#!/usr/bin/perl -w

#   Author: Paul Fitzpatrick, paulfitz@ai.mit.edu
#   Copyright (c) 2003 Paul Fitzpatrick
#
#   This file is part of CosmicOS.
#
#   CosmicOS is free software; you can redistribute it and/or modify
#   it under the terms of the GNU General Public License as published by
#   the Free Software Foundation; either version 2 of the License, or
#   (at your option) any later version.
#
#   CosmicOS is distributed in the hope that it will be useful,
#   but WITHOUT ANY WARRANTY; without even the implied warranty of
#   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
#   GNU General Public License for more details.
#
#   You should have received a copy of the GNU General Public License
#   along with CosmicOS; if not, write to the Free Software
#   Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA




use strict;

my %token;

# library of tokens (symbol sequences) used for designer's convenience.
# make sure names are uniquely decodable, or put in spaces!

$token{";"} = "7\n";   # end of line -- not strictly necessary
$token{" "} = "";      # whitespace is ignored - no translation
$token{"\n"} = "";
$token{"\r"} = "";
$token{"\t"} = "";
$token{"0"} = "0";     # zero      - constant zero
$token{"."} = "1";     # increment - add one
$token{":"} = "2";     # double    - multiply by two
$token{"("} = "3";
$token{")"} = "4";
$token{"?"} = "5";     # lambda
$token{"^"} = "6";     # identifier

sub irand {
  return int(rand(shift));
};

sub prand {
  my $top = shift;
  my $crop = $top;
  if ($#_>=0)
    {
      $crop = shift;
    }
  my @lst = (0 .. ($top-1));
  my @lst_out = ();
  for (my $i=$top; $i>0; $i--)
    {
      my $sel = irand($i);
      push(@lst_out,$lst[$sel]);
      if ($sel<$i-1)
	{
	  $lst[$sel] = $lst[$i-1];
	}
    }
  if ($crop<$top)
    {
      @lst_out = @lst_out[0 .. ($crop-1)];
    }
  return @lst_out;
};


sub Tokens2Msg {
  my $msg = "";
  foreach my $t (@_)
    {
      if (!($t =~ /\[/))
	{
	  $msg .= $token{$t};
	}
    }
  return $msg;
};

my $first_high = 0;
my %translate_high;
my %translate_back;

sub Text2Tokens {
  my $txt = shift;
  my $base = 0;
  my @tokens = ();
  $txt =~ s/\#.*//g;
  #$txt =~ s/\[[^\]]*\]//g;
  while ($txt =~ /([a-zA-Z_\+\*\-\/\=\>\<\!][a-zA-Z_\+\*\-\/\=\>\<\!0-9]*)/)
    {
      my $x = $1;
      my $qx = quotemeta($x);
      if (!defined($translate_high{$x}))
	{
	  $translate_high{$x} = "^$first_high";
	  $translate_back{$first_high} = $x;
	  $first_high++;
	}
      my $qy = $translate_high{$x};
      $txt =~ s/$qx/$qy/;
    }
  while ($txt =~ /([1-9][0-9]*)/)
    {
      my $n = $1;
      my $t = ShowBinaryVerbose($n);
      $txt =~ s/$n/$t/;
    }
  while ($txt =~ /(\{\^([^\}]*)\})/)
    {
      my $x = $1;
      my $qy = $2;
      my $qx = quotemeta($x);
      $txt =~ s/$qx/$qy/g;
#      print "$qx -> $qy\n";
#      die;
    }
  my $line = 0;
  #print "MESSAGE before tokenizing is:\n$txt\n";
  for (my $i=0; $i<length($txt); $i++)
    {
      if (substr($txt,$i,1) eq "\n")
	{
	  $line++;
	  push(@tokens,"[$line]");
	}
      my $tok = substr($txt,$base,$i-$base+1);
      if (defined($token{$tok}))
	{
	  push(@tokens,$tok);
	  $base = $i+1;
	}
      elsif ($tok =~ /^\#.*\n/)
	{
	  $base = $i+1;
	}
    }
  return @tokens;
};

sub EvalBinary {
  my $txt = shift;
  my $x = 0;
  for (my $i=length($txt)-2; $i>=0; $i--)
    {
      my $ch = substr($txt,$i,1);
      if ($ch eq ":") { $x *= 2; }
      if ($ch eq ".") { $x += 1; }
    }
  return $x;
};

sub Decompile {
  # decompile a message to make sure it is sane;
  my $txt = shift;
  my $src = "";
  
  my %detoken;

  foreach my $k (keys %token)
    {
      $detoken{$token{$k}} = $k;
    }
  $detoken{'7'} = ";\n";

  for (my $i=0; $i<length($txt); $i++)
    {
      my $ch = substr($txt,$i,1);
      if (defined($detoken{$ch}))
	{
	  $src .= $detoken{$ch};
	  #print "token $ch -> $detoken{$ch}\n";
	}
    }
  while ($src =~ /\^([\:\.]*0)/)
    {
      my $t = $1;
      my $q = quotemeta($t);
      my $n = EvalBinary($t);
      my $id = $translate_back{$n};
      $src =~ s/\^$q/ $id /g;
    }
  while ($src =~ /[^\:\.]([\:\.]+0)/)
    {
      my $t = $1;
      my $q = quotemeta($t);
      my $n = EvalBinary($t);
      $src =~ s/([^\:\.])$q/$1 $n /g;
    }

  return $src;
};


sub ShowUnary {
  my $txt = "0";
  my $ct = shift;
  for (my $i=0; $i<$ct; $i++)
    {
      $txt = "." . $txt;
    }
  return $txt;
};


sub ShowBinary {
  my $txt = "";
  my $i = shift;
  $txt .= "[$i]";
  return $txt;
};


sub ShowBinaryVerbose {
  my $txt = "0";
  my $i = shift;
  my $val = $i;
  if ($i>0)
    {
      my $p = int(log($val)/log(2));
      for (my $j=$p; $j>=0; $j--)
	{
	  if ($j<$p)
	    {
	      $txt = ":" . $txt;
	    }
	  if ($val>=(2**$j))
	    {
		  $txt = "." . $txt;
		  $val -= (2**$j);
		}
	}
    }
#  $txt .= "[$i]";
  return $txt;
};

sub ShowTerm {
  return join(" ",@_);
};

sub Paren {
  return "(" . ShowTerm(@_) . ")";
};

sub ShowLine {
  return ShowTerm(@_) . ";\n";
};


sub Op1 {
  my $cmp = shift;
  my $o1 = shift;
  return Paren($cmp, $o1);
};

sub BareOp1 {
  my $cmp = shift;
  my $o1 = shift;
  return "$cmp$o1";
};

sub Op2 {
  my $cmp = shift;
  my $o1 = shift;
  my $o2 = shift;
  return Paren($cmp, $o1, $o2);
};

sub Op {
  return Paren(@_);
};


sub Lit {
  my $x = shift;
  return $x;
};

sub Tag {
  my $x = shift;
  return "{$x}";
};

sub Num {
  my $x = shift;
  return "$x";
};

sub Proc {
  return Paren("?", @_);
};

sub ProcMultiple {
  my $plist = shift;
  my @args = @$plist;
  my $txt = "";
  foreach my $arg (@args)
    {
      $txt .= "?" . $arg;
    }
  return Paren($txt, @_);
};

sub Apply {
  return Paren(@_);
};


sub ShowUnaryLesson {
  my $txt = "";

  $txt .= "# MATH introduce numbers (in unary notation)\n";
  for (my $i=0; $i<=27; $i++)
    {
      $txt .= ShowLine(Op("intro",ShowUnary($i)));
    }
  
  for (my $i=27; $i>=0; $i--)
    {
      $txt .= ShowLine(Op("intro",ShowUnary($i)));
    }

  foreach my $i (0, 1, 2, 3, 5, 7, 11, 13, 17, 19, 23)
    {
      $txt .= ShowLine(Op("intro",ShowUnary($i)));
    }

  foreach my $i (0, 1, 4, 9, 16, 25)
    {
      $txt .= ShowLine(Op("intro",ShowUnary($i)));
    }

  foreach my $i (0, 1, 8, 27)
    {
      $txt .= ShowLine(Op("intro",ShowUnary($i)));
    }


  $txt .= "# MATH now show equality\n";

  $txt .= ShowLine(Op("intro","="));
  my @examples = prand(10,5);
  for (my $i=0; $i<=$#examples; $i++)
    {
      my $r = $examples[$i];
      $txt .= ShowLine(Op2("=",ShowUnary($r),ShowUnary($r)));
    }

  $txt .= "# MATH now show other relational operators\n";

  $txt .= ShowLine(Op("intro",">"));
  for (my $i=0; $i<=10; $i++)
    {
      my $r = irand(6);
      my $r2 = irand($r);
      $txt .= ShowLine(Op2(">",ShowUnary($r+1),ShowUnary($r2)));
    }
  $txt .= ShowLine(Op("intro","<"));
  for (my $i=0; $i<=10; $i++)
    {
      my $r = irand(6);
      my $r2 = irand($r);
      $txt .= ShowLine(Op2("<",ShowUnary($r2),ShowUnary($r+1)));
    }
  for (my $i=0; $i<=10; $i++)
    {
      my $r = irand(6);
      my $r2 = irand(6);
      my $cmp = "=";
      if ($r>$r2)
	{
	  $cmp = ">";
	}
      elsif ($r<$r2)
	{
	  $cmp = "<";
	}
      $txt .= ShowLine(Op2($cmp,ShowUnary($r),ShowUnary($r2)));
    }

  return $txt;
};




sub ShowNotLogicLesson {
  my $txt = "";
  $txt .= "# MATH introduce the NOT logical operator\n";
  $txt .= ShowLine(Op("intro","not"));
  for (my $i=0; $i<=5; $i++)
    {
      my $r = irand(6);
      $txt .= ShowLine(Op2("=",ShowUnary($r),ShowUnary($r)));
      $txt .= ShowLine(Op1("not",Op2("<",ShowUnary($r),ShowUnary($r))));
      $txt .= ShowLine(Op1("not",Op2(">",ShowUnary($r),ShowUnary($r))));
    }
  for (my $i=0; $i<=5; $i++)
    {
      my $r = irand(6);
      my $r2 = $r+1+irand(3);
      $txt .= ShowLine(Op1("not",Op2("=",ShowUnary($r),ShowUnary($r2))));
      $txt .= ShowLine(Op1("<",ShowUnary($r),ShowUnary($r2)));
      $txt .= ShowLine(Op1("not",Op2(">",ShowUnary($r),ShowUnary($r2))));
    }
  for (my $i=0; $i<=5; $i++)
    {
      my $r = irand(6);
      my $r2 = $r+1+irand(3);
      $txt .= ShowLine(Op1("not",Op2("=",ShowUnary($r2),ShowUnary($r))));
      $txt .= ShowLine(Op2(">",ShowUnary($r2),ShowUnary($r)));
      $txt .= ShowLine(Op1("not",Op2("<",ShowUnary($r2),ShowUnary($r))));
    }

  return $txt;
};




sub ShowTrueComparison {
  my $txt = "";
  my $c = irand(3);
  if ($c==0)
    {
      my $r = irand(6);
      $txt .= Op2("=",ShowUnary($r),ShowUnary($r));
    }
  elsif ($c==1)
    {
      my $r = irand(6);
      my $r2 = $r+1+irand(3);
      $txt .= Op2("<",ShowUnary($r),ShowUnary($r2));
    }
  else
    {
      my $r = irand(6);
      my $r2 = $r+1+irand(3);
      $txt .= Op2(">",ShowUnary($r2),ShowUnary($r));
    }

  return $txt;
}



sub ShowFalseComparison {
  my $txt = "";
  my $c = irand(3);
  if ($c==0)
    {
      my $r = irand(6);
      my $r2 = irand(6);
      if ($r == $r2)
	{
	  if(irand(2)==1)
	    {
	      $r++;
	    }
	  else
	    {
	      $r2++;
	    }
	}
      $txt .= Op2("=",ShowUnary($r),ShowUnary($r2));
    }
  else
    {
      my $r = irand(7);
      my $r2 = irand(7);
      my $cmp = ">";
      if ($r>$r2)
	{
	  $cmp = "<";
	}
      else
	{
	  $cmp = ">";
	}
      $txt .= Op2($cmp,ShowUnary($r),ShowUnary($r2));      
    }

  return $txt;
}



sub ShowAndLogicLesson {
  my $txt = "";
  $txt .= "# MATH introduce the AND logical operator\n";
  
  $txt .= ShowLine(Op("intro","and"));
  for (my $i=0; $i<10; $i++)
    {
      $txt .= ShowLine(Op2("and",ShowTrueComparison(),ShowTrueComparison()));
    }

  for (my $i=0; $i<5; $i++)
    {
      $txt .= ShowLine(Op1("not",
			   Op2("and",
			       ShowTrueComparison(),
			       ShowFalseComparison())));
    }

  for (my $i=0; $i<5; $i++)
    {
      $txt .= ShowLine(Op1("not",
			   Op2("and",
			       ShowFalseComparison(),
			       ShowTrueComparison())));
    }

  for (my $i=0; $i<5; $i++)
    {
      $txt .= ShowLine(Op1("not",
			   Op2("and",
			       ShowFalseComparison(),
			       ShowFalseComparison())));
    }

  for (my $i=0; $i<10; $i++)
    {
      my $t1 = irand(2);
      my $t2 = irand(2);
      my $c1 = "";
      my $c2 = "";
      if ($t1==1)
	{
	  $c1 = ShowTrueComparison();
	}
      else
	{
	  $c1 = ShowFalseComparison();
	}
      if ($t2==1)
	{
	  $c2 = ShowTrueComparison();
	}
      else
	{
	  $c2 = ShowFalseComparison();
	}
      my $c = Op2("and",$c1,$c2);
      
      if (!(($t1==1)&&($t2==1)))
	{
	  $c = Op1("not",$c);
	}
      $txt .= ShowLine($c);
    }

  return $txt;
}



sub ShowOrLogicLesson {
  my $txt = "";
  $txt .= "# MATH introduce the OR logical operator\n";
  
  $txt .= ShowLine(Op("intro","or"));
  for (my $i=0; $i<10; $i++)
    {
      $txt .= ShowLine(Op2("or",ShowTrueComparison(),ShowTrueComparison()));
    }

  for (my $i=0; $i<5; $i++)
    {
      $txt .= ShowLine(Op2("or",ShowTrueComparison(),ShowFalseComparison()));
    }

  for (my $i=0; $i<5; $i++)
    {
      $txt .= ShowLine(Op2("or",ShowFalseComparison(),ShowTrueComparison()));
    }

  for (my $i=0; $i<5; $i++)
    {
      $txt .= ShowLine(Op1("not",
			   Op2("or",
			       ShowFalseComparison(),
			       ShowFalseComparison())));
    }

  for (my $i=0; $i<10; $i++)
    {
      my $t1 = irand(2);
      my $t2 = irand(2);
      my $c1 = "";
      my $c2 = "";
      if ($t1==1)
	{
	  $c1 = ShowTrueComparison();
	}
      else
	{
	  $c1 = ShowFalseComparison();
	}
      if ($t2==1)
	{
	  $c2 = ShowTrueComparison();
	}
      else
	{
	  $c2 = ShowFalseComparison();
	}
      my $c = Op2("or",$c1,$c2);
      
      if (!(($t1==1)||($t2==1)))
	{
	  $c = Op1("not",$c);
	}
      $txt .= ShowLine($c);
    }

  return $txt;
}





sub ShowTrueFalseLesson {
  my $txt = "";
  $txt .= "# MATH use equality for truth values\n";
  for (my $i=0; $i<5; $i++)
    {
      $txt .= ShowLine(Op2("=",ShowTrueComparison(),ShowTrueComparison()));
    }
  for (my $i=0; $i<5; $i++)
    {
      $txt .= ShowLine(Op2("=",ShowFalseComparison(),ShowFalseComparison()));
    }
  for (my $i=0; $i<5; $i++)
    {
      $txt .= ShowLine(Op1("not",
			   Op2("=",
			       ShowFalseComparison(),
			       ShowTrueComparison())));
    }
  for (my $i=0; $i<5; $i++)
    {
      $txt .= ShowLine(Op1("not",
			   Op2("=",
			       ShowTrueComparison(),
			       ShowFalseComparison())));
    }
  $txt .= ShowLine(Op("intro","true"));
  $txt .= ShowLine(Op("intro","false"));
  for (my $i=0; $i<5; $i++)
    {
      $txt .= ShowLine(Op2("=","true",ShowTrueComparison()));
    }
  for (my $i=0; $i<5; $i++)
    {
      $txt .= ShowLine(Op2("=",ShowTrueComparison(),"true"));
    }
  for (my $i=0; $i<5; $i++)
    {
      $txt .= ShowLine(Op2("=","false",ShowFalseComparison()));
    }
  for (my $i=0; $i<5; $i++)
    {
      $txt .= ShowLine(Op2("=",ShowFalseComparison(),"false"));
    }
  $txt .= ShowLine(Op2("=","true","true"));
  $txt .= ShowLine(Op2("=","false","false"));
  $txt .= ShowLine(Op1("not",Op2("=","true","false")));
  $txt .= ShowLine(Op1("not",Op2("=","false","true")));

  return $txt;
};

sub ShowQuantifierLesson {
  my $txt = "";
  $txt .= "# MATH introduce universal quantifier\n";
  $txt .= "# really need to link with sets for true correctness\n";
  $txt .= "# and the examples here are REALLY sparse, need much more\n";
  $txt .= ShowLine(Op("intro","forall"));
  for (my $i=5; $i>=0; $i--)
    {
      $txt .= ShowLine(Op2("<",
			   Num($i),
			   Op2("+",Num($i),Num(1))));
    }
  $txt .= ShowLine(Op("forall",
		      Proc(Lit("x"),
			   Op2("<",
			       Lit("x"),
			       Op2("+",Lit("x"),Num(1))))));
  for (my $i=5; $i>=0; $i--)
    {
      my $txt0 = Op2("<",
		     Num($i),
		     Op2("*",Num($i),Num(2)));
      if (!($i<$i*2))
	{
	  $txt0 = Op1("not",$txt0);
	}
      $txt .= ShowLine($txt0);
    }
  $txt .= ShowLine(Op1("not",
		       Op("forall",
			  Proc(Lit("x"),
			       Op2("<",
				   Lit("x"),
				   Op2("*",Lit("x"),Num(2)))))));
  $txt .= "# MATH introduce existential quantifier\n";
  $txt .= "# really need to link with sets for true correctness\n";
  $txt .= "# and the examples here are REALLY sparse, need much more\n";
  for (my $i=5; $i>=0; $i--)
    {
      my $txt0 = Op2("=",
		     Num($i),
		     Op2("*",Num(2),Num(2)));
      if (!($i==2*2))
	{
	  $txt0 = Op1("not",$txt0);
	}
      $txt .= ShowLine($txt0);
    }
  $txt .= ShowLine(Op("intro","exists"));
  $txt .= ShowLine(Op("exists",
		      Proc(Lit("x"),
			   Op2("=",
			       Lit("x"),
			       Op2("*",Num(2),Num(2))))));

  for (my $i=5; $i>=0; $i--)
    {
      my $txt0 = Op2("=",
		     Num($i),
		     Op2("+",Num($i),Num(2)));
      if (!($i==$i+1))
	{
	  $txt0 = Op1("not",$txt0);
	}
      $txt .= ShowLine($txt0);
    }
  $txt .= ShowLine(Op("not",
		      Op("exists",
			 Proc(Lit("x"),
			      Op2("=",
				  Lit("x"),
				  Op2("+",Lit("x"),Num(2)))))));

  return $txt;
};

sub ShowImplicationLesson {
  my $txt = "";
  $txt .= "# MATH introduce logical implication\n";
  $txt .= ShowLine(Op("intro","=>"));
  $txt .= ShowLine(Op2("=>","true","true"));
  $txt .= ShowLine(Op1("not",Op2("=>","true","false")));
  $txt .= ShowLine(Op2("=>","false","true"));
  $txt .= ShowLine(Op2("=>","false","false"));
  $txt .= ShowLine(Op("forall",
		      Lit("x"),
		      Op("forall",
			 Lit("y"),
			 Op2("=>",
			     Op2("=>",
				 Lit("x"),
				 Lit("y")),
			     Op2("=>",
				 Op1("not",Lit("y")),
				 Op1("not",Lit("x")))))));
  return $txt;
};


sub ShowAdditionLesson {
  my $txt = "";
  $txt .= "# MATH introduce addition\n";
  $txt .= ShowLine(Op("intro","+"));
  for (my $i=0; $i<10; $i++)
    {
      my $r = irand(5);
      my $r2 = irand(5);
      $txt .= ShowLine(Op2("=",
			   Op2("+",
			       ShowUnary($r),
			       ShowUnary($r2)),
			   ShowUnary($r+$r2)));
    }
  return $txt;
};


sub ShowSubtractionLesson {
  my $txt = "";
  $txt .= "# MATH introduce subtraction\n";
  $txt .= ShowLine(Op("intro","-"));
  for (my $i=0; $i<10; $i++)
    {
      my $r = irand(5);
      my $r2 = irand(5);
      $txt .= ShowLine(Op2("=",
			   Op2("-",
			       ShowUnary($r+$r2),
			       ShowUnary($r2)),
			   ShowUnary($r)));
    }
  return $txt;
};


sub ShowMultiplicationLesson {
  my $txt = "";
  $txt .= "# MATH introduce multiplication\n";
  $txt .= ShowLine(Op("intro","*"));
  for (my $i=0; $i<=3; $i++)
    {
      for (my $j=0; $j<=3; $j++)
	{
	  $txt .= ShowLine(Op2("=",
			       Op2("*",
				   ShowUnary($i),
				   ShowUnary($j)),
			       ShowUnary($i*$j)));
	}
    }
  for (my $i=0; $i<10; $i++)
    {
      my $r = irand(4);
      my $r2 = irand(4);
      $txt .= ShowLine(Op2("=",
			   Op2("*",
			       ShowUnary($r),
			       ShowUnary($r2)),
			   ShowUnary($r*$r2)));
    }
  return $txt;
};


sub ShowDoubleLesson {
  my $txt = "";
  $txt .= "# MATH introduce doubling as a special case of multiplication\n";
  $txt .= "# as prelude to binary representation\n";
  $txt .= ShowLine(Op("intro",":"));
  for (my $i=0; $i<=4; $i++)
    {
      $txt .= ShowLine(Op2("=",Op1(":",ShowUnary($i)),ShowUnary($i*2)));
    }  
  for (my $i=0; $i<=4; $i++)
    {
      $txt .= ShowLine(Op2("=",ShowUnary($i*2),Op1(":",ShowUnary($i))));
    }  
  for (my $i=0; $i<=4; $i++)
    {
      $txt .= ShowLine(Op2("=",
			   Op2("*",ShowUnary($i),ShowUnary(2)),
			   Op1(":",ShowUnary($i))));
    }  
  for (my $i=0; $i<=4; $i++)
    {
      $txt .= ShowLine(Op2("=",
			   BareOp1(":",ShowUnary($i)),
			   Op1(":",ShowUnary($i))));
    }  
  return $txt;
};


sub ShowBinaryLesson {
  my $txt = "";
  $txt .= "# MATH introduce a simple form of binary notation\n";
  $txt .= "# After this lesson, in the higher-level version of the message,\n";
  $txt .= "# will expand decimal to stand for the binary notation given.\n";
  for (my $i=0; $i<16; $i++)
    {
      $txt .= ShowLine(Op2("=",ShowUnary($i),ShowBinaryVerbose($i)));
    }
  for (my $i=0; $i<16; $i++)
    {
      my $j = irand(16);
      $txt .= ShowLine(Op2("=",ShowBinaryVerbose($j),ShowUnary($j)));
    }
  for (my $i=0; $i<8; $i++)
    {
      my $r = irand(16);
      my $r2 = irand(16);
      $txt .= ShowLine(Op2("=",
			   Op2("+",
			       ShowBinaryVerbose($r),
			       ShowBinaryVerbose($r2)),
			   ShowBinaryVerbose($r+$r2)));			       
    }
  for (my $i=0; $i<8; $i++)
    {
      my $r = irand(16);
      my $r2 = irand(16);
      $txt .= ShowLine(Op2("=",
			   Op2("*",
			       ShowBinaryVerbose($r),
			       ShowBinaryVerbose($r2)),
			   ShowBinaryVerbose($r*$r2)));
    }
  return $txt;
};



sub ShowEvaluationLesson {
  my $txt = "";
  $txt .= "# MATH demonstrate idea of leaving gaps in an expression\n";
  $txt .= "# and then filling them in afterwards\n";
  $txt .= "# the examples given leave a lot to be desired!\n";
  for (my $i=0; $i<8; $i++)
    {
      my $r = irand(16);
      my $r2 = irand(16);
      $txt .= ShowLine(Apply(Proc(Lit("x"),
				  Op2("=",
				      Op2("+",Num($r),Lit("x")),
				      Num($r+$r2))),
			     Num($r2)));
    }
  for (my $i=0; $i<8; $i++)
    {
      my $r = irand(16);
      my $r2 = irand(16);
      $txt .= ShowLine(Apply(Apply(Proc(Lit("x"),
					Proc(Lit("y"),
					     Op2("=",
						 Op2("*",
						     Lit("x"),
						     Lit("y")),
						 Num($r*$r2)))),
				   Num($r)),
			     Num($r2)));
    }
  for (my $i=0; $i<8; $i++)
    {
      my $r = irand(16);
      my $r2 = irand(16);
      $txt .= ShowLine(Apply(Apply(Apply(Proc(Lit("x"),
					      Proc(Lit("y"),
						   Proc(Lit("z"),
							Op2("=",
							    Op2("*",
								Lit("x"),
								Lit("y")),
							    Lit("z"))))),
					 Num($r*$r2)),
				   Num($r)),
			     Num($r2)));
    }
  return $txt;
};



sub ShowDefineFunctionLesson {
  my $txt = "";
  $txt .= "# MATH show some simple function calls\n";
  $txt .= "# and show a way to remember functions across statements\n";
  for (my $i=0; $i<8; $i++)
    {
      my $r = irand(10);
      $txt .= ShowLine(Op2("=",
			   Apply(Proc(Lit("square"),
				      Apply(Lit("square"),
					    Num($r))),
				 Proc(Lit("x"),
				      Op2("*", Lit("x"), Lit("x")))),
			   Num($r*$r)));
    }
  $txt .= ShowLine(Op2("define",
		       Lit("square"),
		       Proc(Lit("x"),
			    Op2("*", Lit("x"), Lit("x")))));
  for (my $i=0; $i<4; $i++)
    {
      my $r = irand(10);
      $txt .= ShowLine(Op2("=",
			   Apply(Lit("square"),
				 Num($r)),
			   Num($r*$r)));
    }
  $txt .= ShowLine(Op2("define",
		       Lit("plusone"),
		       Proc(Lit("x"),
			    Op2("+", Lit("x"), Lit("1")))));
  for (my $i=0; $i<4; $i++)
    {
      my $r = irand(10);
      $txt .= ShowLine(Op2("=",
			   Apply(Lit("plusone"),
				 Num($r)),
			   Num($r+1)));
    }

  return $txt;
};


sub ShowIfLesson {
  my $txt = "";
  $txt .= "# MATH show mechanisms for branching\n";

  $txt .= ShowLine(Op("intro","if"));
  for (my $i=0; $i<16; $i++)
    {
      my $r1 = irand(2);
      my $r2 = irand(10);
      my $r3 = irand(10);
      my $cmp = "true";
      my $out = "";
      if ($r1)
	{
	  $cmp = "true";
	}
      else
	{
	  $cmp = "false";
	}
      if ($r1)
	{
	  $out .= Num($r2);
	}
      else
	{
	  $out = Num($r3);
	}
      $txt .= ShowLine(Op2("=",
			   Op("if",
			      $cmp,
			      Num($r2),
			      Num($r3)),
			   $out));
    }

  return $txt;
};


sub Factorial {
  my $r = 1;
  my $x = shift;
  if ($x>0)
    {
      $r = $x*Factorial($x-1);
    }
  return $r;
};

sub ShowRecursionLesson {
  my $txt = "";
  $txt .= "# MATH show an example of recursive evaluation\n";
  $txt .= "# skipping over a lot of definitions and desugarings\n";
  $txt .= ShowLine(Op2("define",
		       Lit("factorial"),
		       Proc(Lit("x"),
			    (Op("if",
				Op2(">",Lit("x"),Num(0)),
				Op2("*",
				    Lit("x"),
				    Apply(Lit("factorial"),
					  Op2("-",Lit("x"),Num(1)))),
				1)))));
  for (my $i=0; $i<=5; $i++)
    {
      $txt .= ShowLine(Op2("=",
			   Apply("factorial",
				 Num($i)),
			   Factorial($i)));
    }

  return $txt;
};




sub ShowSetLesson {
  my $txt = "";
  $txt .= "# MATH introduce sets and set membership\n";
  for (my $i=0; $i<5; $i++)
    {
      my %hset;
      for (my $j=0; $j<6; $j++)
	{
	  $hset{irand(10)} = 1;
	}
      my @set = keys %hset;
      for (my $j=0; $j<3; $j++)
	{
	  my $mem = $set[irand($#set+1)];
	  $txt .= ShowLine(Op("element",
			      Num($mem),
			      Op("set",
				 @set)));
	}
    }
  for (my $i=0; $i<5; $i++)
    {
      my %hset;
      for (my $j=0; $j<6; $j++)
	{
	  $hset{irand(10)} = 1;
	}
      my @set = keys %hset;
      (my $mem, @set) = @set;
      $txt .= ShowLine(Op1("not",
			   Op("element",
			      Num($mem),
			      Op("set",
				 @set))));
    }
  $txt .= ShowLine(Op2("=",
		       Op("set", "1", "5", "9"),
		       Op("set", "5", "1", "9")));
  $txt .= ShowLine(Op2("=",
		       Op("set", "1", "5", "9"),
		       Op("set", "9", "1", "5")));
  $txt .= ShowLine(Op1("not",
		       Op2("=",
			   Op("set", "1", "5", "9"),
			   Op("set", "1", "5"))));

  $txt .= ShowLine(Op2("element",
		       Num(5),
		       Op("all",
			  Proc(Lit("x"),
			       Op("=",
				  Op2("+",
				      Lit("x"),
				      Num(10)),
				  Num(15))))));
  $txt .= ShowLine(Op2("element",
		       Num(3),
		       Op("all",
			  Proc(Lit("x"),
			       Op("=",
				  Op2("*",
				      Lit("x"),
				      Num(3)),
				  Op2("+",
				      Lit("x"),
				      Num(6)))))));


  $txt .= ShowLine(Op("define",
		      Lit("empty_set"),
		      Op("set")));

  $txt .= ShowLine(Op2("element",
		       Num(0),
		       Lit("natural_set")));
  $txt .= ShowLine(Op("forall",
		      Proc(Lit("x"),
			   Op2("=>",
			       Op2("element",
				   Lit("x"),
				   Lit("natural_set")),
			       Op2("element",
				   Op2("+", Lit("x"), Num(1)),
				   Lit("natural_set"))))));

  for (my $i=1; $i<10; $i++)
    {
      $txt .= ShowLine(Op2("element",
			   Num($i),
			   Lit("natural_set")));      
    }

  $txt .= ShowLine(Op1("not",
		       Op2("element",
			   "true",
			   Lit("natural_set"))));

  $txt .= ShowLine(Op1("not",
		       Op2("element",
			   "false",
			   Lit("natural_set"))));

  $txt .= ShowLine(Op("define",
		      Lit("boolean_set"),
		      Op("set", "true", "false")));

  $txt .= ShowLine(Op2("element",
		       Lit("true"),
		       Lit("boolean_set")));
  
  $txt .= ShowLine(Op2("element",
		       Lit("false"),
		       Lit("boolean_set")));
  
  $txt .= ShowLine(Op1("not",
		       Op2("element",
			   "0",
			   Lit("boolean_set"))));
  

  $txt .= ShowLine(Op("define",
		      Lit("even_natural_set"),
		      Op1("all",
			  Proc(Lit("x"),
			       Op1("exists",
				   Proc(Lit("y"),
					Op2("and",
					    Op2("element", "y", "natural_set"),
					    Op2("equals",
						Op2("*",2,"y"),
						"x"))))))));

  for (my $i=0; $i<=6; $i++)
    {
      my $txt0 = Op2("element",
		  Num($i),
		  Lit("even_natural_set"));
      if (($i%2)!=0)
	{
	  $txt0 = Op1("not",$txt0);
	}
      $txt .= ShowLine(Op2("element",
			   Num($i),
			   Lit("natural_set")));      
      $txt .= ShowLine($txt0);
    }

  
  return $txt;
};


sub ShowListLesson {
  my $txt = "";
  $txt .= "# MATH illustrate lists and some list operators\n";
  $txt .= "# still using examples rather than definition by formula -\n";
  $txt .= "# could change this to reduce ambiguity, but that would create\n";
  $txt .= "# more order constraints in the lessons\n";

  for (my $i=0; $i<10; $i++)
    {
      my $len = irand(10)+1;
      my @lst = ();
      for (my $j=0; $j<$len; $j++)
	{
	  push(@lst,irand(20));
	}
      my ($head, @tail) = @lst;
      $txt .= ShowLine(Op2("=",
			   Op1("head",
			       Op("list", @lst)),
			   $head));
      $txt .= ShowLine(Op2("=",
			   Op1("tail",
			       Op("list", @lst)),
			   Op("list", @tail)));

    }
  for (my $i=0; $i<10; $i++)
    {
      my $len = irand(10)+1;
      my @lst = ();
      for (my $j=0; $j<$len; $j++)
	{
	  push(@lst,irand(20));
	}
      my $idx = irand($len);
      my $val = $lst[$idx];
      $txt .= ShowLine(Op2("=",
			   Op2("list-ref",
			       Op("list", @lst),
			       $idx),
			   $val));
    }
  for (my $i=0; $i<5; $i++)
    {
      my $len = $i;
      my @lst = ();
      my $cmp = "=";
      for (my $j=0; $j<$len; $j++)
	{
	  push(@lst,irand(20));
	}
      my $idx = irand($len);
      my $val = $lst[$idx];
      $txt .= ShowLine(Op2($cmp,
			   Op("list", @lst),
			   Op("list", @lst)));
    }
  $txt .= "# this next batch of examples are a bit misleading, should streamline\n";
  for (my $i=0; $i<5; $i++)
    {
      my $len = $i;
      my @lst = ();
      my $cmp = "=";
      for (my $j=0; $j<$len; $j++)
	{
	  push(@lst,irand(20));
	}
      my $idx = irand($len);
      my $val = $lst[$idx];
      $txt .= ShowLine(Op1("not",
			   Op2($cmp,
			       Op("list", @lst),
			       Op("list", (irand(10), @lst)))));
      $txt .= ShowLine(Op1("not",
			   Op2($cmp,
			       Op("list", @lst),
			       Op("list", (@lst, irand(10))))));
    }

  $txt .= "# some helpful functions\n";

  $txt .= ShowLine(Op2("define",
		       "list-length",
		       Proc("x",
			    Op("if",
			       Op2("=",
				   "x",
				   Op("list")),
			       0,
			       Op2("+",
				   1,
				   Op1("list-length",
				       Op1("tail","x")))))));

  my @examples = prand(10,5);
  for (my $i=0; $i<=$#examples; $i++)
    {
      my $r = $examples[$i];
      $txt .= ShowLine(Op2("=",
			   Op1("list-length",
			       Op("list", prand(10,$r))),
			   $r));
    }

  $txt .= ShowLine(Op2("define",
		       "pair",
		       Proc("x",
			    Proc("y",
				 Op("list", "x", "y")))));

  @examples = prand(10,3);
  my @examples2 = prand(10,$#examples+1);
  for (my $i=0; $i<=$#examples; $i++)
    {
      my $r = $examples[$i];
      my $r2 = $examples2[$i];
      $txt .= ShowLine(Op2("=",
			   Op2("pair", $r, $r2),
			   Op2("list", $r, $r2)));
      $txt .= ShowLine(Op2("=",
			   Op1("first",Op2("pair", $r, $r2)),
			   $r));
      $txt .= ShowLine(Op2("=",
			   Op1("second",Op2("pair", $r, $r2)),
			   $r2));
    }
    
  return $txt;
};


sub ShowMultipleParameterLesson {
  my $txt = "";
  $txt .= "# MATH build up functions of several variables\n";
  $txt .= "# there should be nothing actually new here, if the basic\n";
  $txt .= "# symbols are interpreted correctly - but this isn't obvious\n";
  for (my $i=0; $i<5; $i++)
    {
      my $r2 = irand(10);
      my $r1 = irand(10)+$r2;
      $txt .= ShowLine(Op2("=",
			   Apply(ProcMultiple(["x","y"],
					      Op2("-","x","y")),
				 $r1,
				 $r2),
			   Num($r1-$r2)));
    }
  $txt .= ShowLine(Op2("define",
		       "apply",
		       ProcMultiple(["x","y"],
				    Op("if",
				       Op2("=",
					   "y",
					   Op("list")),
				       "x",
				       Op2("apply",
					   Apply("x",
						 Op1("head", "y")),
					   Op1("tail", "y"))))));
					   
  for (my $i=0; $i<5; $i++)
    {
      my $r2 = irand(10);
      my $r1 = irand(10)+$r2;
      $txt .= ShowLine(Op2("=",
			   Op2("apply",
			       ProcMultiple(["x","y"],
					    Op2("-","x","y")),
			       Op("list", 
				  $r1,
				  $r2)),
			   Num($r1-$r2)));
    }
  return $txt;
};

sub ShowHashLesson {
  my $txt = "";
  $txt .= "# MATH introduce environment/hashmap structure\n";
  $txt .= "# note that something written as {name} is just converted to a number\n";
  $txt .= "# it does NOT yield an identifier\n";
  $txt .= "# this section needs a LOT more examples :-)\n";
  $txt .= ShowLine(Op2("define",
		       "hash-add",
		       ProcMultiple(["h","x","y","z"],
				    Op("if",
				       Op2("=","z","x"),
				       "y",
				       Op("h", "z")))));
  $txt .= ShowLine(Op2("define",
		       "hash-ref",
		       ProcMultiple(["h","x"],
				    Op("h", "x"))));

  $txt .= ShowLine(Op2("define",
		       "hash-null",
		       Proc("z","undefined")));
  
  $txt .= ShowLine(Op2("define",
		       "test-hash",
		       Op("hash-add",
			  Op("hash-add",
			     "hash-null",
			     3, 2),
			  4,
			  9)));

  $txt .= ShowLine(Op2("=",
		       Op("hash-ref",
			  "test-hash",
			  4),
		       9));
			
  $txt .= ShowLine(Op2("=",
		       Op("hash-ref",
			  "test-hash",
			  3),
		       2));
			
  $txt .= ShowLine(Op2("=",
		       Op("hash-ref",
			  "test-hash",
			  8),
		       "undefined"));
			
  $txt .= ShowLine(Op2("=",
		       Op("hash-ref",
			  "test-hash",
			  15),
		       "undefined"));
			
  $txt .= ShowLine(Op2("=",
		       Op("hash-ref",
			  Op("hash-add",
			     "test-hash",
			     15,
			     33),
			  15),
		       33));
			
  $txt .= ShowLine(Op2("=",
		       Op("hash-ref",
			  "test-hash",
			  15),
		       "undefined"));

  $txt .= ShowLine(Op2("define",
		       "make-hash",
		       Proc("x",
			    Op2("=","x",Op("list")),
			    "hash-null",
			    Op("hash-add",
			       Op("make-hash", Op1("tail", "x")),
			       Op1("first",Op1("head","x")),
			       Op1("second",Op1("head","x"))))));

  $txt .= ShowLine(Op2("=",
		       Op2("hash-ref",
			   Op1("make-hash",
			       Op("list",
				  Op2("pair", 3, 10),
				  Op2("pair", 2, 20),
				  Op2("pair", 1, 30))),
			   3),
		       10));
  $txt .= ShowLine(Op2("=",
		       Op2("hash-ref",
			   Op1("make-hash",
			       Op("list",
				  Op2("pair", 3, 10),
				  Op2("pair", 2, 20),
				  Op2("pair", 1, 30))),
			   1),
		       30));
			
  return $txt;
};


sub ShowMutableLesson {
  my $txt = "";
  $txt .= "# MATH introduce mutable objects, and side-effects\n";
  $txt .= ShowLine(Op("intro","make-cell"));
  $txt .= ShowLine(Op("intro","set!"));
  $txt .= ShowLine(Op("intro","get!"));
  $txt .= ShowLine(Op("define",
		      "demo-mut1",
		      Op("make-cell", 0)));
  $txt .= ShowLine(Op2("set!",
		       "demo-mut1",
		       15));
  $txt .= ShowLine(Op2("=",
		       Op1("get!", "demo-mut1"),
		       15));
  $txt .= ShowLine(Op2("set!",
		       "demo-mut1",
		       5));
  $txt .= ShowLine(Op2("set!",
		       "demo-mut1",
		       7));
  $txt .= ShowLine(Op2("=",
		       Op1("get!", "demo-mut1"),
		       7));
  $txt .= ShowLine(Op("define",
		      "demo-mut2",
		      Op("make-cell", 11)));
  $txt .= ShowLine(Op2("=",
		       Op1("get!", "demo-mut2"),
		       11));
  $txt .= ShowLine(Op2("set!",
		       "demo-mut2",
		       22));
  $txt .= ShowLine(Op2("=",
		       Op1("get!", "demo-mut2"),
		       22));
  $txt .= ShowLine(Op2("=",
		       Op1("get!", "demo-mut1"),
		       7));
  $txt .= ShowLine(Op2("=",
		       Op2("+",
			   Op1("get!", "demo-mut1"),
			   Op1("get!", "demo-mut2")),
		       29));
  $txt .= ShowLine(Op("if",
		      Op("=",
			 Op1("get!",
			     "demo-mut1"),
			 7),
		      Op2("set!", "demo-mut1", 88),
		      Op2("set!", "demo-mut1", 99)));
  $txt .= ShowLine(Op2("=",
		       Op1("get!", "demo-mut1"),
		       88));
  $txt .= ShowLine(Op("if",
		      Op("=",
			 Op1("get!",
			     "demo-mut1"),
			 7),
		      Op2("set!", "demo-mut1", 88),
		      Op2("set!", "demo-mut1", 99)));
  $txt .= ShowLine(Op2("=",
		       Op1("get!", "demo-mut1"),
		       99));

  return $txt;
};

sub ShowGraphLesson {
  my $txt = "";
  $txt .= "#MATH introduce simple graph structures\n";
		      
  return $txt;
};

sub ShowMUDLesson {
  my $txt = "";
  $txt .= "# MUD under development\n";
  $txt .= "# need a lot more structure/record/object abstractions\n";
  $txt .= "# adding these to MATH section...\n";
  $txt .= "# currently just use this section to play around\n";
  
  $txt .= ShowLine(Op("intro","reflect"));
  $txt .= ShowLine(Op2("define",
		       "reflect",
		       Proc("x",
			    Apply("x",
				  "x"))));

#  $txt .= ShowLine(Op("define",
#		      "Point2D",
		      

  return $txt;
};

# generate message

# use consistent random choices
# (really not acceptable to use random numbers, should use
# look-up tables on a per lesson basis, to ensure stability
# of sequences within lessons)
srand(1);

my $txt = "";

$txt .= "#   Author: Paul Fitzpatrick, paulfitz\@ai.mit.edu
#   Copyright (c) 2003 Paul Fitzpatrick
#
#   This file is part of CosmicOS.
#
#   CosmicOS is free software; you can redistribute it and/or modify
#   it under the terms of the GNU General Public License as published by
#   the Free Software Foundation; either version 2 of the License, or
#   (at your option) any later version.
#
#   CosmicOS is distributed in the hope that it will be useful,
#   but WITHOUT ANY WARRANTY; without even the implied warranty of
#   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
#   GNU General Public License for more details.
#
#   You should have received a copy of the GNU General Public License
#   along with CosmicOS; if not, write to the Free Software
#   Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
#

";

$txt .= ShowUnaryLesson();
$txt .= ShowNotLogicLesson();
$txt .= ShowAndLogicLesson();
$txt .= ShowOrLogicLesson();
$txt .= ShowTrueFalseLesson();
$txt .= ShowAdditionLesson();
$txt .= ShowSubtractionLesson();
$txt .= ShowMultiplicationLesson();
$txt .= ShowDoubleLesson();
$txt .= ShowBinaryLesson();
$txt .= ShowEvaluationLesson();
$txt .= ShowDefineFunctionLesson();
$txt .= ShowIfLesson();
$txt .= ShowRecursionLesson();
$txt .= ShowQuantifierLesson();
$txt .= ShowImplicationLesson();
$txt .= ShowSetLesson();
$txt .= ShowListLesson();
$txt .= ShowMultipleParameterLesson();
$txt .= ShowHashLesson();
$txt .= ShowMutableLesson();
$txt .= ShowMUDLesson();

# Establish some terms which will have a fairly short representation.
# Identifying numbers are allocated on a first come first served basis.
Text2Tokens("intro = < > not and or true false x y z => exists forall cell set get if <= >=");

my $msg = Tokens2Msg(Text2Tokens($txt));

$msg =~ s/\n//g;
$msg =~ s/([a-z0-9]{80})/$1\n*** /g;
print "*** $msg\n";
print "$txt\n\n";


# can call Decompile to make sure everything is getting put in
# the final message

#print Decompile($msg);