|
1 (* Title: ZF/ex/term.ML |
|
2 ID: $Id$ |
|
3 Author: Lawrence C Paulson, Cambridge University Computer Laboratory |
|
4 Copyright 1993 University of Cambridge |
|
5 |
|
6 Datatype definition of terms over an alphabet. |
|
7 Illustrates the list functor (essentially the same type as in Trees & Forests) |
|
8 *) |
|
9 |
|
10 structure Term = Datatype_Fun |
|
11 (val thy = List.thy; |
|
12 val rec_specs = |
|
13 [("term", "univ(A)", |
|
14 [(["Apply"], "[i,i]=>i")])]; |
|
15 val rec_styp = "i=>i"; |
|
16 val ext = None |
|
17 val sintrs = ["[| a: A; l: list(term(A)) |] ==> Apply(a,l) : term(A)"]; |
|
18 val monos = [list_mono]; |
|
19 val type_intrs = [SigmaI,Pair_in_univ, list_univ RS subsetD, A_into_univ]; |
|
20 val type_elims = []); |
|
21 |
|
22 val [ApplyI] = Term.intrs; |
|
23 |
|
24 (*Induction on term(A) followed by induction on List *) |
|
25 val major::prems = goal Term.thy |
|
26 "[| t: term(A); \ |
|
27 \ !!x. [| x: A |] ==> P(Apply(x,Nil)); \ |
|
28 \ !!x z zs. [| x: A; z: term(A); zs: list(term(A)); P(Apply(x,zs)) \ |
|
29 \ |] ==> P(Apply(x, Cons(z,zs))) \ |
|
30 \ |] ==> P(t)"; |
|
31 by (rtac (major RS Term.induct) 1); |
|
32 by (etac List.induct 1); |
|
33 by (etac CollectE 2); |
|
34 by (REPEAT (ares_tac (prems@[list_CollectD]) 1)); |
|
35 val term_induct2 = result(); |
|
36 |
|
37 (*Induction on term(A) to prove an equation*) |
|
38 val major::prems = goal (merge_theories(Term.thy,ListFn.thy)) |
|
39 "[| t: term(A); \ |
|
40 \ !!x zs. [| x: A; zs: list(term(A)); map(f,zs) = map(g,zs) |] ==> \ |
|
41 \ f(Apply(x,zs)) = g(Apply(x,zs)) \ |
|
42 \ |] ==> f(t)=g(t)"; |
|
43 by (rtac (major RS Term.induct) 1); |
|
44 by (resolve_tac prems 1); |
|
45 by (REPEAT (eresolve_tac [asm_rl, map_list_Collect, list_CollectD] 1)); |
|
46 val term_induct_eqn = result(); |
|
47 |
|
48 (** Lemmas to justify using "term" in other recursive type definitions **) |
|
49 |
|
50 goalw Term.thy Term.defs "!!A B. A<=B ==> term(A) <= term(B)"; |
|
51 by (rtac lfp_mono 1); |
|
52 by (REPEAT (rtac Term.bnd_mono 1)); |
|
53 by (REPEAT (ares_tac (univ_mono::basic_monos) 1)); |
|
54 val term_mono = result(); |
|
55 |
|
56 (*Easily provable by induction also*) |
|
57 goalw Term.thy (Term.defs@Term.con_defs) "term(univ(A)) <= univ(A)"; |
|
58 by (rtac lfp_lowerbound 1); |
|
59 by (rtac (A_subset_univ RS univ_mono) 2); |
|
60 by (safe_tac ZF_cs); |
|
61 by (REPEAT (ares_tac [Pair_in_univ, list_univ RS subsetD] 1)); |
|
62 val term_univ = result(); |
|
63 |
|
64 val term_subset_univ = standard |
|
65 (term_mono RS (term_univ RSN (2,subset_trans))); |
|
66 |