--- a/src/HOL/Tools/res_hol_clause.ML Thu Mar 18 13:57:00 2010 +0100
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,531 +0,0 @@
-(* Title: HOL/Tools/res_hol_clause.ML
- Author: Jia Meng, NICTA
-
-FOL clauses translated from HOL formulae.
-*)
-
-signature RES_HOL_CLAUSE =
-sig
- val ext: thm
- val comb_I: thm
- val comb_K: thm
- val comb_B: thm
- val comb_C: thm
- val comb_S: thm
- val minimize_applies: bool
- type axiom_name = string
- type polarity = bool
- type clause_id = int
- datatype combterm =
- CombConst of string * Res_Clause.fol_type * Res_Clause.fol_type list (*Const and Free*)
- | CombVar of string * Res_Clause.fol_type
- | CombApp of combterm * combterm
- datatype literal = Literal of polarity * combterm
- datatype clause = Clause of {clause_id: clause_id, axiom_name: axiom_name, th: thm,
- kind: Res_Clause.kind,literals: literal list, ctypes_sorts: typ list}
- val type_of_combterm: combterm -> Res_Clause.fol_type
- val strip_comb: combterm -> combterm * combterm list
- val literals_of_term: theory -> term -> literal list * typ list
- exception TOO_TRIVIAL
- val make_conjecture_clauses: bool -> theory -> thm list -> clause list
- val make_axiom_clauses: bool ->
- theory ->
- (thm * (axiom_name * clause_id)) list -> (axiom_name * clause) list
- val get_helper_clauses: bool ->
- theory ->
- bool ->
- clause list * (thm * (axiom_name * clause_id)) list * string list ->
- clause list
- val tptp_write_file: bool -> Path.T ->
- clause list * clause list * clause list * clause list *
- Res_Clause.classrelClause list * Res_Clause.arityClause list ->
- int * int
- val dfg_write_file: bool -> Path.T ->
- clause list * clause list * clause list * clause list *
- Res_Clause.classrelClause list * Res_Clause.arityClause list ->
- int * int
-end
-
-structure Res_HOL_Clause: RES_HOL_CLAUSE =
-struct
-
-structure RC = Res_Clause; (* FIXME avoid structure alias *)
-
-(* theorems for combinators and function extensionality *)
-val ext = thm "HOL.ext";
-val comb_I = thm "ATP_Linkup.COMBI_def";
-val comb_K = thm "ATP_Linkup.COMBK_def";
-val comb_B = thm "ATP_Linkup.COMBB_def";
-val comb_C = thm "ATP_Linkup.COMBC_def";
-val comb_S = thm "ATP_Linkup.COMBS_def";
-val fequal_imp_equal = thm "ATP_Linkup.fequal_imp_equal";
-val equal_imp_fequal = thm "ATP_Linkup.equal_imp_fequal";
-
-
-(* Parameter t_full below indicates that full type information is to be
-exported *)
-
-(*If true, each function will be directly applied to as many arguments as possible, avoiding
- use of the "apply" operator. Use of hBOOL is also minimized.*)
-val minimize_applies = true;
-
-fun min_arity_of const_min_arity c = the_default 0 (Symtab.lookup const_min_arity c);
-
-(*True if the constant ever appears outside of the top-level position in literals.
- If false, the constant always receives all of its arguments and is used as a predicate.*)
-fun needs_hBOOL const_needs_hBOOL c =
- not minimize_applies orelse
- the_default false (Symtab.lookup const_needs_hBOOL c);
-
-
-(******************************************************)
-(* data types for typed combinator expressions *)
-(******************************************************)
-
-type axiom_name = string;
-type polarity = bool;
-type clause_id = int;
-
-datatype combterm = CombConst of string * RC.fol_type * RC.fol_type list (*Const and Free*)
- | CombVar of string * RC.fol_type
- | CombApp of combterm * combterm
-
-datatype literal = Literal of polarity * combterm;
-
-datatype clause =
- Clause of {clause_id: clause_id,
- axiom_name: axiom_name,
- th: thm,
- kind: RC.kind,
- literals: literal list,
- ctypes_sorts: typ list};
-
-
-(*********************************************************************)
-(* convert a clause with type Term.term to a clause with type clause *)
-(*********************************************************************)
-
-fun isFalse (Literal(pol, CombConst(c,_,_))) =
- (pol andalso c = "c_False") orelse
- (not pol andalso c = "c_True")
- | isFalse _ = false;
-
-fun isTrue (Literal (pol, CombConst(c,_,_))) =
- (pol andalso c = "c_True") orelse
- (not pol andalso c = "c_False")
- | isTrue _ = false;
-
-fun isTaut (Clause {literals,...}) = exists isTrue literals;
-
-fun type_of dfg (Type (a, Ts)) =
- let val (folTypes,ts) = types_of dfg Ts
- in (RC.Comp(RC.make_fixed_type_const dfg a, folTypes), ts) end
- | type_of _ (tp as TFree (a, _)) =
- (RC.AtomF (RC.make_fixed_type_var a), [tp])
- | type_of _ (tp as TVar (v, _)) =
- (RC.AtomV (RC.make_schematic_type_var v), [tp])
-and types_of dfg Ts =
- let val (folTyps,ts) = ListPair.unzip (map (type_of dfg) Ts)
- in (folTyps, RC.union_all ts) end;
-
-(* same as above, but no gathering of sort information *)
-fun simp_type_of dfg (Type (a, Ts)) =
- RC.Comp(RC.make_fixed_type_const dfg a, map (simp_type_of dfg) Ts)
- | simp_type_of _ (TFree (a, _)) = RC.AtomF(RC.make_fixed_type_var a)
- | simp_type_of _ (TVar (v, _)) = RC.AtomV(RC.make_schematic_type_var v);
-
-
-fun const_type_of dfg thy (c,t) =
- let val (tp,ts) = type_of dfg t
- in (tp, ts, map (simp_type_of dfg) (Sign.const_typargs thy (c,t))) end;
-
-(* convert a Term.term (with combinators) into a combterm, also accummulate sort info *)
-fun combterm_of dfg thy (Const(c,t)) =
- let val (tp,ts,tvar_list) = const_type_of dfg thy (c,t)
- val c' = CombConst(RC.make_fixed_const dfg c, tp, tvar_list)
- in (c',ts) end
- | combterm_of dfg _ (Free(v,t)) =
- let val (tp,ts) = type_of dfg t
- val v' = CombConst(RC.make_fixed_var v, tp, [])
- in (v',ts) end
- | combterm_of dfg _ (Var(v,t)) =
- let val (tp,ts) = type_of dfg t
- val v' = CombVar(RC.make_schematic_var v,tp)
- in (v',ts) end
- | combterm_of dfg thy (P $ Q) =
- let val (P',tsP) = combterm_of dfg thy P
- val (Q',tsQ) = combterm_of dfg thy Q
- in (CombApp(P',Q'), union (op =) tsP tsQ) end
- | combterm_of _ _ (t as Abs _) = raise RC.CLAUSE ("HOL CLAUSE", t);
-
-fun predicate_of dfg thy ((Const("Not",_) $ P), polarity) = predicate_of dfg thy (P, not polarity)
- | predicate_of dfg thy (t,polarity) = (combterm_of dfg thy (Envir.eta_contract t), polarity);
-
-fun literals_of_term1 dfg thy args (Const("Trueprop",_) $ P) = literals_of_term1 dfg thy args P
- | literals_of_term1 dfg thy args (Const("op |",_) $ P $ Q) =
- literals_of_term1 dfg thy (literals_of_term1 dfg thy args P) Q
- | literals_of_term1 dfg thy (lits,ts) P =
- let val ((pred,ts'),pol) = predicate_of dfg thy (P,true)
- in
- (Literal(pol,pred)::lits, union (op =) ts ts')
- end;
-
-fun literals_of_term_dfg dfg thy P = literals_of_term1 dfg thy ([],[]) P;
-val literals_of_term = literals_of_term_dfg false;
-
-(* Problem too trivial for resolution (empty clause) *)
-exception TOO_TRIVIAL;
-
-(* making axiom and conjecture clauses *)
-fun make_clause dfg thy (clause_id,axiom_name,kind,th) =
- let val (lits,ctypes_sorts) = literals_of_term_dfg dfg thy (prop_of th)
- in
- if forall isFalse lits
- then raise TOO_TRIVIAL
- else
- Clause {clause_id = clause_id, axiom_name = axiom_name, th = th, kind = kind,
- literals = lits, ctypes_sorts = ctypes_sorts}
- end;
-
-
-fun add_axiom_clause dfg thy ((th,(name,id)), pairs) =
- let val cls = make_clause dfg thy (id, name, RC.Axiom, th)
- in
- if isTaut cls then pairs else (name,cls)::pairs
- end;
-
-fun make_axiom_clauses dfg thy = List.foldl (add_axiom_clause dfg thy) [];
-
-fun make_conjecture_clauses_aux _ _ _ [] = []
- | make_conjecture_clauses_aux dfg thy n (th::ths) =
- make_clause dfg thy (n,"conjecture", RC.Conjecture, th) ::
- make_conjecture_clauses_aux dfg thy (n+1) ths;
-
-fun make_conjecture_clauses dfg thy = make_conjecture_clauses_aux dfg thy 0;
-
-
-(**********************************************************************)
-(* convert clause into ATP specific formats: *)
-(* TPTP used by Vampire and E *)
-(* DFG used by SPASS *)
-(**********************************************************************)
-
-(*Result of a function type; no need to check that the argument type matches.*)
-fun result_type (RC.Comp ("tc_fun", [_, tp2])) = tp2
- | result_type _ = error "result_type"
-
-fun type_of_combterm (CombConst (_, tp, _)) = tp
- | type_of_combterm (CombVar (_, tp)) = tp
- | type_of_combterm (CombApp (t1, _)) = result_type (type_of_combterm t1);
-
-(*gets the head of a combinator application, along with the list of arguments*)
-fun strip_comb u =
- let fun stripc (CombApp(t,u), ts) = stripc (t, u::ts)
- | stripc x = x
- in stripc(u,[]) end;
-
-val type_wrapper = "ti";
-
-fun head_needs_hBOOL const_needs_hBOOL (CombConst(c,_,_)) = needs_hBOOL const_needs_hBOOL c
- | head_needs_hBOOL _ _ = true;
-
-fun wrap_type t_full (s, tp) =
- if t_full then
- type_wrapper ^ RC.paren_pack [s, RC.string_of_fol_type tp]
- else s;
-
-fun apply ss = "hAPP" ^ RC.paren_pack ss;
-
-fun rev_apply (v, []) = v
- | rev_apply (v, arg::args) = apply [rev_apply (v, args), arg];
-
-fun string_apply (v, args) = rev_apply (v, rev args);
-
-(*Apply an operator to the argument strings, using either the "apply" operator or
- direct function application.*)
-fun string_of_applic t_full cma (CombConst (c, _, tvars), args) =
- let val c = if c = "equal" then "c_fequal" else c
- val nargs = min_arity_of cma c
- val args1 = List.take(args, nargs)
- handle Subscript => error ("string_of_applic: " ^ c ^ " has arity " ^
- Int.toString nargs ^ " but is applied to " ^
- space_implode ", " args)
- val args2 = List.drop(args, nargs)
- val targs = if not t_full then map RC.string_of_fol_type tvars
- else []
- in
- string_apply (c ^ RC.paren_pack (args1@targs), args2)
- end
- | string_of_applic _ _ (CombVar (v, _), args) = string_apply (v, args)
- | string_of_applic _ _ _ = error "string_of_applic";
-
-fun wrap_type_if t_full cnh (head, s, tp) =
- if head_needs_hBOOL cnh head then wrap_type t_full (s, tp) else s;
-
-fun string_of_combterm (params as (t_full, cma, cnh)) t =
- let val (head, args) = strip_comb t
- in wrap_type_if t_full cnh (head,
- string_of_applic t_full cma (head, map (string_of_combterm (params)) args),
- type_of_combterm t)
- end;
-
-(*Boolean-valued terms are here converted to literals.*)
-fun boolify params t =
- "hBOOL" ^ RC.paren_pack [string_of_combterm params t];
-
-fun string_of_predicate (params as (_,_,cnh)) t =
- case t of
- (CombApp(CombApp(CombConst("equal",_,_), t1), t2)) =>
- (*DFG only: new TPTP prefers infix equality*)
- ("equal" ^ RC.paren_pack [string_of_combterm params t1, string_of_combterm params t2])
- | _ =>
- case #1 (strip_comb t) of
- CombConst(c,_,_) => if needs_hBOOL cnh c then boolify params t else string_of_combterm params t
- | _ => boolify params t;
-
-
-(*** tptp format ***)
-
-fun tptp_of_equality params pol (t1,t2) =
- let val eqop = if pol then " = " else " != "
- in string_of_combterm params t1 ^ eqop ^ string_of_combterm params t2 end;
-
-fun tptp_literal params (Literal(pol, CombApp(CombApp(CombConst("equal",_,_), t1), t2))) =
- tptp_of_equality params pol (t1,t2)
- | tptp_literal params (Literal(pol,pred)) =
- RC.tptp_sign pol (string_of_predicate params pred);
-
-(*Given a clause, returns its literals paired with a list of literals concerning TFrees;
- the latter should only occur in conjecture clauses.*)
-fun tptp_type_lits params pos (Clause{literals, ctypes_sorts, ...}) =
- (map (tptp_literal params) literals,
- map (RC.tptp_of_typeLit pos) (RC.add_typs ctypes_sorts));
-
-fun clause2tptp params (cls as Clause {axiom_name, clause_id, kind, ...}) =
- let val (lits,tylits) = tptp_type_lits params (kind = RC.Conjecture) cls
- in
- (RC.gen_tptp_cls(clause_id,axiom_name,kind,lits,tylits), tylits)
- end;
-
-
-(*** dfg format ***)
-
-fun dfg_literal params (Literal(pol,pred)) = RC.dfg_sign pol (string_of_predicate params pred);
-
-fun dfg_type_lits params pos (Clause{literals, ctypes_sorts, ...}) =
- (map (dfg_literal params) literals,
- map (RC.dfg_of_typeLit pos) (RC.add_typs ctypes_sorts));
-
-fun get_uvars (CombConst _) vars = vars
- | get_uvars (CombVar(v,_)) vars = (v::vars)
- | get_uvars (CombApp(P,Q)) vars = get_uvars P (get_uvars Q vars);
-
-fun get_uvars_l (Literal(_,c)) = get_uvars c [];
-
-fun dfg_vars (Clause {literals,...}) = RC.union_all (map get_uvars_l literals);
-
-fun clause2dfg params (cls as Clause{axiom_name,clause_id,kind,ctypes_sorts,...}) =
- let val (lits,tylits) = dfg_type_lits params (kind = RC.Conjecture) cls
- val vars = dfg_vars cls
- val tvars = RC.get_tvar_strs ctypes_sorts
- in
- (RC.gen_dfg_cls(clause_id, axiom_name, kind, lits, tylits, tvars@vars), tylits)
- end;
-
-
-(** For DFG format: accumulate function and predicate declarations **)
-
-fun addtypes tvars tab = List.foldl RC.add_foltype_funcs tab tvars;
-
-fun add_decls (t_full, cma, cnh) (CombConst (c, _, tvars), (funcs, preds)) =
- if c = "equal" then (addtypes tvars funcs, preds)
- else
- let val arity = min_arity_of cma c
- val ntys = if not t_full then length tvars else 0
- val addit = Symtab.update(c, arity+ntys)
- in
- if needs_hBOOL cnh c then (addtypes tvars (addit funcs), preds)
- else (addtypes tvars funcs, addit preds)
- end
- | add_decls _ (CombVar(_,ctp), (funcs,preds)) =
- (RC.add_foltype_funcs (ctp,funcs), preds)
- | add_decls params (CombApp(P,Q),decls) = add_decls params (P,add_decls params (Q,decls));
-
-fun add_literal_decls params (Literal(_,c), decls) = add_decls params (c,decls);
-
-fun add_clause_decls params (Clause {literals, ...}, decls) =
- List.foldl (add_literal_decls params) decls literals
- handle Symtab.DUP a => error ("function " ^ a ^ " has multiple arities")
-
-fun decls_of_clauses params clauses arity_clauses =
- let val init_functab = Symtab.update (type_wrapper,2) (Symtab.update ("hAPP",2) RC.init_functab)
- val init_predtab = Symtab.update ("hBOOL",1) Symtab.empty
- val (functab,predtab) = (List.foldl (add_clause_decls params) (init_functab, init_predtab) clauses)
- in
- (Symtab.dest (List.foldl RC.add_arityClause_funcs functab arity_clauses),
- Symtab.dest predtab)
- end;
-
-fun add_clause_preds (Clause {ctypes_sorts, ...}, preds) =
- List.foldl RC.add_type_sort_preds preds ctypes_sorts
- handle Symtab.DUP a => error ("predicate " ^ a ^ " has multiple arities")
-
-(*Higher-order clauses have only the predicates hBOOL and type classes.*)
-fun preds_of_clauses clauses clsrel_clauses arity_clauses =
- Symtab.dest
- (List.foldl RC.add_classrelClause_preds
- (List.foldl RC.add_arityClause_preds
- (List.foldl add_clause_preds Symtab.empty clauses)
- arity_clauses)
- clsrel_clauses)
-
-
-(**********************************************************************)
-(* write clauses to files *)
-(**********************************************************************)
-
-val init_counters =
- Symtab.make [("c_COMBI", 0), ("c_COMBK", 0),
- ("c_COMBB", 0), ("c_COMBC", 0),
- ("c_COMBS", 0)];
-
-fun count_combterm (CombConst (c, _, _), ct) =
- (case Symtab.lookup ct c of NONE => ct (*no counter*)
- | SOME n => Symtab.update (c,n+1) ct)
- | count_combterm (CombVar _, ct) = ct
- | count_combterm (CombApp(t1,t2), ct) = count_combterm(t1, count_combterm(t2, ct));
-
-fun count_literal (Literal(_,t), ct) = count_combterm(t,ct);
-
-fun count_clause (Clause{literals,...}, ct) = List.foldl count_literal ct literals;
-
-fun count_user_clause user_lemmas (Clause{axiom_name,literals,...}, ct) =
- if axiom_name mem_string user_lemmas then List.foldl count_literal ct literals
- else ct;
-
-fun cnf_helper_thms thy =
- Res_Axioms.cnf_rules_pairs thy o map Res_Axioms.pairname
-
-fun get_helper_clauses dfg thy isFO (conjectures, axcls, user_lemmas) =
- if isFO then [] (*first-order*)
- else
- let
- val axclauses = map #2 (make_axiom_clauses dfg thy axcls)
- val ct0 = List.foldl count_clause init_counters conjectures
- val ct = List.foldl (count_user_clause user_lemmas) ct0 axclauses
- fun needed c = the (Symtab.lookup ct c) > 0
- val IK = if needed "c_COMBI" orelse needed "c_COMBK"
- then cnf_helper_thms thy [comb_I,comb_K]
- else []
- val BC = if needed "c_COMBB" orelse needed "c_COMBC"
- then cnf_helper_thms thy [comb_B,comb_C]
- else []
- val S = if needed "c_COMBS"
- then cnf_helper_thms thy [comb_S]
- else []
- val other = cnf_helper_thms thy [fequal_imp_equal,equal_imp_fequal]
- in
- map #2 (make_axiom_clauses dfg thy (other @ IK @ BC @ S))
- end;
-
-(*Find the minimal arity of each function mentioned in the term. Also, note which uses
- are not at top level, to see if hBOOL is needed.*)
-fun count_constants_term toplev t (const_min_arity, const_needs_hBOOL) =
- let val (head, args) = strip_comb t
- val n = length args
- val (const_min_arity, const_needs_hBOOL) = fold (count_constants_term false) args (const_min_arity, const_needs_hBOOL)
- in
- case head of
- CombConst (a,_,_) => (*predicate or function version of "equal"?*)
- let val a = if a="equal" andalso not toplev then "c_fequal" else a
- val const_min_arity = Symtab.map_default (a, n) (Integer.min n) const_min_arity
- in
- if toplev then (const_min_arity, const_needs_hBOOL)
- else (const_min_arity, Symtab.update (a,true) (const_needs_hBOOL))
- end
- | _ => (const_min_arity, const_needs_hBOOL)
- end;
-
-(*A literal is a top-level term*)
-fun count_constants_lit (Literal (_,t)) (const_min_arity, const_needs_hBOOL) =
- count_constants_term true t (const_min_arity, const_needs_hBOOL);
-
-fun count_constants_clause (Clause{literals,...}) (const_min_arity, const_needs_hBOOL) =
- fold count_constants_lit literals (const_min_arity, const_needs_hBOOL);
-
-fun display_arity const_needs_hBOOL (c,n) =
- Res_Axioms.trace_msg (fn () => "Constant: " ^ c ^ " arity:\t" ^ Int.toString n ^
- (if needs_hBOOL const_needs_hBOOL c then " needs hBOOL" else ""));
-
-fun count_constants (conjectures, _, extra_clauses, helper_clauses, _, _) =
- if minimize_applies then
- let val (const_min_arity, const_needs_hBOOL) =
- fold count_constants_clause conjectures (Symtab.empty, Symtab.empty)
- |> fold count_constants_clause extra_clauses
- |> fold count_constants_clause helper_clauses
- val _ = List.app (display_arity const_needs_hBOOL) (Symtab.dest (const_min_arity))
- in (const_min_arity, const_needs_hBOOL) end
- else (Symtab.empty, Symtab.empty);
-
-(* tptp format *)
-
-fun tptp_write_file t_full file clauses =
- let
- val (conjectures, axclauses, _, helper_clauses,
- classrel_clauses, arity_clauses) = clauses
- val (cma, cnh) = count_constants clauses
- val params = (t_full, cma, cnh)
- val (tptp_clss,tfree_litss) = ListPair.unzip (map (clause2tptp params) conjectures)
- val tfree_clss = map RC.tptp_tfree_clause (List.foldl (uncurry (union (op =))) [] tfree_litss)
- val _ =
- File.write_list file (
- map (#1 o (clause2tptp params)) axclauses @
- tfree_clss @
- tptp_clss @
- map RC.tptp_classrelClause classrel_clauses @
- map RC.tptp_arity_clause arity_clauses @
- map (#1 o (clause2tptp params)) helper_clauses)
- in (length axclauses + 1, length tfree_clss + length tptp_clss)
- end;
-
-
-(* dfg format *)
-
-fun dfg_write_file t_full file clauses =
- let
- val (conjectures, axclauses, _, helper_clauses,
- classrel_clauses, arity_clauses) = clauses
- val (cma, cnh) = count_constants clauses
- val params = (t_full, cma, cnh)
- val (dfg_clss, tfree_litss) = ListPair.unzip (map (clause2dfg params) conjectures)
- and probname = Path.implode (Path.base file)
- val axstrs = map (#1 o (clause2dfg params)) axclauses
- val tfree_clss = map RC.dfg_tfree_clause (RC.union_all tfree_litss)
- val helper_clauses_strs = map (#1 o (clause2dfg params)) helper_clauses
- val (funcs,cl_preds) = decls_of_clauses params (helper_clauses @ conjectures @ axclauses) arity_clauses
- and ty_preds = preds_of_clauses axclauses classrel_clauses arity_clauses
- val _ =
- File.write_list file (
- RC.string_of_start probname ::
- RC.string_of_descrip probname ::
- RC.string_of_symbols (RC.string_of_funcs funcs)
- (RC.string_of_preds (cl_preds @ ty_preds)) ::
- "list_of_clauses(axioms,cnf).\n" ::
- axstrs @
- map RC.dfg_classrelClause classrel_clauses @
- map RC.dfg_arity_clause arity_clauses @
- helper_clauses_strs @
- ["end_of_list.\n\nlist_of_clauses(conjectures,cnf).\n"] @
- tfree_clss @
- dfg_clss @
- ["end_of_list.\n\n",
- (*VarWeight=3 helps the HO problems, probably by counteracting the presence of hAPP*)
- "list_of_settings(SPASS).\n{*\nset_flag(VarWeight,3).\n*}\nend_of_list.\n\n",
- "end_problem.\n"])
-
- in (length axclauses + length classrel_clauses + length arity_clauses +
- length helper_clauses + 1, length tfree_clss + length dfg_clss)
- end;
-
-end;
-