nominal2: comparison Quot/QuotMain.thy

equal deleted inserted replaced

-:bb5d3278f02e
+:ec37a279ca55
 (* the auxiliary data for the quotient types *)
 use "quotient_info.ML"
 declare [[map * = (prod_fun, prod_rel)]]
 declare [[map "fun" = (fun_map, fun_rel)]]
-(* FIXME: This should throw an exception:
-declare [[map "option" = (bla, blu)]]
+(* FIXME: This should throw an exception: *)
-*)
+(* declare [[map "option" = (bla, blu)]] *)
 (* identity quotient is not here as it has to be applied first *)
 lemmas [quotient_thm] =
 fun_quotient prod_quotient
 | (Abs (_, T, t), Abs (_, T', t')) => matches_typ (T, T') andalso matches_term (t, t')
 | (t $ s, t' $ s') => matches_term (t, t') andalso matches_term (s, s')
 | _ => false
 *}
-section {* Regularization *}
+section {* Computation of the Regularize Goal *}
 (*
 Regularizing an rtrm means:
 - quantifiers over a type that needs lifting are replaced by
 bounded quantifiers, for example:
 | (rt, qt) =>
 raise (LIFT_MATCH "regularize (default)")
 *}
+section {* Regularize Tactic *}
 ML {*
 fun equiv_tac ctxt =
 (K (print_tac "equiv tac")) THEN'
 REPEAT_ALL_NEW (resolve_tac (equiv_rules_get ctxt))
 *}
 lemma eq_imp_rel:
 shows "equivp R \<Longrightarrow> a = b \<longrightarrow> R a b"
 by (simp add: equivp_reflp)
-(* FIXME/TODO: How does regularizing work? *)
-(* FIXME/TODO: needs to be adapted
+(* Regularize Tactic *)
-To prove that the raw theorem implies the regularised one,
+(* 0. preliminary simplification step according to *)
-we try in order:
+thm ball_reg_eqv bex_reg_eqv babs_reg_eqv (* the latter of no use *)
+ball_reg_eqv_range bex_reg_eqv_range
-- Reflexivity of the relation
+(* 1. eliminating simple Ball/Bex instances*)
-- Assumption
+thm ball_reg_right bex_reg_left
-- Elimnating quantifiers on both sides of toplevel implication
+(* 2. monos *)
-- Simplifying implications on both sides of toplevel implication
+(* 3. commutation rules for ball and bex *)
-- Ball (Respects ?E) ?P = All ?P
+thm ball_all_comm bex_ex_comm
-- (\<And>x. ?R x \<Longrightarrow> ?P x \<longrightarrow> ?Q x) \<Longrightarrow> All ?P \<longrightarrow> Ball ?R ?Q
+(* 4. then rel-equality (which need to be instantiated to avoid loops *)
+thm eq_imp_rel
-*)
+(* 5. then simplification like 0 *)
+(* finally jump back to 1 *)
 ML {*
 fun regularize_tac ctxt =
 let
 val thy = ProofContext.theory_of ctxt
 val pat_ball = @{term "Ball (Respects (R1 ===> R2)) P"}
 val simpset = (mk_minimal_ss ctxt)
 addsimps @{thms ball_reg_eqv bex_reg_eqv babs_reg_eqv}
 addsimprocs [simproc] addSolver equiv_solver
 (* TODO: Make sure that there are no list_rel, pair_rel etc involved *)
 (* can this cause loops in equiv_tac ? *)
-val eq_eqvs = map (fn x => @{thm eq_imp_rel} OF [x]) (equiv_rules_get ctxt)
+val eq_eqvs = map (OF1 @{thm eq_imp_rel}) (equiv_rules_get ctxt)
 in
 simp_tac simpset THEN'
 REPEAT_ALL_NEW (CHANGED o FIRST' [
-rtac @{thm ball_reg_right},
+resolve_tac @{thms ball_reg_right bex_reg_left},
-rtac @{thm bex_reg_left},
 resolve_tac (Inductive.get_monos ctxt),
-rtac @{thm ball_all_comm},
+resolve_tac @{thms ball_all_comm bex_ex_comm},
-rtac @{thm bex_ex_comm},
 resolve_tac eq_eqvs,
-(* should be equivalent to the above, but causes loops:   *)
-(* rtac @{thm eq_imp_rel} THEN' SOLVES' (equiv_tac ctxt), *)
-(* the culprit is aslread rtac @{thm eq_imp_rel}          *)
 simp_tac simpset])
 end
 *}
-section {* Injections of rep and abses *}
+section {* Calculation of the Injected Goal *}
 (*
 Injecting repabs means:
 For abstractions:
 end
 | _ => raise (LIFT_MATCH "injection")
 *}
-section {* RepAbs Injection Tactic *}
+section {* Injection Tactic *}
 ML {*
 fun quotient_tac ctxt =
 REPEAT_ALL_NEW (FIRST'
 [rtac @{thm identity_quotient},
 *}
 ML {*
 fun inj_repabs_tac ctxt =
 let
-val rel_refl = map (fn x => @{thm equivp_reflp} OF [x]) (equiv_rules_get ctxt)
+val rel_refl = map (OF1 @{thm equivp_reflp}) (equiv_rules_get ctxt)
-val trans2 = map (fn x => @{thm equals_rsp} OF [x]) (quotient_rules_get ctxt)
+val trans2 = map (OF1 @{thm equals_rsp}) (quotient_rules_get ctxt)
 in
 inj_repabs_step_tac ctxt rel_refl trans2
 end
 *}
 More_Conv.top_conv lambda_prs_simple_conv
 fun lambda_prs_tac ctxt = CONVERSION (lambda_prs_conv ctxt)
 *}
-(*
+(* 1. conversion (is not a pattern) *)
-Cleaning the theorem consists of three rewriting steps.
+thm lambda_prs
-The first two need to be done before fun_map is unfolded
+(* 2. folding of definitions: (rep ---> abs) oldConst == newconst *)
+(*    and simplification with                                     *)
-1) lambda_prs:
+thm all_prs ex_prs
-(Rep1 ---> Abs2) (\<lambda>x. Rep2 (f (Abs1 x)))  ---->  f
+(* 3. simplification with *)
+thm fun_map.simps id_simps Quotient_abs_rep Quotient_rel_rep
-Implemented as conversion since it is not a pattern.
+(* 4. Test for refl *)
-2) all_prs (the same for exists):
-Ball (Respects R) ((abs ---> id) f)  ---->  All f
-Rewriting with definitions from the argument defs
-(rep ---> abs) oldConst ----> newconst
-3) Quotient_rel_rep:
-Rel (Rep x) (Rep y)  ---->  x = y
-Quotient_abs_rep:
-Abs (Rep x)  ---->  x
-id_simps; fun_map.simps
-*)
 ML {*
 fun clean_tac lthy =
 let
 val thy = ProofContext.theory_of lthy;
 simp_tac (simps thms2),
 TRY o rtac refl]
 end
 *}
-section {* Genralisation of free variables in a goal *}
+section {* Tactic for genralisation of free variables in a goal *}
 ML {*
 fun inst_spec ctrm =
 Drule.instantiate' [SOME (ctyp_of_term ctrm)] [NONE, SOME ctrm] @{thm spec}
 in
 rtac rule i
 end)
 *}
-section {* General outline of the lifting procedure *}
+section {* 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                *)
 assumes a: "A"
 and     b: "A \<longrightarrow> B"
 and     c: "B = C"
 and     d: "C = D"
 shows   "D"
 using a b c d
 by simp
 ML {*
 fun lift_match_error ctxt fun_str rtrm qtrm =
 let
 val rtrm_str = Syntax.string_of_term ctxt rtrm
 val rtrm' = HOLogic.dest_Trueprop rtrm
 val qtrm' = HOLogic.dest_Trueprop qtrm
 val reg_goal =
 Syntax.check_term ctxt (regularize_trm ctxt rtrm' qtrm')
 handle (LIFT_MATCH s) => lift_match_error ctxt s rtrm qtrm
-val _ = warning "Regularization done."
 val inj_goal =
 Syntax.check_term ctxt (inj_repabs_trm ctxt (reg_goal, qtrm'))
 handle (LIFT_MATCH s) => lift_match_error ctxt s rtrm qtrm
-val _ = warning "RepAbs Injection done."
 in
 Drule.instantiate' []
 [SOME (cterm_of thy rtrm'),
 SOME (cterm_of thy reg_goal),
 SOME (cterm_of thy inj_goal)] @{thm lifting_procedure}
 end
 *}
-(* Left for debugging *)
+ML {*
-ML {*
+(* leaves three subgoales to be proved *)
 fun procedure_tac ctxt rthm =
-ObjectLogic.full_atomize_tac
-THEN' gen_frees_tac ctxt
-THEN' CSUBGOAL (fn (gl, i) =>
-let
-val rthm' = atomize_thm rthm
-val rule = procedure_inst ctxt (prop_of rthm') (term_of gl)
-val thm = Drule.instantiate' [] [SOME (snd (Thm.dest_comb gl))] @{thm QUOT_TRUE_i}
-in
-(rtac rule THEN' RANGE [rtac rthm', (fn _ => all_tac), rtac thm]) i
-end)
-*}
-ML {*
-fun lift_tac ctxt rthm =
 ObjectLogic.full_atomize_tac
 THEN' gen_frees_tac ctxt
 THEN' CSUBGOAL (fn (goal, i) =>
 let
 val rthm' = atomize_thm rthm
 val rule = procedure_inst ctxt (prop_of rthm') (term_of goal)
-val thm = Drule.instantiate' [] [SOME (snd (Thm.dest_comb goal))] @{thm QUOT_TRUE_i}
+val bare_goal = snd (Thm.dest_comb goal)
+val quot_weak = Drule.instantiate' [] [SOME bare_goal] @{thm QUOT_TRUE_i}
 in
-(rtac rule THEN'
+(rtac rule THEN' RANGE [rtac rthm', K all_tac, rtac quot_weak]) i
-RANGE [rtac rthm',
-regularize_tac ctxt,
-rtac thm THEN' all_inj_repabs_tac ctxt,
-clean_tac ctxt]) i
 end)
 *}
-end
+ML {*
+(* automated tactics *)
+fun lift_tac ctxt rthm =
+procedure_tac ctxt rthm
+THEN' RANGE [regularize_tac ctxt,
+all_inj_repabs_tac ctxt,
+clean_tac ctxt]
+*}
+end

changeset 612	ec37a279ca55
parent 611	bb5d3278f02e
child 613	018aabbffd08