(* Author: Jia Meng, Cambridge University Computer Laboratory
ID: $Id$
Copyright 2004 University of Cambridge
Transformation of axiom rules (elim/intro/etc) into CNF forms.
*)
signature RES_AXIOMS =
sig
val cnf_axiom: thm -> thm list
val pairname: thm -> string * thm
val multi_base_blacklist: string list
val skolem_thm: thm -> thm list
val cnf_rules_pairs: (string * thm) list -> (thm * (string * int)) list
val cnf_rules_of_ths: thm list -> thm 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 setup: theory -> theory
end;
structure ResAxioms: RES_AXIOMS =
struct
(* FIXME legacy *)
fun freeze_thm th = #1 (Drule.freeze_thaw th);
(**** 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);
(*Converts an elim-rule into an equivalent theorem that does not have the
predicate variable. Leaves other theorems unchanged. We simply instantiate the
conclusion variable to False.*)
fun transform_elim th =
case concl_of th of (*conclusion variable*)
Const("Trueprop",_) $ (v as Var(_,Type("bool",[]))) =>
Thm.instantiate ([], [(cterm_of HOL.thy v, cfalse)]) th
| v as Var(_, Type("prop",[])) =>
Thm.instantiate ([], [(cterm_of HOL.thy v, ctp_false)]) th
| _ => th;
(*To enforce single-threading*)
exception Clausify_failure of theory;
(**** SKOLEMIZATION BY INFERENCE (lcp) ****)
fun rhs_extra_types lhsT rhs =
let val lhs_vars = Term.add_tfreesT lhsT []
fun add_new_TFrees (TFree v) =
if member (op =) lhs_vars v then I else insert (op =) (TFree v)
| add_new_TFrees _ = I
val rhs_consts = fold_aterms (fn Const c => insert (op =) c | _ => I) rhs []
in fold (#2 #> Term.fold_atyps add_new_TFrees) rhs_consts [] end;
(*Traverse a theorem, declaring Skolem function definitions. String s is the suggested
prefix for the Skolem constant. Result is a new theory*)
fun declare_skofuns s th thy =
let val nref = ref 0
fun dec_sko (Const ("Ex",_) $ (xtp as Abs(_,T,p))) (thy, axs) =
(*Existential: declare a Skolem function, then insert into body and continue*)
let val cname = "sko_" ^ s ^ "_" ^ Int.toString (inc nref)
val args0 = term_frees xtp (*get the formal parameter list*)
val Ts = map type_of args0
val extraTs = rhs_extra_types (Ts ---> T) xtp
val _ = if null extraTs then () else
warning ("Skolemization: extra type vars: " ^
commas_quote (map (Sign.string_of_typ thy) extraTs));
val argsx = map (fn T => Free(gensym"vsk", T)) extraTs
val args = argsx @ args0
val cT = extraTs ---> Ts ---> T
val c = Const (Sign.full_name thy cname, cT)
val rhs = list_abs_free (map dest_Free args, HOLogic.choice_const T $ xtp)
(*Forms a lambda-abstraction over the formal parameters*)
val _ = Output.debug (fn () => "declaring the constant " ^ cname)
val thy' =
Sign.add_consts_authentic [Markup.property_internal] [(cname, cT, NoSyn)] thy
(*Theory is augmented with the constant, then its def*)
val cdef = cname ^ "_def"
val thy'' = Theory.add_defs_i true false [(cdef, equals cT $ c $ rhs)] thy'
handle ERROR _ => raise Clausify_failure thy'
in dec_sko (subst_bound (list_comb(c,args), p))
(thy'', Thm.get_axiom_i thy'' (Sign.full_name thy'' cdef) :: axs)
end
| dec_sko (Const ("All",_) $ (xtp as Abs(a,T,p))) thx =
(*Universal quant: insert a free variable into body and continue*)
let val fname = Name.variant (add_term_names (p,[])) a
in dec_sko (subst_bound (Free(fname,T), p)) thx end
| dec_sko (Const ("op &", _) $ p $ q) thx = dec_sko q (dec_sko p thx)
| dec_sko (Const ("op |", _) $ p $ q) thx = dec_sko q (dec_sko p thx)
| dec_sko (Const ("Trueprop", _) $ p) thx = dec_sko p thx
| dec_sko t thx = thx (*Do nothing otherwise*)
in dec_sko (prop_of th) (thy,[]) end;
(*Traverse a theorem, accumulating Skolem function definitions.*)
fun assume_skofuns s th =
let val sko_count = ref 0
fun dec_sko (Const ("Ex",_) $ (xtp as Abs(_,T,p))) defs =
(*Existential: declare a Skolem function, then insert into body and continue*)
let val skos = map (#1 o Logic.dest_equals) defs (*existing sko fns*)
val args = term_frees xtp \\ skos (*the formal parameters*)
val Ts = map type_of args
val cT = Ts ---> T
val id = "sko_" ^ s ^ "_" ^ Int.toString (inc sko_count)
val c = Free (id, cT)
val rhs = list_abs_free (map dest_Free args,
HOLogic.choice_const T $ xtp)
(*Forms a lambda-abstraction over the formal parameters*)
val def = equals cT $ c $ rhs
in dec_sko (subst_bound (list_comb(c,args), p))
(def :: defs)
end
| dec_sko (Const ("All",_) $ (xtp as Abs(a,T,p))) defs =
(*Universal quant: insert a free variable into body and continue*)
let val fname = Name.variant (add_term_names (p,[])) a
in dec_sko (subst_bound (Free(fname,T), p)) defs end
| dec_sko (Const ("op &", _) $ p $ q) defs = dec_sko q (dec_sko p defs)
| dec_sko (Const ("op |", _) $ p $ q) defs = dec_sko q (dec_sko p defs)
| dec_sko (Const ("Trueprop", _) $ p) defs = dec_sko p defs
| dec_sko t defs = defs (*Do nothing otherwise*)
in dec_sko (prop_of th) [] end;
(**** REPLACING ABSTRACTIONS BY COMBINATORS ****)
(*Returns the vars of a theorem*)
fun vars_of_thm th =
map (Thm.cterm_of (theory_of_thm th) o Var) (Thm.fold_terms Term.add_vars th []);
(*Make a version of fun_cong with a given variable name*)
local
val fun_cong' = fun_cong RS asm_rl; (*renumber f, g to prevent clashes with (a,0)*)
val cx = hd (vars_of_thm fun_cong');
val ty = typ_of (ctyp_of_term cx);
val thy = theory_of_thm fun_cong;
fun mkvar a = cterm_of thy (Var((a,0),ty));
in
fun xfun_cong x = Thm.instantiate ([], [(cx, mkvar x)]) fun_cong'
end;
(*Removes the lambdas from an equation of the form t = (%x. u). A non-negative n,
serves as an upper bound on how many to remove.*)
fun strip_lambdas 0 th = th
| strip_lambdas n th =
case prop_of th of
_ $ (Const ("op =", _) $ _ $ Abs (x,_,_)) =>
strip_lambdas (n-1) (freeze_thm (th RS xfun_cong x))
| _ => th;
fun assert_eta_free ct =
let val t = term_of ct
in if (t aconv Envir.eta_contract t) then ()
else error ("Eta redex in term: " ^ string_of_cterm ct)
end;
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));
(*FIXME: requires more use of cterm constructors*)
fun abstract ct =
let 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
in
case body of
Const _ => makeK()
| Free _ => makeK()
| Var _ => makeK() (*though Var isn't expected*)
| Bound 0 => instantiate' [SOME cxT] [] abs_I (*identity: I*)
| rator$rand =>
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')
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')
in
Thm.transitive abs_C' (Conv.fun_conv (Conv.arg_conv abstract) rhs)
end
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 abs_B' = cterm_instantiate [(f_B, cterm_of thy rator),(g_B,crand)] 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"
end;
(*Traverse a theorem, declaring abstraction function definitions. String s is the suggested
prefix for the constants. Resulting theory is returned in the first theorem. *)
fun combinators_aux ct =
if lambda_free (term_of ct) then reflexive ct
else
case term_of ct of
Abs _ =>
let val _ = assert_eta_free ct;
val (cv,cta) = Thm.dest_abs NONE ct
val (v,Tv) = (dest_Free o term_of) cv
val _ = Output.debug (fn()=>" recursion: " ^ string_of_cterm cta);
val u_th = combinators_aux cta
val _ = Output.debug (fn()=>" returned " ^ string_of_thm u_th);
val cu = Thm.rhs_of u_th
val comb_eq = abstract (Thm.cabs cv cu)
in Output.debug (fn()=>" abstraction result: " ^ 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
else
let val _ = Output.debug (fn()=>"Conversion to combinators: " ^ string_of_thm th);
val th = Drule.eta_contraction_rule th
val eqth = combinators_aux (cprop_of th)
val _ = Output.debug (fn()=>"Conversion result: " ^ string_of_thm eqth);
in equal_elim eqth th end;
(*cterms are used throughout for efficiency*)
val cTrueprop = Thm.cterm_of HOL.thy HOLogic.Trueprop;
(*cterm version of mk_cTrueprop*)
fun c_mkTrueprop A = Thm.capply cTrueprop A;
(*Given an abstraction over n variables, replace the bound variables by free
ones. Return the body, along with the list of free variables.*)
fun c_variant_abs_multi (ct0, vars) =
let val (cv,ct) = Thm.dest_abs NONE ct0
in c_variant_abs_multi (ct, cv::vars) end
handle CTERM _ => (ct0, rev vars);
(*Given the definition of a Skolem function, return a theorem to replace
an existential formula by a use of that function.
Example: "EX x. x : A & x ~: B ==> sko A B : A & sko A B ~: B" [.] *)
fun skolem_of_def def =
let val (c,rhs) = Thm.dest_equals (cprop_of (freeze_thm def))
val (ch, frees) = c_variant_abs_multi (rhs, [])
val (chilbert,cabs) = Thm.dest_comb ch
val {thy,t, ...} = rep_cterm chilbert
val T = case t of Const ("Hilbert_Choice.Eps", Type("fun",[_,T])) => T
| _ => raise THM ("skolem_of_def: expected Eps", 0, [def])
val cex = Thm.cterm_of thy (HOLogic.exists_const T)
val ex_tm = c_mkTrueprop (Thm.capply cex cabs)
and conc = c_mkTrueprop (Drule.beta_conv cabs (Drule.list_comb(c,frees)));
fun tacf [prem] = rewrite_goals_tac [def] THEN rtac (prem RS someI_ex) 1
in Goal.prove_internal [ex_tm] conc tacf
|> forall_intr_list frees
|> forall_elim_vars 0 (*Introduce Vars, but don't discharge defs.*)
|> Thm.varifyT
end;
(*This will refer to the final version of theory ATP_Linkup.*)
val atp_linkup_thy_ref = Theory.check_thy @{theory}
(*Transfer a theorem into theory ATP_Linkup.thy if it is not already
inside that theory -- because it's needed for Skolemization.
If called while ATP_Linkup is being created, it will transfer to the
current version. If called afterward, it will transfer to the final version.*)
fun transfer_to_ATP_Linkup th =
transfer (Theory.deref atp_linkup_thy_ref) th handle THM _ => th;
(*Converts an Isabelle theorem (intro, elim or simp format, even higher-order) into NNF.*)
fun to_nnf th ctxt0 =
let val th1 = th |> transfer_to_ATP_Linkup |> transform_elim |> zero_var_indexes
val ((_,[th2]),ctxt) = Variable.import_thms false [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 =
map (skolem_of_def o assume o (cterm_of (theory_of_thm th))) (assume_skofuns s th);
fun assert_lambda_free ths msg =
case filter (not o lambda_free o prop_of) ths of
[] => ()
| ths' => error (msg ^ "\n" ^ cat_lines (map string_of_thm ths'));
(*Keep the full complexity of the original name*)
fun flatten_name s = space_implode "_X" (NameSpace.explode s);
fun fake_name th =
if PureThy.has_name_hint th then flatten_name (PureThy.get_name_hint th)
else gensym "unknown_thm_";
fun name_or_string th =
if PureThy.has_name_hint th then PureThy.get_name_hint th
else string_of_thm th;
(*Skolemize a named theorem, with Skolem functions as additional premises.*)
fun skolem_thm th =
let val ctxt0 = Variable.thm_context th
val (nnfth,ctxt1) = to_nnf th ctxt0 and s = fake_name th
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 thy th =
let val ctxt0 = Variable.thm_context th
in
Option.map
(fn (nnfth,ctxt1) =>
let val _ = Output.debug (fn () => "skolemizing " ^ name_or_string th ^ ": ")
val _ = Output.debug (fn () => string_of_thm nnfth)
val s = fake_name th
val (thy',defs) = 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 Goal.close_result
in (cnfs', thy') end
handle Clausify_failure thy_e => ([],thy_e)
)
(try (to_nnf th) ctxt0)
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;
fun copy tab : T = tab;
val extend = copy;
fun merge _ (tab1, tab2) : T = Thmtab.merge (K true) (tab1, tab2);
);
(*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 thy (Thm.transfer thy th) 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);
(*Exported function to convert Isabelle theorems into axiom clauses*)
fun cnf_axiom th =
let val thy = Theory.merge (Theory.deref atp_linkup_thy_ref, Thm.theory_of_thm th)
in
case Thmtab.lookup (ThmCache.get thy) th of
NONE => (Output.debug (fn () => "cnf_axiom: " ^ name_or_string th);
map Goal.close_result (skolem_thm th))
| SOME cls => cls
end;
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)
in
Output.debug (fn () => "rules_of_claset intros: " ^ Int.toString(length intros) ^
" elims: " ^ Int.toString(length elims));
map pairname (intros @ elims)
end;
fun rules_of_simpset ss =
let val ({rules,...}, _) = rep_ss ss
val simps = Net.entries rules
in
Output.debug (fn () => "rules_of_simpset: " ^ Int.toString(length simps));
map (fn r => (#name r, #thm r)) simps
end;
fun claset_rules_of ctxt = rules_of_claset (local_claset_of ctxt);
fun simpset_rules_of ctxt = rules_of_simpset (local_simpset_of ctxt);
fun atpset_rules_of ctxt = map pairname (ResAtpset.get ctxt);
(**** Translate a set of theorems into CNF ****)
(* classical rules: works for both FOL and HOL *)
fun cnf_rules [] err_list = ([],err_list)
| cnf_rules ((name,th) :: ths) err_list =
let val (ts,es) = cnf_rules ths err_list
in (cnf_axiom th :: ts,es) handle _ => (ts, (th::es)) end;
fun pair_name_cls k (n, []) = []
| pair_name_cls k (n, cls::clss) = (cls, (n,k)) :: pair_name_cls (k+1) (n, clss)
fun cnf_rules_pairs_aux pairs [] = pairs
| cnf_rules_pairs_aux pairs ((name,th)::ths) =
let val pairs' = (pair_name_cls 0 (name, cnf_axiom th)) @ pairs
handle THM _ => pairs | ResClause.CLAUSE _ => pairs
in cnf_rules_pairs_aux pairs' ths end;
(*The combination of rev and tail recursion preserves the original order*)
fun cnf_rules_pairs l = cnf_rules_pairs_aux [] (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)];
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);
(*Don't count nested lambdas at the level of formulas, as they are quantifiers*)
fun excessive_lambdas_fm Ts (Abs(_,T,t)) = excessive_lambdas_fm (T::Ts) t
| excessive_lambdas_fm Ts t =
if is_formula_type (fastype_of1 (Ts, t))
then exists (excessive_lambdas_fm Ts) (#2 (strip_comb t))
else excessive_lambdas (t, max_lambda_nesting);
fun too_complex t =
Meson.too_many_clauses t orelse excessive_lambdas_fm [] t;
val multi_base_blacklist =
["defs","select_defs","update_defs","induct","inducts","split","splits","split_asm"];
fun skolem_cache th thy =
if PureThy.is_internal th orelse too_complex (prop_of 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;
(*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.*)
(*The new constant is a hack to prevent multiple execution*)
fun clause_cache_endtheory thy =
let val _ = Output.debug (fn () => "RexAxioms end theory action: " ^ Context.str_of_thy thy)
in
Option.map skolem_cache_node (try mark_skolemized thy)
end;
(*** meson proof methods ***)
fun cnf_rules_of_ths ths = List.concat (map cnf_axiom ths);
(*Expand all new*definitions of abstraction or Skolem functions in a proof state.*)
fun is_absko (Const ("==", _) $ Free (a,_) $ u) = String.isPrefix "sko_" a
| is_absko _ = false;
fun is_okdef xs (Const ("==", _) $ t $ u) = (*Definition of Free, not in certain terms*)
is_Free t andalso not (member (op aconv) xs t)
| is_okdef _ _ = false
(*This function tries to cope with open locales, which introduce hypotheses of the form
Free == t, conjecture clauses, which introduce various hypotheses, and also definitions
of sko_ functions. *)
fun expand_defs_tac st0 st =
let val hyps0 = #hyps (rep_thm st0)
val hyps = #hyps (crep_thm st)
val newhyps = filter_out (member (op aconv) hyps0 o Thm.term_of) hyps
val defs = filter (is_absko o Thm.term_of) newhyps
val remaining_hyps = filter_out (member (op aconv) (map Thm.term_of defs))
(map Thm.term_of hyps)
val fixed = term_frees (concl_of st) @
foldl (gen_union (op aconv)) [] (map term_frees remaining_hyps)
in Output.debug (fn _ => "expand_defs_tac: " ^ string_of_thm st);
Output.debug (fn _ => " st0: " ^ string_of_thm st0);
Output.debug (fn _ => " defs: " ^ commas (map string_of_cterm defs));
Seq.of_list [LocalDefs.expand (filter (is_okdef fixed o Thm.term_of) defs) st]
end;
fun meson_general_tac ths i st0 =
let val _ = Output.debug (fn () => "Meson called: " ^ cat_lines (map string_of_thm ths))
in (Meson.meson_claset_tac (cnf_rules_of_ths ths) HOL_cs i THEN expand_defs_tac st0) st0 end;
val meson_method_setup = Method.add_methods
[("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 **)
fun meta_cnf_axiom th = map Meson.make_meta_clause (cnf_axiom th);
fun clausify_rule (th,i) = List.nth (meta_cnf_axiom th, i)
val clausify = Attrib.syntax (Scan.lift Args.nat
>> (fn i => Thm.rule_attribute (fn _ => fn th => clausify_rule (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 =
sts |> Meson.make_clauses |> map combinators |> Meson.finish_cnf;
fun neg_conjecture_clauses st0 n =
let val st = Seq.hd (neg_skolemize_tac n st0)
val (params,_,_) = strip_context (Logic.nth_prem (n, Thm.prop_of st))
in (neg_clausify (Option.valOf (metahyps_thms n st)), params) end
handle Option => raise ERROR "unable to Skolemize subgoal";
(*Conversion of a subgoal to conjecture clauses. Each clause has
leading !!-bound universal variables, to express generality. *)
val neg_clausify_tac =
neg_skolemize_tac THEN'
SUBGOAL
(fn (prop,_) =>
let val ts = Logic.strip_assums_hyp prop
in EVERY1
[METAHYPS
(fn hyps =>
(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;
end;