--- a/src/HOLCF/cfun3.ML Sat Apr 05 17:03:38 2003 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,403 +0,0 @@
-(* Title: HOLCF/cfun3.ML
- ID: $Id$
- Author: Franz Regensburger
- Copyright 1993 Technische Universitaet Muenchen
-*)
-
-open Cfun3;
-
-(* ------------------------------------------------------------------------ *)
-(* the contlub property for fapp its 'first' argument *)
-(* ------------------------------------------------------------------------ *)
-
-val contlub_fapp1 = prove_goal Cfun3.thy "contlub(fapp)"
-(fn prems =>
- [
- (rtac contlubI 1),
- (strip_tac 1),
- (rtac (expand_fun_eq RS iffD2) 1),
- (strip_tac 1),
- (rtac (lub_cfun RS thelubI RS ssubst) 1),
- (atac 1),
- (rtac (Cfunapp2 RS ssubst) 1),
- (etac contX_lubcfun 1),
- (rtac (lub_fun RS thelubI RS ssubst) 1),
- (etac (monofun_fapp1 RS ch2ch_monofun) 1),
- (rtac refl 1)
- ]);
-
-
-(* ------------------------------------------------------------------------ *)
-(* the contX property for fapp in its first argument *)
-(* ------------------------------------------------------------------------ *)
-
-val contX_fapp1 = prove_goal Cfun3.thy "contX(fapp)"
-(fn prems =>
- [
- (rtac monocontlub2contX 1),
- (rtac monofun_fapp1 1),
- (rtac contlub_fapp1 1)
- ]);
-
-
-(* ------------------------------------------------------------------------ *)
-(* contlub, contX properties of fapp in its first argument in mixfix _[_] *)
-(* ------------------------------------------------------------------------ *)
-
-val contlub_cfun_fun = prove_goal Cfun3.thy
-"is_chain(FY) ==>\
-\ lub(range(FY))[x] = lub(range(%i.FY(i)[x]))"
-(fn prems =>
- [
- (cut_facts_tac prems 1),
- (rtac trans 1),
- (etac (contlub_fapp1 RS contlubE RS spec RS mp RS fun_cong) 1),
- (rtac (thelub_fun RS ssubst) 1),
- (etac (monofun_fapp1 RS ch2ch_monofun) 1),
- (rtac refl 1)
- ]);
-
-
-val contX_cfun_fun = prove_goal Cfun3.thy
-"is_chain(FY) ==>\
-\ range(%i.FY(i)[x]) <<| lub(range(FY))[x]"
-(fn prems =>
- [
- (cut_facts_tac prems 1),
- (rtac thelubE 1),
- (etac ch2ch_fappL 1),
- (etac (contlub_cfun_fun RS sym) 1)
- ]);
-
-
-(* ------------------------------------------------------------------------ *)
-(* contlub, contX properties of fapp in both argument in mixfix _[_] *)
-(* ------------------------------------------------------------------------ *)
-
-val contlub_cfun = prove_goal Cfun3.thy
-"[|is_chain(FY);is_chain(TY)|] ==>\
-\ lub(range(FY))[lub(range(TY))] = lub(range(%i.FY(i)[TY(i)]))"
-(fn prems =>
- [
- (cut_facts_tac prems 1),
- (rtac contlub_CF2 1),
- (rtac contX_fapp1 1),
- (rtac allI 1),
- (rtac contX_fapp2 1),
- (atac 1),
- (atac 1)
- ]);
-
-val contX_cfun = prove_goal Cfun3.thy
-"[|is_chain(FY);is_chain(TY)|] ==>\
-\ range(%i.FY(i)[TY(i)]) <<| lub(range(FY))[lub(range(TY))]"
-(fn prems =>
- [
- (cut_facts_tac prems 1),
- (rtac thelubE 1),
- (rtac (monofun_fapp1 RS ch2ch_MF2LR) 1),
- (rtac allI 1),
- (rtac monofun_fapp2 1),
- (atac 1),
- (atac 1),
- (etac (contlub_cfun RS sym) 1),
- (atac 1)
- ]);
-
-
-(* ------------------------------------------------------------------------ *)
-(* contX2contX lemma for fapp *)
-(* ------------------------------------------------------------------------ *)
-
-val contX2contX_fapp = prove_goal Cfun3.thy
- "[|contX(%x.ft(x));contX(%x.tt(x))|] ==> contX(%x.(ft(x))[tt(x)])"
- (fn prems =>
- [
- (cut_facts_tac prems 1),
- (rtac contX2contX_app2 1),
- (rtac contX2contX_app2 1),
- (rtac contX_const 1),
- (rtac contX_fapp1 1),
- (atac 1),
- (rtac contX_fapp2 1),
- (atac 1)
- ]);
-
-
-
-(* ------------------------------------------------------------------------ *)
-(* contX2mono Lemma for %x. LAM y. c1(x,y) *)
-(* ------------------------------------------------------------------------ *)
-
-val contX2mono_LAM = prove_goal Cfun3.thy
- "[|!x.contX(c1(x)); !y.monofun(%x.c1(x,y))|] ==>\
-\ monofun(%x. LAM y. c1(x,y))"
-(fn prems =>
- [
- (cut_facts_tac prems 1),
- (rtac monofunI 1),
- (strip_tac 1),
- (rtac (less_cfun RS ssubst) 1),
- (rtac (less_fun RS ssubst) 1),
- (rtac allI 1),
- (rtac (beta_cfun RS ssubst) 1),
- (etac spec 1),
- (rtac (beta_cfun RS ssubst) 1),
- (etac spec 1),
- (etac ((hd (tl prems)) RS spec RS monofunE RS spec RS spec RS mp) 1)
- ]);
-
-(* ------------------------------------------------------------------------ *)
-(* contX2contX Lemma for %x. LAM y. c1(x,y) *)
-(* ------------------------------------------------------------------------ *)
-
-val contX2contX_LAM = prove_goal Cfun3.thy
- "[| !x.contX(c1(x)); !y.contX(%x.c1(x,y)) |] ==> contX(%x. LAM y. c1(x,y))"
-(fn prems =>
- [
- (cut_facts_tac prems 1),
- (rtac monocontlub2contX 1),
- (etac contX2mono_LAM 1),
- (rtac (contX2mono RS allI) 1),
- (etac spec 1),
- (rtac contlubI 1),
- (strip_tac 1),
- (rtac (thelub_cfun RS ssubst) 1),
- (rtac (contX2mono_LAM RS ch2ch_monofun) 1),
- (atac 1),
- (rtac (contX2mono RS allI) 1),
- (etac spec 1),
- (atac 1),
- (res_inst_tac [("f","fabs")] arg_cong 1),
- (rtac ext 1),
- (rtac (beta_cfun RS ext RS ssubst) 1),
- (etac spec 1),
- (rtac (contX2contlub RS contlubE
- RS spec RS mp ) 1),
- (etac spec 1),
- (atac 1)
- ]);
-
-(* ------------------------------------------------------------------------ *)
-(* elimination of quantifier in premisses of contX2contX_LAM yields good *)
-(* lemma for the contX tactic *)
-(* ------------------------------------------------------------------------ *)
-
-val contX2contX_LAM2 = (allI RSN (2,(allI RS contX2contX_LAM)));
-(*
- [| !!x. contX(?c1.0(x)); !!y. contX(%x. ?c1.0(x,y)) |] ==>
- contX(%x. LAM y. ?c1.0(x,y))
-*)
-
-(* ------------------------------------------------------------------------ *)
-(* contX2contX tactic *)
-(* ------------------------------------------------------------------------ *)
-
-val contX_lemmas = [contX_const, contX_id, contX_fapp2,
- contX2contX_fapp,contX2contX_LAM2];
-
-
-val contX_tac = (fn i => (resolve_tac contX_lemmas i));
-
-val contX_tacR = (fn i => (REPEAT (contX_tac i)));
-
-(* ------------------------------------------------------------------------ *)
-(* function application _[_] is strict in its first arguments *)
-(* ------------------------------------------------------------------------ *)
-
-val strict_fapp1 = prove_goal Cfun3.thy "UU[x] = UU"
- (fn prems =>
- [
- (rtac (inst_cfun_pcpo RS ssubst) 1),
- (rewrite_goals_tac [UU_cfun_def]),
- (rtac (beta_cfun RS ssubst) 1),
- (contX_tac 1),
- (rtac refl 1)
- ]);
-
-
-(* ------------------------------------------------------------------------ *)
-(* results about strictify *)
-(* ------------------------------------------------------------------------ *)
-
-val Istrictify1 = prove_goalw Cfun3.thy [Istrictify_def]
- "Istrictify(f)(UU)=UU"
- (fn prems =>
- [
- (rtac select_equality 1),
- (fast_tac HOL_cs 1),
- (fast_tac HOL_cs 1)
- ]);
-
-val Istrictify2 = prove_goalw Cfun3.thy [Istrictify_def]
- "~x=UU ==> Istrictify(f)(x)=f[x]"
- (fn prems =>
- [
- (cut_facts_tac prems 1),
- (rtac select_equality 1),
- (fast_tac HOL_cs 1),
- (fast_tac HOL_cs 1)
- ]);
-
-val monofun_Istrictify1 = prove_goal Cfun3.thy "monofun(Istrictify)"
- (fn prems =>
- [
- (rtac monofunI 1),
- (strip_tac 1),
- (rtac (less_fun RS iffD2) 1),
- (strip_tac 1),
- (res_inst_tac [("Q","xa=UU")] (excluded_middle RS disjE) 1),
- (rtac (Istrictify2 RS ssubst) 1),
- (atac 1),
- (rtac (Istrictify2 RS ssubst) 1),
- (atac 1),
- (rtac monofun_cfun_fun 1),
- (atac 1),
- (hyp_subst_tac 1),
- (rtac (Istrictify1 RS ssubst) 1),
- (rtac (Istrictify1 RS ssubst) 1),
- (rtac refl_less 1)
- ]);
-
-val monofun_Istrictify2 = prove_goal Cfun3.thy "monofun(Istrictify(f))"
- (fn prems =>
- [
- (rtac monofunI 1),
- (strip_tac 1),
- (res_inst_tac [("Q","x=UU")] (excluded_middle RS disjE) 1),
- (rtac (Istrictify2 RS ssubst) 1),
- (etac notUU_I 1),
- (atac 1),
- (rtac (Istrictify2 RS ssubst) 1),
- (atac 1),
- (rtac monofun_cfun_arg 1),
- (atac 1),
- (hyp_subst_tac 1),
- (rtac (Istrictify1 RS ssubst) 1),
- (rtac minimal 1)
- ]);
-
-
-val contlub_Istrictify1 = prove_goal Cfun3.thy "contlub(Istrictify)"
- (fn prems =>
- [
- (rtac contlubI 1),
- (strip_tac 1),
- (rtac (expand_fun_eq RS iffD2) 1),
- (strip_tac 1),
- (rtac (thelub_fun RS ssubst) 1),
- (etac (monofun_Istrictify1 RS ch2ch_monofun) 1),
- (res_inst_tac [("Q","x=UU")] (excluded_middle RS disjE) 1),
- (rtac (Istrictify2 RS ssubst) 1),
- (atac 1),
- (rtac (Istrictify2 RS ext RS ssubst) 1),
- (atac 1),
- (rtac (thelub_cfun RS ssubst) 1),
- (atac 1),
- (rtac (beta_cfun RS ssubst) 1),
- (rtac contX_lubcfun 1),
- (atac 1),
- (rtac refl 1),
- (hyp_subst_tac 1),
- (rtac (Istrictify1 RS ssubst) 1),
- (rtac (Istrictify1 RS ext RS ssubst) 1),
- (rtac (chain_UU_I_inverse RS sym) 1),
- (rtac (refl RS allI) 1)
- ]);
-
-val contlub_Istrictify2 = prove_goal Cfun3.thy "contlub(Istrictify(f))"
- (fn prems =>
- [
- (rtac contlubI 1),
- (strip_tac 1),
- (res_inst_tac [("Q","lub(range(Y))=UU")] classical2 1),
- (res_inst_tac [("t","lub(range(Y))")] subst 1),
- (rtac sym 1),
- (atac 1),
- (rtac (Istrictify1 RS ssubst) 1),
- (rtac sym 1),
- (rtac chain_UU_I_inverse 1),
- (strip_tac 1),
- (res_inst_tac [("t","Y(i)"),("s","UU")] subst 1),
- (rtac sym 1),
- (rtac (chain_UU_I RS spec) 1),
- (atac 1),
- (atac 1),
- (rtac Istrictify1 1),
- (rtac (Istrictify2 RS ssubst) 1),
- (atac 1),
- (res_inst_tac [("s","lub(range(%i. f[Y(i)]))")] trans 1),
- (rtac contlub_cfun_arg 1),
- (atac 1),
- (rtac lub_equal2 1),
- (rtac (chain_mono2 RS exE) 1),
- (atac 2),
- (rtac chain_UU_I_inverse2 1),
- (atac 1),
- (rtac exI 1),
- (strip_tac 1),
- (rtac (Istrictify2 RS sym) 1),
- (fast_tac HOL_cs 1),
- (rtac ch2ch_monofun 1),
- (rtac monofun_fapp2 1),
- (atac 1),
- (rtac ch2ch_monofun 1),
- (rtac monofun_Istrictify2 1),
- (atac 1)
- ]);
-
-
-val contX_Istrictify1 = (contlub_Istrictify1 RS
- (monofun_Istrictify1 RS monocontlub2contX));
-
-val contX_Istrictify2 = (contlub_Istrictify2 RS
- (monofun_Istrictify2 RS monocontlub2contX));
-
-
-val strictify1 = prove_goalw Cfun3.thy [strictify_def]
- "strictify[f][UU]=UU"
- (fn prems =>
- [
- (rtac (beta_cfun RS ssubst) 1),
- (contX_tac 1),
- (rtac contX_Istrictify2 1),
- (rtac contX2contX_CF1L 1),
- (rtac contX_Istrictify1 1),
- (rtac (beta_cfun RS ssubst) 1),
- (rtac contX_Istrictify2 1),
- (rtac Istrictify1 1)
- ]);
-
-val strictify2 = prove_goalw Cfun3.thy [strictify_def]
- "~x=UU ==> strictify[f][x]=f[x]"
- (fn prems =>
- [
- (rtac (beta_cfun RS ssubst) 1),
- (contX_tac 1),
- (rtac contX_Istrictify2 1),
- (rtac contX2contX_CF1L 1),
- (rtac contX_Istrictify1 1),
- (rtac (beta_cfun RS ssubst) 1),
- (rtac contX_Istrictify2 1),
- (rtac Istrictify2 1),
- (resolve_tac prems 1)
- ]);
-
-
-(* ------------------------------------------------------------------------ *)
-(* Instantiate the simplifier *)
-(* ------------------------------------------------------------------------ *)
-
-val Cfun_rews = [minimal,refl_less,beta_cfun,strict_fapp1,strictify1,
- strictify2];
-
-(* ------------------------------------------------------------------------ *)
-(* use contX_tac as autotac. *)
-(* ------------------------------------------------------------------------ *)
-
-val Cfun_ss = HOL_ss
- addsimps Cfun_rews
- setsolver
- (fn thms => (resolve_tac (TrueI::refl::thms)) ORELSE' atac ORELSE'
- (fn i => DEPTH_SOLVE_1 (contX_tac i))
- );