#!/usr/bin/perl -w
use strict;
use warnings;

# ====================================================================
+==========
# Fixpoint
# f(x): x -> (('x)('x))
# In LISP: 
# define (f x)
#    let y [be] cons "' cons x nil [y is ('x) ]
#    [return] cons y cons y nil    [return (('x)('x))]

# In Perl:
my $f = sub { my $x = $_[0]; return "$x('$x')"; };

print &$f('x'), "\n";
print &$f('&$f'), "\n";
print eval &$f('&$f'), "\n";
print eval eval eval eval eval &$f('&$f'), "\n";
print '&$f(\'&$f\')' eq eval eval eval eval eval &$f('&$f'), "\n";

# Run :
# x('x')
# &$f('&$f')
# &$f('&$f')
# &$f('&$f')
# 1


# ====================================================================
+==========
# Gödel
# g(x): x -> (is-unprovable (value-of (('x)('x))))]
# In LISP:
# define (g x) 
#   let (L x y) cons x cons y nil  [Makes x and y into list]
#   (L is-unprovable 
#   (L value-of (L (L "' x) (L "' x))))

# In Perl:
my $is_unprovable = '$is_unprovable';
my $value_of      = '$value_of';
sub cadr { return ($_[0]) =~ /\(\'(.*)\'\)/; };

my $L = sub {  my ($x, $y) = @_; return "$x('$y')"; };
my $g = sub {  my $x = $_[0];
               &$L($is_unprovable, &$L($value_of, "$x('$x')")); };

print '&$g(\'x\')   -> ', &$g('x'), "\n";
print '&$g(\'&$g\') -> ', &$g('&$g'), "\n";
print cadr cadr &$g('&$g'), "\n";
print eval cadr cadr &$g('&$g'), "\n";    ### expected return:
                                          ### $is_unprovable('$value_o
+f('&$g('&$g')')')
#"\n", &$g('&$g') eq eval cadr cadr &$g('&$g');

# Run :
# &$g('x')   -> $is_unprovable('$value_of('x('x')')')
# &$g('&$g') -> $is_unprovable('$value_of('&$g('&$g')')')
# &$g('&$g')
# 1                                       ### but it returns 1 ???
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