src/HOL/Tools/res_axioms.ML
author paulson
Tue Oct 09 18:14:00 2007 +0200 (2007-10-09)
changeset 24937 340523598914
parent 24854 0ebcd575d3c6
child 24959 119793c84647
permissions -rw-r--r--
context-based treatment of generalization; also handling TFrees in axiom clauses
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(*  Author: Jia Meng, Cambridge University Computer Laboratory
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    ID: $Id$
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    Copyright 2004 University of Cambridge
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Transformation of axiom rules (elim/intro/etc) into CNF forms.
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*)
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signature RES_AXIOMS =
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sig
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  val cnf_axiom: thm -> thm list
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  val pairname: thm -> string * thm
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  val multi_base_blacklist: string list 
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  val skolem_thm: thm -> thm list
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  val cnf_rules_pairs: (string * thm) list -> (thm * (string * int)) list
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  val cnf_rules_of_ths: thm list -> thm list
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  val neg_clausify: thm list -> thm list
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  val expand_defs_tac: thm -> tactic
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  val combinators: thm -> thm
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  val neg_conjecture_clauses: thm -> int -> thm list * (string * typ) list
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  val claset_rules_of: Proof.context -> (string * thm) list   (*FIXME DELETE*)
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  val simpset_rules_of: Proof.context -> (string * thm) list  (*FIXME DELETE*)
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  val atpset_rules_of: Proof.context -> (string * thm) list
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  val meson_method_setup: theory -> theory
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  val clause_cache_endtheory: theory -> theory option
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  val setup: theory -> theory
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end;
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structure ResAxioms: RES_AXIOMS =
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struct
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(* FIXME legacy *)
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fun freeze_thm th = #1 (Drule.freeze_thaw th);
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(**** Transformation of Elimination Rules into First-Order Formulas****)
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val cfalse = cterm_of HOL.thy HOLogic.false_const;
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val ctp_false = cterm_of HOL.thy (HOLogic.mk_Trueprop HOLogic.false_const);
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(*Converts an elim-rule into an equivalent theorem that does not have the
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  predicate variable.  Leaves other theorems unchanged.  We simply instantiate the
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  conclusion variable to False.*)
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fun transform_elim th =
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  case concl_of th of    (*conclusion variable*)
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       Const("Trueprop",_) $ (v as Var(_,Type("bool",[]))) =>
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           Thm.instantiate ([], [(cterm_of HOL.thy v, cfalse)]) th
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    | v as Var(_, Type("prop",[])) =>
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           Thm.instantiate ([], [(cterm_of HOL.thy v, ctp_false)]) th
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    | _ => th;
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(*To enforce single-threading*)
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exception Clausify_failure of theory;
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(**** SKOLEMIZATION BY INFERENCE (lcp) ****)
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fun rhs_extra_types lhsT rhs =
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  let val lhs_vars = Term.add_tfreesT lhsT []
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      fun add_new_TFrees (TFree v) =
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            if member (op =) lhs_vars v then I else insert (op =) (TFree v)
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        | add_new_TFrees _ = I
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      val rhs_consts = fold_aterms (fn Const c => insert (op =) c | _ => I) rhs []
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  in fold (#2 #> Term.fold_atyps add_new_TFrees) rhs_consts [] end;
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(*Traverse a theorem, declaring Skolem function definitions. String s is the suggested
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  prefix for the Skolem constant. Result is a new theory*)
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fun declare_skofuns s th thy =
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  let val nref = ref 0
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      fun dec_sko (Const ("Ex",_) $ (xtp as Abs(_,T,p))) (thy, axs) =
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            (*Existential: declare a Skolem function, then insert into body and continue*)
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            let val cname = "sko_" ^ s ^ "_" ^ Int.toString (inc nref)
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                val args0 = term_frees xtp  (*get the formal parameter list*)
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                val Ts = map type_of args0
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                val extraTs = rhs_extra_types (Ts ---> T) xtp
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                val _ = if null extraTs then () else
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                   warning ("Skolemization: extra type vars: " ^
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                            commas_quote (map (Sign.string_of_typ thy) extraTs));
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                val argsx = map (fn T => Free(gensym"vsk", T)) extraTs
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                val args = argsx @ args0
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                val cT = extraTs ---> Ts ---> T
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                val c = Const (Sign.full_name thy cname, cT)
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                val rhs = list_abs_free (map dest_Free args, HOLogic.choice_const T $ xtp)
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                        (*Forms a lambda-abstraction over the formal parameters*)
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                val _ = Output.debug (fn () => "declaring the constant " ^ cname)
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                val thy' =
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                  Sign.add_consts_authentic [Markup.property_internal] [(cname, cT, NoSyn)] thy
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                           (*Theory is augmented with the constant, then its def*)
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                val cdef = cname ^ "_def"
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                val thy'' = Theory.add_defs_i true false [(cdef, equals cT $ c $ rhs)] thy'
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                            handle ERROR _ => raise Clausify_failure thy'
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            in dec_sko (subst_bound (list_comb(c,args), p))
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                               (thy'', Thm.get_axiom_i thy'' (Sign.full_name thy'' cdef) :: axs)
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            end
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        | dec_sko (Const ("All",_) $ (xtp as Abs(a,T,p))) thx =
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            (*Universal quant: insert a free variable into body and continue*)
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            let val fname = Name.variant (add_term_names (p,[])) a
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            in dec_sko (subst_bound (Free(fname,T), p)) thx end
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        | dec_sko (Const ("op &", _) $ p $ q) thx = dec_sko q (dec_sko p thx)
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        | dec_sko (Const ("op |", _) $ p $ q) thx = dec_sko q (dec_sko p thx)
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        | dec_sko (Const ("Trueprop", _) $ p) thx = dec_sko p thx
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        | dec_sko t thx = thx (*Do nothing otherwise*)
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  in  dec_sko (prop_of th) (thy,[])  end;
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(*Traverse a theorem, accumulating Skolem function definitions.*)
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fun assume_skofuns s th =
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  let val sko_count = ref 0
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      fun dec_sko (Const ("Ex",_) $ (xtp as Abs(_,T,p))) defs =
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            (*Existential: declare a Skolem function, then insert into body and continue*)
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            let val skos = map (#1 o Logic.dest_equals) defs  (*existing sko fns*)
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                val args = term_frees xtp \\ skos  (*the formal parameters*)
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                val Ts = map type_of args
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                val cT = Ts ---> T
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                val id = "sko_" ^ s ^ "_" ^ Int.toString (inc sko_count)
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                val c = Free (id, cT)
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                val rhs = list_abs_free (map dest_Free args,
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                                         HOLogic.choice_const T $ xtp)
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                      (*Forms a lambda-abstraction over the formal parameters*)
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                val def = equals cT $ c $ rhs
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            in dec_sko (subst_bound (list_comb(c,args), p))
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                       (def :: defs)
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            end
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        | dec_sko (Const ("All",_) $ (xtp as Abs(a,T,p))) defs =
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            (*Universal quant: insert a free variable into body and continue*)
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            let val fname = Name.variant (add_term_names (p,[])) a
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            in dec_sko (subst_bound (Free(fname,T), p)) defs end
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        | dec_sko (Const ("op &", _) $ p $ q) defs = dec_sko q (dec_sko p defs)
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        | dec_sko (Const ("op |", _) $ p $ q) defs = dec_sko q (dec_sko p defs)
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        | dec_sko (Const ("Trueprop", _) $ p) defs = dec_sko p defs
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        | dec_sko t defs = defs (*Do nothing otherwise*)
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  in  dec_sko (prop_of th) []  end;
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(**** REPLACING ABSTRACTIONS BY COMBINATORS ****)
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(*Returns the vars of a theorem*)
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fun vars_of_thm th =
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  map (Thm.cterm_of (theory_of_thm th) o Var) (Thm.fold_terms Term.add_vars th []);
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(*Make a version of fun_cong with a given variable name*)
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local
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    val fun_cong' = fun_cong RS asm_rl; (*renumber f, g to prevent clashes with (a,0)*)
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    val cx = hd (vars_of_thm fun_cong');
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    val ty = typ_of (ctyp_of_term cx);
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    val thy = theory_of_thm fun_cong;
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    fun mkvar a = cterm_of thy (Var((a,0),ty));
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in
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fun xfun_cong x = Thm.instantiate ([], [(cx, mkvar x)]) fun_cong'
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end;
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(*Removes the lambdas from an equation of the form t = (%x. u).  A non-negative n,
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  serves as an upper bound on how many to remove.*)
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fun strip_lambdas 0 th = th
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  | strip_lambdas n th =
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      case prop_of th of
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          _ $ (Const ("op =", _) $ _ $ Abs (x,_,_)) =>
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              strip_lambdas (n-1) (freeze_thm (th RS xfun_cong x))
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        | _ => th;
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fun assert_eta_free ct =
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  let val t = term_of ct
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  in if (t aconv Envir.eta_contract t) then ()
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     else error ("Eta redex in term: " ^ string_of_cterm ct)
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  end;
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val lambda_free = not o Term.has_abs;
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val monomorphic = not o Term.exists_type (Term.exists_subtype Term.is_TVar);
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val abs_S = @{thm"abs_S"};
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val abs_K = @{thm"abs_K"};
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val abs_I = @{thm"abs_I"};
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val abs_B = @{thm"abs_B"};
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val abs_C = @{thm"abs_C"};
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val [f_B,g_B] = map (cterm_of @{theory}) (term_vars (prop_of abs_B));
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val [g_C,f_C] = map (cterm_of @{theory}) (term_vars (prop_of abs_C));
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val [f_S,g_S] = map (cterm_of @{theory}) (term_vars (prop_of abs_S));
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(*FIXME: requires more use of cterm constructors*)
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fun abstract ct =
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  let val Abs(x,_,body) = term_of ct
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      val thy = theory_of_cterm ct
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      val Type("fun",[xT,bodyT]) = typ_of (ctyp_of_term ct)
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      val cxT = ctyp_of thy xT and cbodyT = ctyp_of thy bodyT
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      fun makeK() = instantiate' [SOME cxT, SOME cbodyT] [SOME (cterm_of thy body)] abs_K
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  in
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      case body of
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          Const _ => makeK()
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        | Free _ => makeK()
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        | Var _ => makeK()  (*though Var isn't expected*)
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        | Bound 0 => instantiate' [SOME cxT] [] abs_I (*identity: I*)
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        | rator$rand =>
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	    if loose_bvar1 (rator,0) then (*C or S*) 
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	       if loose_bvar1 (rand,0) then (*S*)
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	         let val crator = cterm_of thy (Abs(x,xT,rator))
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	             val crand = cterm_of thy (Abs(x,xT,rand))
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	             val abs_S' = cterm_instantiate [(f_S,crator),(g_S,crand)] abs_S
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	             val (_,rhs) = Thm.dest_equals (cprop_of abs_S') 
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	         in
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	           Thm.transitive abs_S' (Conv.binop_conv abstract rhs)
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	         end
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	       else (*C*)
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	         let val crator = cterm_of thy (Abs(x,xT,rator))
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	             val abs_C' = cterm_instantiate [(f_C,crator),(g_C,cterm_of thy rand)] abs_C
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	             val (_,rhs) = Thm.dest_equals (cprop_of abs_C') 
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	         in
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	           Thm.transitive abs_C' (Conv.fun_conv (Conv.arg_conv abstract) rhs)
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	         end
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	    else if loose_bvar1 (rand,0) then (*B or eta*) 
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	       if rand = Bound 0 then eta_conversion ct
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	       else (*B*)
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	         let val crand = cterm_of thy (Abs(x,xT,rand))
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	             val abs_B' = cterm_instantiate [(f_B, cterm_of thy rator),(g_B,crand)] abs_B
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	             val (_,rhs) = Thm.dest_equals (cprop_of abs_B') 
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	         in
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	           Thm.transitive abs_B' (Conv.arg_conv abstract rhs)
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	         end
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	    else makeK()
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        | _ => error "abstract: Bad term"
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  end;
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(*Traverse a theorem, declaring abstraction function definitions. String s is the suggested
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  prefix for the constants. Resulting theory is returned in the first theorem. *)
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fun combinators_aux ct =
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  if lambda_free (term_of ct) then reflexive ct
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  else
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  case term_of ct of
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      Abs _ =>
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	let val _ = assert_eta_free ct;
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	    val (cv,cta) = Thm.dest_abs NONE ct
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	    val (v,Tv) = (dest_Free o term_of) cv
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	    val _ = Output.debug (fn()=>"  recursion: " ^ string_of_cterm cta);
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	    val u_th = combinators_aux cta
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	    val _ = Output.debug (fn()=>"  returned " ^ string_of_thm u_th);
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	    val cu = Thm.rhs_of u_th
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	    val comb_eq = abstract (Thm.cabs cv cu)
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	in Output.debug (fn()=>"  abstraction result: " ^ string_of_thm comb_eq);
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	   (transitive (abstract_rule v cv u_th) comb_eq) end
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    | t1 $ t2 =>
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	let val (ct1,ct2) = Thm.dest_comb ct
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	in  combination (combinators_aux ct1) (combinators_aux ct2)  end;
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fun combinators th =
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  if lambda_free (prop_of th) then th 
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  else
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    let val _ = Output.debug (fn()=>"Conversion to combinators: " ^ string_of_thm th);
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	val th = Drule.eta_contraction_rule th
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	val eqth = combinators_aux (cprop_of th)
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	val _ = Output.debug (fn()=>"Conversion result: " ^ string_of_thm eqth);
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    in  equal_elim eqth th   end;
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(*cterms are used throughout for efficiency*)
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val cTrueprop = Thm.cterm_of HOL.thy HOLogic.Trueprop;
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(*cterm version of mk_cTrueprop*)
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fun c_mkTrueprop A = Thm.capply cTrueprop A;
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(*Given an abstraction over n variables, replace the bound variables by free
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  ones. Return the body, along with the list of free variables.*)
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fun c_variant_abs_multi (ct0, vars) =
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      let val (cv,ct) = Thm.dest_abs NONE ct0
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      in  c_variant_abs_multi (ct, cv::vars)  end
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      handle CTERM _ => (ct0, rev vars);
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(*Given the definition of a Skolem function, return a theorem to replace
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  an existential formula by a use of that function.
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   Example: "EX x. x : A & x ~: B ==> sko A B : A & sko A B ~: B"  [.] *)
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fun skolem_of_def def =
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  let val (c,rhs) = Thm.dest_equals (cprop_of (freeze_thm def))
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      val (ch, frees) = c_variant_abs_multi (rhs, [])
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      val (chilbert,cabs) = Thm.dest_comb ch
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      val {thy,t, ...} = rep_cterm chilbert
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      val T = case t of Const ("Hilbert_Choice.Eps", Type("fun",[_,T])) => T
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                      | _ => raise THM ("skolem_of_def: expected Eps", 0, [def])
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      val cex = Thm.cterm_of thy (HOLogic.exists_const T)
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      val ex_tm = c_mkTrueprop (Thm.capply cex cabs)
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      and conc =  c_mkTrueprop (Drule.beta_conv cabs (Drule.list_comb(c,frees)));
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      fun tacf [prem] = rewrite_goals_tac [def] THEN rtac (prem RS someI_ex) 1
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  in  Goal.prove_internal [ex_tm] conc tacf
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       |> forall_intr_list frees
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       |> forall_elim_vars 0  (*Introduce Vars, but don't discharge defs.*)
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       |> Thm.varifyT
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  end;
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   283
paulson@24742
   284
paulson@24742
   285
(*This will refer to the final version of theory ATP_Linkup.*)
paulson@24742
   286
val atp_linkup_thy_ref = Theory.check_thy @{theory}
paulson@24742
   287
paulson@24742
   288
(*Transfer a theorem into theory ATP_Linkup.thy if it is not already
paulson@24742
   289
  inside that theory -- because it's needed for Skolemization.
paulson@24742
   290
  If called while ATP_Linkup is being created, it will transfer to the
paulson@24742
   291
  current version. If called afterward, it will transfer to the final version.*)
paulson@24742
   292
fun transfer_to_ATP_Linkup th =
paulson@24742
   293
    transfer (Theory.deref atp_linkup_thy_ref) th handle THM _ => th;
paulson@24742
   294
paulson@20863
   295
(*Converts an Isabelle theorem (intro, elim or simp format, even higher-order) into NNF.*)
paulson@24937
   296
fun to_nnf th ctxt0 =
paulson@24937
   297
  let val th1 = th |> transfer_to_ATP_Linkup |> transform_elim |> zero_var_indexes
paulson@24937
   298
      val ((_,[th2]),ctxt) = Variable.import_thms false [th1] ctxt0
paulson@24937
   299
      val th3 = th2 |> Conv.fconv_rule ObjectLogic.atomize |> Meson.make_nnf |> strip_lambdas ~1
paulson@24937
   300
  in  (th3, ctxt)  end;
paulson@16009
   301
paulson@18141
   302
(*Generate Skolem functions for a theorem supplied in nnf*)
paulson@24937
   303
fun assume_skolem_of_def s th =
paulson@22731
   304
  map (skolem_of_def o assume o (cterm_of (theory_of_thm th))) (assume_skofuns s th);
paulson@18141
   305
wenzelm@24669
   306
fun assert_lambda_free ths msg =
paulson@20863
   307
  case filter (not o lambda_free o prop_of) ths of
paulson@20863
   308
      [] => ()
paulson@22731
   309
    | ths' => error (msg ^ "\n" ^ cat_lines (map string_of_thm ths'));
paulson@20457
   310
paulson@21071
   311
(*Keep the full complexity of the original name*)
wenzelm@21858
   312
fun flatten_name s = space_implode "_X" (NameSpace.explode s);
paulson@21071
   313
paulson@22731
   314
fun fake_name th =
wenzelm@24669
   315
  if PureThy.has_name_hint th then flatten_name (PureThy.get_name_hint th)
paulson@22731
   316
  else gensym "unknown_thm_";
paulson@22731
   317
paulson@24742
   318
fun name_or_string th =
paulson@24742
   319
  if PureThy.has_name_hint th then PureThy.get_name_hint th
paulson@24742
   320
  else string_of_thm th;
paulson@24742
   321
paulson@22731
   322
(*Skolemize a named theorem, with Skolem functions as additional premises.*)
paulson@22731
   323
fun skolem_thm th =
paulson@24937
   324
  let val ctxt0 = Variable.thm_context th
paulson@24937
   325
      val (nnfth,ctxt1) = to_nnf th ctxt0 and s = fake_name th
paulson@24937
   326
      val (cnfs,ctxt2) = Meson.make_cnf (assume_skolem_of_def s nnfth) nnfth ctxt1
paulson@24937
   327
  in  cnfs |> map combinators |> Variable.export ctxt2 ctxt0 |> Meson.finish_cnf  end
paulson@22731
   328
  handle THM _ => [];
paulson@22731
   329
paulson@18510
   330
(*Declare Skolem functions for a theorem, supplied in nnf and with its name.
paulson@18510
   331
  It returns a modified theory, unless skolemization fails.*)
paulson@22471
   332
fun skolem thy th =
paulson@24937
   333
  let val ctxt0 = Variable.thm_context th
paulson@24937
   334
  in
paulson@22731
   335
     Option.map
paulson@24937
   336
        (fn (nnfth,ctxt1) =>
paulson@24742
   337
          let val _ = Output.debug (fn () => "skolemizing " ^ name_or_string th ^ ": ")
paulson@24742
   338
              val _ = Output.debug (fn () => string_of_thm nnfth)
paulson@24742
   339
              val s = fake_name th
paulson@22731
   340
              val (thy',defs) = declare_skofuns s nnfth thy
paulson@24937
   341
              val (cnfs,ctxt2) = Meson.make_cnf (map skolem_of_def defs) nnfth ctxt1
paulson@24742
   342
              val _ = Output.debug (fn () => Int.toString (length cnfs) ^ " clauses yielded")
paulson@24937
   343
              val cnfs' = cnfs |> map combinators |> Variable.export ctxt2 ctxt0 
paulson@24937
   344
                               |> Meson.finish_cnf |> map Goal.close_result
paulson@24937
   345
          in (cnfs', thy') end
paulson@24742
   346
          handle Clausify_failure thy_e => ([],thy_e)
paulson@24742
   347
        )
paulson@24937
   348
      (try (to_nnf th) ctxt0)
paulson@24937
   349
  end;
paulson@16009
   350
paulson@24742
   351
(*The cache prevents repeated clausification of a theorem, and also repeated declaration of
paulson@24742
   352
  Skolem functions.*)
paulson@22516
   353
structure ThmCache = TheoryDataFun
wenzelm@22846
   354
(
paulson@24742
   355
  type T = (thm list) Thmtab.table;
paulson@24742
   356
  val empty = Thmtab.empty;
paulson@24742
   357
  fun copy tab : T = tab;
paulson@22516
   358
  val extend = copy;
paulson@24742
   359
  fun merge _ (tab1, tab2) : T = Thmtab.merge (K true) (tab1, tab2);
wenzelm@22846
   360
);
paulson@22516
   361
paulson@18510
   362
(*Populate the clause cache using the supplied theorem. Return the clausal form
paulson@18510
   363
  and modified theory.*)
paulson@24742
   364
fun skolem_cache_thm th thy =
paulson@24742
   365
  case Thmtab.lookup (ThmCache.get thy) th of
wenzelm@20461
   366
      NONE =>
paulson@22471
   367
        (case skolem thy (Thm.transfer thy th) of
wenzelm@20461
   368
             NONE => ([th],thy)
wenzelm@24669
   369
           | SOME (cls,thy') =>
wenzelm@24785
   370
                 (Output.debug (fn () => "skolem_cache_thm: " ^ Int.toString (length cls) ^
paulson@24742
   371
                                         " clauses inserted into cache: " ^ name_or_string th);
wenzelm@24821
   372
                  (cls, ThmCache.map (Thmtab.update (th,cls)) thy')))
paulson@22471
   373
    | SOME cls => (cls,thy);
wenzelm@20461
   374
wenzelm@20461
   375
(*Exported function to convert Isabelle theorems into axiom clauses*)
paulson@22471
   376
fun cnf_axiom th =
paulson@24742
   377
  let val thy = Theory.merge (Theory.deref atp_linkup_thy_ref, Thm.theory_of_thm th)
paulson@22516
   378
  in
paulson@24742
   379
      case Thmtab.lookup (ThmCache.get thy) th of
wenzelm@24821
   380
          NONE => (Output.debug (fn () => "cnf_axiom: " ^ name_or_string th);
wenzelm@24821
   381
                   map Goal.close_result (skolem_thm th))
wenzelm@24821
   382
        | SOME cls => cls
paulson@22516
   383
  end;
paulson@15347
   384
wenzelm@21646
   385
fun pairname th = (PureThy.get_name_hint th, th);
paulson@18141
   386
paulson@15872
   387
(**** Extract and Clausify theorems from a theory's claset and simpset ****)
paulson@15347
   388
paulson@17484
   389
fun rules_of_claset cs =
paulson@17484
   390
  let val {safeIs,safeEs,hazIs,hazEs,...} = rep_cs cs
paulson@19175
   391
      val intros = safeIs @ hazIs
wenzelm@18532
   392
      val elims  = map Classical.classical_rule (safeEs @ hazEs)
paulson@17404
   393
  in
wenzelm@22130
   394
     Output.debug (fn () => "rules_of_claset intros: " ^ Int.toString(length intros) ^
paulson@17484
   395
            " elims: " ^ Int.toString(length elims));
paulson@20017
   396
     map pairname (intros @ elims)
paulson@17404
   397
  end;
paulson@15347
   398
paulson@17484
   399
fun rules_of_simpset ss =
paulson@17484
   400
  let val ({rules,...}, _) = rep_ss ss
paulson@17484
   401
      val simps = Net.entries rules
wenzelm@20461
   402
  in
wenzelm@22130
   403
    Output.debug (fn () => "rules_of_simpset: " ^ Int.toString(length simps));
wenzelm@22130
   404
    map (fn r => (#name r, #thm r)) simps
paulson@17484
   405
  end;
paulson@17484
   406
wenzelm@21505
   407
fun claset_rules_of ctxt = rules_of_claset (local_claset_of ctxt);
wenzelm@21505
   408
fun simpset_rules_of ctxt = rules_of_simpset (local_simpset_of ctxt);
mengj@19196
   409
wenzelm@24042
   410
fun atpset_rules_of ctxt = map pairname (ResAtpset.get ctxt);
wenzelm@20774
   411
paulson@15347
   412
paulson@22471
   413
(**** Translate a set of theorems into CNF ****)
paulson@15347
   414
paulson@19894
   415
(* classical rules: works for both FOL and HOL *)
paulson@19894
   416
fun cnf_rules [] err_list = ([],err_list)
wenzelm@20461
   417
  | cnf_rules ((name,th) :: ths) err_list =
paulson@19894
   418
      let val (ts,es) = cnf_rules ths err_list
paulson@22471
   419
      in  (cnf_axiom th :: ts,es) handle  _ => (ts, (th::es))  end;
paulson@15347
   420
paulson@19894
   421
fun pair_name_cls k (n, []) = []
paulson@19894
   422
  | pair_name_cls k (n, cls::clss) = (cls, (n,k)) :: pair_name_cls (k+1) (n, clss)
wenzelm@20461
   423
paulson@19894
   424
fun cnf_rules_pairs_aux pairs [] = pairs
paulson@19894
   425
  | cnf_rules_pairs_aux pairs ((name,th)::ths) =
paulson@22471
   426
      let val pairs' = (pair_name_cls 0 (name, cnf_axiom th)) @ pairs
wenzelm@20461
   427
                       handle THM _ => pairs | ResClause.CLAUSE _ => pairs
paulson@19894
   428
      in  cnf_rules_pairs_aux pairs' ths  end;
wenzelm@20461
   429
paulson@21290
   430
(*The combination of rev and tail recursion preserves the original order*)
paulson@21290
   431
fun cnf_rules_pairs l = cnf_rules_pairs_aux [] (rev l);
mengj@19353
   432
mengj@19196
   433
mengj@18198
   434
(**** Convert all theorems of a claset/simpset into clauses (ResClause.clause, or ResHolClause.clause) ****)
paulson@15347
   435
paulson@20419
   436
(*Setup function: takes a theory and installs ALL known theorems into the clause cache*)
paulson@20457
   437
paulson@24742
   438
val mark_skolemized = Sign.add_consts_i [("ResAxioms_endtheory", HOLogic.boolT, NoSyn)];
paulson@24742
   439
paulson@24827
   440
val max_lambda_nesting = 3;
paulson@24827
   441
     
paulson@24827
   442
fun excessive_lambdas (f$t, k) = excessive_lambdas (f,k) orelse excessive_lambdas (t,k)
paulson@24827
   443
  | excessive_lambdas (Abs(_,_,t), k) = k=0 orelse excessive_lambdas (t,k-1)
paulson@24827
   444
  | excessive_lambdas _ = false;
paulson@24827
   445
paulson@24827
   446
fun is_formula_type T = (T = HOLogic.boolT orelse T = propT);
paulson@24827
   447
paulson@24827
   448
(*Don't count nested lambdas at the level of formulas, as they are quantifiers*)
paulson@24827
   449
fun excessive_lambdas_fm Ts (Abs(_,T,t)) = excessive_lambdas_fm (T::Ts) t
paulson@24827
   450
  | excessive_lambdas_fm Ts t =
paulson@24827
   451
      if is_formula_type (fastype_of1 (Ts, t))
paulson@24827
   452
      then exists (excessive_lambdas_fm Ts) (#2 (strip_comb t))
paulson@24827
   453
      else excessive_lambdas (t, max_lambda_nesting);
paulson@24827
   454
paulson@24827
   455
fun too_complex t = 
paulson@24827
   456
  Meson.too_many_clauses t orelse excessive_lambdas_fm [] t;
paulson@24827
   457
  
paulson@24854
   458
val multi_base_blacklist =
paulson@24854
   459
  ["defs","select_defs","update_defs","induct","inducts","split","splits","split_asm"];
paulson@24854
   460
wenzelm@24821
   461
fun skolem_cache th thy =
paulson@24827
   462
  if PureThy.is_internal th orelse too_complex (prop_of th) then thy
wenzelm@24821
   463
  else #2 (skolem_cache_thm th thy);
paulson@24742
   464
paulson@24854
   465
fun skolem_cache_list (a,ths) thy =
paulson@24854
   466
  if (Sign.base_name a) mem_string multi_base_blacklist then thy
paulson@24854
   467
  else fold skolem_cache ths thy;
paulson@24854
   468
paulson@24854
   469
val skolem_cache_theorems_of = Symtab.fold skolem_cache_list o #2 o PureThy.theorems_of;
wenzelm@24821
   470
fun skolem_cache_node thy = skolem_cache_theorems_of thy thy;
wenzelm@24821
   471
fun skolem_cache_all thy = fold skolem_cache_theorems_of (thy :: Theory.ancestors_of thy) thy;
paulson@20457
   472
paulson@22516
   473
(*The cache can be kept smaller by inspecting the prop of each thm. Can ignore all that are
paulson@22516
   474
  lambda_free, but then the individual theory caches become much bigger.*)
paulson@21071
   475
paulson@24742
   476
(*The new constant is a hack to prevent multiple execution*)
paulson@24742
   477
fun clause_cache_endtheory thy =
paulson@24742
   478
  let val _ = Output.debug (fn () => "RexAxioms end theory action: " ^ Context.str_of_thy thy)
paulson@24742
   479
  in
wenzelm@24821
   480
    Option.map skolem_cache_node (try mark_skolemized thy)
paulson@24742
   481
  end;
paulson@16563
   482
paulson@16563
   483
(*** meson proof methods ***)
paulson@16563
   484
paulson@22516
   485
fun cnf_rules_of_ths ths = List.concat (map cnf_axiom ths);
paulson@16563
   486
paulson@22731
   487
(*Expand all new*definitions of abstraction or Skolem functions in a proof state.*)
paulson@24827
   488
fun is_absko (Const ("==", _) $ Free (a,_) $ u) = String.isPrefix "sko_" a
paulson@22731
   489
  | is_absko _ = false;
paulson@22731
   490
paulson@22731
   491
fun is_okdef xs (Const ("==", _) $ t $ u) =   (*Definition of Free, not in certain terms*)
paulson@22731
   492
      is_Free t andalso not (member (op aconv) xs t)
paulson@22731
   493
  | is_okdef _ _ = false
paulson@22724
   494
paulson@24215
   495
(*This function tries to cope with open locales, which introduce hypotheses of the form
paulson@24215
   496
  Free == t, conjecture clauses, which introduce various hypotheses, and also definitions
paulson@24827
   497
  of sko_ functions. *)
paulson@22731
   498
fun expand_defs_tac st0 st =
paulson@22731
   499
  let val hyps0 = #hyps (rep_thm st0)
paulson@22731
   500
      val hyps = #hyps (crep_thm st)
paulson@22731
   501
      val newhyps = filter_out (member (op aconv) hyps0 o Thm.term_of) hyps
paulson@22731
   502
      val defs = filter (is_absko o Thm.term_of) newhyps
wenzelm@24669
   503
      val remaining_hyps = filter_out (member (op aconv) (map Thm.term_of defs))
paulson@22731
   504
                                      (map Thm.term_of hyps)
paulson@22731
   505
      val fixed = term_frees (concl_of st) @
paulson@22731
   506
                  foldl (gen_union (op aconv)) [] (map term_frees remaining_hyps)
paulson@22731
   507
  in  Output.debug (fn _ => "expand_defs_tac: " ^ string_of_thm st);
paulson@22731
   508
      Output.debug (fn _ => "  st0: " ^ string_of_thm st0);
paulson@22731
   509
      Output.debug (fn _ => "  defs: " ^ commas (map string_of_cterm defs));
paulson@22731
   510
      Seq.of_list [LocalDefs.expand (filter (is_okdef fixed o Thm.term_of) defs) st]
paulson@22731
   511
  end;
paulson@22724
   512
paulson@22731
   513
paulson@22731
   514
fun meson_general_tac ths i st0 =
paulson@22731
   515
 let val _ = Output.debug (fn () => "Meson called: " ^ cat_lines (map string_of_thm ths))
paulson@22731
   516
 in  (Meson.meson_claset_tac (cnf_rules_of_ths ths) HOL_cs i THEN expand_defs_tac st0) st0 end;
paulson@22724
   517
wenzelm@21588
   518
val meson_method_setup = Method.add_methods
wenzelm@21588
   519
  [("meson", Method.thms_args (fn ths =>
paulson@22724
   520
      Method.SIMPLE_METHOD' (CHANGED_PROP o meson_general_tac ths)),
wenzelm@21588
   521
    "MESON resolution proof procedure")];
paulson@15347
   522
paulson@21102
   523
(** Attribute for converting a theorem into clauses **)
paulson@18510
   524
paulson@22471
   525
fun meta_cnf_axiom th = map Meson.make_meta_clause (cnf_axiom th);
paulson@18510
   526
paulson@21102
   527
fun clausify_rule (th,i) = List.nth (meta_cnf_axiom th, i)
paulson@21102
   528
paulson@21102
   529
val clausify = Attrib.syntax (Scan.lift Args.nat
paulson@21102
   530
  >> (fn i => Thm.rule_attribute (fn _ => fn th => clausify_rule (th, i))));
paulson@21102
   531
paulson@21999
   532
paulson@21999
   533
(*** Converting a subgoal into negated conjecture clauses. ***)
paulson@21999
   534
wenzelm@24300
   535
val neg_skolemize_tac = EVERY' [rtac ccontr, ObjectLogic.atomize_prems_tac, Meson.skolemize_tac];
paulson@22471
   536
paulson@24937
   537
fun neg_clausify sts =
paulson@24937
   538
  sts |> Meson.make_clauses |> map combinators |> Meson.finish_cnf;
paulson@21999
   539
paulson@21999
   540
fun neg_conjecture_clauses st0 n =
paulson@21999
   541
  let val st = Seq.hd (neg_skolemize_tac n st0)
paulson@21999
   542
      val (params,_,_) = strip_context (Logic.nth_prem (n, Thm.prop_of st))
paulson@22516
   543
  in (neg_clausify (Option.valOf (metahyps_thms n st)), params) end
paulson@22516
   544
  handle Option => raise ERROR "unable to Skolemize subgoal";
paulson@21999
   545
wenzelm@24669
   546
(*Conversion of a subgoal to conjecture clauses. Each clause has
paulson@21999
   547
  leading !!-bound universal variables, to express generality. *)
wenzelm@24669
   548
val neg_clausify_tac =
wenzelm@24669
   549
  neg_skolemize_tac THEN'
paulson@21999
   550
  SUBGOAL
paulson@21999
   551
    (fn (prop,_) =>
paulson@21999
   552
     let val ts = Logic.strip_assums_hyp prop
wenzelm@24669
   553
     in EVERY1
wenzelm@24669
   554
         [METAHYPS
wenzelm@24669
   555
            (fn hyps =>
paulson@21999
   556
              (Method.insert_tac
paulson@21999
   557
                (map forall_intr_vars (neg_clausify hyps)) 1)),
wenzelm@24669
   558
          REPEAT_DETERM_N (length ts) o (etac thin_rl)]
paulson@21999
   559
     end);
paulson@21999
   560
paulson@21102
   561
(** The Skolemization attribute **)
paulson@18510
   562
paulson@18510
   563
fun conj2_rule (th1,th2) = conjI OF [th1,th2];
paulson@18510
   564
paulson@20457
   565
(*Conjoin a list of theorems to form a single theorem*)
paulson@20457
   566
fun conj_rule []  = TrueI
paulson@20445
   567
  | conj_rule ths = foldr1 conj2_rule ths;
paulson@18510
   568
paulson@20419
   569
fun skolem_attr (Context.Theory thy, th) =
paulson@24742
   570
      let val (cls, thy') = skolem_cache_thm th thy
wenzelm@18728
   571
      in (Context.Theory thy', conj_rule cls) end
paulson@22724
   572
  | skolem_attr (context, th) = (context, th)
paulson@18510
   573
paulson@18510
   574
val setup_attrs = Attrib.add_attributes
paulson@21102
   575
  [("skolem", Attrib.no_args skolem_attr, "skolemization of a theorem"),
paulson@21999
   576
   ("clausify", clausify, "conversion of theorem to clauses")];
paulson@21999
   577
paulson@21999
   578
val setup_methods = Method.add_methods
wenzelm@24669
   579
  [("neg_clausify", Method.no_args (Method.SIMPLE_METHOD' neg_clausify_tac),
paulson@21999
   580
    "conversion of goal to conjecture clauses")];
wenzelm@24669
   581
paulson@24742
   582
val setup = mark_skolemized #> skolem_cache_all #> ThmCache.init #> setup_attrs #> setup_methods;
paulson@18510
   583
wenzelm@20461
   584
end;