diff -r f04b33ce250f -r a4dc62a46ee4 List.thy --- 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