--- 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