diff -r 872f866e630f -r d9527f97246e ex/Term.ML --- a/ex/Term.ML Wed Aug 24 18:49:29 1994 +0200 +++ b/ex/Term.ML Thu Aug 25 10:47:33 1994 +0200 @@ -1,9 +1,9 @@ -(* Title: HOL/ex/term +(* Title: HOL/ex/Term ID: $Id$ Author: Lawrence C Paulson, Cambridge University Computer Laboratory Copyright 1992 University of Cambridge -For term.thy. illustrates List functor +Terms over a given alphabet -- function applications; illustrates list functor (essentially the same type as in Trees & Forests) *) @@ -11,85 +11,83 @@ (*** Monotonicity and unfolding of the function ***) -goal Term.thy "mono(%Z. A <*> List(Z))"; -by (REPEAT (ares_tac [monoI, subset_refl, List_mono, uprod_mono] 1)); -val Term_fun_mono = result(); +goal Term.thy "term(A) = A <*> list(term(A))"; +by (fast_tac (univ_cs addSIs (equalityI :: term.intrs) + addEs [term.elim]) 1); +val term_unfold = result(); -val Term_unfold = Term_fun_mono RS (Term_def RS def_lfp_Tarski); - -(*This justifies using Term in other recursive type definitions*) -goalw Term.thy [Term_def] "!!A B. A<=B ==> Term(A) <= Term(B)"; -by (REPEAT (ares_tac [lfp_mono, subset_refl, List_mono, uprod_mono] 1)); -val Term_mono = result(); +(*This justifies using term in other recursive type definitions*) +goalw Term.thy term.defs "!!A B. A<=B ==> term(A) <= term(B)"; +by (REPEAT (ares_tac ([lfp_mono, list_mono] @ basic_monos) 1)); +val term_mono = result(); -(** Type checking rules -- Term creates well-founded sets **) +(** Type checking -- term creates well-founded sets **) -val prems = goalw Term.thy [Term_def] "Term(Sexp) <= Sexp"; +goalw Term.thy term.defs "term(sexp) <= sexp"; by (rtac lfp_lowerbound 1); -by (fast_tac (univ_cs addIs [Sexp_SconsI, List_Sexp RS subsetD]) 1); -val Term_Sexp = result(); +by (fast_tac (univ_cs addIs [sexp.SconsI, list_sexp RS subsetD]) 1); +val term_sexp = result(); -(* A <= Sexp ==> Term(A) <= Sexp *) -val Term_subset_Sexp = standard - (Term_mono RS (Term_Sexp RSN (2,subset_trans))); +(* A <= sexp ==> term(A) <= sexp *) +val term_subset_sexp = standard ([term_mono, term_sexp] MRS subset_trans); -(** Elimination -- structural induction on the set Term(A) **) +(** Elimination -- structural induction on the set term(A) **) -(*Induction for the set Term(A) *) +(*Induction for the set term(A) *) val [major,minor] = goal Term.thy - "[| M: Term(A); \ -\ !!x zs. [| x: A; zs: List(Term(A)); zs: List({x.R(x)}) \ + "[| M: term(A); \ +\ !!x zs. [| x: A; zs: list(term(A)); zs: list({x.R(x)}) \ \ |] ==> R(x$zs) \ \ |] ==> R(M)"; -by (rtac (major RS (Term_def RS def_induct)) 1); -by (rtac Term_fun_mono 1); -by (REPEAT (eresolve_tac ([uprodE, ssubst, minor] @ - ([Int_lower1,Int_lower2] RL [List_mono RS subsetD])) 1)); -val Term_induct = result(); +by (rtac (major RS term.induct) 1); +by (REPEAT (eresolve_tac ([minor] @ + ([Int_lower1,Int_lower2] RL [list_mono RS subsetD])) 1)); +(*Proof could also use mono_Int RS subsetD RS IntE *) +val term_induct = result(); -(*Induction on Term(A) followed by induction on List *) +(*Induction on term(A) followed by induction on list *) val major::prems = goal Term.thy - "[| M: Term(A); \ + "[| M: term(A); \ \ !!x. [| x: A |] ==> R(x$NIL); \ -\ !!x z zs. [| x: A; z: Term(A); zs: List(Term(A)); R(x$zs) \ +\ !!x z zs. [| x: A; z: term(A); zs: list(term(A)); R(x$zs) \ \ |] ==> R(x $ CONS(z,zs)) \ \ |] ==> R(M)"; -by (rtac (major RS Term_induct) 1); -by (etac List_induct 1); +by (rtac (major RS term_induct) 1); +by (etac list.induct 1); by (REPEAT (ares_tac prems 1)); -val Term_induct2 = result(); +val term_induct2 = result(); (*** Structural Induction on the abstract type 'a term ***) val list_all_ss = map_ss addsimps [list_all_Nil, list_all_Cons]; -val Rep_Term_in_Sexp = - Rep_Term RS (range_Leaf_subset_Sexp RS Term_subset_Sexp RS subsetD); +val Rep_term_in_sexp = + Rep_term RS (range_Leaf_subset_sexp RS term_subset_sexp RS subsetD); (*Induction for the abstract type 'a term*) -val prems = goalw Term.thy [App_def,Rep_TList_def,Abs_TList_def] +val prems = goalw Term.thy [App_def,Rep_Tlist_def,Abs_Tlist_def] "[| !!x ts. list_all(R,ts) ==> R(App(x,ts)) \ \ |] ==> R(t)"; -by (rtac (Rep_Term_inverse RS subst) 1); (*types force good instantiation*) -by (res_inst_tac [("P","Rep_Term(t) : Sexp")] conjunct2 1); -by (rtac (Rep_Term RS Term_induct) 1); -by (REPEAT (ares_tac [conjI, Sexp_SconsI, Term_subset_Sexp RS - List_subset_Sexp,range_Leaf_subset_Sexp] 1 +by (rtac (Rep_term_inverse RS subst) 1); (*types force good instantiation*) +by (res_inst_tac [("P","Rep_term(t) : sexp")] conjunct2 1); +by (rtac (Rep_term RS term_induct) 1); +by (REPEAT (ares_tac [conjI, sexp.SconsI, term_subset_sexp RS + list_subset_sexp, range_Leaf_subset_sexp] 1 ORELSE etac rev_subsetD 1)); -by (eres_inst_tac [("A1","Term(?u)"), ("f1","Rep_Term"), ("g1","Abs_Term")] +by (eres_inst_tac [("A1","term(?u)"), ("f1","Rep_term"), ("g1","Abs_term")] (Abs_map_inverse RS subst) 1); -by (rtac (range_Leaf_subset_Sexp RS Term_subset_Sexp) 1); -by (etac Abs_Term_inverse 1); +by (rtac (range_Leaf_subset_sexp RS term_subset_sexp) 1); +by (etac Abs_term_inverse 1); by (etac rangeE 1); by (hyp_subst_tac 1); by (resolve_tac prems 1); -by (etac List_induct 1); +by (etac list.induct 1); by (etac CollectE 2); by (stac Abs_map_CONS 2); by (etac conjunct1 2); by (etac rev_subsetD 2); -by (rtac List_subset_Sexp 2); +by (rtac list_subset_sexp 2); by (fast_tac set_cs 2); by (ALLGOALS (asm_simp_tac list_all_ss)); val term_induct = result(); @@ -111,66 +109,56 @@ rename_last_tac a ["1","s"] (i+1)]; -(** Introduction rule for Term **) -(* c : A <*> List(Term(A)) ==> c : Term(A) *) -val TermI = standard (Term_unfold RS equalityD2 RS subsetD); - -(*The constant APP is not declared; it is simply . *) -val prems = goal Term.thy "[| M: A; N : List(Term(A)) |] ==> M$N : Term(A)"; -by (REPEAT (resolve_tac (prems@[TermI, ListI, uprodI]) 1)); -val APP_I = result(); - - -(*** Term_rec -- by wf recursion on pred_Sexp ***) +(*** Term_rec -- by wf recursion on pred_sexp ***) val Term_rec_unfold = - wf_pred_Sexp RS wf_trancl RS (Term_rec_def RS def_wfrec); + wf_pred_sexp RS wf_trancl RS (Term_rec_def RS def_wfrec); (** conversion rules **) val [prem] = goal Term.thy - "N: List(Term(A)) ==> \ -\ !M. : pred_Sexp^+ --> \ -\ Abs_map(cut(h, pred_Sexp^+, M), N) = \ + "N: list(term(A)) ==> \ +\ !M. : pred_sexp^+ --> \ +\ Abs_map(cut(h, pred_sexp^+, M), N) = \ \ Abs_map(h,N)"; -by (rtac (prem RS List_induct) 1); +by (rtac (prem RS list.induct) 1); by (simp_tac list_all_ss 1); by (strip_tac 1); -by (etac (pred_Sexp_CONS_D RS conjE) 1); -by (asm_simp_tac (list_all_ss addsimps [trancl_pred_SexpD1, cut_apply]) 1); +by (etac (pred_sexp_CONS_D RS conjE) 1); +by (asm_simp_tac (list_all_ss addsimps [trancl_pred_sexpD1, cut_apply]) 1); val Abs_map_lemma = result(); -val [prem1,prem2,A_subset_Sexp] = goal Term.thy - "[| M: Sexp; N: List(Term(A)); A<=Sexp |] ==> \ +val [prem1,prem2,A_subset_sexp] = goal Term.thy + "[| M: sexp; N: list(term(A)); A<=sexp |] ==> \ \ Term_rec(M$N, d) = d(M, N, Abs_map(%Z. Term_rec(Z,d), N))"; by (rtac (Term_rec_unfold RS trans) 1); by (simp_tac (HOL_ss addsimps [Split, - prem2 RS Abs_map_lemma RS spec RS mp, pred_SexpI2 RS r_into_trancl, - prem1, prem2 RS rev_subsetD, List_subset_Sexp, - Term_subset_Sexp, A_subset_Sexp])1); + prem2 RS Abs_map_lemma RS spec RS mp, pred_sexpI2 RS r_into_trancl, + prem1, prem2 RS rev_subsetD, list_subset_sexp, + term_subset_sexp, A_subset_sexp])1); val Term_rec = result(); (*** term_rec -- by Term_rec ***) local val Rep_map_type1 = read_instantiate_sg (sign_of Term.thy) - [("f","Rep_Term")] Rep_map_type; - val Rep_TList = Rep_Term RS Rep_map_type1; - val Rep_Term_rec = range_Leaf_subset_Sexp RSN (2,Rep_TList RSN(2,Term_rec)); + [("f","Rep_term")] Rep_map_type; + val Rep_Tlist = Rep_term RS Rep_map_type1; + val Rep_Term_rec = range_Leaf_subset_sexp RSN (2,Rep_Tlist RSN(2,Term_rec)); - (*Now avoids conditional rewriting with the premise N: List(Term(A)), + (*Now avoids conditional rewriting with the premise N: list(term(A)), since A will be uninstantiated and will cause rewriting to fail. *) val term_rec_ss = HOL_ss - addsimps [Rep_TList RS (rangeI RS APP_I RS Abs_Term_inverse), - Rep_Term_in_Sexp, Rep_Term_rec, Rep_Term_inverse, + addsimps [Rep_Tlist RS (rangeI RS term.APP_I RS Abs_term_inverse), + Rep_term_in_sexp, Rep_Term_rec, Rep_term_inverse, inj_Leaf, Inv_f_f, - Abs_Rep_map, map_ident, Sexp_LeafI] + Abs_Rep_map, map_ident, sexp.LeafI] in val term_rec = prove_goalw Term.thy - [term_rec_def, App_def, Rep_TList_def, Abs_TList_def] + [term_rec_def, App_def, Rep_Tlist_def, Abs_Tlist_def] "term_rec(App(f,ts), d) = d(f, ts, map (%t. term_rec(t,d), ts))" (fn _ => [simp_tac term_rec_ss 1])