
diff -r ca37f4b6457c -r 8dfae5d97387 Quot/QuotMain.thy
--- a/Quot/QuotMain.thy	Tue Dec 08 11:17:56 2009 +0100
+++ b/Quot/QuotMain.thy	Tue Dec 08 11:20:01 2009 +0100
@@ -144,11 +144,10 @@
 
 declare [[map * = (prod_fun, prod_rel)]]
 declare [[map "fun" = (fun_map, fun_rel)]]
-(* FIXME: This should throw an exception:
-declare [[map "option" = (bla, blu)]]
-*)
 
-(* identity quotient is not here as it has to be applied first *)
+(* Throws now an exception:              *)
+(* declare [[map "option" = (bla, blu)]] *)
+
 lemmas [quotient_thm] =
   fun_quotient prod_quotient
 
@@ -160,22 +159,17 @@
 lemmas [quotient_equiv] =
   identity_equivp prod_equivp
 
-ML {* maps_lookup @{theory} "*" *}
-ML {* maps_lookup @{theory} "fun" *}
-
-
 (* definition of the quotient types *)
 (* FIXME: should be called quotient_typ.ML *)
 use "quotient.ML"
 
-
 (* lifting of constants *)
 use "quotient_def.ML"
 
 section {* Simset setup *}
 
-(* since HOL_basic_ss is too "big", we need to set up *)
-(* our own minimal simpset                            *)
+(* Since HOL_basic_ss is too "big" for us, *)
+(* we set up our own minimal simpset.      *)
 ML {*
 fun  mk_minimal_ss ctxt =
   Simplifier.context ctxt empty_ss
@@ -184,11 +178,10 @@
 *}
 
 ML {*
-(* TODO/FIXME not needed anymore? *)
-fun SOLVES' tac = tac THEN_ALL_NEW (fn _ => no_tac)
+fun OF1 thm1 thm2 = thm2 RS thm1
 *}
 
-section {* atomize *}
+section {* Atomize Infrastructure *}
 
 lemma atomize_eqv[atomize]:
   shows "(Trueprop A \<equiv> Trueprop B) \<equiv> (A \<equiv> B)"
@@ -220,24 +213,20 @@
 end
 *}
 
-section {* infrastructure about id *}
+section {* Infrastructure about id *}
+
+print_attributes
 
 (* TODO: think where should this be *)
 lemma prod_fun_id: "prod_fun id id \<equiv> id"
   by (rule eq_reflection) (simp add: prod_fun_def)
 
-(* FIXME: make it a list and add map_id to it *)
-lemmas id_simps =
+lemmas [id_simps] = 
   fun_map_id[THEN eq_reflection]
   id_apply[THEN eq_reflection]
   id_def[THEN eq_reflection,symmetric]
   prod_fun_id
 
-ML {*
-fun simp_ids thm =
-  MetaSimplifier.rewrite_rule @{thms id_simps} thm
-*}
-
 section {* Debugging infrastructure for testing tactics *}
 
 ML {*
@@ -265,7 +254,7 @@
 fun NDT ctxt s tac thm = tac thm  
 *}
 
-section {* Matching of terms and types *}
+section {* Matching of Terms and Types *}
 
 ML {*
 fun matches_typ (ty, ty') =
@@ -278,9 +267,7 @@
        then (List.all matches_typ (tys ~~ tys')) 
        else false
   | _ => false
-*}
 
-ML {*
 fun matches_term (trm, trm') = 
    case (trm, trm') of 
      (_, Var _) => true
@@ -292,37 +279,7 @@
    | _ => false
 *}
 
-section {* Infrastructure for collecting theorems for starting the lifting *}
-
-ML {*
-fun lookup_quot_data lthy qty =
-  let
-    val qty_name = fst (dest_Type qty)
-    val SOME quotdata = quotdata_lookup lthy qty_name
-    (* TODO: Should no longer be needed *)
-    val rty = Logic.unvarifyT (#rtyp quotdata)
-    val rel = #rel quotdata
-    val rel_eqv = #equiv_thm quotdata
-    val rel_refl = @{thm equivp_reflp} OF [rel_eqv]
-  in
-    (rty, rel, rel_refl, rel_eqv)
-  end
-*}
-
-ML {*
-fun lookup_quot_thms lthy qty_name =
-  let
-    val thy = ProofContext.theory_of lthy;
-    val trans2 = PureThy.get_thm thy ("QUOT_TYPE_I_" ^ qty_name ^ ".R_trans2")
-    val reps_same = PureThy.get_thm thy ("QUOT_TYPE_I_" ^ qty_name ^ ".REPS_same")
-    val absrep = PureThy.get_thm thy ("QUOT_TYPE_I_" ^ qty_name ^ ".thm10")
-    val quot = PureThy.get_thm thy ("Quotient_" ^ qty_name)
-  in
-    (trans2, reps_same, absrep, quot)
-  end
-*}
-
-section {* Regularization *} 
+section {* Computation of the Regularize Goal *} 
 
 (*
 Regularizing an rtrm means:
@@ -489,13 +446,13 @@
        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))
-*}
 
-ML {*
 fun equiv_solver_tac ss = equiv_tac (Simplifier.the_context ss)
 val equiv_solver = Simplifier.mk_solver' "Equivalence goal solver" equiv_solver_tac
 *}
@@ -537,7 +494,7 @@
   SOME thm2
 end
 handle _ => NONE
-(* FIXME/TODO: what is the place where the exception can be raised: matching_prs? *)
+(* FIXME/TODO: what is the place where the exception is raised: matching_prs? *)
 *}
 
 ML {*
@@ -560,20 +517,23 @@
   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
 
-To prove that the raw theorem implies the regularised one, 
-we try in order:
+(* Regularize Tactic *)
 
- - Reflexivity of the relation
- - Assumption
- - Elimnating quantifiers on both sides of toplevel implication
- - Simplifying implications on both sides of toplevel implication
- - Ball (Respects ?E) ?P = All ?P
- - (\<And>x. ?R x \<Longrightarrow> ?P x \<longrightarrow> ?Q x) \<Longrightarrow> All ?P \<longrightarrow> Ball ?R ?Q
+(* 0. preliminary simplification step according to *)
+thm ball_reg_eqv bex_reg_eqv babs_reg_eqv (* the latter of no use *)
+    ball_reg_eqv_range bex_reg_eqv_range
+(* 1. eliminating simple Ball/Bex instances*)
+thm ball_reg_right bex_reg_left
+(* 2. monos *)
+(* 3. commutation rules for ball and bex *)
+thm ball_all_comm bex_ex_comm
+(* 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
@@ -586,24 +546,19 @@
                        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},
-    rtac @{thm bex_reg_left},
+    resolve_tac @{thms ball_reg_right bex_reg_left},
     resolve_tac (Inductive.get_monos ctxt),
-    rtac @{thm ball_all_comm},
-    rtac @{thm bex_ex_comm},
+    resolve_tac @{thms ball_all_comm 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:
@@ -658,8 +613,7 @@
         val yvar = Free (y, T)
         val result = Term.lambda_name (y, yvar) (inj_repabs_trm lthy (s, s'))
       in
-        if rty = qty 
-        then result
+        if rty = qty then result
         else mk_repabs lthy (rty, qty) result
       end
 
@@ -667,8 +621,7 @@
        (inj_repabs_trm lthy (t, t')) $ (inj_repabs_trm lthy (s, s'))
 
   | (Free (_, T), Free (_, T')) => 
-        if T = T' 
-        then rtrm 
+        if T = T' then rtrm 
         else mk_repabs lthy (T, T') rtrm
 
   | (_, Const (@{const_name "op ="}, _)) => rtrm
@@ -678,35 +631,33 @@
       let
         val rty = fastype_of rtrm
       in 
-        if rty = T'                    
-        then rtrm
+        if rty = T' then rtrm
         else mk_repabs lthy (rty, T') rtrm
       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},
      resolve_tac (quotient_rules_get ctxt)])
-*}
 
-(* solver for the simplifier *)
-ML {*
 fun quotient_solver_tac ss = quotient_tac (Simplifier.the_context ss)
 val quotient_solver = Simplifier.mk_solver' "Quotient goal solver" quotient_solver_tac
 *}
 
 ML {*
 fun solve_quotient_assums ctxt thm =
-  let val gl = hd (Drule.strip_imp_prems (cprop_of thm)) in
-  thm OF [Goal.prove_internal [] gl (fn _ => quotient_tac ctxt 1)]
-  end
-  handle _ => error "solve_quotient_assums failed. Maybe a quotient_thm is missing"
+let 
+  val goal = hd (Drule.strip_imp_prems (cprop_of thm)) 
+in
+  thm OF [Goal.prove_internal [] goal (fn _ => quotient_tac ctxt 1)]
+end
+handle _ => error "solve_quotient_assums failed. Maybe a quotient_thm is missing"
 *}
 
 (* Not used *)
@@ -914,9 +865,9 @@
 
     (* reflexivity of operators arising from Cong_tac *)
 | Const (@{const_name "op ="},_) $ _ $ _ 
-      => rtac @{thm refl} ORELSE'
+      => rtac @{thm refl} (*ORELSE'
           (resolve_tac trans2 THEN' RANGE [
-            quot_true_tac ctxt (fst o dest_bcomb), quot_true_tac ctxt (snd o dest_bcomb)])
+            quot_true_tac ctxt (fst o dest_bcomb), quot_true_tac ctxt (snd o dest_bcomb)])*)
 
 (* TODO: These patterns should should be somehow combined and generalized... *)
 | (Const (@{const_name fun_rel}, _) $ _ $ _) $
@@ -943,32 +894,49 @@
 *}
 
 ML {*
-fun inj_repabs_tac ctxt rel_refl trans2 =
+fun inj_repabs_step_tac ctxt rel_refl trans2 =
   (FIRST' [
-    inj_repabs_tac_match ctxt trans2,
+    NDT ctxt "0" (inj_repabs_tac_match ctxt trans2),
     (* R (t $ \<dots>) (t' $ \<dots>) ----> apply_rsp   provided type of t needs lifting *)
+    
     NDT ctxt "A" (apply_rsp_tac ctxt THEN'
-                (RANGE [quot_true_tac ctxt (fst o dest_comb), quot_true_tac ctxt (snd o dest_comb)])),
+                 RANGE [quot_true_tac ctxt (fst o dest_comb), quot_true_tac ctxt (snd o dest_comb)]),
+    
+    (* TODO/FIXME: I had to move this after the apply_rsp_tac - is this right *)
+    NDT ctxt "B" (resolve_tac trans2 THEN' 
+                 RANGE [quot_true_tac ctxt (fst o dest_bcomb), quot_true_tac ctxt (snd o dest_bcomb)]),
+
     (* (op =) (t $ \<dots>) (t' $ \<dots>) ----> Cong   provided type of t does not need lifting *)
     (* merge with previous tactic *)
-    NDT ctxt "B" (Cong_Tac.cong_tac @{thm cong} THEN'
+    NDT ctxt "C" (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 =) (\<lambda>x\<dots>) (\<lambda>x\<dots>) ----> (op =) (\<dots>) (\<dots>) *)
-    NDT ctxt "C" (rtac @{thm ext} THEN' quot_true_tac ctxt unlam),
+    NDT ctxt "D" (rtac @{thm ext} THEN' quot_true_tac ctxt unlam),
+    
     (* resolving with R x y assumptions *)
     NDT ctxt "E" (atac),
+    
     (* reflexivity of the basic relations *)
     (* R \<dots> \<dots> *)
-    NDT ctxt "D" (resolve_tac rel_refl)
+    NDT ctxt "F" (resolve_tac rel_refl)
     ])
 *}
 
 ML {*
-fun all_inj_repabs_tac ctxt rel_refl trans2 =
-  REPEAT_ALL_NEW (inj_repabs_tac ctxt rel_refl trans2)
+fun inj_repabs_tac ctxt =
+let
+  val rel_refl = map (OF1 @{thm equivp_reflp}) (equiv_rules_get ctxt)
+  val trans2 = map (OF1 @{thm equals_rsp}) (quotient_rules_get ctxt)
+in
+  inj_repabs_step_tac ctxt rel_refl trans2
+end
+
+fun all_inj_repabs_tac ctxt =
+  REPEAT_ALL_NEW (inj_repabs_tac ctxt)
 *}
 
-section {* Cleaning of the theorem *}
+section {* Cleaning of the Theorem *}
 
 ML {*
 fun make_inst lhs t =
@@ -1017,7 +985,7 @@
        val _ = tracing ("te rule:\n" ^ (Syntax.string_of_term ctxt (prop_of te)));
        val ti =
          (let
-           val ts = MetaSimplifier.rewrite_rule @{thms id_simps} te
+           val ts = MetaSimplifier.rewrite_rule (id_simps_get ctxt) te
            val (insp, inst) = make_inst (term_of (Thm.lhs_of ts)) (term_of ctrm)
          in
            Drule.instantiate ([], [(cterm_of thy insp, cterm_of thy inst)]) ts
@@ -1026,7 +994,7 @@
            val (insp, inst) = make_inst2 (term_of (Thm.lhs_of te)) (term_of ctrm)
            val td = Drule.instantiate ([], [(cterm_of thy insp, cterm_of thy inst)]) te
          in
-           MetaSimplifier.rewrite_rule @{thms id_simps} td
+           MetaSimplifier.rewrite_rule (id_simps_get ctxt) td
          end);
        val _ = if not (Term.is_Const a2 andalso fst (dest_Const a2) = @{const_name "id"}) then
                   (tracing "lambda_prs";
@@ -1049,39 +1017,24 @@
 fun lambda_prs_tac ctxt = CONVERSION (lambda_prs_conv ctxt)
 *}
 
-(*
- Cleaning the theorem consists of three rewriting steps.
- The first two need to be done before fun_map is unfolded
-
- 1) lambda_prs:
-     (Rep1 ---> Abs2) (\<lambda>x. Rep2 (f (Abs1 x)))  ---->  f
-
-    Implemented as conversion since it is not a pattern.
-
- 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
-*)
+(* 1. conversion (is not a pattern) *)
+thm lambda_prs
+(* 2. folding of definitions: (rep ---> abs) oldConst == newconst *)
+(*    and simplification with                                     *)
+thm all_prs ex_prs 
+(* 3. simplification with *)
+thm fun_map.simps Quotient_abs_rep Quotient_rel_rep id_simps
+(* 4. Test for refl *)
 
 ML {*
 fun clean_tac lthy =
   let
     val thy = ProofContext.theory_of lthy;
     val defs = map (Thm.varifyT o symmetric o #def) (qconsts_dest thy)
-      (* FIXME: shouldn't the definitions already be varified? *)
+      (* FIXME: why is the Thm.varifyT needed: example where it fails is LamEx *)
     val thms1 = @{thms all_prs ex_prs} @ defs
-    val thms2 = @{thms eq_reflection[OF fun_map.simps]} 
-                @ @{thms id_simps Quotient_abs_rep Quotient_rel_rep} 
+    val thms2 = @{thms eq_reflection[OF fun_map.simps]} @ (id_simps_get lthy)
+                @ @{thms Quotient_abs_rep Quotient_rel_rep} 
     fun simps thms = (mk_minimal_ss lthy) addsimps thms addSolver quotient_solver
   in
     EVERY' [lambda_prs_tac lthy,
@@ -1091,7 +1044,7 @@
   end
 *}
 
-section {* Genralisation of free variables in a goal *}
+section {* Tactic for genralisation of free variables in a goal *}
 
 ML {*
 fun inst_spec ctrm =
@@ -1121,7 +1074,7 @@
   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           *)
@@ -1138,8 +1091,8 @@
   and     c: "B = C"
   and     d: "C = D"
   shows   "D"
-  using a b c d
-  by simp
+using a b c d
+by simp
 
 ML {*
 fun lift_match_error ctxt fun_str rtrm qtrm =
@@ -1162,11 +1115,9 @@
   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'),
@@ -1175,42 +1126,40 @@
 end
 *}
 
-(* Left for debugging *)
 ML {*
+(* the tactic leaves three subgoals to be proved *)
 fun procedure_tac ctxt rthm =
   ObjectLogic.full_atomize_tac
   THEN' gen_frees_tac ctxt
-  THEN' CSUBGOAL (fn (gl, i) =>
+  THEN' CSUBGOAL (fn (goal, 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}
+      val rule = procedure_inst ctxt (prop_of rthm') (term_of goal)
+      val bare_goal = snd (Thm.dest_comb goal)
+      val quot_weak = Drule.instantiate' [] [SOME bare_goal] @{thm QUOT_TRUE_i}
     in
-      (rtac rule THEN' RANGE [rtac rthm', (fn _ => all_tac), rtac thm]) i
+      (rtac rule THEN' RANGE [rtac rthm', K all_tac, rtac quot_weak]) i
     end)
 *}
 
+(* automatic proofs *)
+ML {*
+fun SOLVES' tac = tac THEN_ALL_NEW (K no_tac)
+
+fun WARN (tac, msg) i st =
+ case Seq.pull ((SOLVES' tac) i st) of
+     NONE    => (warning msg; Seq.single st)
+   | seqcell => Seq.make (fn () => seqcell)
+
+fun RANGE_WARN xs = RANGE (map WARN xs)
+*}
+
 ML {*
-(* FIXME/TODO should only get as arguments the rthm like procedure_tac *)
-
 fun lift_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 rel_refl = map (fn x => @{thm equivp_reflp} OF [x]) (equiv_rules_get ctxt)
-      val quotients = quotient_rules_get ctxt
-      val trans2 = map (fn x => @{thm equals_rsp} OF [x]) quotients
-      val thm = Drule.instantiate' [] [SOME (snd (Thm.dest_comb gl))] @{thm QUOT_TRUE_i}
-    in
-      (rtac rule THEN'
-       RANGE [rtac rthm',
-              regularize_tac ctxt,
-              rtac thm THEN' all_inj_repabs_tac ctxt rel_refl trans2,
-              clean_tac ctxt]) i
-    end)
+  procedure_tac ctxt rthm
+  THEN' RANGE_WARN [(regularize_tac ctxt,     "Regularize proof failed."),
+                    (all_inj_repabs_tac ctxt, "Injection proof failed."),
+                    (clean_tac ctxt,          "Cleaning proof failed.")]
 *}
 
 end




