src/HOL/List.thy

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/List.thy	Fri Mar 03 12:02:25 1995 +0100
@@ -0,0 +1,83 @@
+(*  Title:      HOL/List.thy
+    ID:         $Id$
+    Author:     Tobias Nipkow
+    Copyright   1994 TU Muenchen
+
+Definition of type 'a list as a datatype. This allows primrec to work.
+
+*)
+
+List = Arith +
+
+datatype 'a list = "[]" ("[]") | "#"('a,'a list) (infixr 65)
+
+consts
+
+  null      :: "'a list => bool"
+  hd        :: "'a list => 'a"
+  tl,ttl    :: "'a list => 'a list"
+  mem       :: "['a, 'a list] => bool"			(infixl 55)
+  list_all  :: "('a => bool) => ('a list => bool)"
+  map       :: "('a=>'b) => ('a list => 'b list)"
+  "@"	    :: "['a list, 'a list] => 'a list"		(infixr 65)
+  filter    :: "['a => bool, 'a list] => 'a list"
+  foldl     :: "[['b,'a] => 'b, 'b, 'a list] => 'b"
+  length    :: "'a list => nat"
+  flat      :: "'a list list => 'a list"
+  nth       :: "[nat, 'a list] => 'a"
+
+syntax
+  (* list Enumeration *)
+  "@list"   :: "args => 'a list"                        ("[(_)]")
+
+  (* Special syntax for list_all and filter *)
+  "@Alls"	:: "[idt, 'a list, bool] => bool"	("(2Alls _:_./ _)" 10)
+  "@filter"	:: "[idt, 'a list, bool] => 'a list"	("(1[_:_ ./ _])")
+
+translations
+  "[x, xs]"     == "x#[xs]"
+  "[x]"         == "x#[]"
+
+  "[x:xs . P]"	== "filter (%x.P) xs"
+  "Alls x:xs.P"	== "list_all (%x.P) xs"
+
+primrec null list
+  null_Nil "null([]) = True"
+  null_Cons "null(x#xs) = False"
+primrec hd list
+  hd_Nil  "hd([]) = (@x.False)"
+  hd_Cons "hd(x#xs) = x"
+primrec tl list
+  tl_Nil  "tl([]) = (@x.False)"
+  tl_Cons "tl(x#xs) = xs"
+primrec ttl list
+  (* a "total" version of tl: *)
+  ttl_Nil  "ttl([]) = []"
+  ttl_Cons "ttl(x#xs) = xs"
+primrec "op mem" list
+  mem_Nil  "x mem [] = False"
+  mem_Cons "x mem (y#ys) = if (y=x) True (x mem ys)"
+primrec list_all list
+  list_all_Nil  "list_all P [] = True"
+  list_all_Cons "list_all P (x#xs) = (P(x) & list_all P xs)"
+primrec map list
+  map_Nil  "map f [] = []"
+  map_Cons "map f (x#xs) = f(x)#map f xs"
+primrec "op @" list
+  append_Nil  "[] @ ys = ys"
+  append_Cons "(x#xs)@ys = x#(xs@ys)"
+primrec filter list
+  filter_Nil  "filter P [] = []"
+  filter_Cons "filter P (x#xs) = if (P x) (x#filter P xs) (filter P xs)"
+primrec foldl list
+  foldl_Nil  "foldl f a [] = a"
+  foldl_Cons "foldl f a (x#xs) = foldl f (f a x) xs"
+primrec length list
+  length_Nil  "length([]) = 0"
+  length_Cons "length(x#xs) = Suc(length(xs))"
+primrec flat list
+  flat_Nil  "flat([]) = []"
+  flat_Cons "flat(x#xs) = x @ flat(xs)"
+defs
+  nth_def "nth(n) == nat_rec n hd (%m r xs. r(tl(xs)))"
+end