How to resolve the algorithm Ternary logic step by step in the Perl programming language

Published on 12 May 2024 09:40 PM

How to resolve the algorithm Ternary logic step by step in the Perl programming language

Table of Contents

Problem Statement

In logic, a three-valued logic (also trivalent, ternary, or trinary logic, sometimes abbreviated 3VL) is any of several many-valued logic systems in which there are three truth values indicating true, false and some indeterminate third value.
This is contrasted with the more commonly known bivalent logics (such as classical sentential or boolean logic) which provide only for true and false. Conceptual form and basic ideas were initially created by Łukasiewicz, Lewis and Sulski. These were then re-formulated by Grigore Moisil in an axiomatic algebraic form, and also extended to n-valued logics in 1945.

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

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Ternary logic step by step in the Perl programming language

Source code in the perl programming language

use v5.36;

package Trit;
use List::Util qw(min max);

our @ISA = qw(Exporter);
our @EXPORT = qw(%E);

my %E = (true => 1, false => -1, maybe => 0);

use overload
'<=>' => sub ($a,$b)       { $a->cmp($b)   },
'cmp' => sub ($a,$b)       { $a->cmp($b)   },
'=='  => sub ($a,$b,$)     { $$a == $$b    },
'eq'  => sub ($a,$b,$)     { $a->equiv($b) },
'>'   => sub ($a,$b,$)     { $$a >  $E{$b} },
'<'   => sub ($a,$b,$)     { $$a <  $E{$b} },
'>='  => sub ($a,$b,$)     { $$a >= $$b    },
'<='  => sub ($a,$b,$)     { $$a <= $$b    },
'|'   => sub ($a,$b,$,$,$) { $a->or($b)    },
'&'   => sub ($a,$b,$,$,$) { $a->and($b)   },
'!'   => sub ($a,$,$)      { $a->not()     },
'~'   => sub ($a,$,$,$,$)  { $a->not()     },
'neg' => sub ($a,$,$)      { -$$a          },
'""'  => sub ($a,$,$)      { $a->tostr()   },
'0+'  => sub ($a,$,$)      { $a->tonum()   },
;

sub eqv ($a,$b) {
    $$a == $E{maybe} || $E{$b} == $E{maybe} ? $E{maybe} :       # either arg 'maybe', return 'maybe'
    $$a == $E{false} && $E{$b} == $E{false} ? $E{true}  :       #  both args 'false', return 'true'
                                              min $$a, $E{$b}   # either arg 'false', return 'false', otherwise 'true'
}

# do tests in a manner that avoids overloaded operators
sub new ($class, $v) {
    my $value =
        ! defined $v    ? $E{maybe} :
        $v =~ /true/    ? $E{true}  :
        $v =~ /false/   ? $E{false} :
        $v =~ /maybe/   ? $E{maybe} :
        $v gt $E{maybe} ? $E{true}  :
        $v lt $E{maybe} ? $E{false} :
                          $E{maybe} ;
    bless \$value, $class;
}

sub tostr ($a) { $$a > $E{maybe} ? 'true' : $$a < $E{maybe} ? 'false' : 'maybe' }
sub tonum ($a) { $$a }

sub not   ($a)    { Trit->new( -$a        ) }
sub cmp   ($a,$b) { Trit->new( $a <=> $b  ) }
sub and   ($a,$b) { Trit->new( min $a, $b ) }
sub or    ($a,$b) { Trit->new( max $a, $b ) }
sub equiv ($a,$b) { Trit->new( eqv $a, $b ) }

package main;
Trit->import;

my @a = ( Trit->new($E{true}), Trit->new($E{maybe}), Trit->new($E{false}) );
printf "Codes for logic values: %6s = %d %6s = %d %6s = %d\n", @a[0, 0, 1, 1, 2, 2];

# prefix ! (not) ['~' also can be used]
say "\na\tNOT a";
print "$_\t".(!$_)."\n" for @a;

# infix & (and)
say "\nAND\t" . join("\t",@a);
for my $a (@a) { print $a; print "\t" . ($a & $_)  for @a; say '' }

# infix | (or)
say "\nOR\t" . join("\t",@a);
for my $a (@a) { print $a; print "\t" . ($a | $_)  for @a; say '' }

# infix eq (equivalence)
say "\nEQV\t" . join("\t",@a);
for my $a (@a) { print $a; print "\t" . ($a eq $_) for @a; say '' }

# infix == (equality)
say "\n==\t" . join("\t",@a);
for my $a (@a) { print $a; print "\t" . ($a == $_) for @a; say '' }


  

You may also check:How to resolve the algorithm Loops/With multiple ranges step by step in the Arturo programming language
You may also check:How to resolve the algorithm Arithmetic-geometric mean step by step in the Julia programming language
You may also check:How to resolve the algorithm Window creation step by step in the GUISS programming language
You may also check:How to resolve the algorithm Apply a callback to an array step by step in the ALGOL W programming language
You may also check:How to resolve the algorithm Filter step by step in the Scheme programming language