diff -r f04b33ce250f -r a4dc62a46ee4 ex/SList.thy --- a/ex/SList.thy Tue Oct 24 14:59:17 1995 +0100 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,120 +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" - 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" - - (* list Enumeration *) - - "[]" :: "'a list" ("[]") - "@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#[]" - "[]" == "Nil" - - "case xs of Nil => a | y#ys => b" == "list_case(a, %y ys.b, xs)" - - "[x:xs . P]" == "filter(%x.P,xs)" - "Alls x:xs.P" == "list_all(%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), M, - List_case(%g.c, %x y g. d(x, y, g(y))))" - - 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)" - - mem_def "x mem xs == - list_rec(xs, False, %y ys r. if(y=x, True, r))" - list_all_def "list_all(P, xs) == list_rec(xs, True, %x l r. P(x) & 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), x#r, r))" - - list_case_def "list_case(a, f, xs) == list_rec(xs, a, %x xs r.f(x, xs))" - -end