src/HOL/Tools/res_axioms.ML

 
 signature RES_AXIOMS =
 sig
   val cnf_axiom: theory -> thm -> thm list
   val pairname: thm -> string * thm
-  val multi_base_blacklist: string list 
+  val multi_base_blacklist: string list
   val bad_for_atp: thm -> bool
   val type_has_empty_sort: typ -> bool
   val cnf_rules_pairs: theory -> (string * thm) list -> (thm * (string * int)) list
   val neg_clausify: thm list -> thm list
   val expand_defs_tac: thm -> tactic
   val combinators: thm -> thm
   val neg_conjecture_clauses: thm -> int -> thm list * (string * typ) list
   val claset_rules_of: Proof.context -> (string * thm) list   (*FIXME DELETE*)
   val simpset_rules_of: Proof.context -> (string * thm) list  (*FIXME DELETE*)
   val atpset_rules_of: Proof.context -> (string * thm) list
-  val meson_method_setup: theory -> theory
-  val clause_cache_endtheory: theory -> theory option
   val suppress_endtheory: bool ref     (*for emergency use where endtheory causes problems*)
   val setup: theory -> theory
 end;
 
 structure ResAxioms: RES_AXIOMS =

 
 fun type_has_empty_sort (TFree (_, [])) = true
   | type_has_empty_sort (TVar (_, [])) = true
   | type_has_empty_sort (Type (_, Ts)) = exists type_has_empty_sort Ts
   | type_has_empty_sort _ = false;
-  
+
 (**** Transformation of Elimination Rules into First-Order Formulas****)
 
 val cfalse = cterm_of HOL.thy HOLogic.false_const;
 val ctp_false = cterm_of HOL.thy (HOLogic.mk_Trueprop HOLogic.false_const);
 

 
 val lambda_free = not o Term.has_abs;
 
 val monomorphic = not o Term.exists_type (Term.exists_subtype Term.is_TVar);
 
-val abs_S = @{thm"abs_S"};
-val abs_K = @{thm"abs_K"};
-val abs_I = @{thm"abs_I"};
-val abs_B = @{thm"abs_B"};
-val abs_C = @{thm"abs_C"};
-
-val [f_B,g_B] = map (cterm_of @{theory}) (term_vars (prop_of abs_B));
-val [g_C,f_C] = map (cterm_of @{theory}) (term_vars (prop_of abs_C));
-val [f_S,g_S] = map (cterm_of @{theory}) (term_vars (prop_of abs_S));
+val [f_B,g_B] = map (cterm_of @{theory}) (term_vars (prop_of @{thm abs_B}));
+val [g_C,f_C] = map (cterm_of @{theory}) (term_vars (prop_of @{thm abs_C}));
+val [f_S,g_S] = map (cterm_of @{theory}) (term_vars (prop_of @{thm abs_S}));
 
 (*FIXME: requires more use of cterm constructors*)
 fun abstract ct =
   let val _ = Output.debug (fn()=>"  abstraction: " ^ Display.string_of_cterm ct)
       val Abs(x,_,body) = term_of ct
       val thy = theory_of_cterm ct
       val Type("fun",[xT,bodyT]) = typ_of (ctyp_of_term ct)
       val cxT = ctyp_of thy xT and cbodyT = ctyp_of thy bodyT
-      fun makeK() = instantiate' [SOME cxT, SOME cbodyT] [SOME (cterm_of thy body)] abs_K
+      fun makeK() = instantiate' [SOME cxT, SOME cbodyT] [SOME (cterm_of thy body)] @{thm abs_K}
   in
       case body of
           Const _ => makeK()
         | Free _ => makeK()
         | Var _ => makeK()  (*though Var isn't expected*)
-        | Bound 0 => instantiate' [SOME cxT] [] abs_I (*identity: I*)
+        | Bound 0 => instantiate' [SOME cxT] [] @{thm abs_I} (*identity: I*)
         | rator$rand =>
-            if loose_bvar1 (rator,0) then (*C or S*) 
+            if loose_bvar1 (rator,0) then (*C or S*)
                if loose_bvar1 (rand,0) then (*S*)
                  let val crator = cterm_of thy (Abs(x,xT,rator))
                      val crand = cterm_of thy (Abs(x,xT,rand))
-                     val abs_S' = cterm_instantiate [(f_S,crator),(g_S,crand)] abs_S
-                     val (_,rhs) = Thm.dest_equals (cprop_of abs_S') 
+                     val abs_S' = cterm_instantiate [(f_S,crator),(g_S,crand)] @{thm abs_S}
+                     val (_,rhs) = Thm.dest_equals (cprop_of abs_S')
                  in
                    Thm.transitive abs_S' (Conv.binop_conv abstract rhs)
                  end
                else (*C*)
                  let val crator = cterm_of thy (Abs(x,xT,rator))
-                     val abs_C' = cterm_instantiate [(f_C,crator),(g_C,cterm_of thy rand)] abs_C
-                     val (_,rhs) = Thm.dest_equals (cprop_of abs_C') 
+                     val abs_C' = cterm_instantiate [(f_C,crator),(g_C,cterm_of thy rand)] @{thm abs_C}
+                     val (_,rhs) = Thm.dest_equals (cprop_of abs_C')
                  in
                    Thm.transitive abs_C' (Conv.fun_conv (Conv.arg_conv abstract) rhs)
                  end
-            else if loose_bvar1 (rand,0) then (*B or eta*) 
+            else if loose_bvar1 (rand,0) then (*B or eta*)
                if rand = Bound 0 then eta_conversion ct
                else (*B*)
                  let val crand = cterm_of thy (Abs(x,xT,rand))
                      val crator = cterm_of thy rator
-                     val abs_B' = cterm_instantiate [(f_B,crator),(g_B,crand)] abs_B
-                     val (_,rhs) = Thm.dest_equals (cprop_of abs_B') 
+                     val abs_B' = cterm_instantiate [(f_B,crator),(g_B,crand)] @{thm abs_B}
+                     val (_,rhs) = Thm.dest_equals (cprop_of abs_B')
                  in
                    Thm.transitive abs_B' (Conv.arg_conv abstract rhs)
                  end
             else makeK()
         | _ => error "abstract: Bad term"

         in Output.debug (fn()=>"  abstraction result: " ^ Display.string_of_thm comb_eq);
            (transitive (abstract_rule v cv u_th) comb_eq) end
     | t1 $ t2 =>
         let val (ct1,ct2) = Thm.dest_comb ct
         in  combination (combinators_aux ct1) (combinators_aux ct2)  end;
-            
+
 fun combinators th =
-  if lambda_free (prop_of th) then th 
+  if lambda_free (prop_of th) then th
   else
     let val _ = Output.debug (fn()=>"Conversion to combinators: " ^ Display.string_of_thm th);
         val th = Drule.eta_contraction_rule th
         val eqth = combinators_aux (cprop_of th)
         val _ = Output.debug (fn()=>"Conversion result: " ^ Display.string_of_thm eqth);
     in  equal_elim eqth th   end
-    handle THM (msg,_,_) => 
+    handle THM (msg,_,_) =>
       (warning ("Error in the combinator translation of " ^ Display.string_of_thm th);
        warning ("  Exception message: " ^ msg);
        TrueI);  (*A type variable of sort {} will cause make abstraction fail.*)
 
 (*cterms are used throughout for efficiency*)

 
 
 (*Converts an Isabelle theorem (intro, elim or simp format, even higher-order) into NNF.*)
 fun to_nnf th ctxt0 =
   let val th1 = th |> transform_elim |> zero_var_indexes
-      val ((_,[th2]),ctxt) = Variable.import_thms false [th1] ctxt0
+      val ((_,[th2]),ctxt) = Variable.import_thms true [th1] ctxt0
       val th3 = th2 |> Conv.fconv_rule ObjectLogic.atomize |> Meson.make_nnf |> strip_lambdas ~1
   in  (th3, ctxt)  end;
 
 (*Generate Skolem functions for a theorem supplied in nnf*)
 fun assume_skolem_of_def s th =

   case filter (not o lambda_free o prop_of) ths of
       [] => ()
     | ths' => error (msg ^ "\n" ^ cat_lines (map Display.string_of_thm ths'));
 
 
-(*** Blacklisting (duplicated in ResAtp? ***)
+(*** Blacklisting (duplicated in ResAtp?) ***)
 
 val max_lambda_nesting = 3;
-     
+
 fun excessive_lambdas (f$t, k) = excessive_lambdas (f,k) orelse excessive_lambdas (t,k)
   | excessive_lambdas (Abs(_,_,t), k) = k=0 orelse excessive_lambdas (t,k-1)
   | excessive_lambdas _ = false;
 
 fun is_formula_type T = (T = HOLogic.boolT orelse T = propT);

       then exists (excessive_lambdas_fm Ts) (#2 (strip_comb t))
       else excessive_lambdas (t, max_lambda_nesting);
 
 (*The max apply_depth of any metis call in MetisExamples (on 31-10-2007) was 11.*)
 val max_apply_depth = 15;
-     
+
 fun apply_depth (f$t) = Int.max (apply_depth f, apply_depth t + 1)
   | apply_depth (Abs(_,_,t)) = apply_depth t
   | apply_depth _ = 0;
 
-fun too_complex t = 
-  apply_depth t > max_apply_depth orelse 
+fun too_complex t =
+  apply_depth t > max_apply_depth orelse
   Meson.too_many_clauses NONE t orelse
   excessive_lambdas_fm [] t;
-  
+
 fun is_strange_thm th =
   case head_of (concl_of th) of
       Const (a,_) => (a <> "Trueprop" andalso a <> "==")
     | _ => false;
 
-fun bad_for_atp th = 
-  PureThy.is_internal th     
-  orelse too_complex (prop_of th)   
-  orelse exists_type type_has_empty_sort (prop_of th)  
+fun bad_for_atp th =
+  PureThy.is_internal th
+  orelse too_complex (prop_of th)
+  orelse exists_type type_has_empty_sort (prop_of th)
   orelse is_strange_thm th;
 
 val multi_base_blacklist =
   ["defs","select_defs","update_defs","induct","inducts","split","splits","split_asm",
    "cases","ext_cases"];  (*FIXME: put other record thms here, or use the "Internal" marker*)

 
 fun name_or_string th =
   if PureThy.has_name_hint th then PureThy.get_name_hint th
   else Display.string_of_thm th;
 
+(*Skolemize a named theorem, with Skolem functions as additional premises.*)
+fun skolem_thm (s, th) =
+  if member (op =) multi_base_blacklist (Sign.base_name s) orelse bad_for_atp th then []
+  else
+    let
+      val ctxt0 = Variable.thm_context th
+      val (nnfth, ctxt1) = to_nnf th ctxt0
+      val (cnfs, ctxt2) = Meson.make_cnf (assume_skolem_of_def s nnfth) nnfth ctxt1
+    in  cnfs |> map combinators |> Variable.export ctxt2 ctxt0 |> Meson.finish_cnf  end
+    handle THM _ => [];
+
 (*Declare Skolem functions for a theorem, supplied in nnf and with its name.
   It returns a modified theory, unless skolemization fails.*)
-fun skolem th0 thy =
+fun skolem (name, th0) thy =
   let
     val th = Thm.transfer thy th0
     val ctxt0 = Variable.thm_context th
-    val _ = Output.debug (fn () => "skolemizing " ^ name_or_string th)
   in
-     Option.map
-        (fn (nnfth,ctxt1) =>
-          let 
-              val _ = Output.debug (fn () => "  initial nnf: " ^ Display.string_of_thm nnfth)
-              val s = fake_name th
-              val (defs,thy') = declare_skofuns s nnfth thy
-              val (cnfs,ctxt2) = Meson.make_cnf (map skolem_of_def defs) nnfth ctxt1
-              val _ = Output.debug (fn () => Int.toString (length cnfs) ^ " clauses yielded")
-              val cnfs' = cnfs |> map combinators |> Variable.export ctxt2 ctxt0 
-                               |> Meson.finish_cnf |> map Thm.close_derivation
-          in (cnfs', thy') end
-          handle Clausify_failure thy_e => ([],thy_e)
-        )
-      (try (to_nnf th) ctxt0)
+    try (to_nnf th) ctxt0 |> Option.map (fn (nnfth, ctxt1) =>
+      let
+        val s = flatten_name name
+        val (defs, thy') = declare_skofuns s nnfth thy
+        val (cnfs, ctxt2) = Meson.make_cnf (map skolem_of_def defs) nnfth ctxt1
+        val cnfs' = cnfs |> map combinators |> Variable.export ctxt2 ctxt0
+                         |> Meson.finish_cnf |> map Thm.close_derivation
+      in (cnfs', thy') end
+      handle Clausify_failure thy_e => ([], thy_e))   (* FIXME !? *)
   end;
 
 (*The cache prevents repeated clausification of a theorem, and also repeated declaration of
   Skolem functions.*)
 structure ThmCache = TheoryDataFun
 (
-  type T = thm list Thmtab.table;
-  val empty = Thmtab.empty;
+  type T = thm list Thmtab.table * unit Symtab.table
+  val empty = (Thmtab.empty, Symtab.empty)
   val copy = I;
   val extend = I;
-  fun merge _ tabs : T = Thmtab.merge (K true) tabs;
+  fun merge _ ((cache1, seen1), (cache2, seen2)) : T =
+    (Thmtab.merge (K true) (cache1, cache2), Symtab.merge (K true) (seen1, seen2));
 );
 
-(*Populate the clause cache using the supplied theorem. Return the clausal form
-  and modified theory.*)
-fun skolem_cache_thm th thy =
-  case Thmtab.lookup (ThmCache.get thy) th of
-      NONE =>
-        (case skolem th thy of
-             NONE => ([th],thy)
-           | SOME (cls,thy') =>
-                 (Output.debug (fn () => "skolem_cache_thm: " ^ Int.toString (length cls) ^
-                                         " clauses inserted into cache: " ^ name_or_string th);
-                  (cls, ThmCache.map (Thmtab.update (th,cls)) thy')))
-    | SOME cls => (cls,thy);
-
-(*Skolemize a named theorem, with Skolem functions as additional premises.*)
-fun skolem_thm (s,th) =
-  if (Sign.base_name s) mem_string multi_base_blacklist orelse bad_for_atp th then []
-  else 
-      let val ctxt0 = Variable.thm_context th
-          val (nnfth,ctxt1) = to_nnf th ctxt0
-          val (cnfs,ctxt2) = Meson.make_cnf (assume_skolem_of_def s nnfth) nnfth ctxt1
-      in  cnfs |> map combinators |> Variable.export ctxt2 ctxt0 |> Meson.finish_cnf  end
-      handle THM _ => [];
+val lookup_cache = Thmtab.lookup o #1 o ThmCache.get;
+val already_seen = Symtab.defined o #2 o ThmCache.get;
+
+val update_cache = ThmCache.map o apfst o Thmtab.update;
+fun mark_seen name = ThmCache.map (apsnd (Symtab.update (name, ())));
 
 (*Exported function to convert Isabelle theorems into axiom clauses*)
 fun cnf_axiom thy th0 =
-  let val th = Thm.transfer thy th0
-  in
-      case Thmtab.lookup (ThmCache.get thy) th of
-          NONE => (Output.debug (fn () => "cnf_axiom: " ^ name_or_string th);
-                   map Thm.close_derivation (skolem_thm (fake_name th, th)))
-        | SOME cls => cls
-  end;
+  let val th = Thm.transfer thy th0 in
+    case lookup_cache thy th of
+      NONE => map Thm.close_derivation (skolem_thm (fake_name th, th))
+    | SOME cls => cls
+  end;
+
+
+(**** Extract and Clausify theorems from a theory's claset and simpset ****)
 
 fun pairname th = (PureThy.get_name_hint th, th);
-
-(**** Extract and Clausify theorems from a theory's claset and simpset ****)
 
 fun rules_of_claset cs =
   let val {safeIs,safeEs,hazIs,hazEs,...} = rep_cs cs
       val intros = safeIs @ hazIs
       val elims  = map Classical.classical_rule (safeEs @ hazEs)

 
 (*The combination of rev and tail recursion preserves the original order*)
 fun cnf_rules_pairs thy l = cnf_rules_pairs_aux thy [] (rev l);
 
 
-(**** Convert all theorems of a claset/simpset into clauses (ResClause.clause, or ResHolClause.clause) ****)
-
-(*Setup function: takes a theory and installs ALL known theorems into the clause cache*)
-
-val mark_skolemized = Sign.add_consts_i [("ResAxioms_endtheory", HOLogic.boolT, NoSyn)];
-
-fun skolem_cache th thy =
-  if bad_for_atp th then thy else #2 (skolem_cache_thm th thy);
-
-fun skolem_cache_list (a,ths) thy =
-  if (Sign.base_name a) mem_string multi_base_blacklist then thy
-  else fold skolem_cache ths thy;
-
-val skolem_cache_theorems_of = Symtab.fold skolem_cache_list o #2 o PureThy.theorems_of;
-fun skolem_cache_node thy = skolem_cache_theorems_of thy thy;
-fun skolem_cache_all thy = fold skolem_cache_theorems_of (thy :: Theory.ancestors_of thy) thy;
+(**** Convert all facts of the theory into clauses (ResClause.clause, or ResHolClause.clause) ****)
+
+(*Populate the clause cache using the supplied theorem. Return the clausal form
+  and modified theory.*)
+fun skolem_cache_thm (name, th) thy =
+  if bad_for_atp th then thy
+  else
+    (case lookup_cache thy th of
+      SOME _ => thy
+    | NONE =>
+        (case skolem (name, th) thy of
+          NONE => thy
+        | SOME (cls, thy') => update_cache (th, cls) thy'));
+
+fun skolem_cache_fact (name, ths) (changed, thy) =
+  if (Sign.base_name name) mem_string multi_base_blacklist orelse already_seen thy name
+  then (changed, thy)
+  else (true, thy |> mark_seen name |> fold skolem_cache_thm (PureThy.name_multi name ths));
+
+fun saturate_skolem_cache thy =
+  (case Facts.fold_static skolem_cache_fact (PureThy.facts_of thy) (false, thy) of
+    (false, _) => NONE
+  | (true, thy') => SOME thy');
+
+
+val suppress_endtheory = ref false;
+
+fun clause_cache_endtheory thy =
+  if ! suppress_endtheory then NONE
+  else saturate_skolem_cache thy;
+
 
 (*The cache can be kept smaller by inspecting the prop of each thm. Can ignore all that are
   lambda_free, but then the individual theory caches become much bigger.*)
-
-val suppress_endtheory = ref false;
-
-(*The new constant is a hack to prevent multiple execution*)
-fun clause_cache_endtheory thy =
-  if !suppress_endtheory then NONE
-  else
-   (Output.debug (fn () => "RexAxioms end theory action: " ^ Context.str_of_thy thy);
-    Option.map skolem_cache_node (try mark_skolemized thy) );
 
 
 (*** meson proof methods ***)
 
 (*Expand all new*definitions of abstraction or Skolem functions in a proof state.*)

   [("meson", Method.thms_args (fn ths =>
       Method.SIMPLE_METHOD' (CHANGED_PROP o meson_general_tac ths)),
     "MESON resolution proof procedure")];
 
 
-(** Attribute for converting a theorem into clauses **)
-
-val clausify = Attrib.syntax (Scan.lift Args.nat
-  >> (fn i => Thm.rule_attribute (fn context => fn th =>
-      Meson.make_meta_clause (nth (cnf_axiom (Context.theory_of context) th) i))));
-
-
 (*** Converting a subgoal into negated conjecture clauses. ***)
 
 val neg_skolemize_tac = EVERY' [rtac ccontr, ObjectLogic.atomize_prems_tac, Meson.skolemize_tac];
 
 fun neg_clausify sts =

               (Method.insert_tac
                 (map forall_intr_vars (neg_clausify hyps)) 1)),
           REPEAT_DETERM_N (length ts) o (etac thin_rl)]
      end);
 
-
-(** The Skolemization attribute **)
-
-fun conj2_rule (th1,th2) = conjI OF [th1,th2];
-
-(*Conjoin a list of theorems to form a single theorem*)
-fun conj_rule []  = TrueI
-  | conj_rule ths = foldr1 conj2_rule ths;
-
-fun skolem_attr (Context.Theory thy, th) =
-      let val (cls, thy') = skolem_cache_thm th thy
-      in (Context.Theory thy', conj_rule cls) end
-  | skolem_attr (context, th) = (context, th)
-
-val setup_attrs = Attrib.add_attributes
-  [("skolem", Attrib.no_args skolem_attr, "skolemization of a theorem"),
-   ("clausify", clausify, "conversion of theorem to clauses")];
-
 val setup_methods = Method.add_methods
   [("neg_clausify", Method.no_args (Method.SIMPLE_METHOD' neg_clausify_tac),
     "conversion of goal to conjecture clauses")];
 
-val setup = mark_skolemized #> skolem_cache_all #> ThmCache.init #> setup_attrs #> setup_methods;
+
+(** Attribute for converting a theorem into clauses **)
+
+val clausify = Attrib.syntax (Scan.lift Args.nat
+  >> (fn i => Thm.rule_attribute (fn context => fn th =>
+      Meson.make_meta_clause (nth (cnf_axiom (Context.theory_of context) th) i))));
+
+val setup_attrs = Attrib.add_attributes
+  [("clausify", clausify, "conversion of theorem to clauses")];
+
+
+
+(** setup **)
+
+val setup =
+  meson_method_setup #>
+  setup_methods #>
+  setup_attrs #>
+  perhaps saturate_skolem_cache #>
+  Theory.at_end clause_cache_endtheory;
 
 end;
+