diff -r 1c0dfa7ebb72 -r 3f0ab2c306f7 src/HOL/ex/SList.thy --- a/src/HOL/ex/SList.thy Wed May 07 13:50:52 1997 +0200 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,119 +0,0 @@ -(* Title: HOL/ex/SList.thy - ID: $Id$ - Author: Lawrence C Paulson, Cambridge University Computer Laboratory - Copyright 1993 University of Cambridge - -Definition of type 'a list (strict lists) by a least fixed point - -We use list(A) == lfp(%Z. {NUMB(0)} <+> A <*> Z) -and not list == lfp(%Z. {NUMB(0)} <+> range(Leaf) <*> Z) -so that list can serve as a "functor" for defining other recursive types -*) - -SList = Sexp + - -types - 'a list - -arities - list :: (term) term - - -consts - - list :: 'a item set => 'a item set - Rep_list :: 'a list => 'a item - Abs_list :: 'a item => 'a list - NIL :: 'a item - CONS :: ['a item, 'a item] => 'a item - Nil :: 'a list - "#" :: ['a, 'a list] => 'a list (infixr 65) - List_case :: ['b, ['a item, 'a item]=>'b, 'a item] => 'b - List_rec :: ['a item, 'b, ['a item, 'a item, 'b]=>'b] => 'b - list_case :: ['b, ['a, 'a list]=>'b, 'a list] => 'b - list_rec :: ['a list, 'b, ['a, 'a list, 'b]=>'b] => 'b - Rep_map :: ('b => 'a item) => ('b list => 'a item) - Abs_map :: ('a item => 'b) => 'a item => 'b list - null :: 'a list => bool - hd :: 'a list => 'a - tl,ttl :: 'a list => 'a list - set_of_list :: ('a list => 'a set) - mem :: ['a, 'a list] => bool (infixl 55) - map :: ('a=>'b) => ('a list => 'b list) - "@" :: ['a list, 'a list] => 'a list (infixr 65) - filter :: ['a => bool, 'a list] => 'a list - - (* list Enumeration *) - - "[]" :: 'a list ("[]") - "@list" :: args => 'a list ("[(_)]") - - (* Special syntax for filter *) - "@filter" :: [idt, 'a list, bool] => 'a list ("(1[_:_ ./ _])") - -translations - "[x, xs]" == "x#[xs]" - "[x]" == "x#[]" - "[]" == "Nil" - - "case xs of Nil => a | y#ys => b" == "list_case a (%y ys.b) xs" - - "[x:xs . P]" == "filter (%x.P) xs" - -defs - (* Defining the Concrete Constructors *) - NIL_def "NIL == In0(Numb(0))" - CONS_def "CONS M N == In1(M $ N)" - -inductive "list(A)" - intrs - NIL_I "NIL: list(A)" - CONS_I "[| a: A; M: list(A) |] ==> CONS a M : list(A)" - -rules - (* Faking a Type Definition ... *) - Rep_list "Rep_list(xs): list(range(Leaf))" - Rep_list_inverse "Abs_list(Rep_list(xs)) = xs" - Abs_list_inverse "M: list(range(Leaf)) ==> Rep_list(Abs_list(M)) = M" - - -defs - (* Defining the Abstract Constructors *) - Nil_def "Nil == Abs_list(NIL)" - Cons_def "x#xs == Abs_list(CONS (Leaf x) (Rep_list xs))" - - List_case_def "List_case c d == Case (%x.c) (Split d)" - - (* list Recursion -- the trancl is Essential; see list.ML *) - - List_rec_def - "List_rec M c d == wfrec (trancl pred_sexp) - (%g. List_case c (%x y. d x y (g y))) M" - - list_rec_def - "list_rec l c d == - List_rec (Rep_list l) c (%x y r. d (inv Leaf x) (Abs_list y) r)" - - (* Generalized Map Functionals *) - - Rep_map_def "Rep_map f xs == list_rec xs NIL (%x l r. CONS (f x) r)" - Abs_map_def "Abs_map g M == List_rec M Nil (%N L r. g(N)#r)" - - null_def "null(xs) == list_rec xs True (%x xs r.False)" - hd_def "hd(xs) == list_rec xs (@x.True) (%x xs r.x)" - tl_def "tl(xs) == list_rec xs (@xs.True) (%x xs r.xs)" - (* a total version of tl: *) - ttl_def "ttl(xs) == list_rec xs [] (%x xs r.xs)" - - set_of_list_def "set_of_list xs == list_rec xs {} (%x l r. insert x r)" - - mem_def "x mem xs == - list_rec xs False (%y ys r. if y=x then True else r)" - map_def "map f xs == list_rec xs [] (%x l r. f(x)#r)" - append_def "xs@ys == list_rec xs ys (%x l r. x#r)" - filter_def "filter P xs == - list_rec xs [] (%x xs r. if P(x) then x#r else r)" - - list_case_def "list_case a f xs == list_rec xs a (%x xs r.f x xs)" - -end