--- a/Attic/Quot/quotient_tacs.ML Sat Dec 17 16:57:25 2011 +0000
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,665 +0,0 @@
-(* Title: HOL/Tools/Quotient/quotient_tacs.thy
- Author: Cezary Kaliszyk and Christian Urban
-
-Tactics for solving goal arising from lifting theorems to quotient
-types.
-*)
-
-signature QUOTIENT_TACS =
-sig
- val regularize_tac: Proof.context -> int -> tactic
- val injection_tac: Proof.context -> int -> tactic
- val all_injection_tac: Proof.context -> int -> tactic
- val clean_tac: Proof.context -> int -> tactic
- val procedure_tac: Proof.context -> thm -> int -> tactic
- val lift_tac: Proof.context -> thm list -> int -> tactic
- val quotient_tac: Proof.context -> int -> tactic
- val quot_true_tac: Proof.context -> (term -> term) -> int -> tactic
- val lifted_attrib: attribute
-end;
-
-structure Quotient_Tacs: QUOTIENT_TACS =
-struct
-
-open Quotient_Info;
-open Quotient_Term;
-
-
-(** various helper fuctions **)
-
-(* Since HOL_basic_ss is too "big" for us, we *)
-(* need to set up our own minimal simpset. *)
-fun mk_minimal_ss ctxt =
- Simplifier.context ctxt empty_ss
- setsubgoaler asm_simp_tac
- setmksimps (mksimps [])
-
-(* composition of two theorems, used in maps *)
-fun OF1 thm1 thm2 = thm2 RS thm1
-
-(* prints a warning, if the subgoal is not solved *)
-fun WARN (tac, msg) i st =
- case Seq.pull (SOLVED' tac i st) of
- NONE => (warning msg; Seq.single st)
- | seqcell => Seq.make (fn () => seqcell)
-
-fun RANGE_WARN tacs = RANGE (map WARN tacs)
-
-fun atomize_thm thm =
-let
- val thm' = Thm.freezeT (forall_intr_vars thm) (* FIXME/TODO: is this proper Isar-technology? *)
- val thm'' = Object_Logic.atomize (cprop_of thm')
-in
- @{thm equal_elim_rule1} OF [thm'', thm']
-end
-
-
-
-(*** Regularize Tactic ***)
-
-(** solvers for equivp and quotient assumptions **)
-
-fun equiv_tac ctxt =
- REPEAT_ALL_NEW (resolve_tac (equiv_rules_get ctxt))
-
-fun equiv_solver_tac ss = equiv_tac (Simplifier.the_context ss)
-val equiv_solver = Simplifier.mk_solver' "Equivalence goal solver" equiv_solver_tac
-
-fun quotient_tac ctxt =
- (REPEAT_ALL_NEW (FIRST'
- [rtac @{thm identity_quotient},
- resolve_tac (quotient_rules_get ctxt)]))
-
-fun quotient_solver_tac ss = quotient_tac (Simplifier.the_context ss)
-val quotient_solver =
- Simplifier.mk_solver' "Quotient goal solver" quotient_solver_tac
-
-fun solve_quotient_assm ctxt thm =
- case Seq.pull (quotient_tac ctxt 1 thm) of
- SOME (t, _) => t
- | _ => error "Solve_quotient_assm failed. Possibly a quotient theorem is missing."
-
-
-fun prep_trm thy (x, (T, t)) =
- (cterm_of thy (Var (x, T)), cterm_of thy t)
-
-fun prep_ty thy (x, (S, ty)) =
- (ctyp_of thy (TVar (x, S)), ctyp_of thy ty)
-
-fun get_match_inst thy pat trm =
-let
- val univ = Unify.matchers thy [(pat, trm)]
- val SOME (env, _) = Seq.pull univ (* raises Bind, if no unifier *) (* FIXME fragile *)
- val tenv = Vartab.dest (Envir.term_env env)
- val tyenv = Vartab.dest (Envir.type_env env)
-in
- (map (prep_ty thy) tyenv, map (prep_trm thy) tenv)
-end
-
-(* Calculates the instantiations for the lemmas:
-
- ball_reg_eqv_range and bex_reg_eqv_range
-
- Since the left-hand-side contains a non-pattern '?P (f ?x)'
- we rely on unification/instantiation to check whether the
- theorem applies and return NONE if it doesn't.
-*)
-fun calculate_inst ctxt ball_bex_thm redex R1 R2 =
-let
- val thy = ProofContext.theory_of ctxt
- fun get_lhs thm = fst (Logic.dest_equals (Thm.concl_of thm))
- val ty_inst = map (SOME o ctyp_of thy) [domain_type (fastype_of R2)]
- val trm_inst = map (SOME o cterm_of thy) [R2, R1]
-in
- case try (Drule.instantiate' ty_inst trm_inst) ball_bex_thm of
- NONE => NONE
- | SOME thm' =>
- (case try (get_match_inst thy (get_lhs thm')) redex of
- NONE => NONE
- | SOME inst2 => try (Drule.instantiate inst2) thm')
-end
-
-fun ball_bex_range_simproc ss redex =
-let
- val ctxt = Simplifier.the_context ss
-in
- case redex of
- (Const (@{const_name "Ball"}, _) $ (Const (@{const_name "Respects"}, _) $
- (Const (@{const_name "fun_rel"}, _) $ R1 $ R2)) $ _) =>
- calculate_inst ctxt @{thm ball_reg_eqv_range[THEN eq_reflection]} redex R1 R2
-
- | (Const (@{const_name "Bex"}, _) $ (Const (@{const_name "Respects"}, _) $
- (Const (@{const_name "fun_rel"}, _) $ R1 $ R2)) $ _) =>
- calculate_inst ctxt @{thm bex_reg_eqv_range[THEN eq_reflection]} redex R1 R2
-
- | _ => NONE
-end
-
-(* Regularize works as follows:
-
- 0. preliminary simplification step according to
- ball_reg_eqv bex_reg_eqv babs_reg_eqv ball_reg_eqv_range bex_reg_eqv_range
-
- 1. eliminating simple Ball/Bex instances (ball_reg_right bex_reg_left)
-
- 2. monos
-
- 3. commutation rules for ball and bex (ball_all_comm bex_ex_comm)
-
- 4. then rel-equalities, which need to be instantiated with 'eq_imp_rel'
- to avoid loops
-
- 5. then simplification like 0
-
- finally jump back to 1
-*)
-
-fun regularize_tac ctxt =
-let
- val thy = ProofContext.theory_of ctxt
- val ball_pat = @{term "Ball (Respects (R1 ===> R2)) P"}
- val bex_pat = @{term "Bex (Respects (R1 ===> R2)) P"}
- val simproc = Simplifier.simproc_i thy "" [ball_pat, bex_pat] (K (ball_bex_range_simproc))
- val simpset = (mk_minimal_ss ctxt)
- addsimps @{thms ball_reg_eqv bex_reg_eqv babs_reg_eqv babs_simp}
- addsimprocs [simproc]
- addSolver equiv_solver addSolver quotient_solver
- val eq_imp_rel = @{lemma "equivp R ==> a = b --> R a b" by (simp add: equivp_reflp)}
- val eq_eqvs = map (OF1 eq_imp_rel) (equiv_rules_get ctxt)
-in
- simp_tac simpset THEN'
- REPEAT_ALL_NEW (CHANGED o FIRST'
- [resolve_tac @{thms ball_reg_right bex_reg_left bex1_bexeq_reg},
- resolve_tac (Inductive.get_monos ctxt),
- resolve_tac @{thms ball_all_comm bex_ex_comm},
- resolve_tac eq_eqvs,
- simp_tac simpset])
-end
-
-
-
-(*** Injection Tactic ***)
-
-(* Looks for Quot_True assumptions, and in case its parameter
- is an application, it returns the function and the argument.
-*)
-fun find_qt_asm asms =
-let
- fun find_fun trm =
- case trm of
- (Const(@{const_name Trueprop}, _) $ (Const (@{const_name Quot_True}, _) $ _)) => true
- | _ => false
-in
- case find_first find_fun asms of
- SOME (_ $ (_ $ (f $ a))) => SOME (f, a)
- | _ => NONE
-end
-
-fun quot_true_simple_conv ctxt fnctn ctrm =
- case (term_of ctrm) of
- (Const (@{const_name Quot_True}, _) $ x) =>
- let
- val fx = fnctn x;
- val thy = ProofContext.theory_of ctxt;
- val cx = cterm_of thy x;
- val cfx = cterm_of thy fx;
- val cxt = ctyp_of thy (fastype_of x);
- val cfxt = ctyp_of thy (fastype_of fx);
- val thm = Drule.instantiate' [SOME cxt, SOME cfxt] [SOME cx, SOME cfx] @{thm QT_imp}
- in
- Conv.rewr_conv thm ctrm
- end
-
-fun quot_true_conv ctxt fnctn ctrm =
- case (term_of ctrm) of
- (Const (@{const_name Quot_True}, _) $ _) =>
- quot_true_simple_conv ctxt fnctn ctrm
- | _ $ _ => Conv.comb_conv (quot_true_conv ctxt fnctn) ctrm
- | Abs _ => Conv.abs_conv (fn (_, ctxt) => quot_true_conv ctxt fnctn) ctxt ctrm
- | _ => Conv.all_conv ctrm
-
-fun quot_true_tac ctxt fnctn =
- CONVERSION
- ((Conv.params_conv ~1 (fn ctxt =>
- (Conv.prems_conv ~1 (quot_true_conv ctxt fnctn)))) ctxt)
-
-fun dest_comb (f $ a) = (f, a)
-fun dest_bcomb ((_ $ l) $ r) = (l, r)
-
-fun unlam t =
- case t of
- (Abs a) => snd (Term.dest_abs a)
- | _ => unlam (Abs("", domain_type (fastype_of t), (incr_boundvars 1 t) $ (Bound 0)))
-
-fun dest_fun_type (Type("fun", [T, S])) = (T, S)
- | dest_fun_type _ = error "dest_fun_type"
-
-val bare_concl = HOLogic.dest_Trueprop o Logic.strip_assums_concl
-
-(* We apply apply_rsp only in case if the type needs lifting.
- This is the case if the type of the data in the Quot_True
- assumption is different from the corresponding type in the goal.
-*)
-val apply_rsp_tac =
- Subgoal.FOCUS (fn {concl, asms, context,...} =>
- let
- val bare_concl = HOLogic.dest_Trueprop (term_of concl)
- val qt_asm = find_qt_asm (map term_of asms)
- in
- case (bare_concl, qt_asm) of
- (R2 $ (f $ x) $ (g $ y), SOME (qt_fun, qt_arg)) =>
- if fastype_of qt_fun = fastype_of f
- then no_tac
- else
- let
- val ty_x = fastype_of x
- val ty_b = fastype_of qt_arg
- val ty_f = range_type (fastype_of f)
- val thy = ProofContext.theory_of context
- val ty_inst = map (SOME o (ctyp_of thy)) [ty_x, ty_b, ty_f]
- val t_inst = map (SOME o (cterm_of thy)) [R2, f, g, x, y];
- val inst_thm = Drule.instantiate' ty_inst
- ([NONE, NONE, NONE] @ t_inst) @{thm apply_rsp}
- in
- (rtac inst_thm THEN' quotient_tac context) 1
- end
- | _ => no_tac
- end)
-
-(* Instantiates and applies 'equals_rsp'. Since the theorem is
- complex we rely on instantiation to tell us if it applies
-*)
-fun equals_rsp_tac R ctxt =
-let
- val thy = ProofContext.theory_of ctxt
-in
- case try (cterm_of thy) R of (* There can be loose bounds in R *)
- SOME ctm =>
- let
- val ty = domain_type (fastype_of R)
- in
- case try (Drule.instantiate' [SOME (ctyp_of thy ty)]
- [SOME (cterm_of thy R)]) @{thm equals_rsp} of
- SOME thm => rtac thm THEN' quotient_tac ctxt
- | NONE => K no_tac
- end
- | _ => K no_tac
-end
-
-fun rep_abs_rsp_tac ctxt =
- SUBGOAL (fn (goal, i) =>
- case (try bare_concl goal) of
- SOME (rel $ _ $ (rep $ (abs $ _))) =>
- let
- val thy = ProofContext.theory_of ctxt;
- val (ty_a, ty_b) = dest_fun_type (fastype_of abs);
- val ty_inst = map (SOME o (ctyp_of thy)) [ty_a, ty_b];
- in
- case try (map (SOME o (cterm_of thy))) [rel, abs, rep] of
- SOME t_inst =>
- (case try (Drule.instantiate' ty_inst t_inst) @{thm rep_abs_rsp} of
- SOME inst_thm => (rtac inst_thm THEN' quotient_tac ctxt) i
- | NONE => no_tac)
- | NONE => no_tac
- end
- | _ => no_tac)
-
-
-
-(* Injection means to prove that the regularised theorem implies
- the abs/rep injected one.
-
- The deterministic part:
- - remove lambdas from both sides
- - prove Ball/Bex/Babs equalities using ball_rsp, bex_rsp, babs_rsp
- - prove Ball/Bex relations unfolding fun_rel_id
- - reflexivity of equality
- - prove equality of relations using equals_rsp
- - use user-supplied RSP theorems
- - solve 'relation of relations' goals using quot_rel_rsp
- - remove rep_abs from the right side
- (Lambdas under respects may have left us some assumptions)
-
- Then in order:
- - split applications of lifted type (apply_rsp)
- - split applications of non-lifted type (cong_tac)
- - apply extentionality
- - assumption
- - reflexivity of the relation
-*)
-fun injection_match_tac ctxt = SUBGOAL (fn (goal, i) =>
-(case (bare_concl goal) of
- (* (R1 ===> R2) (%x...) (%x...) ----> [|R1 x y|] ==> R2 (...x) (...y) *)
- (Const (@{const_name fun_rel}, _) $ _ $ _) $ (Abs _) $ (Abs _)
- => rtac @{thm fun_rel_id} THEN' quot_true_tac ctxt unlam
-
- (* (op =) (Ball...) (Ball...) ----> (op =) (...) (...) *)
-| (Const (@{const_name "op ="},_) $
- (Const(@{const_name Ball},_) $ (Const (@{const_name Respects}, _) $ _) $ _) $
- (Const(@{const_name Ball},_) $ (Const (@{const_name Respects}, _) $ _) $ _))
- => rtac @{thm ball_rsp} THEN' dtac @{thm QT_all}
-
- (* (R1 ===> op =) (Ball...) (Ball...) ----> [|R1 x y|] ==> (Ball...x) = (Ball...y) *)
-| (Const (@{const_name fun_rel}, _) $ _ $ _) $
- (Const(@{const_name Ball},_) $ (Const (@{const_name Respects}, _) $ _) $ _) $
- (Const(@{const_name Ball},_) $ (Const (@{const_name Respects}, _) $ _) $ _)
- => rtac @{thm fun_rel_id} THEN' quot_true_tac ctxt unlam
-
- (* (op =) (Bex...) (Bex...) ----> (op =) (...) (...) *)
-| Const (@{const_name "op ="},_) $
- (Const(@{const_name Bex},_) $ (Const (@{const_name Respects}, _) $ _) $ _) $
- (Const(@{const_name Bex},_) $ (Const (@{const_name Respects}, _) $ _) $ _)
- => rtac @{thm bex_rsp} THEN' dtac @{thm QT_ex}
-
- (* (R1 ===> op =) (Bex...) (Bex...) ----> [|R1 x y|] ==> (Bex...x) = (Bex...y) *)
-| (Const (@{const_name fun_rel}, _) $ _ $ _) $
- (Const(@{const_name Bex},_) $ (Const (@{const_name Respects}, _) $ _) $ _) $
- (Const(@{const_name Bex},_) $ (Const (@{const_name Respects}, _) $ _) $ _)
- => rtac @{thm fun_rel_id} THEN' quot_true_tac ctxt unlam
-
-| (Const (@{const_name fun_rel}, _) $ _ $ _) $
- (Const(@{const_name Bex1_rel},_) $ _) $ (Const(@{const_name Bex1_rel},_) $ _)
- => rtac @{thm bex1_rel_rsp} THEN' quotient_tac ctxt
-
-| (_ $
- (Const(@{const_name Babs},_) $ (Const (@{const_name Respects}, _) $ _) $ _) $
- (Const(@{const_name Babs},_) $ (Const (@{const_name Respects}, _) $ _) $ _))
- => rtac @{thm babs_rsp} THEN' RANGE [quotient_tac ctxt]
-
-| Const (@{const_name "op ="},_) $ (R $ _ $ _) $ (_ $ _ $ _) =>
- (rtac @{thm refl} ORELSE'
- (equals_rsp_tac R ctxt THEN' RANGE [
- quot_true_tac ctxt (fst o dest_bcomb), quot_true_tac ctxt (snd o dest_bcomb)]))
-
- (* reflexivity of operators arising from Cong_tac *)
-| Const (@{const_name "op ="},_) $ _ $ _ => rtac @{thm refl}
-
- (* respectfulness of constants; in particular of a simple relation *)
-| _ $ (Const _) $ (Const _) (* fun_rel, list_rel, etc but not equality *)
- => resolve_tac (rsp_rules_get ctxt) THEN_ALL_NEW quotient_tac ctxt
-
- (* R (...) (Rep (Abs ...)) ----> R (...) (...) *)
- (* observe fun_map *)
-| _ $ _ $ _
- => (rtac @{thm quot_rel_rsp} THEN_ALL_NEW quotient_tac ctxt)
- ORELSE' rep_abs_rsp_tac ctxt
-
-| _ => K no_tac
-) i)
-
-fun injection_step_tac ctxt rel_refl =
- FIRST' [
- injection_match_tac ctxt,
-
- (* R (t $ ...) (t' $ ...) ----> apply_rsp provided type of t needs lifting *)
- apply_rsp_tac ctxt THEN'
- RANGE [quot_true_tac ctxt (fst o dest_comb), quot_true_tac ctxt (snd o dest_comb)],
-
- (* (op =) (t $ ...) (t' $ ...) ----> Cong provided type of t does not need lifting *)
- (* merge with previous tactic *)
- Cong_Tac.cong_tac @{thm cong} THEN'
- RANGE [quot_true_tac ctxt (fst o dest_comb), quot_true_tac ctxt (snd o dest_comb)],
-
- (* (op =) (%x...) (%y...) ----> (op =) (...) (...) *)
- rtac @{thm ext} THEN' quot_true_tac ctxt unlam,
-
- (* resolving with R x y assumptions *)
- atac,
-
- (* reflexivity of the basic relations *)
- (* R ... ... *)
- resolve_tac rel_refl]
-
-fun injection_tac ctxt =
-let
- val rel_refl = map (OF1 @{thm equivp_reflp}) (equiv_rules_get ctxt)
-in
- injection_step_tac ctxt rel_refl
-end
-
-fun all_injection_tac ctxt =
- REPEAT_ALL_NEW (injection_tac ctxt)
-
-
-
-(*** Cleaning of the Theorem ***)
-
-(* expands all fun_maps, except in front of the (bound) variables listed in xs *)
-fun fun_map_simple_conv xs ctrm =
- case (term_of ctrm) of
- ((Const (@{const_name "fun_map"}, _) $ _ $ _) $ h $ _) =>
- if member (op=) xs h
- then Conv.all_conv ctrm
- else Conv.rewr_conv @{thm fun_map_def[THEN eq_reflection]} ctrm
- | _ => Conv.all_conv ctrm
-
-fun fun_map_conv xs ctxt ctrm =
- case (term_of ctrm) of
- _ $ _ => (Conv.comb_conv (fun_map_conv xs ctxt) then_conv
- fun_map_simple_conv xs) ctrm
- | Abs _ => Conv.abs_conv (fn (x, ctxt) => fun_map_conv ((term_of x)::xs) ctxt) ctxt ctrm
- | _ => Conv.all_conv ctrm
-
-fun fun_map_tac ctxt = CONVERSION (fun_map_conv [] ctxt)
-
-(* custom matching functions *)
-fun mk_abs u i t =
- if incr_boundvars i u aconv t then Bound i else
- case t of
- t1 $ t2 => mk_abs u i t1 $ mk_abs u i t2
- | Abs (s, T, t') => Abs (s, T, mk_abs u (i + 1) t')
- | Bound j => if i = j then error "make_inst" else t
- | _ => t
-
-fun make_inst lhs t =
-let
- val _ $ (Abs (_, _, (_ $ ((f as Var (_, Type ("fun", [T, _]))) $ u)))) = lhs;
- val _ $ (Abs (_, _, (_ $ g))) = t;
-in
- (f, Abs ("x", T, mk_abs u 0 g))
-end
-
-fun make_inst_id lhs t =
-let
- val _ $ (Abs (_, _, (f as Var (_, Type ("fun", [T, _]))) $ u)) = lhs;
- val _ $ (Abs (_, _, g)) = t;
-in
- (f, Abs ("x", T, mk_abs u 0 g))
-end
-
-(* Simplifies a redex using the 'lambda_prs' theorem.
- First instantiates the types and known subterms.
- Then solves the quotient assumptions to get Rep2 and Abs1
- Finally instantiates the function f using make_inst
- If Rep2 is an identity then the pattern is simpler and
- make_inst_id is used
-*)
-fun lambda_prs_simple_conv ctxt ctrm =
- case (term_of ctrm) of
- (Const (@{const_name fun_map}, _) $ r1 $ a2) $ (Abs _) =>
- let
- val thy = ProofContext.theory_of ctxt
- val (ty_b, ty_a) = dest_fun_type (fastype_of r1)
- val (ty_c, ty_d) = dest_fun_type (fastype_of a2)
- val tyinst = map (SOME o (ctyp_of thy)) [ty_a, ty_b, ty_c, ty_d]
- val tinst = [NONE, NONE, SOME (cterm_of thy r1), NONE, SOME (cterm_of thy a2)]
- val thm1 = Drule.instantiate' tyinst tinst @{thm lambda_prs[THEN eq_reflection]}
- val thm2 = solve_quotient_assm ctxt (solve_quotient_assm ctxt thm1)
- val thm3 = MetaSimplifier.rewrite_rule @{thms id_apply[THEN eq_reflection]} thm2
- val (insp, inst) =
- if ty_c = ty_d
- then make_inst_id (term_of (Thm.lhs_of thm3)) (term_of ctrm)
- else make_inst (term_of (Thm.lhs_of thm3)) (term_of ctrm)
- val thm4 = Drule.instantiate ([], [(cterm_of thy insp, cterm_of thy inst)]) thm3
- in
- Conv.rewr_conv thm4 ctrm
- end
- | _ => Conv.all_conv ctrm
-
-fun lambda_prs_conv ctxt = More_Conv.top_conv lambda_prs_simple_conv ctxt
-fun lambda_prs_tac ctxt = CONVERSION (lambda_prs_conv ctxt)
-
-
-(* Cleaning consists of:
-
- 1. unfolding of ---> in front of everything, except
- bound variables (this prevents lambda_prs from
- becoming stuck)
-
- 2. simplification with lambda_prs
-
- 3. simplification with:
-
- - Quotient_abs_rep Quotient_rel_rep
- babs_prs all_prs ex_prs ex1_prs
-
- - id_simps and preservation lemmas and
-
- - symmetric versions of the definitions
- (that is definitions of quotient constants
- are folded)
-
- 4. test for refl
-*)
-fun clean_tac lthy =
-let
- val defs = map (symmetric o #def) (qconsts_dest lthy)
- val prs = prs_rules_get lthy
- val ids = id_simps_get lthy
- val thms = @{thms Quotient_abs_rep Quotient_rel_rep babs_prs all_prs ex_prs ex1_prs} @ ids @ prs @ defs
-
- val ss = (mk_minimal_ss lthy) addsimps thms addSolver quotient_solver
-in
- EVERY' [fun_map_tac lthy,
- lambda_prs_tac lthy,
- simp_tac ss,
- TRY o rtac refl]
-end
-
-
-
-(** Tactic for Generalising Free Variables in a Goal **)
-
-fun inst_spec ctrm =
- Drule.instantiate' [SOME (ctyp_of_term ctrm)] [NONE, SOME ctrm] @{thm spec}
-
-fun inst_spec_tac ctrms =
- EVERY' (map (dtac o inst_spec) ctrms)
-
-fun all_list xs trm =
- fold (fn (x, T) => fn t' => HOLogic.mk_all (x, T, t')) xs trm
-
-fun apply_under_Trueprop f =
- HOLogic.dest_Trueprop #> f #> HOLogic.mk_Trueprop
-
-fun gen_frees_tac ctxt =
- SUBGOAL (fn (concl, i) =>
- let
- val thy = ProofContext.theory_of ctxt
- val vrs = Term.add_frees concl []
- val cvrs = map (cterm_of thy o Free) vrs
- val concl' = apply_under_Trueprop (all_list vrs) concl
- val goal = Logic.mk_implies (concl', concl)
- val rule = Goal.prove ctxt [] [] goal
- (K (EVERY1 [inst_spec_tac (rev cvrs), atac]))
- in
- rtac rule i
- end)
-
-
-(** The General Shape of the Lifting Procedure **)
-
-(* - A is the original raw theorem
- - B is the regularized theorem
- - C is the rep/abs injected version of B
- - D is the lifted theorem
-
- - 1st prem is the regularization step
- - 2nd prem is the rep/abs injection step
- - 3rd prem is the cleaning part
-
- the Quot_True premise in 2nd records the lifted theorem
-*)
-val lifting_procedure_thm =
- @{lemma "[|A;
- A --> B;
- Quot_True D ==> B = C;
- C = D|] ==> D"
- by (simp add: Quot_True_def)}
-
-fun lift_match_error ctxt msg rtrm qtrm =
-let
- val rtrm_str = Syntax.string_of_term ctxt rtrm
- val qtrm_str = Syntax.string_of_term ctxt qtrm
- val msg = cat_lines [enclose "[" "]" msg, "The quotient theorem", qtrm_str,
- "", "does not match with original theorem", rtrm_str]
-in
- error msg
-end
-
-fun procedure_inst ctxt rtrm qtrm =
-let
- val thy = ProofContext.theory_of ctxt
- val rtrm' = HOLogic.dest_Trueprop rtrm
- val qtrm' = HOLogic.dest_Trueprop qtrm
- val reg_goal = regularize_trm_chk ctxt (rtrm', qtrm')
- handle (ERROR msg) => lift_match_error ctxt msg rtrm qtrm
- val inj_goal = inj_repabs_trm_chk ctxt (reg_goal, qtrm')
- handle (ERROR msg) => lift_match_error ctxt msg rtrm qtrm
-in
- Drule.instantiate' []
- [SOME (cterm_of thy rtrm'),
- SOME (cterm_of thy reg_goal),
- NONE,
- SOME (cterm_of thy inj_goal)] lifting_procedure_thm
-end
-
-(* the tactic leaves three subgoals to be proved *)
-fun procedure_tac ctxt rthm =
- Object_Logic.full_atomize_tac
- THEN' gen_frees_tac ctxt
- THEN' SUBGOAL (fn (goal, i) =>
- let
- val rthm' = atomize_thm rthm
- val rule = procedure_inst ctxt (prop_of rthm') goal
- in
- (rtac rule THEN' rtac rthm') i
- end)
-
-
-(* Automatic Proofs *)
-
-val msg1 = "The regularize proof failed."
-val msg2 = cat_lines ["The injection proof failed.",
- "This is probably due to missing respects lemmas.",
- "Try invoking the injection method manually to see",
- "which lemmas are missing."]
-val msg3 = "The cleaning proof failed."
-
-fun lift_tac ctxt rthms =
-let
- fun mk_tac rthm =
- procedure_tac ctxt rthm
- THEN' RANGE_WARN
- [(regularize_tac ctxt, msg1),
- (all_injection_tac ctxt, msg2),
- (clean_tac ctxt, msg3)]
-in
- simp_tac (mk_minimal_ss ctxt) (* unfolding multiple &&& *)
- THEN' RANGE (map mk_tac rthms)
-end
-
-(* An Attribute which automatically constructs the qthm *)
-fun lifted_attrib_aux context thm =
-let
- val ctxt = Context.proof_of context
- val ((_, [thm']), ctxt') = Variable.import false [thm] ctxt
- val goal = (quotient_lift_all ctxt' o prop_of) thm'
-in
- Goal.prove ctxt' [] [] goal (K (lift_tac ctxt' [thm] 1))
- |> singleton (ProofContext.export ctxt' ctxt)
-end;
-
-val lifted_attrib = Thm.rule_attribute lifted_attrib_aux
-
-end; (* structure *)