lazylist

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+% Filename: Lambda.sty
+% Author: Alan Jeffrey
+% Last modified: 12 Feb 1990
+% Modified 24 July 2003 by Robin Fairbairns, to change file name and
+%                       licence requirements, at Alan Jeffrey's request
+%
+% This package is (c) 1990 Alan Jeffrey.
+%
+% Version 1.0a
+%
+% Use and distribution are subject to the LaTeX Project Public
+% License (lppl), version 1.2 (or any later version, at your
+% convenience).
+%
+% A copy of the latest version of lppl may be found at
+% http://www.latex-project.org/lppl.txt
+%
+% See the Gnu manifesto for details on why software ought to be free.
+%
+% Tugboat are given permission to publish any or all of this.
+%
+% This package provides a pile of lambda-calculus and list-handling
+% macros of an incredibly obtuse nature.  Read lazylist.tex to find
+% out what they all do and how they do it.  This \TeX\ code was
+% formally verified.
+%
+% Alan Jeffrey, 25 Jan 1990.
+
+\def\Identity#1{#1}
+
+\def\Error%
+   {\errmessage{Abandon verification all 
+                ye who enter here}}
+
+\def\First#1#2{#1}
+\def\Second#1#2{#2}
+
+\def\Compose#1#2#3{#1{#2{#3}}}
+
+\def\Twiddle#1#2#3{#1{#3}{#2}}
+
+\let\True=\First
+\let\False=\Second
+\let\Not=\Twiddle
+
+\def\And#1#2{#1{#2}\False}
+\def\Or#1#2{#1\True{#2}}
+
+\def\Lift#1#2#3#4{#1{#4}{#2}{#3}{#4}}
+
+\def\Lessthan#1#2{\TeXif{\ifnum#1<#2 }}
+
+\def\gobblefalse\else\gobbletrue\fi#1#2%
+   {\fi#1}
+\def\gobbletrue\fi#1#2%
+   {\fi#2}
+\def\TeXif#1%
+   {#1\gobblefalse\else\gobbletrue\fi}
+
+\def\Nil#1#2{#2}
+\def\Cons#1#2#3#4{#3{#1}{#2}}
+\def\Stream#1{\Cons{#1}{\Stream{#1}}}
+\def\Singleton#1{\Cons{#1}\Nil}
+
+\def\Head#1{#1\First\Error}
+\def\Tail#1{#1\Second\Error}
+
+\def\Foldl#1#2#3%
+   {#3{\Foldl@{#1}{#2}}{#2}}
+\def\Foldl@#1#2#3#4%
+   {\Foldl{#1}{#1{#2}{#3}}{#4}}
+\def\Foldr#1#2#3%
+   {#3{\Foldr@{#1}{#2}}{#2}}
+\def\Foldr@#1#2#3#4%
+   {#1{#3}{\Foldr{#1}{#2}{#4}}}
+
+\def\Cat#1#2{\Foldr\Cons{#2}{#1}}
+
+\def\Reverse{\Foldl{\Twiddle\Cons}\Nil}
+
+\def\All#1{\Foldr{\Compose\And{#1}}\True}
+\def\Some#1{\Foldr{\Compose\Or{#1}}\False}
+\def\Isempty{\All{\First\False}}
+
+\def\Filter#1%
+   {\Foldr{\Lift{#1}\Cons\Second}\Nil}
+
+\def\Map#1{\Foldr{\Compose\Cons{#1}}\Nil}
+
+\def\Insert#1#2#3%
+   {#3{\Insert@{#1}{#2}}{\Singleton{#2}}}
+\def\Insert@#1#2#3#4%
+   {#1{#2}{#3}%
+      {\Cons{#2}{\Cons{#3}{#4}}}%
+      {\Cons{#3}{\Insert{#1}{#2}{#4}}}}
+\def\Insertsort#1{\Foldr{\Insert{#1}}\Nil}
+
+\def\Unlistize#1{[#1\Unlistize@{}]}
+\def\Unlistize@#1{#1\Foldr\Commaize{}}
+\def\Commaize#1#2{, #1#2}
+
+\def\Listize[#1]%
+   {\Listize@#1,\relax]}
+\def\Listize@#1,#2]%
+   {\TeXif{\ifx\relax#2}%
+        {\Singleton{#1}}%
+        {\Cons{#1}{\Listize@#2]}}}
+
+\def\Show#1[#2]%
+   {\Unlistize{#1{\Listize[#2]}}}
+
+