--- a/Attic/Unused.thy Sun Jun 19 13:14:37 2011 +0900
+++ b/Attic/Unused.thy Mon Jun 20 08:50:13 2011 +0900
@@ -1,164 +1,11 @@
(*notation ( output) "prop" ("#_" [1000] 1000) *)
notation ( output) "Trueprop" ("#_" [1000] 1000)
-function(sequential)
- akind :: "kind \<Rightarrow> kind \<Rightarrow> bool" ("_ \<approx>ki _" [100, 100] 100)
-and aty :: "ty \<Rightarrow> ty \<Rightarrow> bool" ("_ \<approx>ty _" [100, 100] 100)
-and atrm :: "trm \<Rightarrow> trm \<Rightarrow> bool" ("_ \<approx>tr _" [100, 100] 100)
-where
- a1: "(Type) \<approx>ki (Type) = True"
-| a2: "(KPi A x K) \<approx>ki (KPi A' x' K') = (A \<approx>ty A' \<and> (\<exists>pi. (rfv_kind K - {atom x} = rfv_kind K' - {atom x'} \<and> (rfv_kind K - {atom x})\<sharp>* pi \<and> (pi \<bullet> K) \<approx>ki K' \<and> (pi \<bullet> x) = x')))"
-| "_ \<approx>ki _ = False"
-| a3: "(TConst i) \<approx>ty (TConst j) = (i = j)"
-| a4: "(TApp A M) \<approx>ty (TApp A' M') = (A \<approx>ty A' \<and> M \<approx>tr M')"
-| a5: "(TPi A x B) \<approx>ty (TPi A' x' B') = ((A \<approx>ty A') \<and> (\<exists>pi. rfv_ty B - {atom x} = rfv_ty B' - {atom x'} \<and> (rfv_ty B - {atom x})\<sharp>* pi \<and> (pi \<bullet> B) \<approx>ty B' \<and> (pi \<bullet> x) = x'))"
-| "_ \<approx>ty _ = False"
-| a6: "(Const i) \<approx>tr (Const j) = (i = j)"
-| a7: "(Var x) \<approx>tr (Var y) = (x = y)"
-| a8: "(App M N) \<approx>tr (App M' N') = (M \<approx>tr M' \<and> N \<approx>tr N')"
-| a9: "(Lam A x M) \<approx>tr (Lam A' x' M') = (A \<approx>ty A' \<and> (\<exists>pi. rfv_trm M - {atom x} = rfv_trm M' - {atom x'} \<and> (rfv_trm M - {atom x})\<sharp>* pi \<and> (pi \<bullet> M) \<approx>tr M' \<and> (pi \<bullet> x) = x'))"
-| "_ \<approx>tr _ = False"
-apply (pat_completeness)
-apply simp_all
-done
-termination
-by (size_change)
-
-
-
-lemma regularize_to_injection:
- shows "(QUOT_TRUE l \<Longrightarrow> y) \<Longrightarrow> (l = r) \<longrightarrow> y"
- by(auto simp add: QUOT_TRUE_def)
-
syntax
"Bex1_rel" :: "id \<Rightarrow> ('a \<Rightarrow> 'a \<Rightarrow> bool) \<Rightarrow> ('a \<Rightarrow> bool) \<Rightarrow> bool" ("(3\<exists>!!_\<in>_./ _)" [0, 0, 10] 10)
translations
"\<exists>!!x\<in>A. P" == "Bex1_rel A (%x. P)"
-
-(* Atomize infrastructure *)
-(* FIXME/TODO: is this really needed? *)
-(*
-lemma atomize_eqv:
- shows "(Trueprop A \<equiv> Trueprop B) \<equiv> (A \<equiv> B)"
-proof
- assume "A \<equiv> B"
- then show "Trueprop A \<equiv> Trueprop B" by unfold
-next
- assume *: "Trueprop A \<equiv> Trueprop B"
- have "A = B"
- proof (cases A)
- case True
- have "A" by fact
- then show "A = B" using * by simp
- next
- case False
- have "\<not>A" by fact
- then show "A = B" using * by auto
- qed
- then show "A \<equiv> B" by (rule eq_reflection)
-qed
-*)
-
-
-ML {*
- fun dest_cbinop t =
- let
- val (t2, rhs) = Thm.dest_comb t;
- val (bop, lhs) = Thm.dest_comb t2;
- in
- (bop, (lhs, rhs))
- end
-*}
-
-ML {*
- fun dest_ceq t =
- let
- val (bop, pair) = dest_cbinop t;
- val (bop_s, _) = Term.dest_Const (Thm.term_of bop);
- in
- if bop_s = "op =" then pair else (raise CTERM ("Not an equality", [t]))
- end
-*}
-
-ML {*
- fun split_binop_conv t =
- let
- val (lhs, rhs) = dest_ceq t;
- val (bop, _) = dest_cbinop lhs;
- val [clT, cr2] = bop |> Thm.ctyp_of_term |> Thm.dest_ctyp;
- val [cmT, crT] = Thm.dest_ctyp cr2;
- in
- Drule.instantiate' [SOME clT, SOME cmT, SOME crT] [NONE, NONE, NONE, NONE, SOME bop] @{thm arg_cong2}
- end
-*}
-
-
-ML {*
- fun split_arg_conv t =
- let
- val (lhs, rhs) = dest_ceq t;
- val (lop, larg) = Thm.dest_comb lhs;
- val [caT, crT] = lop |> Thm.ctyp_of_term |> Thm.dest_ctyp;
- in
- Drule.instantiate' [SOME caT, SOME crT] [NONE, NONE, SOME lop] @{thm arg_cong}
- end
-*}
-
-ML {*
- fun split_binop_tac n thm =
- let
- val concl = Thm.cprem_of thm n;
- val (_, cconcl) = Thm.dest_comb concl;
- val rewr = split_binop_conv cconcl;
- in
- rtac rewr n thm
- end
- handle CTERM _ => Seq.empty
-*}
-
-
-ML {*
- fun split_arg_tac n thm =
- let
- val concl = Thm.cprem_of thm n;
- val (_, cconcl) = Thm.dest_comb concl;
- val rewr = split_arg_conv cconcl;
- in
- rtac rewr n thm
- end
- handle CTERM _ => Seq.empty
-*}
-
-
-lemma trueprop_cong:
- shows "(a \<equiv> b) \<Longrightarrow> (Trueprop a \<equiv> Trueprop b)"
- by auto
-
-lemma list_induct_hol4:
- fixes P :: "'a list \<Rightarrow> bool"
- assumes a: "((P []) \<and> (\<forall>t. (P t) \<longrightarrow> (\<forall>h. (P (h # t)))))"
- shows "\<forall>l. (P l)"
- using a
- apply (rule_tac allI)
- apply (induct_tac "l")
- apply (simp)
- apply (metis)
- done
-
-ML {*
-val no_vars = Thm.rule_attribute (fn context => fn th =>
- let
- val ctxt = Variable.set_body false (Context.proof_of context);
- val ((_, [th']), _) = Variable.import true [th] ctxt;
- in th' end);
-*}
-
-(*lemma equality_twice:
- "a = c \<Longrightarrow> b = d \<Longrightarrow> (a = b \<longrightarrow> c = d)"
-by auto*)
-
-
(*interpretation code *)
(*val bindd = ((Binding.make ("", Position.none)), ([]: Attrib.src list))
val ((_, [eqn1pre]), lthy5) = Variable.import true [ABS_def] lthy4;
--- a/Attic/UnusedQuotMain.thy Sun Jun 19 13:14:37 2011 +0900
+++ b/Attic/UnusedQuotMain.thy Mon Jun 20 08:50:13 2011 +0900
@@ -1,687 +1,3 @@
-(* Code for getting the goal *)
-apply (tactic {* (ObjectLogic.full_atomize_tac THEN' gen_frees_tac @{context}) 1 *})
-ML_prf {* val qtm = #concl (fst (Subgoal.focus @{context} 1 (#goal (Isar.goal ())))) *}
-
-
-section {* Infrastructure about definitions *}
-
-(* Does the same as 'subst' in a given theorem *)
-ML {*
-fun eqsubst_thm ctxt thms thm =
- let
- val goalstate = Goal.init (Thm.cprop_of thm)
- val a' = case (SINGLE (EqSubst.eqsubst_tac ctxt [0] thms 1) goalstate) of
- NONE => error "eqsubst_thm"
- | SOME th => cprem_of th 1
- val tac = (EqSubst.eqsubst_tac ctxt [0] thms 1) THEN simp_tac HOL_ss 1
- val goal = Logic.mk_equals (term_of (Thm.cprop_of thm), term_of a');
- val cgoal = cterm_of (ProofContext.theory_of ctxt) goal
- val rt = Goal.prove_internal [] cgoal (fn _ => tac);
- in
- @{thm equal_elim_rule1} OF [rt, thm]
- end
-*}
-
-(* expects atomized definitions *)
-ML {*
-fun add_lower_defs_aux lthy thm =
- let
- val e1 = @{thm fun_cong} OF [thm];
- val f = eqsubst_thm lthy @{thms fun_map.simps} e1;
- val g = simp_ids f
- in
- (simp_ids thm) :: (add_lower_defs_aux lthy g)
- end
- handle _ => [simp_ids thm]
-*}
-
-ML {*
-fun add_lower_defs lthy def =
- let
- val def_pre_sym = symmetric def
- val def_atom = atomize_thm def_pre_sym
- val defs_all = add_lower_defs_aux lthy def_atom
- in
- map Thm.varifyT defs_all
- end
-*}
-
-
-
-ML {*
-fun repeat_eqsubst_thm ctxt thms thm =
- repeat_eqsubst_thm ctxt thms (eqsubst_thm ctxt thms thm)
- handle _ => thm
-*}
-
-
-ML {*
-fun eqsubst_prop ctxt thms t =
- let
- val goalstate = Goal.init (cterm_of (ProofContext.theory_of ctxt) t)
- val a' = case (SINGLE (EqSubst.eqsubst_tac ctxt [0] thms 1) goalstate) of
- NONE => error "eqsubst_prop"
- | SOME th => cprem_of th 1
- in term_of a' end
-*}
-
-ML {*
- fun repeat_eqsubst_prop ctxt thms t =
- repeat_eqsubst_prop ctxt thms (eqsubst_prop ctxt thms t)
- handle _ => t
-*}
-
-
-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)
-*}
+(* Could go in the programming tutorial *)
-
-(* 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 atomize_goal thy gl =
- let
- val vars = map Free (Term.add_frees gl []);
- val all = if fastype_of gl = @{typ bool} then HOLogic.all_const else Term.all;
- fun lambda_all (var as Free(_, T)) trm = (all T) $ lambda var trm;
- val glv = fold lambda_all vars gl
- val gla = (term_of o snd o Thm.dest_equals o cprop_of) (ObjectLogic.atomize (cterm_of thy glv))
- val glf = Type.legacy_freeze gla
- in
- if fastype_of gl = @{typ bool} then @{term Trueprop} $ glf else glf
- end
-*}
-
-
-ML {* atomize_goal @{theory} @{term "x memb [] = False"} *}
-ML {* atomize_goal @{theory} @{term "x = xa ? a # x = a # xa"} *}
-
-
-ML {*
-fun applic_prs lthy absrep (rty, qty) =
- let
- fun mk_rep (T, T') tm = (Quotient_Def.get_fun repF lthy (T, T')) $ tm;
- fun mk_abs (T, T') tm = (Quotient_Def.get_fun absF lthy (T, T')) $ tm;
- val (raty, rgty) = Term.strip_type rty;
- val (qaty, qgty) = Term.strip_type qty;
- val vs = map (fn _ => "x") qaty;
- val ((fname :: vfs), lthy') = Variable.variant_fixes ("f" :: vs) lthy;
- val f = Free (fname, qaty ---> qgty);
- val args = map Free (vfs ~~ qaty);
- val rhs = list_comb(f, args);
- val largs = map2 mk_rep (raty ~~ qaty) args;
- val lhs = mk_abs (rgty, qgty) (list_comb((mk_rep (raty ---> rgty, qaty ---> qgty) f), largs));
- val llhs = Syntax.check_term lthy lhs;
- val eq = Logic.mk_equals (llhs, rhs);
- val ceq = cterm_of (ProofContext.theory_of lthy') eq;
- val sctxt = HOL_ss addsimps (@{thms fun_map.simps id_simps} @ absrep);
- val t = Goal.prove_internal [] ceq (fn _ => simp_tac sctxt 1)
- val t_id = MetaSimplifier.rewrite_rule @{thms id_simps} t;
- in
- singleton (ProofContext.export lthy' lthy) t_id
- end
-*}
-
-ML {*
-fun find_aps_all rtm qtm =
- case (rtm, qtm) of
- (Abs(_, T1, s1), Abs(_, T2, s2)) =>
- find_aps_all (subst_bound ((Free ("x", T1)), s1)) (subst_bound ((Free ("x", T2)), s2))
- | (((f1 as (Free (_, T1))) $ a1), ((f2 as (Free (_, T2))) $ a2)) =>
- let
- val sub = (find_aps_all f1 f2) @ (find_aps_all a1 a2)
- in
- if T1 = T2 then sub else (T1, T2) :: sub
- end
- | ((f1 $ a1), (f2 $ a2)) => (find_aps_all f1 f2) @ (find_aps_all a1 a2)
- | _ => [];
-
-fun find_aps rtm qtm = distinct (op =) (find_aps_all rtm qtm)
-*}
-
-
-
-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 simp_ids_trm trm =
- trm |>
- MetaSimplifier.rewrite false @{thms eq_reflection[OF FUN_MAP_I] eq_reflection[OF id_apply] id_def_sym prod_fun_id map_id}
- |> cprop_of |> Thm.dest_equals |> snd
-
-*}
-
-(* Unused part of the locale *)
-
-lemma R_trans:
- assumes ab: "R a b"
- and bc: "R b c"
- shows "R a c"
-proof -
- have tr: "transp R" using equivp equivp_reflp_symp_transp[of R] by simp
- moreover have ab: "R a b" by fact
- moreover have bc: "R b c" by fact
- ultimately show "R a c" unfolding transp_def by blast
-qed
-
-lemma R_sym:
- assumes ab: "R a b"
- shows "R b a"
-proof -
- have re: "symp R" using equivp equivp_reflp_symp_transp[of R] by simp
- then show "R b a" using ab unfolding symp_def by blast
-qed
-
-lemma R_trans2:
- assumes ac: "R a c"
- and bd: "R b d"
- shows "R a b = R c d"
-using ac bd
-by (blast intro: R_trans R_sym)
-
-lemma REPS_same:
- shows "R (REP a) (REP b) \<equiv> (a = b)"
-proof -
- have "R (REP a) (REP b) = (a = b)"
- proof
- assume as: "R (REP a) (REP b)"
- from rep_prop
- obtain x y
- where eqs: "Rep a = R x" "Rep b = R y" by blast
- from eqs have "R (Eps (R x)) (Eps (R y))" using as unfolding REP_def by simp
- then have "R x (Eps (R y))" using lem9 by simp
- then have "R (Eps (R y)) x" using R_sym by blast
- then have "R y x" using lem9 by simp
- then have "R x y" using R_sym by blast
- then have "ABS x = ABS y" using thm11 by simp
- then have "Abs (Rep a) = Abs (Rep b)" using eqs unfolding ABS_def by simp
- then show "a = b" using rep_inverse by simp
- next
- assume ab: "a = b"
- have "reflp R" using equivp equivp_reflp_symp_transp[of R] by simp
- then show "R (REP a) (REP b)" unfolding reflp_def using ab by auto
- qed
- then show "R (REP a) (REP b) \<equiv> (a = b)" by simp
-qed
-
-
-
-
+ML_prf {* val qtm = #concl (fst (Subgoal.focus @{context} 1 (#goal (Isar.goal ())))) *}