Removed unused things from QuotMain.
--- a/FSet.thy Wed Nov 25 10:52:21 2009 +0100
+++ b/FSet.thy Wed Nov 25 11:41:42 2009 +0100
@@ -176,8 +176,6 @@
term fmap
thm fmap_def
-ML {* prop_of @{thm fmap_def} *}
-
ML {* val defs = @{thms EMPTY_def IN_def FUNION_def CARD_def INSERT_def fmap_def FOLD_def} *}
lemma memb_rsp:
@@ -303,8 +301,6 @@
@{thms ho_memb_rsp ho_cons_rsp ho_card1_rsp ho_map_rsp ho_append_rsp ho_fold_rsp}
@ @{thms ho_all_prs ho_ex_prs} *}
-ML {* fun lift_thm_fset lthy t = lift_thm lthy qty "fset" rsp_thms defs t *}
-ML {* fun lift_thm_g_fset lthy t g = lift_thm_goal lthy qty "fset" rsp_thms defs t g *}
ML {* val (rty, rel, rel_refl, rel_eqv) = lookup_quot_data @{context} qty *}
ML {* val (trans2, reps_same, absrep, quot) = lookup_quot_thms @{context} "fset"; *}
ML {* val consts = lookup_quot_consts defs *}
@@ -378,9 +374,6 @@
ML {* val rsp_thms = @{thms list_rec_rsp list_case_rsp} @ rsp_thms *}
ML {* val defs = @{thms fset_rec_def fset_case_def} @ defs *}
-
-ML {* fun lift_thm_fset lthy t = lift_thm lthy qty "fset" rsp_thms defs t *}
-ML {* fun lift_thm_g_fset lthy t g = lift_thm_goal lthy qty "fset" rsp_thms defs t g *}
ML {* fun lift_tac_fset lthy t = lift_tac lthy t rel_eqv rel_refl rty quot trans2 rsp_thms reps_same defs *}
ML {* val aps = findaps rty (prop_of (atomize_thm @{thm list.recs(2)})) *}
@@ -397,9 +390,6 @@
ML {* val aps = findaps rty (prop_of (atomize_thm @{thm list.cases(2)})) *}
ML {* val app_prs_thms = map (applic_prs @{context} rty qty absrep) aps *}
-
-
-ML {* map (lift_thm_fset @{context}) @{thms list.cases(2)} *}
lemma "fset_case (f1::'t) f2 (INSERT a xa) = f2 a xa"
apply (tactic {* lift_tac_fset @{context} @{thm list.cases(2)} 1 *})
apply (tactic {* REPEAT_ALL_NEW (EqSubst.eqsubst_tac @{context} [0] app_prs_thms) 1 *})
@@ -417,100 +407,14 @@
done
-
-(* Construction site starts here *)
-
+ML {* fun r_mk_comb_tac_fset lthy = r_mk_comb_tac lthy rty quot rel_refl trans2 rsp_thms *}
-ML {* val consts = lookup_quot_consts defs *}
-ML {* val (rty, rel, rel_refl, rel_eqv) = lookup_quot_data @{context} qty *}
-ML {* val (trans2, reps_same, absrep, quot) = lookup_quot_thms @{context} "fset" *}
-
-ML {* val t_a = atomize_thm @{thm list_induct_part} *}
-(* prove {* build_regularize_goal t_a rty rel @{context} *}
- ML_prf {* fun tac ctxt = FIRST' [
- rtac rel_refl,
- atac,
- rtac @{thm universal_twice},
- (rtac @{thm impI} THEN' atac),
- rtac @{thm implication_twice},
- //comented out rtac @{thm equality_twice}, //
- EqSubst.eqsubst_tac ctxt [0]
- [(@{thm equiv_res_forall} OF [rel_eqv]),
- (@{thm equiv_res_exists} OF [rel_eqv])],
- (rtac @{thm impI} THEN' (asm_full_simp_tac (Simplifier.context ctxt HOL_ss)) THEN' rtac rel_refl),
- (rtac @{thm RIGHT_RES_FORALL_REGULAR})
- ]; *}
- apply (atomize(full))
- apply (tactic {* REPEAT_ALL_NEW (tac @{context}) 1 *})
- done *)
-ML {* val t_r = regularize t_a rty rel rel_eqv rel_refl @{context} *}
-ML {*
- val rt = build_repabs_term @{context} t_r consts rty qty
- val rg = Logic.mk_equals ((Thm.prop_of t_r), rt);
-*}
-prove {* Syntax.check_term @{context} rg *}
-ML_prf {* fun r_mk_comb_tac_fset lthy = r_mk_comb_tac lthy rty quot rel_refl trans2 rsp_thms *}
-apply(atomize(full))
-apply (tactic {* REPEAT_ALL_NEW (r_mk_comb_tac_fset @{context}) 1 *})
-done
-ML {*
-val t_t = repabs @{context} t_r consts rty qty quot rel_refl trans2 rsp_thms
-*}
-
-ML {* val abs = findabs rty (prop_of (t_a)) *}
-ML {* val aps = findaps rty (prop_of (t_a)) *}
-ML {* val lam_prs_thms = map (make_simp_prs_thm @{context} quot @{thm LAMBDA_PRS}) abs *}
-ML {* val app_prs_thms = map (applic_prs @{context} rty qty absrep) aps *}
-ML {* val lam_prs_thms = map Thm.varifyT lam_prs_thms *}
-ML {* t_t *}
-ML {* val (alls, exs) = findallex @{context} rty qty (prop_of t_a); *}
-ML {* val allthms = map (make_allex_prs_thm @{context} quot @{thm FORALL_PRS}) alls *}
-ML {* val t_l0 = repeat_eqsubst_thm @{context} (app_prs_thms) t_t *}
-ML app_prs_thms
-ML {* val t_l = repeat_eqsubst_thm @{context} (lam_prs_thms) t_l0 *}
-ML lam_prs_thms
-ML {* val t_id = simp_ids @{context} t_l *}
-thm INSERT_def
-ML {* val defs_sym = flat (map (add_lower_defs @{context}) defs) *}
-ML {* val t_d = repeat_eqsubst_thm @{context} defs_sym t_id *}
-ML allthms
-thm FORALL_PRS
-ML {* val t_al = MetaSimplifier.rewrite_rule (allthms) t_d *}
-ML {* val t_s = MetaSimplifier.rewrite_rule @{thms QUOT_TYPE_I_fset.REPS_same} t_al *}
-ML {* ObjectLogic.rulify t_s *}
-
-ML {* val gl = @{term "P (x :: 'a list) (EMPTY :: 'a fset) \<Longrightarrow> (\<And>e t. P x t \<Longrightarrow> P x (INSERT e t)) \<Longrightarrow> P x l"} *}
-ML {* val gla = atomize_goal @{theory} gl *}
-
-prove t_r: {* mk_REGULARIZE_goal @{context} (prop_of t_a) gla *}
-
-ML_prf {* fun tac ctxt = FIRST' [
- rtac rel_refl,
- atac,
- rtac @{thm universal_twice},
- (rtac @{thm impI} THEN' atac),
- rtac @{thm implication_twice},
- (*rtac @{thm equality_twice},*)
- EqSubst.eqsubst_tac ctxt [0]
- [(@{thm equiv_res_forall} OF [rel_eqv]),
- (@{thm equiv_res_exists} OF [rel_eqv])],
- (rtac @{thm impI} THEN' (asm_full_simp_tac (Simplifier.context ctxt HOL_ss)) THEN' rtac rel_refl),
- (rtac @{thm RIGHT_RES_FORALL_REGULAR})
- ]; *}
-
- apply (atomize(full))
- apply (tactic {* REPEAT_ALL_NEW (tac @{context}) 1 *})
- done
-
-ML {* val t_r = @{thm t_r} OF [t_a] *}
-
-ML {* val ttt = mk_inj_REPABS_goal @{context} (prop_of t_r, gla) *}
-ML {* val si = simp_ids_trm (cterm_of @{theory} ttt) *}
-prove t_t: {* term_of si *}
-ML_prf {* fun r_mk_comb_tac_fset lthy = r_mk_comb_tac lthy rty quot rel_refl trans2 rsp_thms *}
-apply(atomize(full))
+(* Construction site starts here *)
+lemma "P (x :: 'a list) (EMPTY :: 'a fset) \<Longrightarrow> (\<And>e t. P x t \<Longrightarrow> P x (INSERT e t)) \<Longrightarrow> P x l"
+apply (tactic {* procedure_tac @{thm list_induct_part} @{context} 1 *})
+apply (tactic {* regularize_tac @{context} rel_eqv rel_refl 1 *})
apply (tactic {* (APPLY_RSP_TAC rty @{context}) 1 *})
apply (rule FUN_QUOTIENT)
apply (rule FUN_QUOTIENT)
@@ -579,13 +483,7 @@
apply (tactic {* (r_mk_comb_tac_fset @{context}) 1 *})
apply (tactic {* (r_mk_comb_tac_fset @{context}) 1 *})
apply (tactic {* (r_mk_comb_tac_fset @{context}) 1 *})
+apply (tactic {* clean_tac @{context} quot defs reps_same 1 *})
done
-thm t_t
-ML {* val t_t = @{thm Pure.equal_elim_rule1} OF [@{thm t_t}, t_r] *}
-ML {* val t_l = repeat_eqsubst_thm @{context} (lam_prs_thms) t_t *}
-ML {* val t_d = repeat_eqsubst_thm @{context} defs_sym t_l *}
-ML {* val t_al = MetaSimplifier.rewrite_rule (allthms) t_d *}
-ML {* val t_s = MetaSimplifier.rewrite_rule @{thms QUOT_TYPE_I_fset.REPS_same} t_al *}
-
end
--- a/IntEx.thy Wed Nov 25 10:52:21 2009 +0100
+++ b/IntEx.thy Wed Nov 25 11:41:42 2009 +0100
@@ -141,10 +141,6 @@
ML {* val consts = lookup_quot_consts defs *}
ML {*
-fun lift_thm_my_int lthy t =
- lift_thm lthy qty ty_name rsp_thms defs t
-fun lift_thm_g_my_int lthy t g =
- lift_thm_goal lthy qty ty_name rsp_thms defs t g
fun lift_tac_fset lthy t =
lift_tac lthy t rel_eqv rel_refl rty quot trans2 rsp_thms reps_same defs
*}
@@ -164,6 +160,21 @@
by (tactic {* lift_tac_fset @{context} @{thm plus_assoc_pre} 1 *})
+lemma ho_tst: "foldl my_plus x [] = x"
+apply simp
+done
+
+lemma "foldl PLUS x [] = x"
+apply (tactic {* lift_tac_fset @{context} @{thm ho_tst} 1 *})
+prefer 3
+apply(tactic {* clean_tac @{context} quot @{thms PLUS_def} reps_same 1 *})
+sorry
+
+(*
+ FIXME: All below is your construction code; mostly commented out as it
+ does not work.
+*)
+
ML {*
mk_REGULARIZE_goal @{context}
@{term "\<forall>i j k. my_plus (my_plus i j) k \<approx> my_plus i (my_plus j k)"}
@@ -172,13 +183,6 @@
|> writeln
*}
-
-ML {*
-val (rty, rel, rel_refl, rel_eqv) = lookup_quot_data @{context} @{typ "my_int"}
-val (trans2, reps_same, absrep, quot) = lookup_quot_thms @{context} "my_int"
-*}
-
-
lemma "PLUS (PLUS i j) k = PLUS i (PLUS j k)"
apply(tactic {* procedure_tac @{thm plus_assoc_pre} @{context} 1 *})
apply(tactic {* regularize_tac @{context} rel_eqv rel_refl 1 *})
@@ -188,7 +192,7 @@
(*
-does not work.
+
ML {*
fun r_mk_comb_tac ctxt rty quot_thm reflex_thm trans_thm rsp_thms =
(REPEAT1 o FIRST1)
@@ -209,14 +213,6 @@
DT ctxt "E" (WEAK_LAMBDA_RES_TAC ctxt),
DT ctxt "F" (CHANGED' (asm_full_simp_tac (HOL_ss addsimps @{thms FUN_REL_EQ})))]
*}
-*)
-
-ML {*
-val (rty, rel, rel_refl, rel_eqv) = lookup_quot_data @{context} @{typ "my_int"}
-val (trans2, reps_same, absrep, quot) = lookup_quot_thms @{context} "my_int"
-val consts = lookup_quot_consts defs
-*}
-
ML {*
mk_inj_REPABS_goal @{context} (reg_atrm, aqtrm)
@@ -238,66 +234,6 @@
|> writeln
*}
-
-lemma ho_tst: "foldl my_plus x [] = x"
-apply simp
-done
-
-text {* Below is the construction site code used if things do not work *}
-ML {* val (rty, rel, rel_refl, rel_eqv) = lookup_quot_data @{context} qty *}
-ML {* val (trans2, reps_same, absrep, quot) = lookup_quot_thms @{context} "my_int" *}
-(* ML {* val consts = [@{const_name my_plus}] *}*)
-ML {* val consts = lookup_quot_consts defs *}
-ML {* val t_a = atomize_thm @{thm ho_tst} *}
-
-(*
-prove t_r: {* build_regularize_goal t_a rty rel @{context} *}
-ML_prf {* fun tac ctxt =
- (ObjectLogic.full_atomize_tac) THEN'
- REPEAT_ALL_NEW (FIRST' [
- rtac rel_refl,
- atac,
- rtac @{thm universal_twice},
- (rtac @{thm impI} THEN' atac),
- (*rtac @{thm equality_twice},*)
- EqSubst.eqsubst_tac ctxt [0]
- [(@{thm equiv_res_forall} OF [rel_eqv]),
- (@{thm equiv_res_exists} OF [rel_eqv])],
- (rtac @{thm impI} THEN' (asm_full_simp_tac (Simplifier.context ctxt HOL_ss)) THEN' rtac rel_refl),
- (rtac @{thm RIGHT_RES_FORALL_REGULAR})
- ]);*}
-apply (atomize(full))
-apply (tactic {* tac @{context} 1 *})
-apply (auto)
-done
-ML {* val t_r = @{thm t_r} OF [t_a] *}*)
-ML {* val t_r = regularize t_a rty rel rel_eqv rel_refl @{context} *}
-ML {*
- val rt = build_repabs_term @{context} t_r consts rty qty
- val rg = Logic.mk_equals ((Thm.prop_of t_r), rt);
-*}
+*)
-
-prove t_t: rg
-apply(atomize(full))
-ML_prf {* fun r_mk_comb_tac_int lthy = r_mk_comb_tac lthy rty quot rel_refl trans2 rsp_thms *}
-apply (tactic {* REPEAT_ALL_NEW (r_mk_comb_tac_int @{context}) 1 *})
-done
-ML {* val t_t = @{thm Pure.equal_elim_rule1} OF [@{thm t_t},t_r] *}
-ML {* val abs = findabs rty (prop_of t_a) *}
-ML {* val aps = findaps rty (prop_of t_a); *}
-ML {* val simp_lam_prs_thms = map (make_simp_prs_thm @{context} quot @{thm LAMBDA_PRS}) abs *}
-
-(*ML {* val t_t = repabs @{context} @{thm t_r} consts rty qty quot rel_refl trans2 rsp_thms *}*)
-ML findallex
-ML {* val (alls, exs) = findallex @{context} rty qty (prop_of t_a) *}
-ML {* val allthms = map (make_allex_prs_thm @{context} quot @{thm FORALL_PRS}) alls *}
-ML {* val t_a = MetaSimplifier.rewrite_rule (allthms) t_t *}
-ML {* val t_l = repeat_eqsubst_thm @{context} simp_lam_prs_thms t_a *}
-ML {* val defs_sym = flat (map (add_lower_defs @{context}) defs) *}
-ML {* val t_d = repeat_eqsubst_thm @{context} defs_sym t_l *}
-ML {* val t_r = MetaSimplifier.rewrite_rule [reps_same] t_d *}
-ML {* ObjectLogic.rulify t_r *}
-ML {* @{term "Trueprop"} *}
-
--- a/LamEx.thy Wed Nov 25 10:52:21 2009 +0100
+++ b/LamEx.thy Wed Nov 25 11:41:42 2009 +0100
@@ -176,7 +176,6 @@
ML {* val rsp_thms = @{thms perm_rsp fresh_rsp rVar_rsp rApp_rsp rLam_rsp rfv_rsp} @
@{thms ho_all_prs ho_ex_prs} *}
-ML {* fun lift_thm_lam lthy t = lift_thm lthy qty "lam" rsp_thms defs t *}
ML {* val (rty, rel, rel_refl, rel_eqv) = lookup_quot_data @{context} qty *}
ML {* val consts = lookup_quot_consts defs *}
ML {* val (trans2, reps_same, absrep, quot) = lookup_quot_thms @{context} "lam" *}
@@ -268,101 +267,6 @@
(* Construction Site code *)
-ML {* val (rty, rel, rel_refl, rel_eqv) = lookup_quot_data @{context} qty *}
-ML {* val consts = lookup_quot_consts defs *}
-ML {* val (trans2, reps_same, absrep, quot) = lookup_quot_thms @{context} "lam" *}
-
-ML {* val t_a = atomize_thm @{thm alpha.cases} *}
-(* prove {* build_regularize_goal t_a rty rel @{context} *}
-ML_prf {* fun tac ctxt =
- (FIRST' [
- rtac rel_refl,
- atac,
- rtac @{thm universal_twice},
- (rtac @{thm impI} THEN' atac),
- rtac @{thm implication_twice},
- EqSubst.eqsubst_tac ctxt [0]
- [(@{thm equiv_res_forall} OF [rel_eqv]),
- (@{thm equiv_res_exists} OF [rel_eqv])],
- (rtac @{thm impI} THEN' (asm_full_simp_tac (Simplifier.context ctxt HOL_ss)) THEN' rtac rel_refl),
- (rtac @{thm RIGHT_RES_FORALL_REGULAR})
- ]);
- *}
- apply (tactic {* tac @{context} 1 *}) *)
-ML {* val t_r = regularize t_a rty rel rel_eqv rel_refl @{context} *}
-
-ML {*
- val rt = build_repabs_term @{context} t_r consts rty qty
- val rg = Logic.mk_equals ((Thm.prop_of t_r), rt);
-*}
-prove rg
-apply(atomize(full))
-(*ML_prf {*
-fun r_mk_comb_tac ctxt rty quot_thm reflex_thm trans_thm rsp_thms =
- (FIRST' [
- rtac trans_thm,
- LAMBDA_RES_TAC ctxt,
- res_forall_rsp_tac ctxt,
- res_exists_rsp_tac ctxt,
- (
- (simp_tac ((Simplifier.context ctxt HOL_ss) addsimps rsp_thms))
- THEN_ALL_NEW (fn _ => no_tac)
- ),
- (instantiate_tac @{thm REP_ABS_RSP(1)} ctxt THEN' (RANGE [quotient_tac quot_thm])),
- rtac refl,
- (APPLY_RSP_TAC rty ctxt THEN' (RANGE [quotient_tac quot_thm, quotient_tac quot_thm])),
- Cong_Tac.cong_tac @{thm cong},
- rtac @{thm ext},
- rtac reflex_thm,
- atac,
- (
- (simp_tac ((Simplifier.context ctxt HOL_ss) addsimps @{thms FUN_REL.simps}))
- THEN_ALL_NEW (fn _ => no_tac)
- ),
- WEAK_LAMBDA_RES_TAC ctxt
- ]);
-*}*)
-ML_prf {*
- fun r_mk_comb_tac_lam lthy = r_mk_comb_tac lthy rty quot rel_refl trans2 rsp_thms
-*}
-apply (tactic {* (r_mk_comb_tac_lam @{context}) 1 *})
-
-
-
-
-
-
-apply (tactic {* REPEAT_ALL_NEW (r_mk_comb_tac_lam @{context}) 1 *})
-
-
-ML {* val t_t = repabs @{context} t_r consts rty qty quot rel_refl trans2 rsp_thms *}
-ML {* val abs = findabs rty (prop_of (atomize_thm @{thm alpha.induct})) *}
-ML {* val aps = findaps rty (prop_of (atomize_thm @{thm alpha.induct})) *}
-ML {* val (alls, exs) = findallex rty qty (prop_of (atomize_thm @{thm alpha.induct})) *}
-ML {* val allthms = map (make_allex_prs_thm @{context} quot @{thm FORALL_PRS} ) alls *}
-ML {* val exthms = map (make_allex_prs_thm @{context} quot @{thm EXISTS_PRS} ) exs *}
-ML {* val t_a = MetaSimplifier.rewrite_rule allthms t_t *}
-ML {* val simp_app_prs_thms = map (make_simp_prs_thm @{context} quot @{thm APP_PRS}) aps *}
-ML {* val simp_lam_prs_thms = map (make_simp_prs_thm @{context} quot @{thm LAMBDA_PRS}) abs *}
-ML {* val t_l = repeat_eqsubst_thm @{context} (simp_lam_prs_thms) t_a *}
-ML {* val t_l1 = repeat_eqsubst_thm @{context} simp_app_prs_thms t_l *}
-ML {* val defs_sym = add_lower_defs @{context} defs; *}
-ML {* val defs_sym_eq = map (fn x => eq_reflection OF [x]) defs_sym *}
-ML {* val t_d0 = MetaSimplifier.rewrite_rule defs_sym_eq t_l1 *}
-ML {* val t_d = repeat_eqsubst_thm @{context} defs_sym t_d0 *}
-ML {* val t_r = MetaSimplifier.rewrite_rule [reps_same] t_d *}
-ML {* val t_r1 = repeat_eqsubst_thm @{context} @{thms fun_map.simps} t_r *}
-ML {* val t_r2 = MetaSimplifier.rewrite_rule @{thms QUOT_TYPE_I_lam.thm10} t_r1 *}
-ML {* val t_r3 = MetaSimplifier.rewrite_rule @{thms eq_reflection[OF id_apply]} t_r2 *}
-ML {* val alpha_induct = ObjectLogic.rulify t_r3 *}
-
-(*local_setup {*
- Quotient.note (@{binding "alpha_induct"}, alpha_induct) #> snd
-*}*)
-
-thm alpha_induct
-thm alpha.induct
-
@@ -384,6 +288,9 @@
declare [[map noption = (option_map, option_rel)]]
+lemma "option_map id = id"
+sorry
+
lemma OPT_QUOTIENT:
assumes q: "QUOTIENT R Abs Rep"
shows "QUOTIENT (option_rel R) (option_map Abs) (option_map Rep)"
--- a/QuotMain.thy Wed Nov 25 10:52:21 2009 +0100
+++ b/QuotMain.thy Wed Nov 25 11:41:42 2009 +0100
@@ -227,35 +227,6 @@
*)
-text {* tyRel takes a type and builds a relation that a quantifier over this
- type needs to respect. *}
-ML {*
-fun tyRel ty rty rel lthy =
- if Sign.typ_instance (ProofContext.theory_of lthy) (ty, rty)
- then rel
- else (case ty of
- Type (s, tys) =>
- let
- val tys_rel = map (fn ty => ty --> ty --> @{typ bool}) tys;
- val ty_out = ty --> ty --> @{typ bool};
- val tys_out = tys_rel ---> ty_out;
- in
- (case (maps_lookup (ProofContext.theory_of lthy) s) of
- SOME (info) => list_comb (Const (#relfun info, tys_out),
- map (fn ty => tyRel ty rty rel lthy) tys)
- | NONE => HOLogic.eq_const ty
- )
- end
- | _ => HOLogic.eq_const ty)
-*}
-
-(*
-ML {* cterm_of @{theory}
- (tyRel @{typ "'a \<Rightarrow> 'a list \<Rightarrow> 't \<Rightarrow> 't"} (Logic.varifyT @{typ "'a list"})
- @{term "f::('a list \<Rightarrow> 'a list \<Rightarrow> bool)"} @{context})
-*}
-*)
-
definition
Babs :: "('a \<Rightarrow> bool) \<Rightarrow> ('a \<Rightarrow> 'b) \<Rightarrow> 'a \<Rightarrow> 'b"
where
@@ -273,94 +244,6 @@
*}
-ML {*
-fun mk_babs ty ty' = Const (@{const_name "Babs"}, [ty' --> @{typ bool}, ty] ---> ty)
-fun mk_ball ty = Const (@{const_name "Ball"}, [ty, ty] ---> @{typ bool})
-fun mk_bex ty = Const (@{const_name "Bex"}, [ty, ty] ---> @{typ bool})
-fun mk_resp ty = Const (@{const_name Respects}, [[ty, ty] ---> @{typ bool}, ty] ---> @{typ bool})
-*}
-
-(* applies f to the subterm of an abstractions, otherwise to the given term *)
-ML {*
-fun apply_subt f trm =
- case trm of
- Abs (x, T, t) =>
- let
- val (x', t') = Term.dest_abs (x, T, t)
- in
- Term.absfree (x', T, f t')
- end
- | _ => f trm
-*}
-
-(* FIXME: if there are more than one quotient, then you have to look up the relation *)
-ML {*
-fun my_reg lthy rel rty trm =
- case trm of
- Abs (x, T, t) =>
- if (needs_lift rty T) then
- let
- val rrel = tyRel T rty rel lthy
- in
- (mk_babs (fastype_of trm) T) $ (mk_resp T $ rrel) $ (apply_subt (my_reg lthy rel rty) trm)
- end
- else
- Abs(x, T, (apply_subt (my_reg lthy rel rty) t))
- | Const (@{const_name "All"}, ty) $ (t as Abs (x, T, _)) =>
- let
- val ty1 = domain_type ty
- val ty2 = domain_type ty1
- val rrel = tyRel T rty rel lthy
- in
- if (needs_lift rty T) then
- (mk_ball ty1) $ (mk_resp ty2 $ rrel) $ (apply_subt (my_reg lthy rel rty) t)
- else
- Const (@{const_name "All"}, ty) $ apply_subt (my_reg lthy rel rty) t
- end
- | Const (@{const_name "Ex"}, ty) $ (t as Abs (x, T, _)) =>
- let
- val ty1 = domain_type ty
- val ty2 = domain_type ty1
- val rrel = tyRel T rty rel lthy
- in
- if (needs_lift rty T) then
- (mk_bex ty1) $ (mk_resp ty2 $ rrel) $ (apply_subt (my_reg lthy rel rty) t)
- else
- Const (@{const_name "Ex"}, ty) $ apply_subt (my_reg lthy rel rty) t
- end
- | Const (@{const_name "op ="}, ty) $ t =>
- if needs_lift rty (fastype_of t) then
- (tyRel (fastype_of t) rty rel lthy) $ t (* FIXME: t should be regularised too *)
- else Const (@{const_name "op ="}, ty) $ (my_reg lthy rel rty t)
- | t1 $ t2 => (my_reg lthy rel rty t1) $ (my_reg lthy rel rty t2)
- | _ => trm
-*}
-
-(* For polymorphic types we need to find the type of the Relation term. *)
-(* TODO: we assume that the relation is a Constant. Is this always true? *)
-ML {*
-fun my_reg_inst lthy rel rty trm =
- case rel of
- Const (n, _) => Syntax.check_term lthy
- (my_reg lthy (Const (n, dummyT)) (Logic.varifyT rty) trm)
-*}
-
-(*
-ML {*
- val r = Free ("R", dummyT);
- val t = (my_reg_inst @{context} r @{typ "'a list"} @{term "\<forall>(x::'b list). P x"});
- val t2 = Syntax.check_term @{context} t;
- cterm_of @{theory} t2
-*}
-*)
-
-text {* Assumes that the given theorem is atomized *}
-ML {*
- fun build_regularize_goal thm rty rel lthy =
- Logic.mk_implies
- ((prop_of thm),
- (my_reg_inst lthy rel rty (prop_of thm)))
-*}
lemma universal_twice:
assumes *: "\<And>x. (P x \<longrightarrow> Q x)"
@@ -373,32 +256,6 @@
shows "(a \<longrightarrow> b) \<longrightarrow> (c \<longrightarrow> d)"
using a b by auto
-ML {*
-fun regularize thm rty rel rel_eqv rel_refl lthy =
- let
- val goal = build_regularize_goal thm rty rel lthy;
- fun tac ctxt =
- (ObjectLogic.full_atomize_tac) THEN'
- REPEAT_ALL_NEW (FIRST' [
- rtac rel_refl,
- atac,
- rtac @{thm universal_twice},
- (rtac @{thm impI} THEN' atac),
- rtac @{thm implication_twice},
- EqSubst.eqsubst_tac ctxt [0]
- [(@{thm equiv_res_forall} OF [rel_eqv]),
- (@{thm equiv_res_exists} OF [rel_eqv])],
- (* For a = b \<longrightarrow> a \<approx> b *)
- (rtac @{thm impI} THEN' (asm_full_simp_tac HOL_ss) THEN' rtac rel_refl),
- (rtac @{thm RIGHT_RES_FORALL_REGULAR})
- ]);
- val cthm = Goal.prove lthy [] [] goal
- (fn {context, ...} => tac context 1);
- in
- cthm OF [thm]
- end
-*}
-
section {* RepAbs injection *}
(*
@@ -473,16 +330,6 @@
handle TYPE _ => ty (* for dest_Type *)
*}
-(*consts Rl :: "'a list \<Rightarrow> 'a list \<Rightarrow> bool"
-axioms Rl_eq: "EQUIV Rl"
-
-quotient ql = "'a list" / "Rl"
- by (rule Rl_eq)
-ML {*
- ctyp_of @{theory} (exchange_ty @{context} (Logic.varifyT @{typ "'a list"}) (Logic.varifyT @{typ "'a ql"}) @{typ "nat list \<Rightarrow> (nat \<times> nat) list"});
- ctyp_of @{theory} (exchange_ty @{context} (Logic.varifyT @{typ "nat \<times> nat"}) (Logic.varifyT @{typ "int"}) @{typ "nat list \<Rightarrow> (nat \<times> nat) list"})
-*}
-*)
ML {*
fun find_matching_types rty ty =
@@ -535,19 +382,6 @@
| Type (s, tys) => get_fun_aux s (map (get_fun flag qenv lthy) tys)
| _ => error ("no type variables allowed"))
end
-
-(* returns all subterms where two types differ *)
-fun diff (T, S) Ds =
- case (T, S) of
- (TVar v, TVar u) => if v = u then Ds else (T, S)::Ds
- | (TFree x, TFree y) => if x = y then Ds else (T, S)::Ds
- | (Type (a, Ts), Type (b, Us)) =>
- if a = b then diffs (Ts, Us) Ds else (T, S)::Ds
- | _ => (T, S)::Ds
-and diffs (T::Ts, U::Us) Ds = diffs (Ts, Us) (diff (T, U) Ds)
- | diffs ([], []) Ds = Ds
- | diffs _ _ = error "Unequal length of type arguments"
-
*}
ML {*
@@ -609,73 +443,6 @@
ML {* symmetric (eq_reflection OF @{thms id_def}) *}
ML {*
-fun build_repabs_term lthy thm consts rty qty =
- let
- (* TODO: The rty and qty stored in the quotient_info should
- be varified, so this will soon not be needed *)
- val rty = Logic.varifyT rty;
- val qty = Logic.varifyT qty;
-
- fun mk_abs tm =
- let
- val ty = fastype_of tm
- in Syntax.check_term lthy ((get_fun_OLD absF (rty, qty) lthy ty) $ tm) end
- fun mk_repabs tm =
- let
- val ty = fastype_of tm
- in Syntax.check_term lthy ((get_fun_OLD repF (rty, qty) lthy ty) $ (mk_abs tm)) end
-
- fun is_lifted_const (Const (x, _)) = member (op =) consts x
- | is_lifted_const _ = false;
-
- fun build_aux lthy tm =
- case tm of
- Abs (a as (_, vty, _)) =>
- let
- val (vs, t) = Term.dest_abs a;
- val v = Free(vs, vty);
- val t' = lambda v (build_aux lthy t)
- in
- if (not (needs_lift rty (fastype_of tm))) then t'
- else mk_repabs (
- if not (needs_lift rty vty) then t'
- else
- let
- val v' = mk_repabs v;
- (* TODO: I believe 'beta' is not needed any more *)
- val t1 = (* Envir.beta_norm *) (t' $ v')
- in
- lambda v t1
- end)
- end
- | x =>
- case Term.strip_comb tm of
- (Const(@{const_name Respects}, _), _) => tm
- | (opp, tms0) =>
- let
- val tms = map (build_aux lthy) tms0
- val ty = fastype_of tm
- in
- if (is_lifted_const opp andalso needs_lift rty ty) then
- mk_repabs (list_comb (opp, tms))
- else if ((Term.is_Free opp) andalso (length tms > 0) andalso (needs_lift rty ty)) then
- mk_repabs (list_comb (opp, tms))
- else if tms = [] then opp
- else list_comb(opp, tms)
- end
- in
- repeat_eqsubst_prop lthy @{thms id_def_sym}
- (build_aux lthy (Thm.prop_of thm))
- end
-*}
-
-text {* Builds provable goals for regularized theorems *}
-ML {*
-fun build_repabs_goal ctxt thm cons rty qty =
- Logic.mk_equals ((Thm.prop_of thm), (build_repabs_term ctxt thm cons rty qty))
-*}
-
-ML {*
fun instantiate_tac thm = Subgoal.FOCUS (fn {concl, ...} =>
let
val pat = Drule.strip_imp_concl (cprop_of thm)
@@ -801,19 +568,6 @@
])
*}
-ML {*
-fun repabs lthy thm consts rty qty quot_thm reflex_thm trans_thm rsp_thms =
- let
- val rt = build_repabs_term lthy thm consts rty qty;
- val rg = Logic.mk_equals ((Thm.prop_of thm), rt);
- fun tac ctxt = (ObjectLogic.full_atomize_tac) THEN'
- (REPEAT_ALL_NEW (r_mk_comb_tac ctxt rty quot_thm reflex_thm trans_thm rsp_thms));
- val cthm = Goal.prove lthy [] [] rg (fn x => tac (#context x) 1);
- in
- @{thm Pure.equal_elim_rule1} OF [cthm, thm]
- end
-*}
-
section {* Cleaning the goal *}
@@ -854,22 +608,6 @@
end
*}
-(* TODO: Check if it behaves properly with varifyed rty *)
-ML {*
-fun findabs_all rty tm =
- case tm of
- Abs(_, T, b) =>
- let
- val b' = subst_bound ((Free ("x", T)), b);
- val tys = findabs_all rty b'
- val ty = fastype_of tm
- in if needs_lift rty ty then (ty :: tys) else tys
- end
- | f $ a => (findabs_all rty f) @ (findabs_all rty a)
- | _ => [];
-fun findabs rty tm = distinct (op =) (findabs_all rty tm)
-*}
-
ML {*
fun findaps_all rty tm =
case tm of
@@ -882,83 +620,6 @@
fun findaps rty tm = distinct (op =) (findaps_all rty tm)
*}
-(* Currently useful only for LAMBDA_PRS *)
-ML {*
-fun make_simp_prs_thm lthy quot_thm thm typ =
- let
- val (_, [lty, rty]) = dest_Type typ;
- val thy = ProofContext.theory_of lthy;
- val (lcty, rcty) = (ctyp_of thy lty, ctyp_of thy rty)
- val inst = [SOME lcty, NONE, SOME rcty];
- val lpi = Drule.instantiate' inst [] thm;
- val tac =
- (compose_tac (false, lpi, 2)) THEN_ALL_NEW
- (quotient_tac quot_thm);
- val gc = Drule.strip_imp_concl (cprop_of lpi);
- val t = Goal.prove_internal [] gc (fn _ => tac 1)
- in
- MetaSimplifier.rewrite_rule [@{thm eq_reflection} OF @{thms id_apply}] t
- end
-*}
-
-ML {*
-fun findallex_all rty qty tm =
- case tm of
- Const (@{const_name All}, T) $ (s as (Abs(_, _, b))) =>
- let
- val (tya, tye) = findallex_all rty qty s
- in if needs_lift rty T then
- ((T :: tya), tye)
- else (tya, tye) end
- | Const (@{const_name Ex}, T) $ (s as (Abs(_, _, b))) =>
- let
- val (tya, tye) = findallex_all rty qty s
- in if needs_lift rty T then
- (tya, (T :: tye))
- else (tya, tye) end
- | Abs(_, T, b) =>
- findallex_all rty qty (subst_bound ((Free ("x", T)), b))
- | f $ a =>
- let
- val (a1, e1) = findallex_all rty qty f;
- val (a2, e2) = findallex_all rty qty a;
- in (a1 @ a2, e1 @ e2) end
- | _ => ([], []);
-*}
-
-ML {*
-fun findallex lthy rty qty tm =
- let
- val (a, e) = findallex_all rty qty tm;
- val (ad, ed) = (map domain_type a, map domain_type e);
- val (au, eu) = (distinct (op =) ad, distinct (op =) ed);
- val (rty, qty) = (Logic.varifyT rty, Logic.varifyT qty)
- in
- (map (exchange_ty lthy rty qty) au, map (exchange_ty lthy rty qty) eu)
- end
-*}
-
-ML {*
-fun make_allex_prs_thm lthy quot_thm thm typ =
- let
- val (_, [lty, rty]) = dest_Type typ;
- val thy = ProofContext.theory_of lthy;
- val (lcty, rcty) = (ctyp_of thy lty, ctyp_of thy rty)
- val inst = [NONE, SOME lcty];
- val lpi = Drule.instantiate' inst [] thm;
- val tac =
- (compose_tac (false, lpi, 1)) THEN_ALL_NEW
- (quotient_tac quot_thm);
- val gc = Drule.strip_imp_concl (cprop_of lpi);
- val t = Goal.prove_internal [] gc (fn _ => tac 1)
- val t_noid = MetaSimplifier.rewrite_rule
- [@{thm eq_reflection} OF @{thms id_apply}] t;
- val t_sym = @{thm "HOL.sym"} OF [t_noid];
- val t_eq = @{thm "eq_reflection"} OF [t_sym]
- in
- t_eq
- end
-*}
ML {*
fun applic_prs lthy rty qty absrep ty =
@@ -1035,76 +696,6 @@
*}
-ML {*
-fun lift_thm lthy qty qty_name rsp_thms defs rthm =
-let
- val _ = tracing ("raw theorem:\n" ^ Syntax.string_of_term lthy (prop_of rthm))
-
- val (rty, rel, rel_refl, rel_eqv) = lookup_quot_data lthy qty;
- val (trans2, reps_same, absrep, quot) = lookup_quot_thms lthy qty_name;
- val consts = lookup_quot_consts defs;
- val t_a = atomize_thm rthm;
-
- val _ = tracing ("raw atomized theorem:\n" ^ Syntax.string_of_term lthy (prop_of t_a))
-
- val t_r = regularize t_a rty rel rel_eqv rel_refl lthy;
-
- val _ = tracing ("regularised theorem:\n" ^ Syntax.string_of_term lthy (prop_of t_r))
-
- val t_t = repabs lthy t_r consts rty qty quot rel_refl trans2 rsp_thms;
-
- val _ = tracing ("rep/abs injected theorem:\n" ^ Syntax.string_of_term lthy (prop_of t_t))
-
- val (alls, exs) = findallex lthy rty qty (prop_of t_a);
- val allthms = map (make_allex_prs_thm lthy quot @{thm FORALL_PRS}) alls
- val exthms = map (make_allex_prs_thm lthy quot @{thm EXISTS_PRS}) exs
- val t_a = MetaSimplifier.rewrite_rule (allthms @ exthms) t_t
-
- val _ = tracing ("??:\n" ^ Syntax.string_of_term lthy (prop_of t_a))
-
- val abs = findabs rty (prop_of t_a);
- val aps = findaps rty (prop_of t_a);
- val app_prs_thms = map (applic_prs lthy rty qty absrep) aps;
- val lam_prs_thms = map (make_simp_prs_thm lthy quot @{thm LAMBDA_PRS}) abs;
- val t_l = repeat_eqsubst_thm lthy (lam_prs_thms @ app_prs_thms) t_a;
-
- val _ = tracing ("??:\n" ^ Syntax.string_of_term lthy (prop_of t_l))
-
- val defs_sym = flat (map (add_lower_defs lthy) defs);
- val defs_sym_eq = map (fn x => eq_reflection OF [x]) defs_sym;
- val t_id = simp_ids lthy t_l;
-
- val _ = tracing ("??:\n" ^ Syntax.string_of_term lthy (prop_of t_id))
-
- val t_d0 = MetaSimplifier.rewrite_rule defs_sym_eq t_id;
-
- val _ = tracing ("??:\n" ^ Syntax.string_of_term lthy (prop_of t_d0))
-
- val t_d = repeat_eqsubst_thm lthy defs_sym t_d0;
-
- val _ = tracing ("??:\n" ^ Syntax.string_of_term lthy (prop_of t_d))
-
- val t_r = MetaSimplifier.rewrite_rule [reps_same] t_d;
-
- val _ = tracing ("??:\n" ^ Syntax.string_of_term lthy (prop_of t_r))
-
- val t_rv = ObjectLogic.rulify t_r
-
- val _ = tracing ("lifted theorem:\n" ^ Syntax.string_of_term lthy (prop_of t_rv))
-in
- Thm.varifyT t_rv
-end
-*}
-
-ML {*
-fun lift_thm_note qty qty_name rsp_thms defs thm name lthy =
- let
- val lifted_thm = lift_thm lthy qty qty_name rsp_thms defs thm;
- val (_, lthy2) = note (name, lifted_thm) lthy;
- in
- lthy2
- end
-*}
(******************************************)
(******************************************)
@@ -1461,70 +1052,6 @@
*}
ML {*
-fun regularize_goal lthy thm rel_eqv rel_refl qtrm =
- let
- val reg_trm = mk_REGULARIZE_goal lthy (prop_of thm) qtrm;
- fun tac lthy = regularize_tac lthy rel_eqv rel_refl;
- val cthm = Goal.prove lthy [] [] reg_trm
- (fn {context, ...} => tac context 1);
- in
- cthm OF [thm]
- end
-*}
-
-ML {*
-fun repabs_goal lthy thm rty quot_thm reflex_thm trans_thm rsp_thms qtrm =
- let
- val rg = Syntax.check_term lthy (mk_inj_REPABS_goal lthy ((prop_of thm), qtrm));
- fun tac ctxt = (ObjectLogic.full_atomize_tac) THEN'
- (REPEAT_ALL_NEW (r_mk_comb_tac ctxt rty quot_thm reflex_thm trans_thm rsp_thms));
- val cthm = Goal.prove lthy [] [] rg (fn x => tac (#context x) 1);
- in
- @{thm Pure.equal_elim_rule1} OF [cthm, thm]
- end
-*}
-
-ML {*
-fun lift_thm_goal lthy qty qty_name rsp_thms defs rthm goal =
-let
- val (rty, rel, rel_refl, rel_eqv) = lookup_quot_data lthy qty;
- val (trans2, reps_same, absrep, quot) = lookup_quot_thms lthy qty_name;
- val t_a = atomize_thm rthm;
- val goal_a = atomize_goal (ProofContext.theory_of lthy) goal;
- val t_r = regularize_goal lthy t_a rel_eqv rel_refl goal_a;
- val t_t = repabs_goal lthy t_r rty quot rel_refl trans2 rsp_thms goal_a;
- val (alls, exs) = findallex lthy rty qty (prop_of t_a);
- val allthms = map (make_allex_prs_thm lthy quot @{thm FORALL_PRS}) alls
- val exthms = map (make_allex_prs_thm lthy quot @{thm EXISTS_PRS}) exs
- val t_a = MetaSimplifier.rewrite_rule (allthms @ exthms) t_t
- val abs = findabs rty (prop_of t_a);
- val aps = findaps rty (prop_of t_a);
- val app_prs_thms = map (applic_prs lthy rty qty absrep) aps;
- val lam_prs_thms = map (make_simp_prs_thm lthy quot @{thm LAMBDA_PRS}) abs;
- val t_l = repeat_eqsubst_thm lthy (lam_prs_thms @ app_prs_thms) t_a;
- val defs_sym = flat (map (add_lower_defs lthy) defs);
- val defs_sym_eq = map (fn x => eq_reflection OF [x]) defs_sym;
- val t_id = simp_ids lthy t_l;
- val t_d0 = MetaSimplifier.rewrite_rule defs_sym_eq t_id;
- val t_d = repeat_eqsubst_thm lthy defs_sym t_d0;
- val t_r = MetaSimplifier.rewrite_rule [reps_same] t_d;
- val t_rv = ObjectLogic.rulify t_r
-in
- Thm.varifyT t_rv
-end
-*}
-
-ML {*
-fun lift_thm_goal_note lthy qty qty_name rsp_thms defs thm name goal =
- let
- val lifted_thm = lift_thm_goal lthy qty qty_name rsp_thms defs thm goal;
- val (_, lthy2) = note (name, lifted_thm) lthy;
- in
- lthy2
- end
-*}
-
-ML {*
fun inst_spec ctrm =
let
val cty = ctyp_of_term ctrm
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/UnusedQuotMain.thy Wed Nov 25 11:41:42 2009 +0100
@@ -0,0 +1,486 @@
+
+text {* tyRel takes a type and builds a relation that a quantifier over this
+ type needs to respect. *}
+ML {*
+fun tyRel ty rty rel lthy =
+ if Sign.typ_instance (ProofContext.theory_of lthy) (ty, rty)
+ then rel
+ else (case ty of
+ Type (s, tys) =>
+ let
+ val tys_rel = map (fn ty => ty --> ty --> @{typ bool}) tys;
+ val ty_out = ty --> ty --> @{typ bool};
+ val tys_out = tys_rel ---> ty_out;
+ in
+ (case (maps_lookup (ProofContext.theory_of lthy) s) of
+ SOME (info) => list_comb (Const (#relfun info, tys_out),
+ map (fn ty => tyRel ty rty rel lthy) tys)
+ | NONE => HOLogic.eq_const ty
+ )
+ end
+ | _ => HOLogic.eq_const ty)
+*}
+
+(*
+ML {* cterm_of @{theory}
+ (tyRel @{typ "'a \<Rightarrow> 'a list \<Rightarrow> 't \<Rightarrow> 't"} (Logic.varifyT @{typ "'a list"})
+ @{term "f::('a list \<Rightarrow> 'a list \<Rightarrow> bool)"} @{context})
+*}
+*)
+
+
+ML {*
+fun mk_babs ty ty' = Const (@{const_name "Babs"}, [ty' --> @{typ bool}, ty] ---> ty)
+fun mk_ball ty = Const (@{const_name "Ball"}, [ty, ty] ---> @{typ bool})
+fun mk_bex ty = Const (@{const_name "Bex"}, [ty, ty] ---> @{typ bool})
+fun mk_resp ty = Const (@{const_name Respects}, [[ty, ty] ---> @{typ bool}, ty] ---> @{typ bool})
+*}
+
+(* applies f to the subterm of an abstractions, otherwise to the given term *)
+ML {*
+fun apply_subt f trm =
+ case trm of
+ Abs (x, T, t) =>
+ let
+ val (x', t') = Term.dest_abs (x, T, t)
+ in
+ Term.absfree (x', T, f t')
+ end
+ | _ => f trm
+*}
+
+
+
+(* FIXME: if there are more than one quotient, then you have to look up the relation *)
+ML {*
+fun my_reg lthy rel rty trm =
+ case trm of
+ Abs (x, T, t) =>
+ if (needs_lift rty T) then
+ let
+ val rrel = tyRel T rty rel lthy
+ in
+ (mk_babs (fastype_of trm) T) $ (mk_resp T $ rrel) $ (apply_subt (my_reg lthy rel rty) trm)
+ end
+ else
+ Abs(x, T, (apply_subt (my_reg lthy rel rty) t))
+ | Const (@{const_name "All"}, ty) $ (t as Abs (x, T, _)) =>
+ let
+ val ty1 = domain_type ty
+ val ty2 = domain_type ty1
+ val rrel = tyRel T rty rel lthy
+ in
+ if (needs_lift rty T) then
+ (mk_ball ty1) $ (mk_resp ty2 $ rrel) $ (apply_subt (my_reg lthy rel rty) t)
+ else
+ Const (@{const_name "All"}, ty) $ apply_subt (my_reg lthy rel rty) t
+ end
+ | Const (@{const_name "Ex"}, ty) $ (t as Abs (x, T, _)) =>
+ let
+ val ty1 = domain_type ty
+ val ty2 = domain_type ty1
+ val rrel = tyRel T rty rel lthy
+ in
+ if (needs_lift rty T) then
+ (mk_bex ty1) $ (mk_resp ty2 $ rrel) $ (apply_subt (my_reg lthy rel rty) t)
+ else
+ Const (@{const_name "Ex"}, ty) $ apply_subt (my_reg lthy rel rty) t
+ end
+ | Const (@{const_name "op ="}, ty) $ t =>
+ if needs_lift rty (fastype_of t) then
+ (tyRel (fastype_of t) rty rel lthy) $ t (* FIXME: t should be regularised too *)
+ else Const (@{const_name "op ="}, ty) $ (my_reg lthy rel rty t)
+ | t1 $ t2 => (my_reg lthy rel rty t1) $ (my_reg lthy rel rty t2)
+ | _ => trm
+*}
+
+(* For polymorphic types we need to find the type of the Relation term. *)
+(* TODO: we assume that the relation is a Constant. Is this always true? *)
+ML {*
+fun my_reg_inst lthy rel rty trm =
+ case rel of
+ Const (n, _) => Syntax.check_term lthy
+ (my_reg lthy (Const (n, dummyT)) (Logic.varifyT rty) trm)
+*}
+
+(*
+ML {*
+ val r = Free ("R", dummyT);
+ val t = (my_reg_inst @{context} r @{typ "'a list"} @{term "\<forall>(x::'b list). P x"});
+ val t2 = Syntax.check_term @{context} t;
+ cterm_of @{theory} t2
+*}
+*)
+
+text {* Assumes that the given theorem is atomized *}
+ML {*
+ fun build_regularize_goal thm rty rel lthy =
+ Logic.mk_implies
+ ((prop_of thm),
+ (my_reg_inst lthy rel rty (prop_of thm)))
+*}
+
+ML {*
+fun regularize thm rty rel rel_eqv rel_refl lthy =
+ let
+ val goal = build_regularize_goal thm rty rel lthy;
+ fun tac ctxt =
+ (ObjectLogic.full_atomize_tac) THEN'
+ REPEAT_ALL_NEW (FIRST' [
+ rtac rel_refl,
+ atac,
+ rtac @{thm universal_twice},
+ (rtac @{thm impI} THEN' atac),
+ rtac @{thm implication_twice},
+ EqSubst.eqsubst_tac ctxt [0]
+ [(@{thm equiv_res_forall} OF [rel_eqv]),
+ (@{thm equiv_res_exists} OF [rel_eqv])],
+ (* For a = b \<longrightarrow> a \<approx> b *)
+ (rtac @{thm impI} THEN' (asm_full_simp_tac HOL_ss) THEN' rtac rel_refl),
+ (rtac @{thm RIGHT_RES_FORALL_REGULAR})
+ ]);
+ val cthm = Goal.prove lthy [] [] goal
+ (fn {context, ...} => tac context 1);
+ in
+ cthm OF [thm]
+ end
+*}
+
+(*consts Rl :: "'a list \<Rightarrow> 'a list \<Rightarrow> bool"
+axioms Rl_eq: "EQUIV Rl"
+
+quotient ql = "'a list" / "Rl"
+ by (rule Rl_eq)
+ML {*
+ ctyp_of @{theory} (exchange_ty @{context} (Logic.varifyT @{typ "'a list"}) (Logic.varifyT @{typ "'a ql"}) @{typ "nat list \<Rightarrow> (nat \<times> nat) list"});
+ ctyp_of @{theory} (exchange_ty @{context} (Logic.varifyT @{typ "nat \<times> nat"}) (Logic.varifyT @{typ "int"}) @{typ "nat list \<Rightarrow> (nat \<times> nat) list"})
+*}
+*)
+
+ML {*
+(* returns all subterms where two types differ *)
+fun diff (T, S) Ds =
+ case (T, S) of
+ (TVar v, TVar u) => if v = u then Ds else (T, S)::Ds
+ | (TFree x, TFree y) => if x = y then Ds else (T, S)::Ds
+ | (Type (a, Ts), Type (b, Us)) =>
+ if a = b then diffs (Ts, Us) Ds else (T, S)::Ds
+ | _ => (T, S)::Ds
+and diffs (T::Ts, U::Us) Ds = diffs (Ts, Us) (diff (T, U) Ds)
+ | diffs ([], []) Ds = Ds
+ | diffs _ _ = error "Unequal length of type arguments"
+
+*}
+
+ML {*
+fun build_repabs_term lthy thm consts rty qty =
+ let
+ (* TODO: The rty and qty stored in the quotient_info should
+ be varified, so this will soon not be needed *)
+ val rty = Logic.varifyT rty;
+ val qty = Logic.varifyT qty;
+
+ fun mk_abs tm =
+ let
+ val ty = fastype_of tm
+ in Syntax.check_term lthy ((get_fun_OLD absF (rty, qty) lthy ty) $ tm) end
+ fun mk_repabs tm =
+ let
+ val ty = fastype_of tm
+ in Syntax.check_term lthy ((get_fun_OLD repF (rty, qty) lthy ty) $ (mk_abs tm)) end
+
+ fun is_lifted_const (Const (x, _)) = member (op =) consts x
+ | is_lifted_const _ = false;
+
+ fun build_aux lthy tm =
+ case tm of
+ Abs (a as (_, vty, _)) =>
+ let
+ val (vs, t) = Term.dest_abs a;
+ val v = Free(vs, vty);
+ val t' = lambda v (build_aux lthy t)
+ in
+ if (not (needs_lift rty (fastype_of tm))) then t'
+ else mk_repabs (
+ if not (needs_lift rty vty) then t'
+ else
+ let
+ val v' = mk_repabs v;
+ (* TODO: I believe 'beta' is not needed any more *)
+ val t1 = (* Envir.beta_norm *) (t' $ v')
+ in
+ lambda v t1
+ end)
+ end
+ | x =>
+ case Term.strip_comb tm of
+ (Const(@{const_name Respects}, _), _) => tm
+ | (opp, tms0) =>
+ let
+ val tms = map (build_aux lthy) tms0
+ val ty = fastype_of tm
+ in
+ if (is_lifted_const opp andalso needs_lift rty ty) then
+ mk_repabs (list_comb (opp, tms))
+ else if ((Term.is_Free opp) andalso (length tms > 0) andalso (needs_lift rty ty)) then
+ mk_repabs (list_comb (opp, tms))
+ else if tms = [] then opp
+ else list_comb(opp, tms)
+ end
+ in
+ repeat_eqsubst_prop lthy @{thms id_def_sym}
+ (build_aux lthy (Thm.prop_of thm))
+ end
+*}
+
+text {* Builds provable goals for regularized theorems *}
+ML {*
+fun build_repabs_goal ctxt thm cons rty qty =
+ Logic.mk_equals ((Thm.prop_of thm), (build_repabs_term ctxt thm cons rty qty))
+*}
+
+ML {*
+fun repabs lthy thm consts rty qty quot_thm reflex_thm trans_thm rsp_thms =
+ let
+ val rt = build_repabs_term lthy thm consts rty qty;
+ val rg = Logic.mk_equals ((Thm.prop_of thm), rt);
+ fun tac ctxt = (ObjectLogic.full_atomize_tac) THEN'
+ (REPEAT_ALL_NEW (r_mk_comb_tac ctxt rty quot_thm reflex_thm trans_thm rsp_thms));
+ val cthm = Goal.prove lthy [] [] rg (fn x => tac (#context x) 1);
+ in
+ @{thm Pure.equal_elim_rule1} OF [cthm, thm]
+ end
+*}
+
+
+(* TODO: Check if it behaves properly with varifyed rty *)
+ML {*
+fun findabs_all rty tm =
+ case tm of
+ Abs(_, T, b) =>
+ let
+ val b' = subst_bound ((Free ("x", T)), b);
+ val tys = findabs_all rty b'
+ val ty = fastype_of tm
+ in if needs_lift rty ty then (ty :: tys) else tys
+ end
+ | f $ a => (findabs_all rty f) @ (findabs_all rty a)
+ | _ => [];
+fun findabs rty tm = distinct (op =) (findabs_all rty tm)
+*}
+
+
+(* Currently useful only for LAMBDA_PRS *)
+ML {*
+fun make_simp_prs_thm lthy quot_thm thm typ =
+ let
+ val (_, [lty, rty]) = dest_Type typ;
+ val thy = ProofContext.theory_of lthy;
+ val (lcty, rcty) = (ctyp_of thy lty, ctyp_of thy rty)
+ val inst = [SOME lcty, NONE, SOME rcty];
+ val lpi = Drule.instantiate' inst [] thm;
+ val tac =
+ (compose_tac (false, lpi, 2)) THEN_ALL_NEW
+ (quotient_tac quot_thm);
+ val gc = Drule.strip_imp_concl (cprop_of lpi);
+ val t = Goal.prove_internal [] gc (fn _ => tac 1)
+ in
+ MetaSimplifier.rewrite_rule [@{thm eq_reflection} OF @{thms id_apply}] t
+ end
+*}
+
+ML {*
+fun findallex_all rty qty tm =
+ case tm of
+ Const (@{const_name All}, T) $ (s as (Abs(_, _, b))) =>
+ let
+ val (tya, tye) = findallex_all rty qty s
+ in if needs_lift rty T then
+ ((T :: tya), tye)
+ else (tya, tye) end
+ | Const (@{const_name Ex}, T) $ (s as (Abs(_, _, b))) =>
+ let
+ val (tya, tye) = findallex_all rty qty s
+ in if needs_lift rty T then
+ (tya, (T :: tye))
+ else (tya, tye) end
+ | Abs(_, T, b) =>
+ findallex_all rty qty (subst_bound ((Free ("x", T)), b))
+ | f $ a =>
+ let
+ val (a1, e1) = findallex_all rty qty f;
+ val (a2, e2) = findallex_all rty qty a;
+ in (a1 @ a2, e1 @ e2) end
+ | _ => ([], []);
+*}
+
+ML {*
+fun findallex lthy rty qty tm =
+ let
+ val (a, e) = findallex_all rty qty tm;
+ val (ad, ed) = (map domain_type a, map domain_type e);
+ val (au, eu) = (distinct (op =) ad, distinct (op =) ed);
+ val (rty, qty) = (Logic.varifyT rty, Logic.varifyT qty)
+ in
+ (map (exchange_ty lthy rty qty) au, map (exchange_ty lthy rty qty) eu)
+ end
+*}
+
+ML {*
+fun make_allex_prs_thm lthy quot_thm thm typ =
+ let
+ val (_, [lty, rty]) = dest_Type typ;
+ val thy = ProofContext.theory_of lthy;
+ val (lcty, rcty) = (ctyp_of thy lty, ctyp_of thy rty)
+ val inst = [NONE, SOME lcty];
+ val lpi = Drule.instantiate' inst [] thm;
+ val tac =
+ (compose_tac (false, lpi, 1)) THEN_ALL_NEW
+ (quotient_tac quot_thm);
+ val gc = Drule.strip_imp_concl (cprop_of lpi);
+ val t = Goal.prove_internal [] gc (fn _ => tac 1)
+ val t_noid = MetaSimplifier.rewrite_rule
+ [@{thm eq_reflection} OF @{thms id_apply}] t;
+ val t_sym = @{thm "HOL.sym"} OF [t_noid];
+ val t_eq = @{thm "eq_reflection"} OF [t_sym]
+ in
+ t_eq
+ end
+*}
+
+ML {*
+fun lift_thm lthy qty qty_name rsp_thms defs rthm =
+let
+ val _ = tracing ("raw theorem:\n" ^ Syntax.string_of_term lthy (prop_of rthm))
+
+ val (rty, rel, rel_refl, rel_eqv) = lookup_quot_data lthy qty;
+ val (trans2, reps_same, absrep, quot) = lookup_quot_thms lthy qty_name;
+ val consts = lookup_quot_consts defs;
+ val t_a = atomize_thm rthm;
+
+ val _ = tracing ("raw atomized theorem:\n" ^ Syntax.string_of_term lthy (prop_of t_a))
+
+ val t_r = regularize t_a rty rel rel_eqv rel_refl lthy;
+
+ val _ = tracing ("regularised theorem:\n" ^ Syntax.string_of_term lthy (prop_of t_r))
+
+ val t_t = repabs lthy t_r consts rty qty quot rel_refl trans2 rsp_thms;
+
+ val _ = tracing ("rep/abs injected theorem:\n" ^ Syntax.string_of_term lthy (prop_of t_t))
+
+ val (alls, exs) = findallex lthy rty qty (prop_of t_a);
+ val allthms = map (make_allex_prs_thm lthy quot @{thm FORALL_PRS}) alls
+ val exthms = map (make_allex_prs_thm lthy quot @{thm EXISTS_PRS}) exs
+ val t_a = MetaSimplifier.rewrite_rule (allthms @ exthms) t_t
+
+ val _ = tracing ("??:\n" ^ Syntax.string_of_term lthy (prop_of t_a))
+
+ val abs = findabs rty (prop_of t_a);
+ val aps = findaps rty (prop_of t_a);
+ val app_prs_thms = map (applic_prs lthy rty qty absrep) aps;
+ val lam_prs_thms = map (make_simp_prs_thm lthy quot @{thm LAMBDA_PRS}) abs;
+ val t_l = repeat_eqsubst_thm lthy (lam_prs_thms @ app_prs_thms) t_a;
+
+ val _ = tracing ("??:\n" ^ Syntax.string_of_term lthy (prop_of t_l))
+
+ val defs_sym = flat (map (add_lower_defs lthy) defs);
+ val defs_sym_eq = map (fn x => eq_reflection OF [x]) defs_sym;
+ val t_id = simp_ids lthy t_l;
+
+ val _ = tracing ("??:\n" ^ Syntax.string_of_term lthy (prop_of t_id))
+
+ val t_d0 = MetaSimplifier.rewrite_rule defs_sym_eq t_id;
+
+ val _ = tracing ("??:\n" ^ Syntax.string_of_term lthy (prop_of t_d0))
+
+ val t_d = repeat_eqsubst_thm lthy defs_sym t_d0;
+
+ val _ = tracing ("??:\n" ^ Syntax.string_of_term lthy (prop_of t_d))
+
+ val t_r = MetaSimplifier.rewrite_rule [reps_same] t_d;
+
+ val _ = tracing ("??:\n" ^ Syntax.string_of_term lthy (prop_of t_r))
+
+ val t_rv = ObjectLogic.rulify t_r
+
+ val _ = tracing ("lifted theorem:\n" ^ Syntax.string_of_term lthy (prop_of t_rv))
+in
+ Thm.varifyT t_rv
+end
+*}
+
+ML {*
+fun lift_thm_note qty qty_name rsp_thms defs thm name lthy =
+ let
+ val lifted_thm = lift_thm lthy qty qty_name rsp_thms defs thm;
+ val (_, lthy2) = note (name, lifted_thm) lthy;
+ in
+ lthy2
+ end
+*}
+
+
+ML {*
+fun regularize_goal lthy thm rel_eqv rel_refl qtrm =
+ let
+ val reg_trm = mk_REGULARIZE_goal lthy (prop_of thm) qtrm;
+ fun tac lthy = regularize_tac lthy rel_eqv rel_refl;
+ val cthm = Goal.prove lthy [] [] reg_trm
+ (fn {context, ...} => tac context 1);
+ in
+ cthm OF [thm]
+ end
+*}
+
+ML {*
+fun repabs_goal lthy thm rty quot_thm reflex_thm trans_thm rsp_thms qtrm =
+ let
+ val rg = Syntax.check_term lthy (mk_inj_REPABS_goal lthy ((prop_of thm), qtrm));
+ fun tac ctxt = (ObjectLogic.full_atomize_tac) THEN'
+ (REPEAT_ALL_NEW (r_mk_comb_tac ctxt rty quot_thm reflex_thm trans_thm rsp_thms));
+ val cthm = Goal.prove lthy [] [] rg (fn x => tac (#context x) 1);
+ in
+ @{thm Pure.equal_elim_rule1} OF [cthm, thm]
+ end
+*}
+
+ML {*
+fun lift_thm_goal lthy qty qty_name rsp_thms defs rthm goal =
+let
+ val (rty, rel, rel_refl, rel_eqv) = lookup_quot_data lthy qty;
+ val (trans2, reps_same, absrep, quot) = lookup_quot_thms lthy qty_name;
+ val t_a = atomize_thm rthm;
+ val goal_a = atomize_goal (ProofContext.theory_of lthy) goal;
+ val t_r = regularize_goal lthy t_a rel_eqv rel_refl goal_a;
+ val t_t = repabs_goal lthy t_r rty quot rel_refl trans2 rsp_thms goal_a;
+ val (alls, exs) = findallex lthy rty qty (prop_of t_a);
+ val allthms = map (make_allex_prs_thm lthy quot @{thm FORALL_PRS}) alls
+ val exthms = map (make_allex_prs_thm lthy quot @{thm EXISTS_PRS}) exs
+ val t_a = MetaSimplifier.rewrite_rule (allthms @ exthms) t_t
+ val abs = findabs rty (prop_of t_a);
+ val aps = findaps rty (prop_of t_a);
+ val app_prs_thms = map (applic_prs lthy rty qty absrep) aps;
+ val lam_prs_thms = map (make_simp_prs_thm lthy quot @{thm LAMBDA_PRS}) abs;
+ val t_l = repeat_eqsubst_thm lthy (lam_prs_thms @ app_prs_thms) t_a;
+ val defs_sym = flat (map (add_lower_defs lthy) defs);
+ val defs_sym_eq = map (fn x => eq_reflection OF [x]) defs_sym;
+ val t_id = simp_ids lthy t_l;
+ val t_d0 = MetaSimplifier.rewrite_rule defs_sym_eq t_id;
+ val t_d = repeat_eqsubst_thm lthy defs_sym t_d0;
+ val t_r = MetaSimplifier.rewrite_rule [reps_same] t_d;
+ val t_rv = ObjectLogic.rulify t_r
+in
+ Thm.varifyT t_rv
+end
+*}
+
+ML {*
+fun lift_thm_goal_note lthy qty qty_name rsp_thms defs thm name goal =
+ let
+ val lifted_thm = lift_thm_goal lthy qty qty_name rsp_thms defs thm goal;
+ val (_, lthy2) = note (name, lifted_thm) lthy;
+ in
+ lthy2
+ end
+*}
+