--- a/List.thy Tue Oct 24 14:59:17 1995 +0100
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,83 +0,0 @@
-(* 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