
begin
Truth_Table(F => "not"'Access, Name => "Not");
Truth_Table(F => "and"'Access, Name => "And");
Truth_Table(F => "or"'Access, Name => "Or");
Truth_Table(F => Equivalent'Access, Name => "Eq");
Truth_Table(F => Implies'Access, Name => "Implies");
end Test_Tri_Logic;
{{out}}
X | Not(X)
T | F
? | ?
F | T
X | Y | And(X,Y)
T | T | T
T | ? | ?
T | F | F
? | T | ?
? | ? | ?
? | F | F
F | T | F
F | ? | F
F | F | F
... (and so on)
ALGOL 68
{{works with|ALGOL 68|Revision 1 - one minor extension to language used - PRAGMA READ, like C's #include directive.}} {{works with|ALGOL 68G|Any - tested with release [http://sourceforge.net/projects/algol68/files/algol68g/algol68g-1.18.0/algol68g-1.18.0-9h.tiny.el5.centos.fc11.i386.rpm/download 1.18.0-9h.tiny].}} {{wont work with|ELLA ALGOL 68|Any (with appropriate job cards) - tested with release [http://sourceforge.net/projects/algol68/files/algol68toc/algol68toc-1.8.8d/algol68toc-1.8-8d.fc9.i386.rpm/download 1.8-8d] - due to extensive use of '''format'''[ted] ''transput''.}} '''File: Ternary_logic.a68'''
# -*- coding: utf-8 -*- #
INT trit width = 1, trit base = 3;
MODE TRIT = STRUCT(BITS trit);
CO FORMAT trit fmt = $c("?","⌈","⌊",#|"~"#)$; CO
# These values treated are as per "Balanced ternary" #
# eg true=1, maybe=0, false=-1 #
TRIT true =INITTRIT 4r1, maybe=INITTRIT 4r0,
false=INITTRIT 4r2;
# Warning: redefines standard builtins flip & flop #
LONGCHAR flap="?", flip="⌈", flop="⌊";
OP REPR = (TRIT t)LONGCHAR:
[]LONGCHAR(flap, flip, flop)[1+ABS trit OF t];
############################################
# Define some OPerators for coercing MODES #
############################################
OP INITTRIT = (BOOL in)TRIT:
(in|true|false);
OP INITBOOL = (TRIT in)BOOL:
(trit OF in=trit OF true|TRUE|:trit OF in=trit OF false|FALSE|
raise value error(("vague TRIT to BOOL coercion: """, REPR in,""""));~
);
OP B = (TRIT in)BOOL: INITBOOL in;
# These values treated are as per "Balanced ternary" #
# n.b true=1, maybe=0, false=-1 #
# Warning: BOOL ABS FALSE (0) is not the same as TRIT ABS false (-1) #
OP INITINT = (TRIT t)INT:
CASE 1+ABS trit OF t
IN #maybe# 0, #true # 1, #false#-1
OUT raise value error(("invalid TRIT value",REPR t)); ~
ESAC;
OP INITTRIT = (INT in)TRIT: (
TRIT out;
trit OF out:= trit OF
CASE 2+in
IN false, maybe, true
OUT raise value error(("invalid TRIT value",in)); ~
ESAC;
out
);
OP INITTRIT = (BITS b)TRIT:
(TRIT out; trit OF out:=b; out);
##################################################
# Define the LOGICAL OPerators for the TRIT MODE #
##################################################
MODE LOGICAL = TRIT;
PR READ "Template_operators_logical_mixin.a68" PR
COMMENT
Kleene logic truth tables:
END COMMENT
OP AND = (TRIT a,b)TRIT: (
[,]TRIT(
# ∧ ## false, maybe, true #
#false# (false, false, false),
#maybe# (false, maybe, maybe),
#true # (false, maybe, true )
)[@-1,@-1][INITINT a, INITINT b]
);
OP OR = (TRIT a,b)TRIT: (
[,]TRIT(
# ∨ ## false, maybe, true #
#false# (false, maybe, true),
#maybe# (maybe, maybe, true),
#true # (true, true, true)
)[@-1,@-1][INITINT a, INITINT b]
);
PRIO IMPLIES = 1; # PRIO = 1.9 #
OP IMPLIES = (TRIT a,b)TRIT: (
[,]TRIT(
# ⊃ ## false, maybe, true #
#false# (true, true, true),
#maybe# (maybe, maybe, true),
#true # (false, maybe, true)
)[@-1,@-1][INITINT a, INITINT b]
);
PRIO EQV = 1; # PRIO = 1.8 #
OP EQV = (TRIT a,b)TRIT: (
[,]TRIT(
# ≡ ## false, maybe, true #
#false# (true, maybe, false),
#maybe# (maybe, maybe, maybe),
#true # (false, maybe, true )
)[@-1,@-1][INITINT a, INITINT b]
);
'''File: Template_operators_logical_mixin.a68'''
# -*- coding: utf-8 -*- #
OP & = (LOGICAL a,b)LOGICAL: a AND b;
CO # not included as they are treated as SCALAR #
OP EQ = (LOGICAL a,b)LOGICAL: a = b,
NE = (LOGICAL a,b)LOGICAL: a /= b,
≠ = (TRIT a,b)TRIT: a /= b,
¬= = (TRIT a,b)TRIT: a /= b;
END CO
#IF html entities possible THEN
¢ "parked" operators for completeness ¢
OP ¬ = (LOGICAL a)LOGICAL: NOT a,
∧ = (LOGICAL a,b)LOGICAL: a AND b,
/\ = (LOGICAL a,b)LOGICAL: a AND b,
∨ = (LOGICAL a,b)LOGICAL: a OR b,
\/ = (LOGICAL a,b)LOGICAL: a OR b,
⊃ = (TRIT a,b)TRIT: a IMPLIES b,
≡ = (TRIT a,b)TRIT: a EQV b;
FI#
#IF algol68c THEN
OP ~ = (LOGICAL a)LOGICAL: NOT a,
~= = (LOGICAL a,b)LOGICAL: a /= b; SCALAR!
FI#
'''File: test_Ternary_logic.a68'''
#!/usr/local/bin/a68g --script #
# -*- coding: utf-8 -*- #
PR READ "prelude/general.a68" PR
PR READ "Ternary_logic.a68" PR
[]TRIT trits = (false, maybe, true);
FORMAT
col fmt = $" "g" "$,
row fmt = $l3(f(col fmt)"|")f(col fmt)$,
row sep fmt = $l3("---+")"---"l$;
PROC row sep = VOID:
printf(row sep fmt);
PROC title = (STRING op name, LONGCHAR op char)VOID:(
print(("Operator: ",op name));
printf((row fmt,op char,REPR false, REPR maybe, REPR true))
);
PROC print trit op table = (LONGCHAR op char, STRING op name, PROC(TRIT,TRIT)TRIT op)VOID: (
printf($l$);
title(op name, op char);
FOR i FROM LWB trits TO UPB trits DO
row sep;
TRIT ti = trits[i];
printf((col fmt, REPR ti));
FOR j FROM LWB trits TO UPB trits DO
TRIT tj = trits[j];
printf(($"|"$, col fmt, REPR op(ti,tj)))
OD
OD;
printf($l$)
);
printf((
$"Comparitive table of coercions:"l$,
$" TRIT BOOL INT"l$
));
FOR it FROM LWB trits TO UPB trits DO
TRIT t = trits[it];
printf(( $" "g" "$, REPR t,
IF trit OF t = trit OF maybe THEN " " ELSE B t FI,
INITINT t, $l$))
OD;
printf((
$l"Specific test of the IMPLIES operator:"l$,
$" "g" implies "g" is "b("not ","")"a contradiction!"l$,
B false, B false, B(false IMPLIES false),
B false, B true, B(false IMPLIES true),
B false, REPR maybe, B(false IMPLIES maybe),
B true, B false, B(true IMPLIES false),
B true, B true, B(true IMPLIES true),
REPR maybe, Btrue, B(maybe IMPLIES true),
$" "g" implies "g" is "g" a contradiction!"l$,
B true, REPR maybe, REPR (true IMPLIES maybe),
REPR maybe, B false, REPR (maybe IMPLIES false),
REPR maybe, REPR maybe, REPR (maybe IMPLIES maybe),
$l$
));
printf($"Kleene logic truth table samples:"l$);
print trit op table("≡","EQV", (TRIT a,b)TRIT: a EQV b);
print trit op table("⊃","IMPLIES", (TRIT a,b)TRIT: a IMPLIES b);
print trit op table("∧","AND", (TRIT a,b)TRIT: a AND b);
print trit op table("∨","OR", (TRIT a,b)TRIT: a OR b)
{{out}}
Comparitive table of coercions:
TRIT BOOL INT
⌊ F -1
? +0
⌈ T +1
Specific test of the IMPLIES operator:
F implies F is not a contradiction!
F implies T is not a contradiction!
F implies ? is not a contradiction!
T implies F is a contradiction!
T implies T is not a contradiction!
? implies T is not a contradiction!
T implies ? is ? a contradiction!
? implies F is ? a contradiction!
? implies ? is ? a contradiction!
Kleene logic truth table samples:
Operator: EQV
≡ | ⌊ | ? | ⌈
---+---+---+---
⌊ | ⌈ | ? | ⌊
---+---+---+---
? | ? | ? | ?
---+---+---+---
⌈ | ⌊ | ? | ⌈
Operator: IMPLIES
⊃ | ⌊ | ? | ⌈
---+---+---+---
⌊ | ⌈ | ⌈ | ⌈
---+---+---+---
? | ? | ? | ⌈
---+---+---+---
⌈ | ⌊ | ? | ⌈
Operator: AND
∧ | ⌊ | ? | ⌈
---+---+---+---
⌊ | ⌊ | ⌊ | ⌊
---+---+---+---
? | ⌊ | ? | ?
---+---+---+---
⌈ | ⌊ | ? | ⌈
Operator: OR
∨ | ⌊ | ? | ⌈
---+---+---+---
⌊ | ⌊ | ? | ⌈
---+---+---+---
? | ? | ? | ⌈
---+---+---+---
⌈ | ⌈ | ⌈ | ⌈
AutoHotkey
Ternary_Not(a){
SetFormat, Float, 2.1
return Abs(a-1)
}
Ternary_And(a,b){
return a<b?a:b
}
Ternary_Or(a,b){
return a>b?a:b
}
Ternary_IfThen(a,b){
return a=1?b:a=0?1:a+b>1?1:0.5
}
Ternary_Equiv(a,b){
return a=b?1:a=1?b:b=1?a:0.5
}
Examples:
aa:=[1,0.5,0]
bb:=[1,0.5,0]
for index, a in aa
Res .= "`tTernary_Not`t" a "`t=`t" Ternary_Not(a) "`n"
Res .= "-------------`n"
for index, a in aa
for index, b in bb
Res .= a "`tTernary_And`t" b "`t=`t" Ternary_And(a,b) "`n"
Res .= "-------------`n"
for index, a in aa
for index, b in bb
Res .= a "`tTernary_or`t" b "`t=`t" Ternary_Or(a,b) "`n"
Res .= "-------------`n"
for index, a in aa
for index, b in bb
Res .= a "`tTernary_then`t" b "`t=`t" Ternary_IfThen(a,b) "`n"
Res .= "-------------`n"
for index, a in aa
for index, b in bb
Res .= a "`tTernary_equiv`t" b "`t=`t" Ternary_Equiv(a,b) "`n"
StringReplace, Res, Res, 1, true, all
StringReplace, Res, Res, 0.5, maybe, all
StringReplace, Res, Res, 0, false, all
MsgBox % Res
return
{{out}}
Ternary_Not true = false
Ternary_Not maybe = maybe
Ternary_Not false = true
-------------
true Ternary_And true = true
true Ternary_And maybe = maybe
true Ternary_And false = false
maybe Ternary_And true = maybe
maybe Ternary_And maybe = maybe
maybe Ternary_And false = false
false Ternary_And true = false
false Ternary_And maybe = false
false Ternary_And false = false
-------------
true Ternary_or true = true
true Ternary_or maybe = true
true Ternary_or false = true
maybe Ternary_or true = true
maybe Ternary_or maybe = maybe
maybe Ternary_or false = maybe
false Ternary_or true = true
false Ternary_or maybe = maybe
false Ternary_or false = false
-------------
true Ternary_then true = true
true Ternary_then maybe = maybe
true Ternary_then false = false
maybe Ternary_then true = true
maybe Ternary_then maybe = maybe
maybe Ternary_then false = maybe
false Ternary_then true = true
false Ternary_then maybe = true
false Ternary_then false = true
-------------
true Ternary_equiv true = true
true Ternary_equiv maybe = maybe
true Ternary_equiv false = false
maybe Ternary_equiv true = maybe
maybe Ternary_equiv maybe = true
maybe Ternary_equiv false = maybe
false Ternary_equiv true = false
false Ternary_equiv maybe = maybe
false Ternary_equiv false = true
BBC BASIC
{{works with|BBC BASIC for Windows}}
INSTALL @lib$ + "CLASSLIB"
REM Create a ternary class:
DIM trit{tor, tand, teqv, tnot, tnor, s, v}
DEF PRIVATE trit.s (t&) LOCAL t$():DIM t$(2):t$()="FALSE","MAYBE","TRUE":=t$(t&)
DEF PRIVATE trit.v (t$) = INSTR("FALSE MAYBE TRUE", t$) DIV 6
DEF trit.tnot (t$) = FN(trit.s)(2 - FN(trit.v)(t$))
DEF trit.tor (a$,b$) LOCAL t:t=FN(trit.v)(a$)ORFN(trit.v)(b$):=FN(trit.s)(t+(t>2))
DEF trit.tnor (a$,b$) = FN(trit.tnot)(FN(trit.tor)(a$,b$))
DEF trit.tand (a$,b$) = FN(trit.tnor)(FN(trit.tnot)(a$),FN(trit.tnot)(b$))
DEF trit.teqv (a$,b$) = FN(trit.tor)(FN(trit.tand)(a$,b$),FN(trit.tnor)(a$,b$))
PROC_class(trit{})
PROC_new(mytrit{}, trit{})
REM Test it:
PRINT "Testing NOT:"
PRINT "NOT FALSE = " FN(mytrit.tnot)("FALSE")
PRINT "NOT MAYBE = " FN(mytrit.tnot)("MAYBE")
PRINT "NOT TRUE = " FN(mytrit.tnot)("TRUE")
PRINT '"Testing OR:"
PRINT "FALSE OR FALSE = " FN(mytrit.tor)("FALSE","FALSE")
PRINT "FALSE OR MAYBE = " FN(mytrit.tor)("FALSE","MAYBE")
PRINT "FALSE OR TRUE = " FN(mytrit.tor)("FALSE","TRUE")
PRINT "MAYBE OR MAYBE = " FN(mytrit.tor)("MAYBE","MAYBE")
PRINT "MAYBE OR TRUE = " FN(mytrit.tor)("MAYBE","TRUE")
PRINT "TRUE OR TRUE = " FN(mytrit.tor)("TRUE","TRUE")
PRINT '"Testing AND:"
PRINT "FALSE AND FALSE = " FN(mytrit.tand)("FALSE","FALSE")
PRINT "FALSE AND MAYBE = " FN(mytrit.tand)("FALSE","MAYBE")
PRINT "FALSE AND TRUE = " FN(mytrit.tand)("FALSE","TRUE")
PRINT "MAYBE AND MAYBE = " FN(mytrit.tand)("MAYBE","MAYBE")
PRINT "MAYBE AND TRUE = " FN(mytrit.tand)("MAYBE","TRUE")
PRINT "TRUE AND TRUE = " FN(mytrit.tand)("TRUE","TRUE")
PRINT '"Testing EQV (similar to EOR):"
PRINT "FALSE EQV FALSE = " FN(mytrit.teqv)("FALSE","FALSE")
PRINT "FALSE EQV MAYBE = " FN(mytrit.teqv)("FALSE","MAYBE")
PRINT "FALSE EQV TRUE = " FN(mytrit.teqv)("FALSE","TRUE")
PRINT "MAYBE EQV MAYBE = " FN(mytrit.teqv)("MAYBE","MAYBE")
PRINT "MAYBE EQV TRUE = " FN(mytrit.teqv)("MAYBE","TRUE")
PRINT "TRUE EQV TRUE = " FN(mytrit.teqv)("TRUE","TRUE")
PROC_discard(mytrit{})
{{out}}
Testing NOT:
NOT FALSE = TRUE
NOT MAYBE = MAYBE
NOT TRUE = FALSE
Testing OR:
FALSE OR FALSE = FALSE
FALSE OR MAYBE = MAYBE
FALSE OR TRUE = TRUE
MAYBE OR MAYBE = MAYBE
MAYBE OR TRUE = TRUE
TRUE OR TRUE = TRUE
Testing AND:
FALSE AND FALSE = FALSE
FALSE AND MAYBE = FALSE
FALSE AND TRUE = FALSE
MAYBE AND MAYBE = MAYBE
MAYBE AND TRUE = MAYBE
TRUE AND TRUE = TRUE
Testing EQV (similar to EOR):
FALSE EQV FALSE = TRUE
FALSE EQV MAYBE = MAYBE
FALSE EQV TRUE = FALSE
MAYBE EQV MAYBE = MAYBE
MAYBE EQV TRUE = MAYBE
TRUE EQV TRUE = TRUE
C
Implementing logic using lookup tables
#include <stdio.h>
typedef enum {
TRITTRUE, /* In this enum, equivalent to integer value 0 */
TRITMAYBE, /* In this enum, equivalent to integer value 1 */
TRITFALSE /* In this enum, equivalent to integer value 2 */
} trit;
/* We can trivially find the result of the operation by passing
the trinary values as indeces into the lookup tables' arrays. */
trit tritNot[3] = {TRITFALSE , TRITMAYBE, TRITTRUE};
trit tritAnd[3][3] = { {TRITTRUE, TRITMAYBE, TRITFALSE},
{TRITMAYBE, TRITMAYBE, TRITFALSE},
{TRITFALSE, TRITFALSE, TRITFALSE} };
trit tritOr[3][3] = { {TRITTRUE, TRITTRUE, TRITTRUE},
{TRITTRUE, TRITMAYBE, TRITMAYBE},
{TRITTRUE, TRITMAYBE, TRITFALSE} };
trit tritThen[3][3] = { { TRITTRUE, TRITMAYBE, TRITFALSE},
{ TRITTRUE, TRITMAYBE, TRITMAYBE},
{ TRITTRUE, TRITTRUE, TRITTRUE } };
trit tritEquiv[3][3] = { { TRITTRUE, TRITMAYBE, TRITFALSE},
{ TRITMAYBE, TRITMAYBE, TRITMAYBE},
{ TRITFALSE, TRITMAYBE, TRITTRUE } };
/* Everything beyond here is just demonstration */
const char* tritString[3] = {"T", "?", "F"};
void demo_binary_op(trit operator[3][3], const char* name)
{
trit operand1 = TRITTRUE; /* Declare. Initialize for CYA */
trit operand2 = TRITTRUE; /* Declare. Initialize for CYA */
/* Blank line */
printf("\n");
/* Demo this operator */
for( operand1 = TRITTRUE; operand1 <= TRITFALSE; ++operand1 )
{
for( operand2 = TRITTRUE; operand2 <= TRITFALSE; ++operand2 )
{
printf("%s %s %s: %s\n", tritString[operand1],
name,
tritString[operand2],
tritString[operator[operand1][operand2]]);
}
}
}
int main()
{
trit op1 = TRITTRUE; /* Declare. Initialize for CYA */
trit op2 = TRITTRUE; /* Declare. Initialize for CYA */
/* Demo 'not' */
for( op1 = TRITTRUE; op1 <= TRITFALSE; ++op1 )
{
printf("Not %s: %s\n", tritString[op1], tritString[tritNot[op1]]);
}
demo_binary_op(tritAnd, "And");
demo_binary_op(tritOr, "Or");
demo_binary_op(tritThen, "Then");
demo_binary_op(tritEquiv, "Equiv");
return 0;
}
{{out}}
Not T: F
Not ?: ?
Not F: T
T And T: T
T And ?: ?
T And F: F
? And T: ?
? And ?: ?
? And F: F
F And T: F
F And ?: F
F And F: F
T Or T: T
T Or ?: T
T Or F: T
? Or T: T
? Or ?: ?
? Or F: ?
F Or T: T
F Or ?: ?
F Or F: F
T Then T: T
T Then ?: ?
T Then F: F
? Then T: T
? Then ?: ?
? Then F: ?
F Then T: T
F Then ?: T
F Then F: T
T Equiv T: T
T Equiv ?: ?
T Equiv F: F
? Equiv T: ?
? Equiv ?: ?
? Equiv F: ?
F Equiv T: F
F Equiv ?: ?
F Equiv F: T
Using functions
#include <stdio.h>
typedef enum { t_F = -1, t_M, t_T } trit;
trit t_not (trit a) { return -a; }
trit t_and (trit a, trit b) { return a < b ? a : b; }
trit t_or (trit a, trit b) { return a > b ? a : b; }
trit t_eq (trit a, trit b) { return a * b; }
trit t_imply(trit a, trit b) { return -a > b ? -a : b; }
char t_s(trit a) { return "F?T"[a + 1]; }
#define forall(a) for(a = t_F; a <= t_T; a++)
void show_op(trit (*f)(trit, trit), const char *name) {
trit a, b;
printf("\n[%s]\n F ? T\n -------", name);
forall(a) {
printf("\n%c |", t_s(a));
forall(b) printf(" %c", t_s(f(a, b)));
}
puts("");
}
int main(void)
{
trit a;
puts("[Not]");
forall(a) printf("%c | %c\n", t_s(a), t_s(t_not(a)));
show_op(t_and, "And");
show_op(t_or, "Or");
show_op(t_eq, "Equiv");
show_op(t_imply, "Imply");
return 0;
}
{{out}}
[Not]
F | T
? | ?
T | F
[And]
F ? T
-------
F | F F F
? | F ? ?
T | F ? T
[Or]
F ? T
-------
F | F ? T
? | ? ? T
T | T T T
[Equiv]
F ? T
-------
F | T ? F
? | ? ? ?
T | F ? T
[Imply]
F ? T
-------
F | T T T
? | ? ? T
T | F ? T
Variable truthfulness
Represent each possible truth value as a floating point value x,
where the var has x chance of being true and 1 - x chance of being false.
When using if3 conditional on a potential truth varible,
the result is randomly sampled to true or false according to the chance.
(This description is definitely very confusing perhaps).
#include <stdio.h>
#include <stdlib.h>
typedef double half_truth, maybe;
inline maybe not3(maybe a) { return 1 - a; }
inline maybe
and3(maybe a, maybe b) { return a * b; }
inline maybe
or3(maybe a, maybe b) { return a + b - a * b; }
inline maybe
eq3(maybe a, maybe b) { return 1 - a - b + 2 * a * b; }
inline maybe
imply3(maybe a, maybe b) { return or3(not3(a), b); }
#define true3(x) ((x) * RAND_MAX > rand())
#define if3(x) if (true3(x))
int main()
{
maybe roses_are_red = 0.25; /* they can be white or black, too */
maybe violets_are_blue = 1; /* aren't they just */
int i;
puts("Verifying flowery truth for 40 times:\n");
puts("Rose is NOT red:"); /* chance: .75 */
for (i = 0; i < 40 || !puts("\n"); i++)
printf( true3( not3(roses_are_red) ) ? "T" : "_");
/* pick a rose and a violet; */
puts("Rose is red AND violet is blue:");
/* chance of rose being red AND violet being blue is .25 */
for (i = 0; i < 40 || !puts("\n"); i++)
printf( true3( and3(roses_are_red, violets_are_blue) )
? "T" : "_");
/* chance of rose being red OR violet being blue is 1 */
puts("Rose is red OR violet is blue:");
for (i = 0; i < 40 || !puts("\n"); i++)
printf( true3( or3(roses_are_red, violets_are_blue) )
? "T" : "_");
/* pick two roses; chance of em being both red or both not red is .625 */
puts("This rose is as red as that rose:");
for (i = 0; i < 40 || !puts("\n"); i++)
if3(eq3(roses_are_red, roses_are_red)) putchar('T');
else putchar('_');
return 0;
}
C++
Essentially the same logic as the [[#Using functions|Using functions]] implementation above, but using class-based encapsulation and overridden operators.
#include <iostream>
#include <stdlib.h>
class trit {
public:
static const trit False, Maybe, True;
trit operator !() const {
return static_cast<Value>(-value);
}
trit operator &&(const trit &b) const {
return (value < b.value) ? value : b.value;
}
trit operator ||(const trit &b) const {
return (value > b.value) ? value : b.value;
}
trit operator >>(const trit &b) const {
return -value > b.value ? static_cast<Value>(-value) : b.value;
}
trit operator ==(const trit &b) const {
return static_cast<Value>(value * b.value);
}
char chr() const {
return "F?T"[value + 1];
}
protected:
typedef enum { FALSE=-1, MAYBE, TRUE } Value;
Value value;
trit(const Value value) : value(value) { }
};
std::ostream& operator<<(std::ostream &os, const trit &t)
{
os << t.chr();
return os;
}
const trit trit::False = trit(trit::FALSE);
const trit trit::Maybe = trit(trit::MAYBE);
const trit trit::True = trit(trit::TRUE);
int main(int, char**) {
const trit trits[3] = { trit::True, trit::Maybe, trit::False };
#define for_each(name) \
for (size_t name=0; name<3; ++name)
#define show_op(op) \
std::cout << std::endl << #op << " "; \
for_each(a) std::cout << ' ' << trits[a]; \
std::cout << std::endl << " -------"; \
for_each(a) { \
std::cout << std::endl << trits[a] << " |"; \
for_each(b) std::cout << ' ' << (trits[a] op trits[b]); \
} \
std::cout << std::endl;
std::cout << "! ----" << std::endl;
for_each(a) std::cout << trits[a] << " | " << !trits[a] << std::endl;
show_op(&&);
show_op(||);
show_op(>>);
show_op(==);
return EXIT_SUCCESS;
}
{{out}}
! ----
T | F
? | ?
F | T
&& T ? F
-------
T | T ? F
? | ? ? F
F | F F F
|| T ? F
-------
T | T T T
? | T ? ?
F | T ? F
>> T ? F
-------
T | T ? F
? | T ? ?
F | T T T
== T ? F
-------
T | T ? F
? | ? ? ?
F | F ? T
C#
using System;
/// <summary>
/// Extension methods on nullable bool.
/// </summary>
/// <remarks>
/// The operators !, & and | are predefined.
/// </remarks>
public static class NullableBoolExtension
{
public static bool? Implies(this bool? left, bool? right)
{
return !left | right;
}
public static bool? IsEquivalentTo(this bool? left, bool? right)
{
return left.HasValue && right.HasValue ? left == right : default(bool?);
}
public static string Format(this bool? value)
{
return value.HasValue ? value.Value.ToString() : "Maybe";
}
}
public class Program
{
private static void Main()
{
var values = new[] { true, default(bool?), false };
foreach (var left in values)
{
Console.WriteLine("¬{0} = {1}", left.Format(), (!left).Format());
foreach (var right in values)
{
Console.WriteLine("{0} & {1} = {2}", left.Format(), right.Format(), (left & right).Format());
Console.WriteLine("{0} | {1} = {2}", left.Format(), right.Format(), (left | right).Format());
Console.WriteLine("{0} → {1} = {2}", left.Format(), right.Format(), left.Implies(right).Format());
Console.WriteLine("{0} ≡ {1} = {2}", left.Format(), right.Format(), left.IsEquivalentTo(right).Format());
}
}
}
}
{{out}}
¬True = False
True & True = True
True | True = True
True → True = True
True ≡ True = True
True & Maybe = Maybe
True | Maybe = True
True → Maybe = Maybe
True ≡ Maybe = Maybe
True & False = False
True | False = True
True → False = False
True ≡ False = False
¬Maybe = Maybe
Maybe & True = Maybe
Maybe | True = True
Maybe → True = True
Maybe ≡ True = Maybe
Maybe & Maybe = Maybe
Maybe | Maybe = Maybe
Maybe → Maybe = Maybe
Maybe ≡ Maybe = Maybe
Maybe & False = False
Maybe | False = Maybe
Maybe → False = Maybe
Maybe ≡ False = Maybe
¬False = True
False & True = False
False | True = True
False → True = True
False ≡ True = False
False & Maybe = False
False | Maybe = Maybe
False → Maybe = True
False ≡ Maybe = Maybe
False & False = False
False | False = False
False → False = True
False ≡ False = True
Common Lisp
(defun tri-not (x) (- 1 x))
(defun tri-and (&rest x) (apply #'* x))
(defun tri-or (&rest x) (tri-not (apply #'* (mapcar #'tri-not x))))
(defun tri-eq (x y) (+ (tri-and x y) (tri-and (- 1 x) (- 1 y))))
(defun tri-imply (x y) (tri-or (tri-not x) y))
(defun tri-test (x) (< (random 1e0) x))
(defun tri-string (x) (if (= x 1) "T" (if (= x 0) "F" "?")))
;; to say (tri-if (condition) (yes) (no))
(defmacro tri-if (tri ifcase &optional elsecase)
`(if (tri-test ,tri) ,ifcase ,elsecase))
(defun print-table (func header)
(let ((vals '(1 .5 0)))
(format t "~%~a:~%" header)
(format t " ~{~a ~^~}~%---------~%" (mapcar #'tri-string vals))
(loop for row in vals do
(format t "~a | " (tri-string row))
(loop for col in vals do
(format t "~a " (tri-string (funcall func row col))))
(write-line ""))))
(write-line "NOT:")
(loop for row in '(1 .5 0) do
(format t "~a | ~a~%" (tri-string row) (tri-string (tri-not row))))
(print-table #'tri-and "AND")
(print-table #'tri-or "OR")
(print-table #'tri-imply "IMPLY")
(print-table #'tri-eq "EQUAL")
{{out}}
NOT:
T | F
? | ?
F | T
AND:
T ? F
---------
T | T ? F
? | ? ? F
F | F F F
OR:
T ? F
---------
T | T T T
? | T ? ?
F | T ? F
IMPLY:
T ? F
---------
T | T ? F
? | T ? ?
F | T T T
EQUAL:
T ? F
---------
T | T ? F
? | ? ? ?
F | F ? T
D
Partial translation of a C entry:
import std.stdio;
struct Trit {
private enum Val : byte { F = -1, M, T }
private Val t;
alias t this;
static immutable Trit[3] vals = [{Val.F}, {Val.M}, {Val.T}];
static immutable F = Trit(Val.F); // Not necessary but handy.
static immutable M = Trit(Val.M);
static immutable T = Trit(Val.T);
string toString() const pure nothrow {
return "F?T"[t + 1 .. t + 2];
}
Trit opUnary(string op)() const pure nothrow
if (op == "~") {
return Trit(-t);
}
Trit opBinary(string op)(in Trit b) const pure nothrow
if (op == "&") {
return t < b ? this : b;
}
Trit opBinary(string op)(in Trit b) const pure nothrow
if (op == "|") {
return t > b ? this : b;
}
Trit opBinary(string op)(in Trit b) const pure nothrow
if (op == "^") {
return ~(this == b);
}
Trit opEquals(in Trit b) const pure nothrow {
return Trit(cast(Val)(t * b));
}
Trit imply(in Trit b) const pure nothrow {
return -t > b ? ~this : b;
}
}
void showOperation(string op)(in string opName) {
writef("\n[%s]\n F ? T\n -------", opName);
foreach (immutable a; Trit.vals) {
writef("\n%s |", a);
foreach (immutable b; Trit.vals)
static if (op == "==>")
writef(" %s", a.imply(b));
else
writef(" %s", mixin("a " ~ op ~ " b"));
}
writeln();
}
void main() {
writeln("[Not]");
foreach (const a; Trit.vals)
writefln("%s | %s", a, ~a);
showOperation!"&"("And");
showOperation!"|"("Or");
showOperation!"^"("Xor");
showOperation!"=="("Equiv");
showOperation!"==>"("Imply");
}
{{out}}
[Not]
F | T
? | ?
T | F
[And]
F ? T
-------
F | F F F
? | F ? ?
T | F ? T
[Or]
F ? T
-------
F | F ? T
? | ? ? T
T | T T T
[Xor]
F ? T
-------
F | F ? T
? | ? ? ?
T | T ? F
[Equiv]
F ? T
-------
F | T ? F
? | ? ? ?
T | F ? T
[Imply]
F ? T
-------
F | T T T
? | ? ? T
T | F ? T
Delphi
unit TrinaryLogic;
interface
//Define our own type for ternary logic.
//This is actually still a Boolean, but the compiler will use distinct RTTI information.
type
TriBool = type Boolean;
const
TTrue:TriBool = True;
TFalse:TriBool = False;
TMaybe:TriBool = TriBool(2);
function TVL_not(Value: TriBool): TriBool;
function TVL_and(A, B: TriBool): TriBool;
function TVL_or(A, B: TriBool): TriBool;
function TVL_xor(A, B: TriBool): TriBool;
function TVL_eq(A, B: TriBool): TriBool;
implementation
Uses
SysUtils;
function TVL_not(Value: TriBool): TriBool;
begin
if Value = True Then
Result := TFalse
else If Value = False Then
Result := TTrue
else
Result := Value;
end;
function TVL_and(A, B: TriBool): TriBool;
begin
Result := TriBool(Iff(Integer(A * B) > 1, Integer(TMaybe), A * B));
end;
function TVL_or(A, B: TriBool): TriBool;
begin
Result := TVL_not(TVL_and(TVL_not(A), TVL_not(B)));
end;
function TVL_xor(A, B: TriBool): TriBool;
begin
Result := TVL_and(TVL_or(A, B), TVL_not(TVL_or(A, B)));
end;
function TVL_eq(A, B: TriBool): TriBool;
begin
Result := TVL_not(TVL_xor(A, B));
end;
end.
And that's the reason why you never on no account ''ever'' should compare against the values of True or False unless you intent ternary logic!
An alternative version would be using an enum type
type TriBool = (tbFalse, tbMaybe, tbTrue);
and defining a set of constants implementing the above tables:
const
tvl_not: array[TriBool] = (tbTrue, tbMaybe, tbFalse);
tvl_and: array[TriBool, TriBool] = (
(tbFalse, tbFalse, tbFalse),
(tbFalse, tbMaybe, tbMaybe),
(tbFalse, tbMaybe, tbTrue),
);
tvl_or: array[TriBool, TriBool] = (
(tbFalse, tbMaybe, tbTrue),
(tbMaybe, tbMaybe, tbTrue),
(tbTrue, tbTrue, tbTrue),
);
tvl_xor: array[TriBool, TriBool] = (
(tbFalse, tbMaybe, tbTrue),
(tbMaybe, tbMaybe, tbMaybe),
(tbTrue, tbMaybe, tbFalse),
);
tvl_eq: array[TriBool, TriBool] = (
(tbTrue, tbMaybe, tbFalse),
(tbMaybe, tbMaybe, tbMaybe),
(tbFalse, tbMaybe, tbTrue),
);
That's no real fun, but lookup can then be done with
Result := tvl_and[A, B];
Elena
ELENA 4.1 :
import extensions;
import system'routines;
import system'collections;
sealed class Trit
{
bool _value;
bool cast() = _value;
constructor(v)
{
if (v != nil)
{
_value := cast bool(v);
}
}
Trit equivalent(b)
= _value.equal(cast bool(b)) \ back:nilValue;
Trit Inverted
= _value.Inverted \ back:nilValue;
Trit and(b)
{
if (nil == _value)
{
^ b.and:nil \ back:nilValue
}
else
{
^ _value.and(lazy::(cast bool(b))) \ back:nilValue
}
}
Trit or(b)
{
if (nil == _value)
{
^ b.or:nilValue \ back:nilValue
}
else
{
^ _value.or(lazy::(cast bool(b))) \ back:nilValue
}
}
Trit implies(b)
= self.Inverted.or(b);
string Printable = _value.Printable \ back:"maybe";
}
public program()
{
List<Trit> values := new Trit[]::(true, nilValue, false);
values.forEach:(left)
{
console.printLine("¬",left," = ", left.Inverted);
values.forEach:(right)
{
console.printLine(left, " & ", right, " = ", left && right);
console.printLine(left, " | ", right, " = ", left || right);
console.printLine(left, " → ", right, " = ", left.implies:right);
console.printLine(left, " ≡ ", right, " = ", left.equivalent:right)
}
}
}
{{out}}
¬ true = false
true & true = true
true | true = true
true → true = true
true ≡ true = true
true & maybe = maybe
true | maybe = true
true → maybe = maybe
true ≡ maybe = maybe
true & false = false
true | false = true
true → false = false
true ≡ false = false
¬ maybe = maybe
maybe & true = maybe
maybe | true = true
maybe → true = true
maybe ≡ true = maybe
maybe & maybe = maybe
maybe | maybe = maybe
maybe → maybe = maybe
maybe ≡ maybe = maybe
maybe & false = false
maybe | false = maybe
maybe → false = maybe
maybe ≡ false = maybe
¬ false = true
false & true = false
false | true = true
false → true = true
false ≡ true = false
false & maybe = false
false | maybe = maybe
false → maybe = true
false ≡ maybe = maybe
false & false = false
false | false = false
false → false = true
false ≡ false = true
Erlang
% Implemented by Arjun Sunel
-module(ternary).
-export([main/0, nott/1, andd/2,orr/2, then/2, equiv/2]).
main() ->
{ok, [A]} = io:fread("Enter A: ","~s"),
{ok, [B]} = io:fread("Enter B: ","~s"),
andd(A,B).
nott(S) ->
if
S=="T" ->
io : format("F\n");
S=="F" ->
io : format("T\n");
true ->
io: format("?\n")
end.
andd(A, B) ->
if
A=="T", B=="T" ->
io : format("T\n");
A=="F"; B=="F" ->
io : format("F\n");
true ->
io: format("?\n")
end.
orr(A, B) ->
if
A=="T"; B=="T" ->
io : format("T\n");
A=="?"; B=="?" ->
io : format("?\n");
true ->
io: format("F\n")
end.
then(A, B) ->
if
B=="T" ->
io : format("T\n");
A=="?" ->
io : format("?\n");
A=="F" ->
io :format("T\n");
B=="F" ->
io:format("F\n");
true ->
io: format("?\n")
end.
equiv(A, B) ->
if
A=="?" ->
io : format("?\n");
A=="F" ->
io : format("~s\n", [nott(B)]);
true ->
io: format("~s\n", [B])
end.
Factor
For boolean logic, Factor uses ''t'' and ''f'' with the words ''>boolean'', ''not'', ''and'', ''or'', ''xor''. For ternary logic, we add ''m'' and define the words ''>trit'', ''tnot'', ''tand'', ''tor'', ''txor'' and ''t=''. Our new class, ''trit'', is the union class of ''t'', ''m'' and ''f''.
! rosettacode/ternary/ternary.factor
! http://rosettacode.org/wiki/Ternary_logic
USING: combinators kernel ;
IN: rosettacode.ternary
SINGLETON: m
UNION: trit t m POSTPONE: f ;
GENERIC: >trit ( object -- trit )
M: trit >trit ;
: tnot ( trit1 -- trit )
>trit { { t [ f ] } { m [ m ] } { f [ t ] } } case ;
: tand ( trit1 trit2 -- trit )
>trit {
{ t [ >trit ] }
{ m [ >trit { { t [ m ] } { m [ m ] } { f [ f ] } } case ] }
{ f [ >trit drop f ] }
} case ;
: tor ( trit1 trit2 -- trit )
>trit {
{ t [ >trit drop t ] }
{ m [ >trit { { t [ t ] } { m [ m ] } { f [ m ] } } case ] }
{ f [ >trit ] }
} case ;
: txor ( trit1 trit2 -- trit )
>trit {
{ t [ tnot ] }
{ m [ >trit drop m ] }
{ f [ >trit ] }
} case ;
: t= ( trit1 trit2 -- trit )
{
{ t [ >trit ] }
{ m [ >trit drop m ] }
{ f [ tnot ] }
} case ;
Example use:
( scratchpad ) CONSTANT: trits { t m f }
( scratchpad ) trits [ tnot ] map .
{ f m t }
( scratchpad ) trits [ trits swap [ tand ] curry map ] map .
{ { t m f } { m m f } { f f f } }
( scratchpad ) trits [ trits swap [ tor ] curry map ] map .
{ { t t t } { t m m } { t m f } }
( scratchpad ) trits [ trits swap [ txor ] curry map ] map .
{ { f m t } { m m m } { t m f } }
( scratchpad ) trits [ trits swap [ t= ] curry map ] map .
{ { t m f } { m m m } { f m t } }
=={{header|Fōrmulæ}}==
In [http://wiki.formulae.org/Finite-valued_logic this] page you can see the solution of this task.
Fōrmulæ programs are not textual, visualization/edition of programs is done showing/manipulating structures but not text ([http://wiki.formulae.org/Editing_F%C5%8Drmul%C3%A6_expressions more info]). Moreover, there can be multiple visual representations of the same program. Even though it is possible to have textual representation —i.e. XML, JSON— they are intended for transportation effects more than visualization and edition.
The option to show Fōrmulæ programs and their results is showing images. Unfortunately images cannot be uploaded in Rosetta Code.
The solution shown uses [https://en.wikipedia.org/wiki/Finite-valued_logic finite-valued logic], where the n-valued logic can be represented as n equally spaced values between 0 (pure false) and 1 (pure true). As an example, the traditional logic values are represented as 0 and 1, and ternary logic is represented with the values 0 (false), 1/2 (maybe) and 1 (true), and so on.
The solution also shows how to ''redefine'' the logic operations, and how to show the values and the operations using colors.
Fortran
Please find the demonstration and compilation with gfortran at the start of the code. A module contains the ternary logic for easy reuse. Consider input redirection from unixdict.txt as vestigial. Or I could delete it.
!-*- mode: compilation; default-directory: "/tmp/" -*-
!Compilation started at Mon May 20 23:05:46
!
!a=./f && make $a && $a < unixdict.txt
!gfortran -std=f2003 -Wall -ffree-form f.f03 -o f
!
!ternary not
! 1.0 0.5 0.0
!
!
!ternary and
! 0.0 0.0 0.0
! 0.0 0.5 0.5
! 0.0 0.5 1.0
!
!
!ternary or
! 0.0 0.5 1.0
! 0.5 0.5 1.0
! 1.0 1.0 1.0
!
!
!ternary if
! 1.0 1.0 1.0
! 0.5 0.5 1.0
! 0.0 0.5 1.0
!
!
!ternary eq
! 1.0 0.5 0.0
! 0.5 0.5 0.5
! 0.0 0.5 1.0
!
!
!Compilation finished at Mon May 20 23:05:46
!This program is based on the j implementation
!not=: -.
!and=: <.
!or =: >.
!if =: (>. -.)"0~
!eq =: (<.&-. >. <.)"0
module trit
real, parameter :: true = 1, false = 0, maybe = 0.5
contains
real function tnot(y)
real, intent(in) :: y
tnot = 1 - y
end function tnot
real function tand(x, y)
real, intent(in) :: x, y
tand = min(x, y)
end function tand
real function tor(x, y)
real, intent(in) :: x, y
tor = max(x, y)
end function tor
real function tif(x, y)
real, intent(in) :: x, y
tif = tor(y, tnot(x))
end function tif
real function teq(x, y)
real, intent(in) :: x, y
teq = tor(tand(tnot(x), tnot(y)), tand(x, y))
end function teq
end module trit
program ternaryLogic
use trit
integer :: i
real, dimension(3) :: a = [false, maybe, true] ! (/ ... /)
write(6,'(/a)')'ternary not' ; write(6, '(3f4.1/)') (tnot(a(i)), i = 1 , 3)
write(6,'(/a)')'ternary and' ; call table(tand, a, a)
write(6,'(/a)')'ternary or' ; call table(tor, a, a)
write(6,'(/a)')'ternary if' ; call table(tif, a, a)
write(6,'(/a)')'ternary eq' ; call table(teq, a, a)
contains
subroutine table(u, x, y) ! for now, show the table.
real, external :: u
real, dimension(3), intent(in) :: x, y
integer :: i, j
write(6, '(3(3f4.1/))') ((u(x(i), y(j)), j=1,3), i=1,3)
end subroutine table
end program ternaryLogic
Free Pascal
Free Pascal version with lookup. Note equivalence and implication are used as proof, they are solved using the basic set instead of a lookup. Note Since we use a balanced range -1,0,1 multiplication equals EQU
{$mode objfpc}
unit ternarylogic;
interface
type
{ ternary type, balanced }
trit = (tFalse=-1, tMaybe=0, tTrue=1);
{ ternary operators }
{ equivalence = multiplication }
operator * (const a,b:trit):trit;
operator and (const a,b:trit):trit;inline;
operator or (const a,b:trit):trit;inline;
operator not (const a:trit):trit;inline;
operator xor (const a,b:trit):trit;
{ imp ==>}
operator >< (const a,b:trit):trit;
implementation
operator and (const a,b:trit):trit;inline;
const lookupAnd:array[trit,trit] of trit =
((tFalse,tFalse,tFalse),
(tFalse,tMaybe,tMaybe),
(tFalse,tMaybe,tTrue));
begin
Result:= LookupAnd[a,b];
end;
operator or (const a,b:trit):trit;inline;
const lookupOr:array[trit,trit] of trit =
((tFalse,tMaybe,tTrue),
(tMaybe,tMaybe,tTrue),
(tTrue,tTrue,tTrue));
begin
Result := LookUpOr[a,b];
end;
operator not (const a:trit):trit;inline;
const LookupNot:array[trit] of trit =(tTrue,tMaybe,tFalse);
begin
Result:= LookUpNot[a];
end;
operator xor (const a,b:trit):trit;
const LookupXor:array[trit,trit] of trit =
((tFalse,tMaybe,tTrue),
(tMaybe,tMaybe,tMaybe),
(tTrue,tMaybe,tFalse));
begin
Result := LookupXor[a,b];
end;
operator * (const a,b:trit):trit;
begin
result := not (a xor b);
end;
{ imp ==>}
operator >< (const a,b:trit):trit;
begin
result := not(a) or b;
end;
end.
program ternarytests;
{$mode objfpc}
uses
ternarylogic;
begin
writeln(' a AND b');
writeln('F':7,'U':7, 'T':7);
writeln('F|',tFalse and tFalse:7,tFalse and tMaybe:7,tFalse and tTrue:7);
writeln('U|',tMaybe and tFalse:7,tMaybe and tMaybe:7,tMaybe and tTrue:7);
writeln('T|',tTrue and tFalse:7,tTrue and tMaybe:7,tTrue and tTrue:7);
writeln;
writeln(' a OR b');
writeln('F':7,'U':7, 'T':7);
writeln('F|',tFalse or tFalse:7,tFalse or tMaybe:7,tFalse or tTrue:7);
writeln('U|',tMaybe or tFalse:7,tMaybe or tMaybe:7,tMaybe or tTrue:7);
writeln('T|',tTrue or tFalse:7,tTrue or tMaybe:7,tTrue or tTrue:7);
writeln;
writeln(' NOT a');
writeln('F|',not tFalse:7);
writeln('U|',not tMaybe:7);
writeln('T|',not tTrue:7);
writeln;
writeln(' a XOR b');
writeln('F':7,'U':7, 'T':7);
writeln('F|',tFalse xor tFalse:7,tFalse xor tMaybe:7,tFalse xor tTrue:7);
writeln('U|',tMaybe xor tFalse:7,tMaybe xor tMaybe:7,tMaybe xor tTrue:7);
writeln('T|',tTrue xor tFalse:7,tTrue xor tMaybe:7,tTrue xor tTrue:7);
writeln;
writeln('equality/equivalence and multiplication');
writeln('F':7,'U':7, 'T':7);
writeln('F|', tFalse * tFalse:7,tFalse * tMaybe:7, tFalse * tTrue:7);
writeln('U|', tMaybe * tFalse:7,tMaybe * tMaybe:7,tMaybe * tTrue:7);
writeln('T|', tTrue * tFalse:7, tTrue * tMaybe:7, tTrue * tTrue:7);
writeln;
writeln('IMP. a.k.a. IfThen -> not(a) or b');
writeln('F':7,'U':7, 'T':7);
writeln('T|',tTrue >< tTrue:7,tTrue >< tMaybe:7,tTrue >< tFalse:7);
writeln('U|',tMaybe >< tTrue:7,tMaybe >< tMaybe:7,tMaybe >< tFalse:7);
writeln('F|',tFalse >< tTrue:7, tFalse >< tMaybe:7,tFalse >< tFalse:7);
writeln;
end.
Output:
a AND b
F U T
F|tFalse tFalse tFalse
U|tFalse tMaybe tMaybe
T|tFalse tMaybe tTrue
a OR b
F U T
F|tFalse tMaybe tTrue
U|tMaybe tMaybe tTrue
T|tTrue tTrue tTrue
NOT a
F|tTrue
U|tMaybe
T|tFalse
a XOR b
F U T
F|tFalse tMaybe tTrue
U|tMaybe tMaybe tMaybe
T|tTrue tMaybe tFalse
equality/equivalence and multiplication
F U T
F|tTrue tMaybe tFalse
U|tMaybe tMaybe tMaybe
T|tFalse tMaybe tTrue
IMP. a.k.a. IfThen -> not(a) or b
F U T
T|tTrue tMaybe tFalse
U|tTrue tMaybe tMaybe
F|tTrue tTrue tTrue
Go
Go has four operators for the bool type: ==, &&, ||, and !.
package main
import "fmt"
type trit int8
const (
trFalse trit = iota - 1
trMaybe
trTrue
)
func (t trit) String() string {
switch t {
case trFalse:
return "False"
case trMaybe:
return "Maybe"
case trTrue:
return "True "
}
panic("Invalid trit")
}
func trNot(t trit) trit {
return -t
}
func trAnd(s, t trit) trit {
if s < t {
return s
}
return t
}
func trOr(s, t trit) trit {
if s > t {
return s
}
return t
}
func trEq(s, t trit) trit {
return s * t
}
func main() {
trSet := []trit{trFalse, trMaybe, trTrue}
fmt.Println("t not t")
for _, t := range trSet {
fmt.Println(t, trNot(t))
}
fmt.Println("\ns t s and t")
for _, s := range trSet {
for _, t := range trSet {
fmt.Println(s, t, trAnd(s, t))
}
}
fmt.Println("\ns t s or t")
for _, s := range trSet {
for _, t := range trSet {
fmt.Println(s, t, trOr(s, t))
}
}
fmt.Println("\ns t s eq t")
for _, s := range trSet {
for _, t := range trSet {
fmt.Println(s, t, trEq(s, t))
}
}
}
{{out}}
t not t
False True
Maybe Maybe
True False
s t s and t
False False False
False Maybe False
False True False
Maybe False False
Maybe Maybe Maybe
Maybe True Maybe
True False False
True Maybe Maybe
True True True
s t s or t
False False False
False Maybe Maybe
False True True
Maybe False Maybe
Maybe Maybe Maybe
Maybe True True
True False True
True Maybe True
True True True
s t s eq t
False False True
False Maybe Maybe
False True False
Maybe False Maybe
Maybe Maybe Maybe
Maybe True Maybe
True False False
True Maybe Maybe
True True True
Groovy
Solution:
enum Trit {
TRUE, MAYBE, FALSE
private Trit nand(Trit that) {
switch ([this,that]) {
case { FALSE in it }: return TRUE
case { MAYBE in it }: return MAYBE
default : return FALSE
}
}
private Trit nor(Trit that) { this.or(that).not() }
Trit and(Trit that) { this.nand(that).not() }
Trit or(Trit that) { this.not().nand(that.not()) }
Trit not() { this.nand(this) }
Trit imply(Trit that) { this.nand(that.not()) }
Trit equiv(Trit that) { this.and(that).or(this.nor(that)) }
}
Test:
printf 'AND\n '
Trit.values().each { b -> printf ('%6s', b) }
println '\n ----- ----- -----'
Trit.values().each { a ->
printf ('%6s | ', a)
Trit.values().each { b -> printf ('%6s', a.and(b)) }
println()
}
printf '\nOR\n '
Trit.values().each { b -> printf ('%6s', b) }
println '\n ----- ----- -----'
Trit.values().each { a ->
printf ('%6s | ', a)
Trit.values().each { b -> printf ('%6s', a.or(b)) }
println()
}
println '\nNOT'
Trit.values().each {
printf ('%6s | %6s\n', it, it.not())
}
printf '\nIMPLY\n '
Trit.values().each { b -> printf ('%6s', b) }
println '\n ----- ----- -----'
Trit.values().each { a ->
printf ('%6s | ', a)
Trit.values().each { b -> printf ('%6s', a.imply(b)) }
println()
}
printf '\nEQUIV\n '
Trit.values().each { b -> printf ('%6s', b) }
println '\n ----- ----- -----'
Trit.values().each { a ->
printf ('%6s | ', a)
Trit.values().each { b -> printf ('%6s', a.equiv(b)) }
println()
}
{{out}}
AND
TRUE MAYBE FALSE
----- ----- -----
TRUE | TRUE MAYBE FALSE
MAYBE | MAYBE MAYBE FALSE
FALSE | FALSE FALSE FALSE
OR
TRUE MAYBE FALSE
----- ----- -----
TRUE | TRUE TRUE TRUE
MAYBE | TRUE MAYBE MAYBE
FALSE | TRUE MAYBE FALSE
NOT
TRUE | FALSE
MAYBE | MAYBE
FALSE | TRUE
IMPLY
TRUE MAYBE FALSE
----- ----- -----
TRUE | TRUE MAYBE FALSE
MAYBE | TRUE MAYBE MAYBE
FALSE | TRUE TRUE TRUE
EQUIV
TRUE MAYBE FALSE
----- ----- -----
TRUE | TRUE MAYBE FALSE
MAYBE | MAYBE MAYBE MAYBE
FALSE | FALSE MAYBE TRUE
Haskell
All operations given in terms of NAND, the functionally-complete operation.
import Prelude hiding (Bool(..), not, (&&), (||), (==))
main = mapM_ (putStrLn . unlines . map unwords)
[ table "not" $ unary not
, table "and" $ binary (&&)
, table "or" $ binary (||)
, table "implies" $ binary (=->)
, table "equals" $ binary (==)
]
data Trit = False | Maybe | True deriving (Show)
False `nand` _ = True
_ `nand` False = True
True `nand` True = False
_ `nand` _ = Maybe
not a = nand a a
a && b = not $ a `nand` b
a || b = not a `nand` not b
a =-> b = a `nand` not b
a == b = (a && b) || (not a && not b)
inputs1 = [True, Maybe, False]
inputs2 = [(a,b) | a <- inputs1, b <- inputs1]
unary f = map (\a -> [a, f a]) inputs1
binary f = map (\(a,b) -> [a, b, f a b]) inputs2
table name xs = map (map pad) . (header :) $ map (map show) xs
where header = map (:[]) (take ((length $ head xs) - 1) ['A'..]) ++ [name]
pad s = s ++ replicate (5 - length s) ' '
{{out}}
A not
True False
Maybe Maybe
False True
A B and
True True True
True Maybe Maybe
True False False
Maybe True Maybe
Maybe Maybe Maybe
Maybe False False
False True False
False Maybe False
False False False
A B or
True True True
True Maybe True
True False True
Maybe True True
Maybe Maybe Maybe
Maybe False Maybe
False True True
False Maybe Maybe
False False False
A B implies
True True True
True Maybe Maybe
True False False
Maybe True True
Maybe Maybe Maybe
Maybe False Maybe
False True True
False Maybe True
False False True
A B equals
True True True
True Maybe Maybe
True False False
Maybe True Maybe
Maybe Maybe Maybe
Maybe False Maybe
False True False
False Maybe Maybe
False False True
=={{header|Icon}} and {{header|Unicon}}== The following example works in both Icon and Unicon. There are a couple of comments on the code that pertain to the task requirements:
- Strictly speaking there are no binary values in Icon and Unicon. There are a number of flow control operations that result in expression success (and a result) or failure which affects flow. As a result there really isn't a set of binary operators to map into ternary. The example provides the minimum required by the task plus xor.
- The code below does not define a data type as it doesn't really make sense in this case. Icon and Unicon can create records which would be overkill and clumsy in this case. Unicon can create objects which would also be overkill. The only remaining option is to reinterpret one of the existing types as ternary values. The code below implements balanced ternary values as integers in order to simplify several of the functions.
- The use of integers doesn't really support strings of trits well. While there is a function showtrit to ease display a converse function to decode character trits in a string is not included.
$define TRUE 1
$define FALSE -1
$define UNKNOWN 0
invocable all
link printf
procedure main() # demonstrate ternary logic
ufunc := ["not3"]
bfunc := ["and3", "or3", "xor3", "eq3", "ifthen3"]
every f := !ufunc do { # display unary functions
printf("\nunary function=%s:\n",f)
every t1 := (TRUE | FALSE | UNKNOWN) do
printf(" %s : %s\n",showtrit(t1),showtrit(not3(t1)))
}
every f := !bfunc do { # display binary functions
printf("\nbinary function=%s:\n ",f)
every t1 := (&null | TRUE | FALSE | UNKNOWN) do {
printf(" %s : ",showtrit(\t1))
every t2 := (TRUE | FALSE | UNKNOWN | &null) do {
if /t1 then printf(" %s",showtrit(\t2)|"\n")
else printf(" %s",showtrit(f(t1,\t2))|"\n")
}
}
}
end
procedure showtrit(a) #: return printable trit of error if invalid
return case a of {TRUE:"T";FALSE:"F";UNKNOWN:"?";default:runerr(205,a)}
end
procedure istrit(a) #: return value of trit or error if invalid
return (TRUE|FALSE|UNKNOWN|runerr(205,a)) = a
end
procedure not3(a) #: not of trit or error if invalid
return FALSE * istrit(a)
end
procedure and3(a,b) #: and of two trits or error if invalid
return min(istrit(a),istrit(b))
end
procedure or3(a,b) #: or of two trits or error if invalid
return max(istrit(a),istrit(b))
end
procedure eq3(a,b) #: equals of two trits or error if invalid
return istrit(a) * istrit(b)
end
procedure ifthen3(a,b) #: if trit then trit or error if invalid
return case istrit(a) of { TRUE: istrit(b) ; UNKNOWN: or3(a,b); FALSE: TRUE }
end
procedure xor3(a,b) #: xor of two trits or error if invalid
return not3(eq3(a,b))
end
{{libheader|Icon Programming Library}} [http://www.cs.arizona.edu/icon/library/src/procs/printf.icn printf.icn provides support for the printf family of functions]
{{out}}
unary function=not3:
T : F
F : T
? : ?
binary function=and3:
T F ?
T : T F ?
F : F F F
? : ? F ?
binary function=or3:
T F ?
T : T T T
F : T F ?
? : T ? ?
binary function=xor3:
T F ?
T : F T ?
F : T F ?
? : ? ? ?
binary function=eq3:
T F ?
T : T F ?
F : F T ?
? : ? ? ?
binary function=ifthen3:
T F ?
T : T F ?
F : T T T
? : T ? ?
J
The designers of J felt that user defined types were harmful, so that part of the task will not be supported here.
Instead:
true: 1 false: 0 maybe: 0.5
not=: -.
and=: <.
or =: >.
if =: (>. -.)"0~
eq =: (<.&-. >. <.)"0
Example use:
not 0 0.5 1
1 0.5 0
0 0.5 1 and/ 0 0.5 1
0 0 0
0 0.5 0.5
0 0.5 1
0 0.5 1 or/ 0 0.5 1
0 0.5 1
0.5 0.5 1
1 1 1
0 0.5 1 if/ 0 0.5 1
1 1 1
0.5 0.5 1
0 0.5 1
0 0.5 1 eq/ 0 0.5 1
1 0.5 0
0.5 0.5 0.5
0 0.5 1
Note that this implementation is a special case of "[[wp:fuzzy logic|fuzzy logic]]" (using a limited set of values).
Note that while >. and <. could be used for boolean operations instead of J's +. and *., the identity elements for >. and <. are not boolean values, but are negative and positive infinity. See also: [[wp:Boolean ring|Boolean ring]]
Note that we might instead define values between 0 and 1 to represent independent probabilities:
not=: -.
and=: *
or=: *&.-.
if =: (or -.)"0~
eq =: (*&-. or *)"0
However, while this might be a more intellectually satisfying approach, this gives us some different results from the task requirement, for the combination of two "maybe" values (we could "fix" this by adding some "logic" which replaced any non-integer value with "0.5" - this would satisfy literal compliance with the task specification and might even be a valid engineering choice if we are implementing in hardware, for example):
not 0 0.5 1
1 0.5 0
0 0.5 1 and/ 0 0.5 1
0 0 0
0 0.25 0.5
0 0.5 1
0 0.5 1 or/ 0 0.5 1
0 0.5 1
0.5 0.75 1
1 1 1
0 0.5 1 if/ 0 0.5 1
1 1 1
0.5 0.75 1
0 0.5 1
0 0.5 1 eq/ 0 0.5 1
1 0.5 0
0.5 0.4375 0.5
0 0.5 1
Another interesting possibility would involve using George Boole's original operations. This leaves us without any "not", (if we include the definition of logical negation which was later added to the definition of Boolean algebra, then the only numbers which can be used with Boolean algebra are 1 and 0). So, it's not clear how we would implement "if" or "eq". However, "and" and "or" would look like this:
and=: *.
or=: +.
And, the boolean result tables would look like this:
0 0.5 1 and/ 0 0.5 1
0 0 0
0 0.5 1
0 1 1
0 0.5 1 or/ 0 0.5 1
0 0.5 1
0.5 0.5 0.5
1 0.5 1
Java
{{works with|Java|1.5+}}
public class Logic{
public static enum Trit{
TRUE, MAYBE, FALSE;
public Trit and(Trit other){
if(this == TRUE){
return other;
}else if(this == MAYBE){
return (other == FALSE) ? FALSE : MAYBE;
}else{
return FALSE;
}
}
public Trit or(Trit other){
if(this == TRUE){
return TRUE;
}else if(this == MAYBE){
return (other == TRUE) ? TRUE : MAYBE;
}else{
return other;
}
}
public Trit tIf(Trit other){
if(this == TRUE){
return other;
}else if(this == MAYBE){
return (other == TRUE) ? TRUE : MAYBE;
}else{
return TRUE;
}
}
public Trit not(){
if(this == TRUE){
return FALSE;
}else if(this == MAYBE){
return MAYBE;
}else{
return TRUE;
}
}
public Trit equals(Trit other){
if(this == TRUE){
return other;
}else if(this == MAYBE){
return MAYBE;
}else{
return other.not();
}
}
}
public static void main(String[] args){
for(Trit a:Trit.values()){
System.out.println("not " + a + ": " + a.not());
}
for(Trit a:Trit.values()){
for(Trit b:Trit.values()){
System.out.println(a+" and "+b+": "+a.and(b)+
"\t "+a+" or "+b+": "+a.or(b)+
"\t "+a+" implies "+b+": "+a.tIf(b)+
"\t "+a+" = "+b+": "+a.equals(b));
}
}
}
}
{{out}}
not TRUE: FALSE
not MAYBE: MAYBE
not FALSE: TRUE
TRUE and TRUE: TRUE TRUE or TRUE: TRUE TRUE implies TRUE: TRUE TRUE = TRUE: TRUE
TRUE and MAYBE: MAYBE TRUE or MAYBE: TRUE TRUE implies MAYBE: MAYBE TRUE = MAYBE: MAYBE
TRUE and FALSE: FALSE TRUE or FALSE: TRUE TRUE implies FALSE: FALSE TRUE = FALSE: FALSE
MAYBE and TRUE: MAYBE MAYBE or TRUE: TRUE MAYBE implies TRUE: TRUE MAYBE = TRUE: MAYBE
MAYBE and MAYBE: MAYBE MAYBE or MAYBE: MAYBE MAYBE implies MAYBE: MAYBE MAYBE = MAYBE: MAYBE
MAYBE and FALSE: FALSE MAYBE or FALSE: MAYBE MAYBE implies FALSE: MAYBE MAYBE = FALSE: MAYBE
FALSE and TRUE: FALSE FALSE or TRUE: TRUE FALSE implies TRUE: TRUE FALSE = TRUE: FALSE
FALSE and MAYBE: FALSE FALSE or MAYBE: MAYBE FALSE implies MAYBE: TRUE FALSE = MAYBE: MAYBE
FALSE and FALSE: FALSE FALSE or FALSE: FALSE FALSE implies FALSE: TRUE FALSE = FALSE: TRUE
JavaScript
Let's use the trit already available in JavaScript: true, false (both boolean) and undefined…
var L3 = new Object();
L3.not = function(a) {
if (typeof a == "boolean") return !a;
if (a == undefined) return undefined;
throw("Invalid Ternary Expression.");
}
L3.and = function(a, b) {
if (typeof a == "boolean" && typeof b == "boolean") return a && b;
if ((a == true && b == undefined) || (a == undefined && b == true)) return undefined;
if ((a == false && b == undefined) || (a == undefined && b == false)) return false;
if (a == undefined && b == undefined) return undefined;
throw("Invalid Ternary Expression.");
}
L3.or = function(a, b) {
if (typeof a == "boolean" && typeof b == "boolean") return a || b;
if ((a == true && b == undefined) || (a == undefined && b == true)) return true;
if ((a == false && b == undefined) || (a == undefined && b == false)) return undefined;
if (a == undefined && b == undefined) return undefined;
throw("Invalid Ternary Expression.");
}
// A -> B is equivalent to -A or B
L3.ifThen = function(a, b) {
return L3.or(L3.not(a), b);
}
// A <=> B is equivalent to (A -> B) and (B -> A)
L3.iff = function(a, b) {
return L3.and(L3.ifThen(a, b), L3.ifThen(b, a));
}
… and try these:
L3.and(true, a) // undefined
L3.or(a, 2 == 3) // false
L3.ifThen(true, a) // undefined
L3.iff(a, 2 == 2) // undefined
## jq
jq itself does not have an extensible type system, so we'll use false, "maybe", and true
as the three values since ternary logic agrees with Boolean logic for true and false, and because jq prints these three values consistently.
For consistency, all the ternary logic operators are defined here with the prefix "ternary_", but such a prefix is only needed for "not", "and", and "or", as these are jq keywords.
```jq
def ternary_nand(a; b):
if a == false or b == false then true
elif a == "maybe" or b == "maybe" then "maybe"
else false
end ;
def ternary_not(a): ternary_nand(a; a);
def ternary_or(a; b): ternary_nand( ternary_not(a); ternary_not(b) );
def ternary_nor(a; b): ternary_not( ternary_or(a;b) );
def ternary_and(a; b): ternary_not( ternary_nand(a; b) );
def ternary_imply(this; that):
ternary_nand(this, ternary_not(that));
def ternary_equiv(this; that):
ternary_or( ternary_and(this; that); ternary_nor(this; that) );
def display_and(a; b):
a as $a | b as $b
| "\($a) and \($b) is \( ternary_and($a; $b) )";
def display_equiv(a; b):
a as $a | b as $b
| "\($a) equiv \($b) is \( ternary_equiv($a; $b) )";
# etc etc
# Invoke the display functions:
display_and( (false, "maybe", true ); (false, "maybe", true) ),
display_equiv( (false, "maybe", true ); (false, "maybe", true) ),
"etc etc"
{{out}}
"false and false is false"
"false and maybe is false"
"false and true is false"
"maybe and false is false"
"maybe and maybe is maybe"
"maybe and true is maybe"
"true and false is false"
"true and maybe is maybe"
"true and true is true"
"false equiv false is true"
"false equiv maybe is maybe"
"false equiv true is false"
"maybe equiv false is maybe"
"maybe equiv maybe is maybe"
"maybe equiv true is maybe"
"true equiv false is false"
"true equiv maybe is maybe"
"true equiv true is true"
"etc etc"
Julia
{{works with|Julia|0.6}}
@enum Trit False Maybe True
const trits = (False, Maybe, True)
Base.:!(a::Trit) = a == False ? True : a == Maybe ? Maybe : False
∧(a::Trit, b::Trit) = a == b == True ? True : (a, b) ∋ False ? False : Maybe
∨(a::Trit, b::Trit) = a == b == False ? False : (a, b) ∋ True ? True : Maybe
⊃(a::Trit, b::Trit) = a == False || b == True ? True : (a, b) ∋ Maybe ? Maybe : False
≡(a::Trit, b::Trit) = (a, b) ∋ Maybe ? Maybe : a == b ? True : False
println("Not (!):")
println(join(@sprintf("%10s%s is %5s", "!", t, !t) for t in trits))
println("And (∧):")
for a in trits
println(join(@sprintf("%10s ∧ %5s is %5s", a, b, a ∧ b) for b in trits))
end
println("Or (∨):")
for a in trits
println(join(@sprintf("%10s ∨ %5s is %5s", a, b, a ∨ b) for b in trits))
end
println("If Then (⊃):")
for a in trits
println(join(@sprintf("%10s ⊃ %5s is %5s", a, b, a ⊃ b) for b in trits))
end
println("Equivalent (≡):")
for a in trits
println(join(@sprintf("%10s ≡ %5s is %5s", a, b, a ≡ b) for b in trits))
end
{{out}}
Not (!):
!False is True !Maybe is Maybe !True is False
And (∧):
False ∧ False is False False ∧ Maybe is False False ∧ True is False
Maybe ∧ False is False Maybe ∧ Maybe is Maybe Maybe ∧ True is Maybe
True ∧ False is False True ∧ Maybe is Maybe True ∧ True is True
Or (∨):
False ∨ False is False False ∨ Maybe is Maybe False ∨ True is True
Maybe ∨ False is Maybe Maybe ∨ Maybe is Maybe Maybe ∨ True is True
True ∨ False is True True ∨ Maybe is True True ∨ True is True
If Then (⊃):
False ⊃ False is True False ⊃ Maybe is True False ⊃ True is True
Maybe ⊃ False is Maybe Maybe ⊃ Maybe is Maybe Maybe ⊃ True is True
True ⊃ False is False True ⊃ Maybe is Maybe True ⊃ True is True
Equivalent (≡):
False ≡ False is True False ≡ Maybe is Maybe False ≡ True is False
Maybe ≡ False is Maybe Maybe ≡ Maybe is Maybe Maybe ≡ True is Maybe
True ≡ False is False True ≡ Maybe is Maybe True ≡ True is True
== Alternative version == {{works with|Julia|0.7}}
With Julia 1.0 and the new type missing, three-value logic is implemented by default
# built-in: true, false and missing
using Printf
const tril = (true, missing, false)
@printf("\n%8s | %8s\n", "A", "¬A")
for A in tril
@printf("%8s | %8s\n", A, !A)
end
@printf("\n%8s | %8s | %8s\n", "A", "B", "A ∧ B")
for (A, B) in Iterators.product(tril, tril)
@printf("%8s | %8s | %8s\n", A, B, A & B)
end
@printf("\n%8s | %8s | %8s\n", "A", "B", "A ∨ B")
for (A, B) in Iterators.product(tril, tril)
@printf("%8s | %8s | %8s\n", A, B, A | B)
end
@printf("\n%8s | %8s | %8s\n", "A", "B", "A ≡ B")
for (A, B) in Iterators.product(tril, tril)
@printf("%8s | %8s | %8s\n", A, B, A == B)
end
⊃(A, B) = B | !A
@printf("\n%8s | %8s | %8s\n", "A", "B", "A ⊃ B")
for (A, B) in Iterators.product(tril, tril)
@printf("%8s | %8s | %8s\n", A, B, A ⊃ B)
end
{{out}}
A | ¬A
true | false
missing | missing
false | true
A | B | A ∧ B
true | true | true
missing | true | missing
false | true | false
true | missing | missing
missing | missing | missing
false | missing | false
true | false | false
missing | false | false
false | false | false
A | B | A ∨ B
true | true | true
missing | true | true
false | true | true
true | missing | true
missing | missing | missing
false | missing | missing
true | false | true
missing | false | missing
false | false | false
A | B | A ≡ B
true | true | true
missing | true | missing
false | true | false
true | missing | missing
missing | missing | missing
false | missing | missing
true | false | false
missing | false | missing
false | false | true
A | B | A ⊃ B
true | true | true
missing | true | true
false | true | true
true | missing | missing
missing | missing | missing
false | missing | true
true | false | false
missing | false | missing
Kotlin
// version 1.1.2
enum class Trit {
TRUE, MAYBE, FALSE;
operator fun not() = when (this) {
TRUE -> FALSE
MAYBE -> MAYBE
FALSE -> TRUE
}
infix fun and(other: Trit) = when (this) {
TRUE -> other
MAYBE -> if (other == FALSE) FALSE else MAYBE
FALSE -> FALSE
}
infix fun or(other: Trit) = when (this) {
TRUE -> TRUE
MAYBE -> if (other == TRUE) TRUE else MAYBE
FALSE -> other
}
infix fun imp(other: Trit) = when (this) {
TRUE -> other
MAYBE -> if (other == TRUE) TRUE else MAYBE
FALSE -> TRUE
}
infix fun eqv(other: Trit) = when (this) {
TRUE -> other
MAYBE -> MAYBE
FALSE -> !other
}
override fun toString() = this.name[0].toString()
}
fun main(args: Array<String>) {
val ta = arrayOf(Trit.TRUE, Trit.MAYBE, Trit.FALSE)
// not
println("not")
println("-------")
for (t in ta) println(" $t | ${!t}")
println()
// and
println("and | T M F")
println("-------------")
for (t in ta) {
print(" $t | ")
for (tt in ta) print("${t and tt} ")
println()
}
println()
// or
println("or | T M F")
println("-------------")
for (t in ta) {
print(" $t | ")
for (tt in ta) print("${t or tt} ")
println()
}
println()
// imp
println("imp | T M F")
println("-------------")
for (t in ta) {
print(" $t | ")
for (tt in ta) print("${t imp tt} ")
println()
}
println()
// eqv
println("eqv | T M F")
println("-------------")
for (t in ta) {
print(" $t | ")
for (tt in ta) print("${t eqv tt} ")
println()
}
}
{{out}}
not
-------
T | F
M | M
F | T
and | T M F
-------------
T | T M F
M | M M F
F | F F F
or | T M F
-------------
T | T T T
M | T M M
F | T M F
imp | T M F
-------------
T | T M F
M | T M M
F | T T T
eqv | T M F
-------------
T | T M F
M | M M M
F | F M T
Liberty BASIC
'ternary logic
'0 1 2
'F ? T
'False Don't know True
'LB has NOT AND OR XOR, so we implement them.
'LB has no EQ, but XOR could be expressed via EQ. In 'normal' boolean at least.
global tFalse, tDontKnow, tTrue
tFalse = 0
tDontKnow = 1
tTrue = 2
print "Short and long names for ternary logic values"
for i = tFalse to tTrue
print shortName3$(i);" ";longName3$(i)
next
print
print "Single parameter functions"
print "x";" ";"=x";" ";"not(x)"
for i = tFalse to tTrue
print shortName3$(i);" ";shortName3$(i);" ";shortName3$(not3(i))
next
print
print "Double parameter fuctions"
print "x";" ";"y";" ";"x AND y";" ";"x OR y";" ";"x EQ y";" ";"x XOR y"
for a = tFalse to tTrue
for b = tFalse to tTrue
print shortName3$(a);" ";shortName3$(b);" "; _
shortName3$(and3(a,b));" "; shortName3$(or3(a,b));" "; _
shortName3$(eq3(a,b));" "; shortName3$(xor3(a,b))
next
next
function and3(a,b)
and3 = min(a,b)
end function
function or3(a,b)
or3 = max(a,b)
end function
function eq3(a,b)
select case
case a=tDontKnow or b=tDontKnow
eq3 = tDontKnow
case a=b
eq3 = tTrue
case else
eq3 = tFalse
end select
end function
function xor3(a,b)
xor3 = not3(eq3(a,b))
end function
function not3(b)
not3 = 2-b
end function
'------------------------------------------------
function shortName3$(i)
shortName3$ = word$("F ? T", i+1)
end function
function longName3$(i)
longName3$ = word$("False,Don't know,True", i+1, ",")
end function
{{out}}
Short and long names for ternary logic values
F False
? Don't know
T True
Single parameter functions
x =x not(x)
F F T
? ? ?
T T F
Double parameter fuctions
x y x AND y x OR y x EQ y x XOR y
F F F F T F
F ? F ? ? ?
F T F T F T
? F F ? ? ?
? ? ? ? ? ?
? T ? T ? ?
T F F T F T
T ? ? T ? ?
T T T T T F
Maple
The logic system in Maple is implicitly ternary with truth values '''true''', '''false''', and '''FAIL'''.
The following script generates all truth tables for Maple logical operations. Note that in addition to the usual built-in logical operators for '''not''', '''or''', '''and''', and '''xor''', Maple also has '''implies'''.
tv := [true, false, FAIL];
NotTable := Array(1..3, i->not tv[i] );
AndTable := Array(1..3, 1..3, (i,j)->tv[i] and tv[j] );
OrTable := Array(1..3, 1..3, (i,j)->tv[i] or tv[j] );
XorTable := Array(1..3, 1..3, (i,j)->tv[i] xor tv[j] );
ImpliesTable := Array(1..3, 1..3, (i,j)->tv[i] implies tv[j] );
{{Out}}
tv := [true, false, FAIL];
tv := [true, false, FAIL]
> NotTable := Array(1..3, i->not tv[i] );
NotTable := [false, true, FAIL]
> AndTable := Array(1..3, 1..3, (i,j)->tv[i] and tv[j] );
[true false FAIL ]
[ ]
AndTable := [false false false]
[ ]
[FAIL false FAIL ]
> OrTable := Array(1..3, 1..3, (i,j)->tv[i] or tv[j] );
[true true true]
[ ]
OrTable := [true false FAIL]
[ ]
[true FAIL FAIL]
> XorTable := Array(1..3, 1..3, (i,j)->tv[i] xor tv[j] );
[false true FAIL]
[ ]
XorTable := [true false FAIL]
[ ]
[FAIL FAIL FAIL]
> ImpliesTable := Array(1..3, 1..3, (i,j)->tv[i] implies tv[j] );
[true false FAIL]
[ ]
ImpliesTable := [true true true]
[ ]
[true FAIL FAIL]
Mathematica
Type definition is not allowed in Mathematica. We can just use the build-in symbols "True" and "False", and add a new symbol "Maybe".
Maybe /: ! Maybe = Maybe;
Maybe /: (And | Or | Nand | Nor | Xor | Xnor | Implies | Equivalent)[Maybe, Maybe] = Maybe;
Example:
trits = {True, Maybe, False};
Print@Grid[
ArrayFlatten[{{{{Not}}, {{Null}}}, {List /@ trits,
List /@ Not /@ trits}}]];
Do[Print@Grid[
ArrayFlatten[{{{{operator}}, {{Null, Null,
Null}}}, {{{Null}}, {trits}}, {List /@ trits,
Outer[operator, trits, trits]}}]], {operator, {And, Or, Nand,
Nor, Xor, Xnor, Implies, Equivalent}}]
{{out}}
Not
True False
Maybe Maybe
False True
And
True Maybe False
True True Maybe False
Maybe Maybe Maybe False
False False False False
Or
True Maybe False
True True True True
Maybe True Maybe Maybe
False True Maybe False
Nand
True Maybe False
True False Maybe True
Maybe Maybe Maybe True
False True True True
Nor
True Maybe False
True False False False
Maybe False Maybe Maybe
False False Maybe True
Xor
True Maybe False
True False Maybe True
Maybe Maybe Maybe Maybe
False True Maybe False
Xnor
True Maybe False
True True Maybe False
Maybe Maybe Maybe Maybe
False False Maybe True
Implies
True Maybe False
True True Maybe False
Maybe True Maybe Maybe
False True True True
Equivalent
True Maybe False
True True Maybe False
Maybe Maybe Maybe Maybe
False False Maybe True
=={{header|MK-61/52}}==
- 3 x^y ИП0 <-> / [x] ^ ^ 3 / [x] 3 * - 1 - С/П 1 5 6 3 3 БП 00 1 9 5 6 9 БП 00 1 5 9 2 9 БП 00 1 5 6 6 5 БП 00 /-/ ЗН С/П
<u>Instruction</u>:
''БП <u>XX</u> С/П a ^ b С/П'',
where <u>XX</u> = 28 for ''AND''; 35 for ''OR''; 42 for ''implies''; 49 for ''equivalent''; 56 for ''NOT'';
''a'', ''b'' ∈ {-1, 0, 1}.
## Nim
```nim
type Trit* = enum ttrue, tmaybe, tfalse
proc `$`*(a: Trit): string =
case a
of ttrue: "T"
of tmaybe: "?"
of tfalse: "F"
proc `not`*(a: Trit): Trit =
case a
of ttrue: tfalse
of tmaybe: tmaybe
of tfalse: ttrue
proc `and`*(a, b: Trit): Trit =
const t: array[Trit, array[Trit, Trit]] =
[ [ttrue, tmaybe, tfalse]
, [tmaybe, tmaybe, tfalse]
, [tfalse, tfalse, tfalse] ]
t[a][b]
proc `or`*(a, b: Trit): Trit =
const t: array[Trit, array[Trit, Trit]] =
[ [ttrue, ttrue, ttrue]
, [ttrue, tmaybe, tmaybe]
, [ttrue, tmaybe, tfalse] ]
t[a][b]
proc then*(a, b: Trit): Trit =
const t: array[Trit, array[Trit, Trit]] =
[ [ttrue, tmaybe, tfalse]
, [ttrue, tmaybe, tmaybe]
, [ttrue, ttrue, ttrue] ]
t[a][b]
proc equiv*(a, b: Trit): Trit =
const t: array[Trit, array[Trit, Trit]] =
[ [ttrue, tmaybe, tfalse]
, [tmaybe, tmaybe, tmaybe]
, [tfalse, tmaybe, ttrue] ]
t[a][b]
import strutils
var
op1 = ttrue
op2 = ttrue
for t in Trit:
echo "Not ", t , ": ", not t
for op1 in Trit:
for op2 in Trit:
echo "$# and $#: $#".format(op1, op2, op1 and op2)
echo "$# or $#: $#".format(op1, op2, op1 or op2)
echo "$# then $#: $#".format(op1, op2, op1.then op2)
echo "$# equiv $#: $#".format(op1, op2, op1.equiv op2)
{{out}}
Not T: F
Not ?: ?
Not F: T
T and T: T
T or T: T
T then T: T
T equiv T: T
T and ?: ?
T or ?: T
T then ?: ?
T equiv ?: ?
T and F: F
T or F: T
T then F: F
T equiv F: F
? and T: ?
? or T: T
? then T: T
? equiv T: ?
? and ?: ?
? or ?: ?
? then ?: ?
? equiv ?: ?
? and F: F
? or F: ?
? then F: ?
? equiv F: ?
F and T: F
F or T: T
F then T: T
F equiv T: F
F and ?: F
F or ?: ?
F then ?: T
F equiv ?: ?
F and F: F
F or F: F
F then F: T
F equiv F: T
OCaml
type trit = True | False | Maybe
let t_not = function
| True -> False
| False -> True
| Maybe -> Maybe
let t_and a b = match (a,b) with
| (True,True) -> True
| (False,_) | (_,False) -> False
| _ -> Maybe
let t_or a b = t_not (t_and (t_not a) (t_not b))
let t_eq a b = match (a,b) with
| (True,True) | (False,False) -> True
| (False,True) | (True,False) -> False
| _ -> Maybe
let t_imply a b = t_or (t_not a) b
let string_of_trit = function
| True -> "True"
| False -> "False"
| Maybe -> "Maybe"
let () =
let values = [| True; Maybe; False |] in
let f = string_of_trit in
Array.iter (fun v -> Printf.printf "Not %s: %s\n" (f v) (f (t_not v))) values;
print_newline ();
let print op str =
Array.iter (fun a ->
Array.iter (fun b ->
Printf.printf "%s %s %s: %s\n" (f a) str (f b) (f (op a b))
) values
) values;
print_newline ()
in
print t_and "And";
print t_or "Or";
print t_imply "Then";
print t_eq "Equiv";
;;
{{out}}
Not True: False
Not Maybe: Maybe
Not False: True
True And True: True
True And Maybe: Maybe
True And False: False
Maybe And True: Maybe
Maybe And Maybe: Maybe
Maybe And False: False
False And True: False
False And Maybe: False
False And False: False
True Or True: True
True Or Maybe: True
True Or False: True
Maybe Or True: True
Maybe Or Maybe: Maybe
Maybe Or False: Maybe
False Or True: True
False Or Maybe: Maybe
False Or False: False
True Then True: True
True Then Maybe: Maybe
True Then False: False
Maybe Then True: True
Maybe Then Maybe: Maybe
Maybe Then False: Maybe
False Then True: True
False Then Maybe: True
False Then False: True
True Equiv True: True
True Equiv Maybe: Maybe
True Equiv False: False
Maybe Equiv True: Maybe
Maybe Equiv Maybe: Maybe
Maybe Equiv False: Maybe
False Equiv True: False
False Equiv Maybe: Maybe
False Equiv False: True
=== Using a general binary -> ternary transform === Instead of writing all of the truth-tables by hand, we can construct a general binary -> ternary transform and apply it to any logical function we want:
type trit = True | False | Maybe
let to_bin = function True -> [true] | False -> [false] | Maybe -> [true;false]
let eval f x =
List.fold_left (fun l c -> List.fold_left (fun m d -> ((d c) :: m)) l f) [] x
let rec from_bin =
function [true] -> True | [false] -> False
| h :: t -> (match (h, from_bin t) with
(true,True) -> True | (false,False) -> False | _ -> Maybe)
| _ -> Maybe
let to_ternary1 uop = fun x -> from_bin (eval [uop] (to_bin x))
let to_ternary2 bop = fun x y -> from_bin (eval (eval [bop] (to_bin x)) (to_bin y))
let t_not = to_ternary1 (not)
let t_and = to_ternary2 (&&)
let t_or = to_ternary2 (||)
let t_equiv = to_ternary2 (=)
let t_imply = to_ternary2 (fun p q -> (not p) || q)
let str = function True -> "True " | False -> "False" | Maybe -> "Maybe"
let iterv f = List.iter f [True; False; Maybe]
let table1 s u =
print_endline ("\n"^s^":");
iterv (fun v -> print_endline (" "^(str v)^" -> "^(str (u v))));;
let table2 s b =
print_endline ("\n"^s^":");
iterv (fun u ->
iterv (fun v ->
print_endline (" "^(str u)^" "^(str v)^" -> "^(str (b u v)))));;
table1 "not" t_not;;
table2 "and" t_and;;
table2 "or" t_or;;
table2 "equiv" t_equiv;;
table2 "implies" t_imply;;
{{out}}
not:
True -> False
False -> True
Maybe -> Maybe
and:
True True -> True
True False -> False
True Maybe -> Maybe
False True -> False
False False -> False
False Maybe -> False
Maybe True -> Maybe
Maybe False -> False
Maybe Maybe -> Maybe
or:
True True -> True
True False -> True
True Maybe -> True
False True -> True
False False -> False
False Maybe -> Maybe
Maybe True -> True
Maybe False -> Maybe
Maybe Maybe -> Maybe
equiv:
True True -> True
True False -> False
True Maybe -> Maybe
False True -> False
False False -> True
False Maybe -> Maybe
Maybe True -> Maybe
Maybe False -> Maybe
Maybe Maybe -> Maybe
implies:
True True -> True
True False -> False
True Maybe -> Maybe
False True -> True
False False -> True
False Maybe -> True
Maybe True -> True
Maybe False -> Maybe
Maybe Maybe -> Maybe
ooRexx
tritValues = .array~of(.trit~true, .trit~false, .trit~maybe)
tab = '09'x
say "not operation (\)"
loop a over tritValues
say "\"a":" (\a)
end
say
say "and operation (&)"
loop aa over tritValues
loop bb over tritValues
say (aa" & "bb":" (aa&bb))
end
end
say
say "or operation (|)"
loop aa over tritValues
loop bb over tritValues
say (aa" | "bb":" (aa|bb))
end
end
say
say "implies operation (&&)"
loop aa over tritValues
loop bb over tritValues
say (aa" && "bb":" (aa&&bb))
end
end
say
say "equals operation (=)"
loop aa over tritValues
loop bb over tritValues
say (aa" = "bb":" (aa=bb))
end
end
::class trit
-- making this a private method so we can control the creation
-- of these. We only allow 3 instances to exist
::method new class private
forward class(super)
::method init class
expose true false maybe
-- delayed creation
true = .nil
false = .nil
maybe = .nil
-- read only attribute access to the instances.
-- these methods create the appropriate singleton on the first call
::attribute true class get
expose true
if true == .nil then true = self~new("True")
return true
::attribute false class get
expose false
if false == .nil then false = self~new("False")
return false
::attribute maybe class get
expose maybe
if maybe == .nil then maybe = self~new("Maybe")
return maybe
-- create an instance
::method init
expose value
use arg value
-- string method to return the value of the instance
::method string
expose value
return value
-- "and" method using the operator overload
::method "&"
use strict arg other
if self == .trit~true then return other
else if self == .trit~maybe then do
if other == .trit~false then return .trit~false
else return .trit~maybe
end
else return .trit~false
-- "or" method using the operator overload
::method "|"
use strict arg other
if self == .trit~true then return .trit~true
else if self == .trit~maybe then do
if other == .trit~true then return .trit~true
else return .trit~maybe
end
else return other
-- implies method...using the XOR operator for this
::method "&&"
use strict arg other
if self == .trit~true then return other
else if self == .trit~maybe then do
if other == .trit~true then return .trit~true
else return .trit~maybe
end
else return .trit~true
-- "not" method using the operator overload
::method "\"
if self == .trit~true then return .trit~false
else if self == .trit~maybe then return .trit~maybe
else return .trit~true
-- "equals" using the "=" override. This makes a distinction between
-- the "==" operator, which is real equality and the "=" operator, which
-- is trinary equality.
::method "="
use strict arg other
if self == .trit~true then return other
else if self == .trit~maybe then return .trit~maybe
else return \other
not operation (\)
\True: False
\False: True
\Maybe: Maybe
and operation (&)
True & True: True
True & False: False
True & Maybe: Maybe
False & True: False
False & False: False
False & Maybe: False
Maybe & True: Maybe
Maybe & False: False
Maybe & Maybe: Maybe
or operation (|)
True | True: True
True | False: True
True | Maybe: True
False | True: True
False | False: False
False | Maybe: Maybe
Maybe | True: True
Maybe | False: Maybe
Maybe | Maybe: Maybe
implies operation (&&)
True && True: True
True && False: False
True && Maybe: Maybe
False && True: True
False && False: True
False && Maybe: True
Maybe && True: True
Maybe && False: Maybe
Maybe && Maybe: Maybe
equals operation (=)
True = True: True
True = False: False
True = Maybe: Maybe
False = True: False
False = False: True
False = Maybe: Maybe
Maybe = True: Maybe
Maybe = False: Maybe
Maybe = Maybe: Maybe
Pascal
Program TernaryLogic (output);
type
trit = (terTrue, terMayBe, terFalse);
function terNot (a: trit): trit;
begin
case a of
terTrue: terNot := terFalse;
terMayBe: terNot := terMayBe;
terFalse: terNot := terTrue;
end;
end;
function terAnd (a, b: trit): trit;
begin
terAnd := terMayBe;
if (a = terFalse) or (b = terFalse) then
terAnd := terFalse
else
if (a = terTrue) and (b = terTrue) then
terAnd := terTrue;
end;
function terOr (a, b: trit): trit;
begin
terOr := terMayBe;
if (a = terTrue) or (b = terTrue) then
terOr := terTrue
else
if (a = terFalse) and (b = terFalse) then
terOr := terFalse;
end;
function terEquals (a, b: trit): trit;
begin
if a = b then
terEquals := terTrue
else
if a <> b then
terEquals := terFalse;
if (a = terMayBe) or (b = terMayBe) then
terEquals := terMayBe;
end;
function terIfThen (a, b: trit): trit;
begin
terIfThen := terMayBe;
if (a = terTrue) or (b = terFalse) then
terIfThen := terTrue
else
if (a = terFalse) and (b = terTrue) then
terIfThen := terFalse;
end;
function terToStr(a: trit): string;
begin
case a of
terTrue: terToStr := 'True ';
terMayBe: terToStr := 'Maybe';
terFalse: terToStr := 'False';
end;
end;
begin
writeln('Ternary logic test:');
writeln;
writeln('NOT ', ' True ', ' Maybe', ' False');
writeln(' ', terToStr(terNot(terTrue)), ' ', terToStr(terNot(terMayBe)), ' ', terToStr(terNot(terFalse)));
writeln;
writeln('AND ', ' True ', ' Maybe', ' False');
writeln('True ', terToStr(terAnd(terTrue,terTrue)), ' ', terToStr(terAnd(terMayBe,terTrue)), ' ', terToStr(terAnd(terFalse,terTrue)));
writeln('Maybe ', terToStr(terAnd(terTrue,terMayBe)), ' ', terToStr(terAnd(terMayBe,terMayBe)), ' ', terToStr(terAnd(terFalse,terMayBe)));
writeln('False ', terToStr(terAnd(terTrue,terFalse)), ' ', terToStr(terAnd(terMayBe,terFalse)), ' ', terToStr(terAnd(terFalse,terFalse)));
writeln;
writeln('OR ', ' True ', ' Maybe', ' False');
writeln('True ', terToStr(terOR(terTrue,terTrue)), ' ', terToStr(terOR(terMayBe,terTrue)), ' ', terToStr(terOR(terFalse,terTrue)));
writeln('Maybe ', terToStr(terOR(terTrue,terMayBe)), ' ', terToStr(terOR(terMayBe,terMayBe)), ' ', terToStr(terOR(terFalse,terMayBe)));
writeln('False ', terToStr(terOR(terTrue,terFalse)), ' ', terToStr(terOR(terMayBe,terFalse)), ' ', terToStr(terOR(terFalse,terFalse)));
writeln;
writeln('IFTHEN', ' True ', ' Maybe', ' False');
writeln('True ', terToStr(terIfThen(terTrue,terTrue)), ' ', terToStr(terIfThen(terMayBe,terTrue)), ' ', terToStr(terIfThen(terFalse,terTrue)));
writeln('Maybe ', terToStr(terIfThen(terTrue,terMayBe)), ' ', terToStr(terIfThen(terMayBe,terMayBe)), ' ', terToStr(terIfThen(terFalse,terMayBe)));
writeln('False ', terToStr(terIfThen(terTrue,terFalse)), ' ', terToStr(terIfThen(terMayBe,terFalse)), ' ', terToStr(terIfThen(terFalse,terFalse)));
writeln;
writeln('EQUAL ', ' True ', ' Maybe', ' False');
writeln('True ', terToStr(terEquals(terTrue,terTrue)), ' ', terToStr(terEquals(terMayBe,terTrue)), ' ', terToStr(terEquals(terFalse,terTrue)));
writeln('Maybe ', terToStr(terEquals(terTrue,terMayBe)), ' ', terToStr(terEquals(terMayBe,terMayBe)), ' ', terToStr(terEquals(terFalse,terMayBe)));
writeln('False ', terToStr(terEquals(terTrue,terFalse)), ' ', terToStr(terEquals(terMayBe,terFalse)), ' ', terToStr(terEquals(terFalse,terFalse)));
writeln;
end.
{{out}}
:> ./TernaryLogic
Ternary logic test:
NOT True Maybe False
False Maybe True
AND True Maybe False
True True Maybe False
Maybe Maybe Maybe False
False False False False
OR True Maybe False
True True True True
Maybe True Maybe Maybe
False True Maybe False
IFTHEN True Maybe False
True True Maybe False
Maybe True Maybe Maybe
False True True True
EQUAL True Maybe False
True True Maybe False
Maybe Maybe Maybe Maybe
False False Maybe True
Perl
File Trit.pm:
package Trit;
# -1 = false ; 0 = maybe ; 1 = true
use Exporter 'import';
our @EXPORT_OK = qw(TRUE FALSE MAYBE is_true is_false is_maybe);
our %EXPORT_TAGS = (
all => \@EXPORT_OK,
const => [qw(TRUE FALSE MAYBE)],
bool => [qw(is_true is_false is_maybe)],
);
use List::Util qw(min max);
use overload
'=' => sub { $_[0]->clone() },
'<=>'=> sub { $_[0]->cmp($_[1]) },
'cmp'=> sub { $_[0]->cmp($_[1]) },
'==' => sub { ${$_[0]} == ${$_[1]} },
'eq' => sub { $_[0]->equiv($_[1]) },
'>' => sub { ${$_[0]} > ${$_[1]} },
'<' => sub { ${$_[0]} < ${$_[1]} },
'>=' => sub { ${$_[0]} >= ${$_[1]} },
'<=' => sub { ${$_[0]} <= ${$_[1]} },
'|' => sub { $_[0]->or($_[1]) },
'&' => sub { $_[0]->and($_[1]) },
'!' => sub { $_[0]->not() },
'~' => sub { $_[0]->not() },
'""' => sub { $_[0]->tostr() },
'0+' => sub { $_[0]->tonum() },
;
sub new
{
my ($class, $v) = @_;
my $ret =
!defined($v) ? 0 :
$v eq 'true' ? 1 :
$v eq 'false'? -1 :
$v eq 'maybe'? 0 :
$v > 0 ? 1 :
$v < 0 ? -1 :
0;
return bless \$ret, $class;
}
sub TRUE() { new Trit( 1) }
sub FALSE() { new Trit(-1) }
sub MAYBE() { new Trit( 0) }
sub clone
{
my $ret = ${$_[0]};
return bless \$ret, ref($_[0]);
}
sub tostr { ${$_[0]} > 0 ? "true" : ${$_[0]} < 0 ? "false" : "maybe" }
sub tonum { ${$_[0]} }
sub is_true { ${$_[0]} > 0 }
sub is_false { ${$_[0]} < 0 }
sub is_maybe { ${$_[0]} == 0 }
sub cmp { ${$_[0]} <=> ${$_[1]} }
sub not { new Trit(-${$_[0]}) }
sub and { new Trit(min(${$_[0]}, ${$_[1]}) ) }
sub or { new Trit(max(${$_[0]}, ${$_[1]}) ) }
sub equiv { new Trit( ${$_[0]} * ${$_[1]} ) }
File test.pl:
use Trit ':all';
my @a = (TRUE(), MAYBE(), FALSE());
print "\na\tNOT a\n";
print "$_\t".(!$_)."\n" for @a; # Example of use of prefix operator NOT. Tilde ~ also can be used.
print "\nAND\t".join("\t",@a)."\n";
for my $a (@a) {
print $a;
for my $b (@a) {
print "\t".($a & $b); # Example of use of infix & (and)
}
print "\n";
}
print "\nOR\t".join("\t",@a)."\n";
for my $a (@a) {
print $a;
for my $b (@a) {
print "\t".($a | $b); # Example of use of infix | (or)
}
print "\n";
}
print "\nEQV\t".join("\t",@a)."\n";
for my $a (@a) {
print $a;
for my $b (@a) {
print "\t".($a eq $b); # Example of use of infix eq (equivalence)
}
print "\n";
}
print "\n==\t".join("\t",@a)."\n";
for my $a (@a) {
print $a;
for my $b (@a) {
print "\t".($a == $b); # Example of use of infix == (equality)
}
print "\n";
}
{{out}}
a NOT a
true false
maybe maybe
false true
AND true maybe false
true true maybe false
maybe maybe maybe false
false false false false
OR true maybe false
true true true true
maybe true maybe maybe
false true maybe false
EQV true maybe false
true true maybe false
maybe maybe maybe maybe
false false maybe true
== true maybe false
true 1
maybe 1
false 1
Perl 6
{{Works with|rakudo|2018.03}}
The precedence of each operator is specified as equivalent to an existing operator. We've taken the liberty of using a double arrow for implication, to avoid confusing it with ⊃, (U+2283 SUPERSET OF).
# Implementation:
enum Trit <Foo Moo Too>;
sub prefix:<¬> (Trit $a) { Trit(1-($a-1)) }
sub infix:<∧> (Trit $a, Trit $b) is equiv(&infix:<*>) { $a min $b }
sub infix:<∨> (Trit $a, Trit $b) is equiv(&infix:<+>) { $a max $b }
sub infix:<⇒> (Trit $a, Trit $b) is equiv(&infix:<..>) { ¬$a max $b }
sub infix:<≡> (Trit $a, Trit $b) is equiv(&infix:<eq>) { Trit(1 + ($a-1) * ($b-1)) }
# Testing:
say '¬';
say "Too {¬Too}";
say "Moo {¬Moo}";
say "Foo {¬Foo}";
sub tbl (&op,$name) {
say '';
say "$name Too Moo Foo";
say " ╔═══════════";
say "Too║{op Too,Too} {op Too,Moo} {op Too,Foo}";
say "Moo║{op Moo,Too} {op Moo,Moo} {op Moo,Foo}";
say "Foo║{op Foo,Too} {op Foo,Moo} {op Foo,Foo}";
}
tbl(&infix:<∧>, '∧');
tbl(&infix:<∨>, '∨');
tbl(&infix:<⇒>, '⇒');
tbl(&infix:<≡>, '≡');
say '';
say 'Precedence tests should all print "Too":';
say ~(
Foo ∧ Too ∨ Too ≡ Too,
Foo ∧ (Too ∨ Too) ≡ Foo,
Too ∨ Too ∧ Foo ≡ Too,
(Too ∨ Too) ∧ Foo ≡ Foo,
¬Too ∧ Too ∨ Too ≡ Too,
¬Too ∧ (Too ∨ Too) ≡ ¬Too,
Too ∨ Too ∧ ¬Too ≡ Too,
(Too ∨ Too) ∧ ¬Too ≡ ¬Too,
Foo ∧ Too ∨ Foo ⇒ Foo ≡ Too,
Foo ∧ Too ∨ Too ⇒ Foo ≡ Foo,
);
{{out}}
¬
Too Foo
Moo Moo
Foo Too
∧ Too Moo Foo
╔═══════════
Too║Too Moo Foo
Moo║Moo Moo Foo
Foo║Foo Foo Foo
∨ Too Moo Foo
╔═══════════
Too║Too Too Too
Moo║Too Moo Moo
Foo║Too Moo Foo
⇒ Too Moo Foo
╔═══════════
Too║Too Moo Foo
Moo║Too Moo Moo
Foo║Too Too Too
≡ Too Moo Foo
╔═══════════
Too║Too Moo Foo
Moo║Moo Moo Moo
Foo║Foo Moo Too
Precedence tests should all print "Too":
Too Too Too Too Too Too Too Too Too Too
Phix
enum type ternary T, M, F end type
function t_not(ternary a)
return F+1-a
end function
function t_and(ternary a, ternary b)
return iff(a=T and b=T?T:iff(a=F or b=F?F:M))
end function
function t_or(ternary a, ternary b)
return iff(a=T or b=T?T:iff(a=F and b=F?F:M))
end function
function t_xor(ternary a, ternary b)
return iff(a=M or b=M?M:iff(a=b?F:T))
end function
function t_implies(ternary a, ternary b)
return iff(a=F or b=T?T:iff(a=T and b=F?F:M))
end function
function t_equal(ternary a, ternary b)
return iff(a=M or b=M?M:iff(a=b?T:F))
end function
function t_string(ternary a)
return iff(a=T?"T":iff(a=M?"?":"F"))
end function
procedure show_truth_table(integer rid, integer unary, string name)
printf(1,"%-3s |%s\n",{name,iff(unary?"":" T | ? | F")})
printf(1,"----+---%s\n",{iff(unary?"":"+---+---")})
for x=T to F do
printf(1," %s ",{t_string(x)})
if unary then
printf(1," | %s",{t_string(call_func(rid,{x}))})
else
for y=T to F do
printf(1," | %s",{t_string(call_func(rid,{x,y}))})
end for
end if
printf(1,"\n")
end for
printf(1,"\n")
end procedure
show_truth_table(routine_id("t_not"),1,"not")
show_truth_table(routine_id("t_and"),0,"and")
show_truth_table(routine_id("t_or"),0,"or")
show_truth_table(routine_id("t_xor"),0,"xor")
show_truth_table(routine_id("t_implies"),0,"imp")
show_truth_table(routine_id("t_equal"),0,"eq")
{{out}}
not |
----+---
T | F
? | ?
F | T
and | T | ? | F
----+---+---+---
T | T | ? | F
? | ? | ? | F
F | F | F | F
or | T | ? | F
----+---+---+---
T | T | T | T
? | T | ? | ?
F | T | ? | F
xor | T | ? | F
----+---+---+---
T | F | ? | T
? | ? | ? | ?
F | T | ? | F
imp | T | ? | F
----+---+---+---
T | T | ? | F
? | T | ? | ?
F | T | T | T
eq | T | ? | F
----+---+---+---
T | T | ? | F
? | ? | ? | ?
F | F | ? | T
PHP
Save the sample code as executable shell script on your *nix system:
#!/usr/bin/php
<?php
# defined as numbers, so I can use max() and min() on it
if (! define('triFalse',0)) trigger_error('Unknown error defining!', E_USER_ERROR);
if (! define('triMaybe',1)) trigger_error('Unknown error defining!', E_USER_ERROR);
if (! define('triTrue', 2)) trigger_error('Unknown error defining!', E_USER_ERROR);
$triNotarray = array(triFalse=>triTrue, triMaybe=>triMaybe, triTrue=>triFalse);
# output helper
function triString ($tri) {
if ($tri===triFalse) return 'false ';
if ($tri===triMaybe) return 'unknown';
if ($tri===triTrue) return 'true ';
trigger_error('triString: parameter not a tri value', E_USER_ERROR);
}
function triAnd() {
if (func_num_args() < 2)
trigger_error('triAnd needs 2 or more parameters', E_USER_ERROR);
return min(func_get_args());
}
function triOr() {
if (func_num_args() < 2)
trigger_error('triOr needs 2 or more parameters', E_USER_ERROR);
return max(func_get_args());
}
function triNot($t) {
global $triNotarray; # using result table
if (in_array($t, $triNotarray)) return $triNotarray[$t];
trigger_error('triNot: Parameter is not a tri value', E_USER_ERROR);
}
function triImplies($a, $b) {
if ($a===triFalse || $b===triTrue) return triTrue;
if ($a===triMaybe || $b===triMaybe) return triMaybe;
# without parameter type check I just would return triFalse here
if ($a===triTrue && $b===triFalse) return triFalse;
trigger_error('triImplies: parameter type error', E_USER_ERROR);
}
function triEquiv($a, $b) {
if ($a===triTrue) return $b;
if ($a===triMaybe) return $a;
if ($a===triFalse) return triNot($b);
trigger_error('triEquiv: parameter type error', E_USER_ERROR);
}
# data sampling
printf("--- Sample output for a equivalent b ---\n\n");
foreach ([triTrue,triMaybe,triFalse] as $a) {
foreach ([triTrue,triMaybe,triFalse] as $b) {
printf("for a=%s and b=%s a equivalent b is %s\n",
triString($a), triString($b), triString(triEquiv($a, $b)));
}
}
Sample output:
--- Sample output for a equivalent b ---
for a=true and b=true a equivalent b is true
for a=true and b=unknown a equivalent b is unknown
for a=true and b=false a equivalent b is false
for a=unknown and b=true a equivalent b is unknown
for a=unknown and b=unknown a equivalent b is unknown
for a=unknown and b=false a equivalent b is unknown
for a=false and b=true a equivalent b is false
for a=false and b=unknown a equivalent b is unknown
for a=false and b=false a equivalent b is true
PicoLisp
In addition for the standard T (for "true") and NIL (for "false") we define 0 (zero, for "maybe").
(de 3not (A)
(or (=0 A) (not A)) )
(de 3and (A B)
(cond
((=T A) B)
((=0 A) (and B 0)) ) )
(de 3or (A B)
(cond
((=T A) T)
((=0 A) (or (=T B) 0))
(T B) ) )
(de 3impl (A B)
(cond
((=T A) B)
((=0 A) (or (=T B) 0))
(T T) ) )
(de 3equiv (A B)
(cond
((=T A) B)
((=0 A) 0)
(T (3not B)) ) )
Test:
(for X '(T 0 NIL)
(println 'not X '-> (3not X)) )
(for Fun '((and . 3and) (or . 3or) (implies . 3impl) (equivalent . 3equiv))
(for X '(T 0 NIL)
(for Y '(T 0 NIL)
(println X (car Fun) Y '-> ((cdr Fun) X Y)) ) ) )
{{out}}
not T -> NIL
not 0 -> 0
not NIL -> T
T and T -> T
T and 0 -> 0
T and NIL -> NIL
0 and T -> 0
0 and 0 -> 0
0 and NIL -> NIL
NIL and T -> NIL
NIL and 0 -> NIL
NIL and NIL -> NIL
T or T -> T
T or 0 -> T
T or NIL -> T
0 or T -> T
0 or 0 -> 0
0 or NIL -> 0
NIL or T -> T
NIL or 0 -> 0
NIL or NIL -> NIL
T implies T -> T
T implies 0 -> 0
T implies NIL -> NIL
0 implies T -> T
0 implies 0 -> 0
0 implies NIL -> 0
NIL implies T -> T
NIL implies 0 -> T
NIL implies NIL -> T
T equivalent T -> T
T equivalent 0 -> 0
T equivalent NIL -> NIL
0 equivalent T -> 0
0 equivalent 0 -> 0
0 equivalent NIL -> 0
NIL equivalent T -> NIL
NIL equivalent 0 -> 0
NIL equivalent NIL -> T
```
## Python
In Python, the keywords 'and', 'not', and 'or' are coerced to always work as boolean operators. I have therefore overloaded the boolean bitwise operators &, |, ^ to provide the required functionality.
```python
class Trit(int):
def __new__(cls, value):
if value == 'TRUE':
value = 1
elif value == 'FALSE':
value = 0
elif value == 'MAYBE':
value = -1
return super(Trit, cls).__new__(cls, value // (abs(value) or 1))
def __repr__(self):
if self > 0:
return 'TRUE'
elif self == 0:
return 'FALSE'
return 'MAYBE'
def __str__(self):
return repr(self)
def __bool__(self):
if self > 0:
return True
elif self == 0:
return False
else:
raise ValueError("invalid literal for bool(): '%s'" % self)
def __or__(self, other):
if isinstance(other, Trit):
return _ttable[(self, other)][1]
else:
try:
return _ttable[(self, Trit(bool(other)))][1]
except:
return NotImplemented
def __ror__(self, other):
if isinstance(other, Trit):
return _ttable[(self, other)][1]
else:
try:
return _ttable[(self, Trit(bool(other)))][1]
except:
return NotImplemented
def __and__(self, other):
if isinstance(other, Trit):
return _ttable[(self, other)][0]
else:
try:
return _ttable[(self, Trit(bool(other)))][0]
except:
return NotImplemented
def __rand__(self, other):
if isinstance(other, Trit):
return _ttable[(self, other)][0]
else:
try:
return _ttable[(self, Trit(bool(other)))][0]
except:
return NotImplemented
def __xor__(self, other):
if isinstance(other, Trit):
return _ttable[(self, other)][2]
else:
try:
return _ttable[(self, Trit(bool(other)))][2]
except:
return NotImplemented
def __rxor__(self, other):
if isinstance(other, Trit):
return _ttable[(self, other)][2]
else:
try:
return _ttable[(self, Trit(bool(other)))][2]
except:
return NotImplemented
def __invert__(self):
return _ttable[self]
def __getattr__(self, name):
if name in ('_n', 'flip'):
# So you can do x._n == x.flip; the inverse of x
# In Python 'not' is strictly boolean so we can't write `not x`
# Same applies to keywords 'and' and 'or'.
return _ttable[self]
else:
raise AttributeError
TRUE, FALSE, MAYBE = Trit(1), Trit(0), Trit(-1)
_ttable = {
# A: -> flip_A
TRUE: FALSE,
FALSE: TRUE,
MAYBE: MAYBE,
# (A, B): -> (A_and_B, A_or_B, A_xor_B)
(MAYBE, MAYBE): (MAYBE, MAYBE, MAYBE),
(MAYBE, FALSE): (FALSE, MAYBE, MAYBE),
(MAYBE, TRUE): (MAYBE, TRUE, MAYBE),
(FALSE, MAYBE): (FALSE, MAYBE, MAYBE),
(FALSE, FALSE): (FALSE, FALSE, FALSE),
(FALSE, TRUE): (FALSE, TRUE, TRUE),
( TRUE, MAYBE): (MAYBE, TRUE, MAYBE),
( TRUE, FALSE): (FALSE, TRUE, TRUE),
( TRUE, TRUE): ( TRUE, TRUE, FALSE),
}
values = ('FALSE', 'TRUE ', 'MAYBE')
print("\nTrit logical inverse, '~'")
for a in values:
expr = '~%s' % a
print(' %s = %s' % (expr, eval(expr)))
for op, ophelp in (('&', 'and'), ('|', 'or'), ('^', 'exclusive-or')):
print("\nTrit logical %s, '%s'" % (ophelp, op))
for a in values:
for b in values:
expr = '%s %s %s' % (a, op, b)
print(' %s = %s' % (expr, eval(expr)))
```
{{out}}
```txt
Trit logical inverse, '~'
~FALSE = TRUE
~TRUE = FALSE
~MAYBE = MAYBE
Trit logical and, '&'
FALSE & FALSE = FALSE
FALSE & TRUE = FALSE
FALSE & MAYBE = FALSE
TRUE & FALSE = FALSE
TRUE & TRUE = TRUE
TRUE & MAYBE = MAYBE
MAYBE & FALSE = FALSE
MAYBE & TRUE = MAYBE
MAYBE & MAYBE = MAYBE
Trit logical or, '|'
FALSE | FALSE = FALSE
FALSE | TRUE = TRUE
FALSE | MAYBE = MAYBE
TRUE | FALSE = TRUE
TRUE | TRUE = TRUE
TRUE | MAYBE = TRUE
MAYBE | FALSE = MAYBE
MAYBE | TRUE = TRUE
MAYBE | MAYBE = MAYBE
Trit logical exclusive-or, '^'
FALSE ^ FALSE = FALSE
FALSE ^ TRUE = TRUE
FALSE ^ MAYBE = MAYBE
TRUE ^ FALSE = TRUE
TRUE ^ TRUE = FALSE
TRUE ^ MAYBE = MAYBE
MAYBE ^ FALSE = MAYBE
MAYBE ^ TRUE = MAYBE
MAYBE ^ MAYBE = MAYBE
```
;Extra doodling in the Python shell:
```txt
>>> values = (TRUE, FALSE, MAYBE)
>>> for a in values:
for b in values:
assert (a & ~b) | (b & ~a) == a ^ b
>>>
```
## Racket
```racket
#lang typed/racket
; to avoid the hassle of adding a maybe value that is as special as
; the two standard booleans, we'll use symbols to make our own
(define-type trit (U 'true 'false 'maybe))
(: not (trit -> trit))
(define (not a)
(case a
[(true) 'false]
[(maybe) 'maybe]
[(false) 'true]))
(: and (trit trit -> trit))
(define (and a b)
(case a
[(false) 'false]
[(maybe) (case b
[(false) 'false]
[else 'maybe])]
[(true) (case b
[(true) 'true]
[(maybe) 'maybe]
[(false) 'false])]))
(: or (trit trit -> trit))
(define (or a b)
(case a
[(true) 'true]
[(maybe) (case b
[(true) 'true]
[else 'maybe])]
[(false) (case b
[(true) 'true]
[(maybe) 'maybe]
[(false) 'false])]))
(: ifthen (trit trit -> trit))
(define (ifthen a b)
(case b
[(true) 'true]
[(maybe) (case a
[(false) 'true]
[else 'maybe])]
[(false) (case a
[(true) 'false]
[(maybe) 'maybe]
[(false) 'true])]))
(: iff (trit trit -> trit))
(define (iff a b)
(case a
[(maybe) 'maybe]
[(true) b]
[(false) (not b)]))
(for: : Void ([a (in-list '(true maybe false))])
(printf "~a ~a = ~a~n" (object-name not) a (not a)))
(for: : Void ([proc (in-list (list and or ifthen iff))])
(for*: : Void ([a (in-list '(true maybe false))]
[b (in-list '(true maybe false))])
(printf "~a ~a ~a = ~a~n" a (object-name proc) b (proc a b))))
```
{{out}}
```txt
not true = false
not maybe = maybe
not false = true
true and true = true
true and maybe = maybe
true and false = false
maybe and true = maybe
maybe and maybe = maybe
maybe and false = false
false and true = false
false and maybe = false
false and false = false
true or true = true
true or maybe = true
true or false = true
maybe or true = true
maybe or maybe = maybe
maybe or false = maybe
false or true = true
false or maybe = maybe
false or false = false
true ifthen true = true
true ifthen maybe = maybe
true ifthen false = false
maybe ifthen true = true
maybe ifthen maybe = maybe
maybe ifthen false = maybe
false ifthen true = true
false ifthen maybe = true
false ifthen false = true
true iff true = true
true iff maybe = maybe
true iff false = false
maybe iff true = maybe
maybe iff maybe = maybe
maybe iff false = maybe
false iff true = false
false iff maybe = maybe
false iff false = true
```
## REXX
This REXX program is a re-worked version of the REXX program used for the Rosetta Code task: ''truth table''.
```rexx
/*REXX program displays a ternary truth table [true, false, maybe] for the variables */
/*──── and one or more expressions. */
/*──── Infix notation is supported with one character propositional constants. */
/*──── Variables (propositional constants) allowed: A ──► Z, a ──► z except u.*/
/*──── All propositional constants are case insensative (except lowercase v). */
parse arg $express /*obtain optional argument from the CL.*/
if $express\='' then do /*Got one? Then show user's expression*/
call truthTable $express /*display the user's truth table──►term*/
exit /*we're all done with the truth table. */
end
call truthTable "a & b ; AND"
call truthTable "a | b ; OR"
call truthTable "a ^ b ; XOR"
call truthTable "a ! b ; NOR"
call truthTable "a ¡ b ; NAND"
call truthTable "a xnor b ; XNOR" /*XNOR is the same as NXOR. */
exit /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
truthTable: procedure; parse arg $ ';' comm 1 $o; $o=strip($o)
$=translate(strip($), '|', "v"); $u=$; upper $u
$u=translate($u, '()()()', "[]{}«»"); $$.=0; PCs=; hdrPCs=
@abc= 'abcdefghijklmnopqrstuvwxyz'; @abcU=@abc; upper @abcU
@= 'ff'x /*─────────infix operators───────*/
op.= /*a single quote (') wasn't */
/* implemented for negation. */
op.0 = 'false boolFALSE' /*unconditionally FALSE */
op.1 = 'and and & *' /* AND, conjunction */
op.2 = 'naimpb NaIMPb' /*not A implies B */
op.3 = 'boolb boolB' /*B (value of) */
op.4 = 'nbimpa NbIMPa' /*not B implies A */
op.5 = 'boola boolA' /*A (value of) */
op.6 = 'xor xor && % ^' /* XOR, exclusive OR */
op.7 = 'or or | + v' /* OR, disjunction */
op.8 = 'nor nor ! ↓' /* NOR, not OR, Pierce operator */
op.9 = 'xnor xnor nxor' /*NXOR, not exclusive OR, not XOR*/
op.10 = 'notb notB' /*not B (value of) */
op.11 = 'bimpa bIMPa' /* B implies A */
op.12 = 'nota notA' /*not A (value of) */
op.13 = 'aimpb aIMPb' /* A implies B */
op.14 = 'nand nand ¡ ↑' /*NAND, not AND, Sheffer operator*/
op.15 = 'true boolTRUE' /*unconditionally TRUE */
/*alphabetic names need changing.*/
op.16 = '\ NOT ~ ─ . ¬' /* NOT, negation */
op.17 = '> GT' /*conditional greater than */
op.18 = '>= GE ─> => ──> ==>' "1a"x /*conditional greater than or eq.*/
op.19 = '< LT' /*conditional less than */
op.20 = '<= LE <─ <= <── <==' /*conditional less then or equal */
op.21 = '\= NE ~= ─= .= ¬=' /*conditional not equal to */
op.22 = '= EQ EQUAL EQUALS =' "1b"x /*biconditional (equals) */
op.23 = '0 boolTRUE' /*TRUEness */
op.24 = '1 boolFALSE' /*FALSEness */
op.25 = 'NOT NOT NEG' /*not, neg (negative) */
do jj=0 while op.jj\=='' | jj<16 /*change opers──►what REXX likes.*/
new=word(op.jj,1)
do kk=2 to words(op.jj) /*handle each token separately. */
_=word(op.jj, kk); upper _
if wordpos(_, $u)==0 then iterate /*no such animal in this string. */
if datatype(new, 'm') then new!=@ /*expresion needs transcribing. */
else new!=new
$u=changestr(_, $u, new!) /*transcribe the function (maybe)*/
if new!==@ then $u=changeFunc($u, @, new) /*use the internal boolean name. */
end /*kk*/
end /*jj*/
$u=translate($u, '()', "{}") /*finish cleaning up transcribing*/
do jj=1 for length(@abcU) /*see what variables are used. */
_=substr(@abcU, jj, 1) /*use available upercase alphabet*/
if pos(_,$u)==0 then iterate /*found one? No, keep looking. */
$$.jj=2 /*found: set upper bound for it.*/
PCs=PCs _ /*also, add to propositional cons*/
hdrPCs=hdrPCS center(_, length('false')) /*build a propositional cons hdr.*/
end /*jj*/
$u=PCs '('$u")" /*sep prop. cons. from expression*/
ptr='_────►_' /*a pointer for the truth table. */
hdrPCs=substr(hdrPCs,2) /*create a header for prop. cons.*/
say hdrPCs left('', length(ptr) -1) $o /*show prop cons hdr +expression.*/
say copies('───── ', words(PCs)) left('', length(ptr)-2) copies('─', length($o))
/*Note: "true"s: right─justified*/
do a=0 to $$.1
do b=0 to $$.2
do c=0 to $$.3
do d=0 to $$.4
do e=0 to $$.5
do f=0 to $$.6
do g=0 to $$.7
do h=0 to $$.8
do i=0 to $$.9
do j=0 to $$.10
do k=0 to $$.11
do l=0 to $$.12
do m=0 to $$.13
do n=0 to $$.14
do o=0 to $$.15
do p=0 to $$.16
do q=0 to $$.17
do r=0 to $$.18
do s=0 to $$.19
do t=0 to $$.20
do u=0 to $$.21
do !=0 to $$.22
do w=0 to $$.23
do x=0 to $$.24
do y=0 to $$.25
do z=0 to $$.26
interpret '_=' $u /*evaluate truth T.*/
_=changestr(0, _, 'false') /*convert 0──►false*/
_=changestr(1, _, '_true') /*convert 1──►_true*/
_=changestr(2, _, 'maybe') /*convert 2──►maybe*/
_=insert(ptr, _, wordindex(_, words(_)) -1) /*──►*/
say translate(_, , '_') /*display truth tab*/
end /*z*/
end /*y*/
end /*x*/
end /*w*/
end /*v*/
end /*u*/
end /*t*/
end /*s*/
end /*r*/
end /*q*/
end /*p*/
end /*o*/
end /*n*/
end /*m*/
end /*l*/
end /*k*/
end /*j*/
end /*i*/
end /*h*/
end /*g*/
end /*f*/
end /*e*/
end /*d*/
end /*c*/
end /*b*/
end /*a*/
say
return
/*──────────────────────────────────────────────────────────────────────────────────────*/
scan: procedure; parse arg x,at; L=length(x); t=L; lp=0; apost=0; quote=0
if at<0 then do; t=1; x= translate(x, '()', ")("); end
do j=abs(at) to t by sign(at); _=substr(x,j,1); __=substr(x,j,2)
if quote then do; if _\=='"' then iterate
if __=='""' then do; j=j+1; iterate; end
quote=0; iterate
end
if apost then do; if _\=="'" then iterate
if __=="''" then do; j=j+1; iterate; end
apost=0; iterate
end
if _=='"' then do; quote=1; iterate; end
if _=="'" then do; apost=1; iterate; end
if _==' ' then iterate
if _=='(' then do; lp=lp+1; iterate; end
if lp\==0 then do; if _==')' then lp=lp-1; iterate; end
if datatype(_,'U') then return j - (at<0)
if at<0 then return j + 1
end /*j*/
return min(j,L)
/*──────────────────────────────────────────────────────────────────────────────────────*/
changeFunc: procedure; parse arg z,fC,newF; funcPos= 0
do forever
funcPos= pos(fC, z, funcPos + 1); if funcPos==0 then return z
origPos= funcPos
z= changestr(fC, z, ",'"newF"',")
funcPos= funcPos + length(newF) + 4
where= scan(z, funcPos) ; z= insert( '}', z, where)
where= scan(z, 1 - origPos) ; z= insert('trit{', z, where)
end /*forever*/
/*──────────────────────────────────────────────────────────────────────────────────────*/
trit: procedure; arg a,$,b; v= \(a==2 | b==2); o= (a==1 | b==1); z= (a==0 | b==0)
select
when $=='FALSE' then return 0
when $=='AND' then if v then return a & b; else return 2
when $=='NAIMPB' then if v then return \(\a & \b); else return 2
when $=='BOOLB' then return b
when $=='NBIMPA' then if v then return \(\b & \a); else return 2
when $=='BOOLA' then return a
when $=='XOR' then if v then return a && b ; else return 2
when $=='OR' then if v then return a | b ; else if o then return 1
else return 2
when $=='NOR' then if v then return \(a | b) ; else return 2
when $=='XNOR' then if v then return \(a && b) ; else return 2
when $=='NOTB' then if v then return \b ; else return 2
when $=='NOTA' then if v then return \a ; else return 2
when $=='AIMPB' then if v then return \(a & \b) ; else return 2
when $=='NAND' then if v then return \(a & b) ; else if z then return 1
else return 2
when $=='TRUE' then return 1
otherwise return -13 /*error, unknown function.*/
end /*select*/
```
Some older REXXes don't have a '''changestr''' BIF, so one is included here ──► [[CHANGESTR.REX]].
'''output'''
```txt
A B a & b ; AND
───── ───── ───────────
false false ────► false
false true ────► false
false maybe ────► maybe
true false ────► false
true true ────► true
true maybe ────► maybe
maybe false ────► maybe
maybe true ────► maybe
maybe maybe ────► maybe
A B a | b ; OR
───── ───── ──────────
false false ────► false
false true ────► true
false maybe ────► maybe
true false ────► true
true true ────► true
true maybe ────► true
maybe false ────► maybe
maybe true ────► true
maybe maybe ────► maybe
A B a ^ b ; XOR
───── ───── ───────────
false false ────► false
false true ────► true
false maybe ────► maybe
true false ────► true
true true ────► false
true maybe ────► maybe
maybe false ────► maybe
maybe true ────► maybe
maybe maybe ────► maybe
A B a ! b ; NOR
───── ───── ───────────
false false ────► true
false true ────► false
false maybe ────► maybe
true false ────► false
true true ────► false
true maybe ────► maybe
maybe false ────► maybe
maybe true ────► maybe
maybe maybe ────► maybe
A B a ¡ b ; NAND
───── ───── ────────────
false false ────► true
false true ────► true
false maybe ────► true
true false ────► true
true true ────► false
true maybe ────► maybe
maybe false ────► true
maybe true ────► maybe
maybe maybe ────► maybe
A B a xnor b ; XNOR
───── ───── ───────────────
false false ────► true
false true ────► false
false maybe ────► maybe
true false ────► false
true true ────► true
true maybe ────► maybe
maybe false ────► maybe
maybe true ────► maybe
maybe maybe ────► maybe
```
## Ruby
Ruby, like Smalltalk, has two boolean classes: TrueClass for true and FalseClass for false. We add a third class, MaybeClass for MAYBE, and define ternary logic for all three classes.
We keep !a, a & b and so on for binary logic. We add !a.trit, a.trit & b and so on for ternary logic. The code for !a.trit uses def !, which works with Ruby 1.9, but fails as a syntax error with Ruby 1.8.
{{works with|Ruby|1.9}}
```ruby
# trit.rb - ternary logic
# http://rosettacode.org/wiki/Ternary_logic
require 'singleton'
# MAYBE, the only instance of MaybeClass, enables a system of ternary
# logic using TrueClass#trit, MaybeClass#trit and FalseClass#trit.
#
# !a.trit # ternary not
# a.trit & b # ternary and
# a.trit | b # ternary or
# a.trit ^ b # ternary exclusive or
# a.trit == b # ternary equal
#
# Though +true+ and +false+ are internal Ruby values, +MAYBE+ is not.
# Programs may want to assign +maybe = MAYBE+ in scopes that use
# ternary logic. Then programs can use +true+, +maybe+ and +false+.
class MaybeClass
include Singleton
# maybe.to_s # => "maybe"
def to_s; "maybe"; end
end
MAYBE = MaybeClass.instance
class TrueClass
TritMagic = Object.new
class << TritMagic
def index; 0; end
def !; false; end
def & other; other; end
def | other; true; end
def ^ other; [false, MAYBE, true][other.trit.index]; end
def == other; other; end
end
# Performs ternary logic. See MaybeClass.
# !true.trit # => false
# true.trit & obj # => obj
# true.trit | obj # => true
# true.trit ^ obj # => false, maybe or true
# true.trit == obj # => obj
def trit; TritMagic; end
end
class MaybeClass
TritMagic = Object.new
class << TritMagic
def index; 1; end
def !; MAYBE; end
def & other; [MAYBE, MAYBE, false][other.trit.index]; end
def | other; [true, MAYBE, MAYBE][other.trit.index]; end
def ^ other; MAYBE; end
def == other; MAYBE; end
end
# Performs ternary logic. See MaybeClass.
# !maybe.trit # => maybe
# maybe.trit & obj # => maybe or false
# maybe.trit | obj # => true or maybe
# maybe.trit ^ obj # => maybe
# maybe.trit == obj # => maybe
def trit; TritMagic; end
end
class FalseClass
TritMagic = Object.new
class << TritMagic
def index; 2; end
def !; true; end
def & other; false; end
def | other; other; end
def ^ other; other; end
def == other; [false, MAYBE, true][other.trit.index]; end
end
# Performs ternary logic. See MaybeClass.
# !false.trit # => true
# false.trit & obj # => false
# false.trit | obj # => obj
# false.trit ^ obj # => obj
# false.trit == obj # => false, maybe or true
def trit; TritMagic; end
end
```
This IRB session shows ternary not, and, or, equal.
```ruby
$ irb
irb(main):001:0> require './trit'
=> true
irb(main):002:0> maybe = MAYBE
=> maybe
irb(main):003:0> !true.trit
=> false
irb(main):004:0> !maybe.trit
=> maybe
irb(main):005:0> maybe.trit & false
=> false
irb(main):006:0> maybe.trit | true
=> true
irb(main):007:0> false.trit == true
=> false
irb(main):008:0> false.trit == maybe
=> maybe
```
This program shows all 9 outcomes from a.trit ^ b.
```ruby
require 'trit'
maybe = MAYBE
[true, maybe, false].each do |a|
[true, maybe, false].each do |b|
printf "%5s ^ %5s => %5s\n", a, b, a.trit ^ b
end
end
```
```txt
$ ruby -I. trit-xor.rb
true ^ true => false
true ^ maybe => maybe
true ^ false => true
maybe ^ true => maybe
maybe ^ maybe => maybe
maybe ^ false => maybe
false ^ true => true
false ^ maybe => maybe
false ^ false => false
```
## Run BASIC
```runbasic
testFalse = 0 ' F
testDoNotKnow = 1 ' ?
testTrue = 2 ' T
print "Short and long names for ternary logic values"
for i = testFalse to testTrue
print shortName3$(i);" ";longName3$(i)
next i
print
print "Single parameter functions"
print "x";" ";"=x";" ";"not(x)"
for i = testFalse to testTrue
print shortName3$(i);" ";shortName3$(i);" ";shortName3$(not3(i))
next
print
print "Double parameter fuctions"
html "| x | y | x AND y | x OR y | x EQ y | x XOR y |
| " html shortName3$(a); " | ";shortName3$(b); " | " html shortName3$(and3(a,b));" | ";shortName3$(or3(a,b)); " | " html shortName3$(eq3(a,b)); " | ";shortName3$(xor3(a,b));" |
| x | y | x AND y | x OR y | x EQ y | x XOR y |
| F | F | F | F | T | F |
| F | ? | F | ? | F | T |
| F | T | F | T | F | T |
| ? | F | F | ? | F | T |
| ? | ? | ? | ? | T | F |
| ? | T | ? | T | F | T |
| T | F | F | T | F | T |
| T | ? | ? | T | F | T |
| T | T | T | T | T | F |