diff --git a/src/HOL/Tools/ATP/atp_problem.ML b/src/HOL/Tools/ATP/atp_problem.ML --- a/src/HOL/Tools/ATP/atp_problem.ML +++ b/src/HOL/Tools/ATP/atp_problem.ML @@ -1,1055 +1,1054 @@ (* Title: HOL/Tools/ATP/atp_problem.ML Author: Jia Meng, Cambridge University Computer Laboratory and NICTA Author: Jasmin Blanchette, TU Muenchen Author: Martin Desharnais, MPI-INF Saarbruecken Abstract representation of ATP problems and TPTP syntax. *) signature ATP_PROBLEM = sig datatype ('a, 'b) atp_term = ATerm of ('a * 'b list) * ('a, 'b) atp_term list | AAbs of (('a * 'b) * ('a, 'b) atp_term) * ('a, 'b) atp_term list datatype atp_quantifier = AForall | AExists datatype atp_connective = ANot | AAnd | AOr | AImplies | AIff datatype ('a, 'b, 'c, 'd) atp_formula = ATyQuant of atp_quantifier * ('b * 'd list) list * ('a, 'b, 'c, 'd) atp_formula | AQuant of atp_quantifier * ('a * 'b option) list * ('a, 'b, 'c, 'd) atp_formula | AConn of atp_connective * ('a, 'b, 'c, 'd) atp_formula list | AAtom of 'c datatype 'a atp_type = AType of ('a * 'a list) * 'a atp_type list | AFun of 'a atp_type * 'a atp_type | APi of 'a list * 'a atp_type type term_order = {is_lpo : bool, gen_weights : bool, gen_prec : bool, gen_simp : bool} type syntax = {with_ite : bool, with_let : bool} datatype fool = Without_FOOL | With_FOOL of syntax datatype polymorphism = Monomorphic | Polymorphic datatype thf_flavor = THF_Lambda_Free | THF_Without_Choice | THF_With_Choice datatype atp_format = CNF | CNF_UEQ | FOF | TFF of polymorphism * fool | THF of polymorphism * syntax * thf_flavor | DFG of polymorphism datatype atp_formula_role = Axiom | Definition | Lemma | Hypothesis | Conjecture | Negated_Conjecture | Plain | Type_Role | Unknown datatype 'a atp_problem_line = Class_Decl of string * 'a * 'a list | Type_Decl of string * 'a * int | Sym_Decl of string * 'a * 'a atp_type | Datatype_Decl of string * ('a * 'a list) list * 'a atp_type * ('a, 'a atp_type) atp_term list * bool | Class_Memb of string * ('a * 'a list) list * 'a atp_type * 'a | Formula of (string * string) * atp_formula_role * ('a, 'a atp_type, ('a, 'a atp_type) atp_term, 'a) atp_formula * (string, string atp_type) atp_term option * (string, string atp_type) atp_term list type 'a atp_problem = (string * 'a atp_problem_line list) list val tptp_cnf : string val tptp_fof : string val tptp_tff : string val tptp_thf : string val tptp_has_type : string val tptp_type_of_types : string val tptp_bool_type : string val tptp_individual_type : string val tptp_fun_type : string val tptp_product_type : string val tptp_forall : string val tptp_ho_forall : string val tptp_pi_binder : string val tptp_exists : string val tptp_ho_exists : string val tptp_choice : string val tptp_ho_choice : string val tptp_hilbert_choice : string val tptp_hilbert_the : string val tptp_not : string val tptp_and : string val tptp_not_and : string val tptp_or : string val tptp_not_or : string val tptp_implies : string val tptp_if : string val tptp_iff : string val tptp_not_iff : string val tptp_ite : string val tptp_let : string val tptp_app : string val tptp_not_infix : string val tptp_equal : string val tptp_not_equal : string val tptp_old_equal : string val tptp_false : string val tptp_true : string val tptp_lambda : string val tptp_empty_list : string type tptp_builtin_desc = {arity : int, is_predicate : bool} val tptp_builtins : tptp_builtin_desc Symtab.table val dfg_individual_type : string val isabelle_info_prefix : string val isabelle_info : bool -> string -> int -> (string, 'a) atp_term list val extract_isabelle_status : (string, 'a) atp_term list -> string option val extract_isabelle_rank : (string, 'a) atp_term list -> int val inductionN : string val introN : string val inductiveN : string val elimN : string val simpN : string val non_rec_defN : string val rec_defN : string val rankN : string val minimum_rank : int val default_rank : int val default_term_order_weight : int val is_tptp_equal : string -> bool val is_built_in_tptp_symbol : string -> bool val is_tptp_variable : string -> bool val is_tptp_user_symbol : string -> bool val bool_atype : (string * string) atp_type val individual_atype : (string * string) atp_type val mk_anot : ('a, 'b, 'c, 'd) atp_formula -> ('a, 'b, 'c, 'd) atp_formula val mk_aconn : atp_connective -> ('a, 'b, 'c, 'd) atp_formula -> ('a, 'b, 'c, 'd) atp_formula -> ('a, 'b, 'c, 'd) atp_formula val mk_app : (string, 'a) atp_term -> (string, 'a) atp_term -> (string, 'a) atp_term val mk_apps : (string, 'a) atp_term -> (string, 'a) atp_term list -> (string, 'a) atp_term val mk_simple_aterm: 'a -> ('a, 'b) atp_term val aconn_fold : bool option -> (bool option -> 'a -> 'b -> 'b) -> atp_connective * 'a list -> 'b -> 'b val aconn_map : bool option -> (bool option -> 'a -> ('b, 'c, 'd, 'e) atp_formula) -> atp_connective * 'a list -> ('b, 'c, 'd, 'e) atp_formula val formula_fold : bool option -> (bool option -> 'c -> 'e -> 'e) -> ('a, 'b, 'c, 'd) atp_formula -> 'e -> 'e val formula_map : ('c -> 'e) -> ('a, 'b, 'c, 'd) atp_formula -> ('a, 'b, 'e, 'd) atp_formula val strip_atype : 'a atp_type -> 'a list * ('a atp_type list * 'a atp_type) val is_format_higher_order : atp_format -> bool val tptp_string_of_format : atp_format -> string val tptp_string_of_role : atp_formula_role -> string val tptp_string_of_line : atp_format -> string atp_problem_line -> string val lines_of_atp_problem : atp_format -> term_order -> (unit -> (string * int) list) -> string atp_problem -> string list val ensure_cnf_problem : (string * string) atp_problem -> (string * string) atp_problem val filter_cnf_ueq_problem : (string * string) atp_problem -> (string * string) atp_problem val declared_in_atp_problem : 'a atp_problem -> ('a list * 'a list) * 'a list val nice_atp_problem : bool -> atp_format -> ('a * (string * string) atp_problem_line list) list -> ('a * string atp_problem_line list) list * (string Symtab.table * string Symtab.table) option end; structure ATP_Problem : ATP_PROBLEM = struct open ATP_Util val parens = enclose "(" ")" (** ATP problem **) datatype ('a, 'b) atp_term = ATerm of ('a * 'b list) * ('a, 'b) atp_term list | AAbs of (('a * 'b) * ('a, 'b) atp_term) * ('a, 'b) atp_term list datatype atp_quantifier = AForall | AExists datatype atp_connective = ANot | AAnd | AOr | AImplies | AIff datatype ('a, 'b, 'c, 'd) atp_formula = ATyQuant of atp_quantifier * ('b * 'd list) list * ('a, 'b, 'c, 'd) atp_formula | AQuant of atp_quantifier * ('a * 'b option) list * ('a, 'b, 'c, 'd) atp_formula | AConn of atp_connective * ('a, 'b, 'c, 'd) atp_formula list | AAtom of 'c datatype 'a atp_type = AType of ('a * 'a list) * 'a atp_type list | AFun of 'a atp_type * 'a atp_type | APi of 'a list * 'a atp_type type term_order = {is_lpo : bool, gen_weights : bool, gen_prec : bool, gen_simp : bool} type syntax = {with_ite : bool, with_let : bool} datatype fool = Without_FOOL | With_FOOL of syntax datatype polymorphism = Monomorphic | Polymorphic datatype thf_flavor = THF_Lambda_Free | THF_Without_Choice | THF_With_Choice datatype atp_format = CNF | CNF_UEQ | FOF | TFF of polymorphism * fool | THF of polymorphism * syntax * thf_flavor | DFG of polymorphism datatype atp_formula_role = Axiom | Definition | Lemma | Hypothesis | Conjecture | Negated_Conjecture | Plain | Type_Role | Unknown datatype 'a atp_problem_line = Class_Decl of string * 'a * 'a list | Type_Decl of string * 'a * int | Sym_Decl of string * 'a * 'a atp_type | Datatype_Decl of string * ('a * 'a list) list * 'a atp_type * ('a, 'a atp_type) atp_term list * bool | Class_Memb of string * ('a * 'a list) list * 'a atp_type * 'a | Formula of (string * string) * atp_formula_role * ('a, 'a atp_type, ('a, 'a atp_type) atp_term, 'a) atp_formula * (string, string atp_type) atp_term option * (string, string atp_type) atp_term list type 'a atp_problem = (string * 'a atp_problem_line list) list (* official TPTP syntax *) val tptp_cnf = "cnf" val tptp_fof = "fof" val tptp_tff = "tff" val tptp_thf = "thf" val tptp_has_type = ":" val tptp_type_of_types = "$tType" val tptp_bool_type = "$o" val tptp_individual_type = "$i" val tptp_fun_type = ">" val tptp_product_type = "*" val tptp_forall = "!" val tptp_ho_forall = "!!" val tptp_pi_binder = "!>" val tptp_exists = "?" val tptp_ho_exists = "??" val tptp_choice = "@+" val tptp_ho_choice = "@@+" val tptp_not = "~" val tptp_and = "&" val tptp_not_and = "~&" val tptp_or = "|" val tptp_not_or = "~|" val tptp_implies = "=>" val tptp_if = "<=" val tptp_iff = "<=>" val tptp_not_iff = "<~>" val tptp_ite = "$ite" val tptp_let = "$let" val tptp_app = "@" val tptp_hilbert_choice = "@+" val tptp_hilbert_the = "@-" val tptp_not_infix = "!" val tptp_equal = "=" val tptp_not_equal = "!=" val tptp_old_equal = "equal" val tptp_false = "$false" val tptp_true = "$true" val tptp_lambda = "^" val tptp_empty_list = "[]" (* A predicate has return type $o (i.e. bool) *) type tptp_builtin_desc = {arity : int, is_predicate : bool} val tptp_builtins = let fun make_builtin arity is_predicate name = (name, {arity = arity, is_predicate = is_predicate}) in map (make_builtin 0 true) [tptp_false, tptp_true] @ map (make_builtin 1 true) [tptp_not, tptp_ho_forall, tptp_ho_exists] @ map (make_builtin 2 true) [tptp_and, tptp_or, tptp_implies, tptp_if, tptp_iff, tptp_not_iff, tptp_equal, tptp_old_equal] @ map (make_builtin 2 false) [tptp_let] @ map (make_builtin 3 false) [tptp_ite] |> Symtab.make end val dfg_individual_type = "iii" (* cannot clash *) val isabelle_info_prefix = "isabelle_" val inductionN = "induction" val introN = "intro" val inductiveN = "inductive" val elimN = "elim" val simpN = "simp" val non_rec_defN = "non_rec_def" val rec_defN = "rec_def" val rankN = "rank" val minimum_rank = 0 val default_rank = 1000 val default_term_order_weight = 1 (* Currently, only SPASS 3.8ds and (to a lesser extent) Metis can process Isabelle metainformation. *) fun isabelle_info generate_info status rank = if generate_info then [] |> rank <> default_rank ? cons (ATerm ((isabelle_info_prefix ^ rankN, []), [ATerm ((string_of_int rank, []), [])])) |> status <> "" ? cons (ATerm ((isabelle_info_prefix ^ status, []), [])) else [] fun extract_isabelle_status (ATerm ((s, []), []) :: _) = try (unprefix isabelle_info_prefix) s | extract_isabelle_status _ = NONE fun extract_isabelle_rank (tms as _ :: _) = (case List.last tms of ATerm ((_, []), [ATerm ((rank, []), [])]) => the (Int.fromString rank) | _ => default_rank) | extract_isabelle_rank _ = default_rank fun is_tptp_equal s = (s = tptp_equal orelse s = tptp_old_equal) fun is_built_in_tptp_symbol s = s = tptp_old_equal orelse not (Char.isAlpha (String.sub (s, 0))) fun is_tptp_variable s = s <> "" andalso Char.isUpper (String.sub (s, 0)) val is_tptp_user_symbol = not o (is_tptp_variable orf is_built_in_tptp_symbol) val bool_atype = AType ((`I tptp_bool_type, []), []) val individual_atype = AType ((`I tptp_individual_type, []), []) fun raw_polarities_of_conn ANot = (SOME false, NONE) | raw_polarities_of_conn AAnd = (SOME true, SOME true) | raw_polarities_of_conn AOr = (SOME true, SOME true) | raw_polarities_of_conn AImplies = (SOME false, SOME true) | raw_polarities_of_conn AIff = (NONE, NONE) fun polarities_of_conn NONE = K (NONE, NONE) | polarities_of_conn (SOME pos) = raw_polarities_of_conn #> not pos ? apply2 (Option.map not) fun mk_anot (AConn (ANot, [phi])) = phi | mk_anot phi = AConn (ANot, [phi]) fun mk_aconn c phi1 phi2 = AConn (c, [phi1, phi2]) fun mk_app t u = ATerm ((tptp_app, []), [t, u]) fun mk_apps f xs = fold (fn x => fn f => mk_app f x) xs f fun mk_simple_aterm p = ATerm ((p, []), []) fun aconn_fold pos f (ANot, [phi]) = f (Option.map not pos) phi | aconn_fold pos f (AImplies, [phi1, phi2]) = f (Option.map not pos) phi1 #> f pos phi2 | aconn_fold pos f (AAnd, phis) = fold (f pos) phis | aconn_fold pos f (AOr, phis) = fold (f pos) phis | aconn_fold _ f (_, phis) = fold (f NONE) phis fun aconn_map pos f (ANot, [phi]) = AConn (ANot, [f (Option.map not pos) phi]) | aconn_map pos f (AImplies, [phi1, phi2]) = AConn (AImplies, [f (Option.map not pos) phi1, f pos phi2]) | aconn_map pos f (AAnd, phis) = AConn (AAnd, map (f pos) phis) | aconn_map pos f (AOr, phis) = AConn (AOr, map (f pos) phis) | aconn_map _ f (c, phis) = AConn (c, map (f NONE) phis) fun formula_fold pos f = let fun fld pos (AQuant (_, _, phi)) = fld pos phi | fld pos (ATyQuant (_, _, phi)) = fld pos phi | fld pos (AConn conn) = aconn_fold pos fld conn | fld pos (AAtom tm) = f pos tm in fld pos end fun formula_map f (AQuant (q, xs, phi)) = AQuant (q, xs, formula_map f phi) | formula_map f (ATyQuant (q, xs, phi)) = ATyQuant (q, xs, formula_map f phi) | formula_map f (AConn (c, phis)) = AConn (c, map (formula_map f) phis) | formula_map f (AAtom tm) = AAtom (f tm) fun strip_api (APi (tys, ty)) = strip_api ty |>> append tys | strip_api ty = ([], ty) fun strip_afun (AFun (ty1, ty2)) = strip_afun ty2 |>> cons ty1 | strip_afun ty = ([], ty) fun strip_atype ty = ty |> strip_api ||> strip_afun fun is_function_atype ty = snd (snd (strip_atype ty)) <> AType ((tptp_bool_type, []), []) fun is_predicate_atype ty = not (is_function_atype ty) fun is_nontrivial_predicate_atype (AType _) = false | is_nontrivial_predicate_atype ty = is_predicate_atype ty fun is_format_higher_order (THF _) = true | is_format_higher_order _ = false fun is_format_higher_order_with_choice (THF (_, _, THF_With_Choice)) = true | is_format_higher_order_with_choice _ = false fun is_format_typed (TFF _) = true | is_format_typed (THF _) = true | is_format_typed (DFG _) = true | is_format_typed _ = false fun is_format_with_fool (THF _) = true | is_format_with_fool (TFF (_, With_FOOL _)) = true | is_format_with_fool _ = false fun tptp_string_of_role Axiom = "axiom" | tptp_string_of_role Definition = "definition" | tptp_string_of_role Lemma = "lemma" | tptp_string_of_role Hypothesis = "hypothesis" | tptp_string_of_role Conjecture = "conjecture" | tptp_string_of_role Negated_Conjecture = "negated_conjecture" | tptp_string_of_role Plain = "plain" | tptp_string_of_role Type_Role = "type" | tptp_string_of_role Unknown = "unknown" fun tptp_string_of_app _ func [] = func | tptp_string_of_app format func args = if is_format_higher_order format then "(" ^ space_implode (" " ^ tptp_app ^ " ") (func :: args) ^ ")" else func ^ "(" ^ commas args ^ ")" fun uncurry_type (APi (tys, ty)) = APi (tys, uncurry_type ty) | uncurry_type (ty as AFun (ty1 as AType _, ty2)) = (case uncurry_type ty2 of AFun (ty' as AType ((s, _), tys), ty) => AFun (AType ((tptp_product_type, []), ty1 :: (if s = tptp_product_type then tys else [ty'])), ty) | _ => ty) | uncurry_type (ty as AType _) = ty | uncurry_type _ = raise Fail "unexpected higher-order type in first-order format" val suffix_type_of_types = suffix (" " ^ tptp_has_type ^ " " ^ tptp_type_of_types) fun str_of_type format ty = let val dfg = (case format of DFG _ => true | _ => false) fun str _ (AType ((s, _), [])) = if dfg andalso s = tptp_individual_type then dfg_individual_type else s | str rhs (AType ((s, _), tys)) = if s = tptp_fun_type then let val [ty1, ty2] = tys in str rhs (AFun (ty1, ty2)) end else let val ss = tys |> map (str false) in if s = tptp_product_type then ss |> space_implode (if dfg then ", " else " " ^ tptp_product_type ^ " ") |> (not dfg andalso length ss > 1) ? parens else tptp_string_of_app format s ss end | str rhs (AFun (ty1, ty2)) = (str false ty1 |> dfg ? parens) ^ " " ^ (if dfg then "" else tptp_fun_type ^ " ") ^ str true ty2 |> not rhs ? parens | str _ (APi (ss, ty)) = if dfg then "[" ^ commas ss ^ "], " ^ str true ty else tptp_pi_binder ^ "[" ^ commas (map suffix_type_of_types ss) ^ "]: " ^ str false ty in str true ty end fun string_of_type (format as THF _) ty = str_of_type format ty | string_of_type format ty = str_of_type format (uncurry_type ty) fun tptp_string_of_quantifier AForall = tptp_forall | tptp_string_of_quantifier AExists = tptp_exists fun tptp_string_of_connective ANot = tptp_not | tptp_string_of_connective AAnd = tptp_and | tptp_string_of_connective AOr = tptp_or | tptp_string_of_connective AImplies = tptp_implies | tptp_string_of_connective AIff = tptp_iff fun string_of_bound_var format (s, ty) = s ^ (if is_format_typed format then " " ^ tptp_has_type ^ " " ^ (ty |> the_default (AType ((tptp_individual_type, []), [])) |> string_of_type format) else "") fun tptp_string_of_term _ (ATerm ((s, []), [])) = s |> Symtab.defined tptp_builtins s ? parens | tptp_string_of_term format (ATerm ((s, tys), ts)) = let val of_type = string_of_type format val of_term = tptp_string_of_term format fun app0 f types args = tptp_string_of_app format (f |> Symtab.defined tptp_builtins f ? parens) (map (of_type #> is_format_higher_order format ? parens) types @ map of_term args) fun app () = app0 s tys ts in if s = tptp_empty_list then (* used for lists in the optional "source" field of a derivation *) "[" ^ commas (map of_term ts) ^ "]" else if is_tptp_equal s then space_implode (" " ^ tptp_equal ^ " ") (map of_term ts) |> (is_format_higher_order format orelse is_format_with_fool format) ? parens else if s = tptp_ho_forall orelse s = tptp_ho_exists then (case ts of [AAbs (((s', ty), tm), [])] => (* Use syntactic sugar "!" and "?" instead of "!!" and "??" whenever possible, to work around LEO-II, Leo-III, and Satallax parser limitation. *) tptp_string_of_formula format (AQuant (if s = tptp_ho_forall then AForall else AExists, [(s', SOME ty)], AAtom tm)) | _ => app ()) else if s = tptp_let then (case ts of t1 :: AAbs (((s', ty), tm), []) :: ts => let val declaration = s' ^ " : " ^ of_type ty val definition = s' ^ " := " ^ of_term t1 val usage = of_term tm in if ts = [] orelse is_format_higher_order format then app0 (s ^ "(" ^ declaration ^ ", " ^ definition ^ ", " ^ usage ^ ")") [] ts else error (tptp_let ^ " is special syntax and more than two arguments is only \ \supported in higher order") end | _ => error (tptp_let ^ " is special syntax and must have at least two arguments")) else if s = tptp_ite then (case ts of t1 :: t2 :: t3 :: ts => if ts = [] orelse is_format_higher_order format then app0 (s ^ "(" ^ of_term t1 ^ ", " ^ of_term t2 ^ ", " ^ of_term t3 ^ ")") [] ts else error (tptp_ite ^ " is special syntax and more than three arguments is only supported \ \in higher order") | _ => error (tptp_ite ^ " is special syntax and must have at least three arguments")) else if s = tptp_choice then (case ts of (AAbs (((s', ty), tm), args) :: ts) => (* There is code in "ATP_Problem_Generate" to ensure that "Eps" is always applied to an abstraction. *) if ts = [] orelse is_format_higher_order_with_choice format then let val declaration = s' ^ " : " ^ of_type ty in app0 ("(" ^ tptp_choice ^ "[" ^ declaration ^ "]: " ^ of_term tm ^ ")") [] (args @ ts) end else error (tptp_choice ^ " is only supported in higher order") | _ => error (tptp_choice ^ " must be followed by a lambda abstraction")) else (case (Symtab.lookup tptp_builtins s, ts) of (SOME {arity = 1, is_predicate = true}, [t]) => (* generate e.g. "~ t" instead of "~ @ t". *) s ^ " " ^ (of_term t |> parens) |> parens | (SOME {arity = 2, is_predicate = true}, [t1, t2]) => (* generate e.g. "t1 & t2" instead of "& @ t1 @ t2". *) (of_term t1 |> parens) ^ " " ^ s ^ " " ^ (of_term t2 |> parens) |> parens | _ => app ()) end | tptp_string_of_term (format as THF _) (AAbs (((s, ty), tm), args)) = tptp_string_of_app format ("(^[" ^ s ^ " : " ^ string_of_type format ty ^ "]: " ^ tptp_string_of_term format tm ^ ")") (map (tptp_string_of_term format) args) | tptp_string_of_term _ _ = raise Fail "unexpected term in first-order format" and tptp_string_of_formula format (ATyQuant (q, xs, phi)) = tptp_string_of_quantifier q ^ "[" ^ commas (map (suffix_type_of_types o string_of_type format o fst) xs) ^ "]: " ^ tptp_string_of_formula format phi |> parens | tptp_string_of_formula format (AQuant (q, xs, phi)) = tptp_string_of_quantifier q ^ "[" ^ commas (map (string_of_bound_var format) xs) ^ "]: " ^ tptp_string_of_formula format phi |> parens | tptp_string_of_formula format (AConn (ANot, [AAtom (ATerm (("=" (* tptp_equal *), []), ts))])) = space_implode (" " ^ tptp_not_infix ^ tptp_equal ^ " ") (map (tptp_string_of_term format) ts) |> is_format_higher_order format ? parens | tptp_string_of_formula format (AConn (c, [phi])) = tptp_string_of_connective c ^ " " ^ - (tptp_string_of_formula format phi - |> is_format_higher_order format ? parens) + (tptp_string_of_formula format phi |> parens) |> parens | tptp_string_of_formula format (AConn (c, phis)) = space_implode (" " ^ tptp_string_of_connective c ^ " ") (map (tptp_string_of_formula format) phis) |> parens | tptp_string_of_formula format (AAtom tm) = tptp_string_of_term format tm fun tptp_string_of_format CNF = tptp_cnf | tptp_string_of_format CNF_UEQ = tptp_cnf | tptp_string_of_format FOF = tptp_fof | tptp_string_of_format (TFF _) = tptp_tff | tptp_string_of_format (THF _) = tptp_thf | tptp_string_of_format (DFG _) = raise Fail "non-TPTP format" val atype_of_types = AType ((tptp_type_of_types, []), []) fun nary_type_decl_type n = funpow n (curry AFun atype_of_types) atype_of_types fun maybe_alt "" = "" | maybe_alt s = " % " ^ s fun tptp_string_of_line format (Type_Decl (ident, ty, ary)) = tptp_string_of_line format (Sym_Decl (ident, ty, nary_type_decl_type ary)) | tptp_string_of_line format (Sym_Decl (ident, sym, ty)) = tptp_string_of_format format ^ "(" ^ ident ^ ", type,\n " ^ sym ^ " : " ^ string_of_type format ty ^ ").\n" | tptp_string_of_line format (Formula ((ident, alt), kind, phi, source, info)) = tptp_string_of_format format ^ "(" ^ ident ^ ", " ^ tptp_string_of_role kind ^ "," ^ "\n (" ^ tptp_string_of_formula format phi ^ ")" ^ (case source of SOME tm => ", " ^ tptp_string_of_term format tm | NONE => if null info then "" else ", []") ^ (case info of [] => "" | tms => ", [" ^ commas (map (tptp_string_of_term format) tms) ^ "]") ^ ")." ^ maybe_alt alt ^ "\n" fun tptp_lines format = maps (fn (_, []) => [] | (heading, lines) => "\n% " ^ heading ^ " (" ^ string_of_int (length lines) ^ ")\n" :: map (tptp_string_of_line format) lines) fun arity_of_type (APi (tys, ty)) = arity_of_type ty |>> Integer.add (length tys) | arity_of_type (AFun (_, ty)) = arity_of_type ty ||> Integer.add 1 | arity_of_type _ = (0, 0) fun string_of_arity (0, n) = string_of_int n | string_of_arity (m, n) = string_of_int m ^ "+" ^ string_of_int n val dfg_class_inter = space_implode " & " fun dfg_string_of_term (ATerm ((s, tys), tms)) = s ^ (if null tys then "" else "<" ^ commas (map (string_of_type (DFG Polymorphic)) tys) ^ ">") ^ (if null tms then "" else "(" ^ commas (map dfg_string_of_term tms) ^ ")") | dfg_string_of_term _ = raise Fail "unexpected atom in first-order format" fun dfg_string_of_formula poly gen_simp info = let val str_of_typ = string_of_type (DFG poly) fun str_of_bound_typ (ty, []) = str_of_typ ty | str_of_bound_typ (ty, cls) = str_of_typ ty ^ " : " ^ dfg_class_inter cls fun suffix_tag top_level s = if top_level then (case extract_isabelle_status info of SOME s' => if s' = non_rec_defN then s ^ ":lt" else if (s' = simpN orelse s' = rec_defN) andalso gen_simp then s ^ ":lr" else s | NONE => s) else s fun str_of_atom top_level (ATerm ((s, tys), tms)) = let val s' = if is_tptp_equal s then "equal" |> suffix_tag top_level else if s = tptp_true then "true" else if s = tptp_false then "false" else s in dfg_string_of_term (ATerm ((s', tys), tms)) end | str_of_atom _ _ = raise Fail "unexpected atom in first-order format" fun str_of_quant AForall = "forall" | str_of_quant AExists = "exists" fun str_of_conn _ ANot = "not" | str_of_conn _ AAnd = "and" | str_of_conn _ AOr = "or" | str_of_conn _ AImplies = "implies" | str_of_conn top_level AIff = "equiv" |> suffix_tag top_level fun str_of_formula top_level (ATyQuant (q, xs, phi)) = str_of_quant q ^ "_sorts([" ^ commas (map str_of_bound_typ xs) ^ "], " ^ str_of_formula top_level phi ^ ")" | str_of_formula top_level (AQuant (q, xs, phi)) = str_of_quant q ^ "([" ^ commas (map (string_of_bound_var (DFG poly)) xs) ^ "], " ^ str_of_formula top_level phi ^ ")" | str_of_formula top_level (AConn (c, phis)) = str_of_conn top_level c ^ "(" ^ commas (map (str_of_formula false) phis) ^ ")" | str_of_formula top_level (AAtom tm) = str_of_atom top_level tm in str_of_formula true end fun maybe_enclose bef aft "" = "% " ^ bef ^ aft | maybe_enclose bef aft s = bef ^ s ^ aft fun dfg_lines poly {is_lpo, gen_weights, gen_prec, gen_simp} ord_info problem = let val typ = string_of_type (DFG poly) val term = dfg_string_of_term fun spair (s, s') = "(" ^ s ^ ", " ^ s' ^ ")" fun tm_ary sym ty = spair (sym, string_of_arity (arity_of_type ty)) fun ty_ary 0 ty = ty | ty_ary n ty = "(" ^ ty ^ ", " ^ string_of_int n ^ ")" fun fun_typ sym ty = "function(" ^ sym ^ ", " ^ typ ty ^ ")." fun pred_typ sym ty = let val (ty_vars, (tys, _)) = strip_atype ty |>> (fn [] => [] | xs => ["[" ^ commas xs ^ "]"]) in "predicate(" ^ commas (sym :: ty_vars @ map typ tys) ^ ")." end fun bound_tvar (ty, []) = ty | bound_tvar (ty, cls) = ty ^ " : " ^ dfg_class_inter cls fun binder_typ xs ty = (if null xs then "" else "[" ^ commas (map bound_tvar xs) ^ "], ") ^ typ ty fun sort_decl xs ty cl = "sort(" ^ binder_typ xs ty ^ ", " ^ cl ^ ")." fun datatype_decl xs ty tms exhaust = "datatype(" ^ commas (binder_typ xs ty :: map term tms @ (if exhaust then [] else ["..."])) ^ ")." fun subclass_of sub super = "subclass(" ^ sub ^ ", " ^ super ^ ")." fun formula pred (Formula ((ident, alt), kind, phi, _, info)) = if pred kind then let val rank = extract_isabelle_rank info in "formula(" ^ dfg_string_of_formula poly gen_simp info phi ^ ", " ^ ident ^ (if rank = default_rank then "" else ", " ^ string_of_int rank) ^ ")." ^ maybe_alt alt |> SOME end else NONE | formula _ _ = NONE fun filt f = problem |> map (map_filter f o snd) |> filter_out null val func_aries = filt (fn Sym_Decl (_, sym, ty) => if is_function_atype ty then SOME (tm_ary sym ty) else NONE | _ => NONE) |> flat |> commas |> maybe_enclose "functions [" "]." val pred_aries = filt (fn Sym_Decl (_, sym, ty) => if is_predicate_atype ty then SOME (tm_ary sym ty) else NONE | _ => NONE) |> flat |> commas |> maybe_enclose "predicates [" "]." val sorts = filt (try (fn Type_Decl (_, ty, ary) => ty_ary ary ty)) @ [[ty_ary 0 dfg_individual_type]] |> flat |> commas |> maybe_enclose "sorts [" "]." val classes = filt (try (fn Class_Decl (_, cl, _) => cl)) |> flat |> commas |> maybe_enclose "classes [" "]." val ord_info = if gen_weights orelse gen_prec then ord_info () else [] val do_term_order_weights = (if gen_weights then ord_info else []) |> map (spair o apsnd string_of_int) |> commas |> maybe_enclose "weights [" "]." val syms = [func_aries, pred_aries, do_term_order_weights, sorts, classes] val func_decls = filt (fn Sym_Decl (_, sym, ty) => if is_function_atype ty then SOME (fun_typ sym ty) else NONE | _ => NONE) |> flat val pred_decls = filt (fn Sym_Decl (_, sym, ty) => if is_nontrivial_predicate_atype ty then SOME (pred_typ sym ty) else NONE | _ => NONE) |> flat val datatype_decls = filt (try (fn Datatype_Decl (_, xs, ty, tms, exhaust) => datatype_decl xs ty tms exhaust)) |> flat val sort_decls = filt (try (fn Class_Memb (_, xs, ty, cl) => sort_decl xs ty cl)) |> flat val subclass_decls = filt (try (fn Class_Decl (_, sub, supers) => map (subclass_of sub) supers)) |> flat |> flat val decls = func_decls @ pred_decls @ datatype_decls @ sort_decls @ subclass_decls val axioms = filt (formula (curry (op <>) Conjecture)) |> separate [""] |> flat val conjs = filt (formula (curry (op =) Conjecture)) |> separate [""] |> flat val settings = (if is_lpo then ["set_flag(Ordering, 1)."] else []) @ (if gen_prec then [ord_info |> map fst |> rev |> commas |> maybe_enclose "set_precedence(" ")."] else []) fun list_of _ [] = [] | list_of heading ss = "list_of_" ^ heading ^ ".\n" :: map (suffix "\n") ss @ ["end_of_list.\n\n"] in "\nbegin_problem(isabelle).\n\n" :: list_of "descriptions" ["name({**}).", "author({**}).", "status(unknown).", "description({**})."] @ list_of "symbols" syms @ list_of "declarations" decls @ list_of "formulae(axioms)" axioms @ list_of "formulae(conjectures)" conjs @ list_of "settings(SPASS)" settings @ ["end_problem.\n"] end fun lines_of_atp_problem format ord ord_info problem = "% This file was generated by Isabelle (most likely Sledgehammer)\n\ \% " ^ timestamp () ^ "\n" :: (case format of DFG poly => dfg_lines poly ord ord_info | _ => tptp_lines format) problem (** CNF (Metis) and CNF UEQ (Waldmeister) **) fun is_line_negated (Formula (_, _, AConn (ANot, _), _, _)) = true | is_line_negated _ = false fun is_line_cnf_ueq (Formula (_, _, AAtom (ATerm (((s, _), _), _)), _, _)) = is_tptp_equal s | is_line_cnf_ueq _ = false fun open_conjecture_term (ATerm (((s, s'), tys), tms)) = ATerm ((if is_tptp_variable s then (s |> Name.desymbolize (SOME false), s') else (s, s'), tys), tms |> map open_conjecture_term) | open_conjecture_term _ = raise Fail "unexpected higher-order term" fun open_formula conj = let (* We are conveniently assuming that all bound variable names are distinct, which should be the case for the formulas we generate. *) fun opn (pos as SOME true) (AQuant (AForall, _, phi)) = opn pos phi | opn (pos as SOME false) (AQuant (AExists, _, phi)) = opn pos phi | opn pos (AConn (ANot, [phi])) = mk_anot (opn (Option.map not pos) phi) | opn pos (AConn (c, [phi1, phi2])) = let val (pos1, pos2) = polarities_of_conn pos c in AConn (c, [opn pos1 phi1, opn pos2 phi2]) end | opn _ (AAtom t) = AAtom (t |> conj ? open_conjecture_term) | opn _ phi = phi in opn (SOME (not conj)) end fun open_formula_line (Formula (ident, kind, phi, source, info)) = Formula (ident, kind, open_formula (kind = Conjecture) phi, source, info) | open_formula_line line = line fun negate_conjecture_line (Formula (ident, Conjecture, phi, source, info)) = Formula (ident, Hypothesis, mk_anot phi, source, info) | negate_conjecture_line line = line exception CLAUSIFY of unit (* This "clausification" only expands syntactic sugar, such as "phi => psi" to "~ phi | psi" and "phi <=> psi" to "~ phi | psi" and "~ psi | phi". We don't attempt to distribute conjunctions over disjunctions. *) fun clausify_formula pos (phi as AAtom _) = [phi |> not pos ? mk_anot] | clausify_formula pos (AConn (ANot, [phi])) = clausify_formula (not pos) phi | clausify_formula true (AConn (AOr, [phi1, phi2])) = (phi1, phi2) |> apply2 (clausify_formula true) |> uncurry (map_product (mk_aconn AOr)) | clausify_formula false (AConn (AAnd, [phi1, phi2])) = (phi1, phi2) |> apply2 (clausify_formula false) |> uncurry (map_product (mk_aconn AOr)) | clausify_formula true (AConn (AImplies, [phi1, phi2])) = clausify_formula true (AConn (AOr, [mk_anot phi1, phi2])) | clausify_formula true (AConn (AIff, phis)) = clausify_formula true (AConn (AImplies, phis)) @ clausify_formula true (AConn (AImplies, rev phis)) | clausify_formula _ _ = raise CLAUSIFY () fun clausify_formula_line (Formula ((ident, alt), kind, phi, source, info)) = let val (n, phis) = phi |> try (clausify_formula true) |> these |> `length in map2 (fn phi => fn j => Formula ((ident ^ replicate_string (j - 1) "x", alt), kind, phi, source, info)) phis (1 upto n) end | clausify_formula_line _ = [] fun ensure_cnf_line line = line |> open_formula_line |> negate_conjecture_line |> clausify_formula_line fun ensure_cnf_problem problem = problem |> map (apsnd (maps ensure_cnf_line)) fun filter_cnf_ueq_problem problem = problem |> map (apsnd (map open_formula_line #> filter is_line_cnf_ueq #> map negate_conjecture_line)) |> (fn problem => let val lines = problem |> maps snd val conjs = lines |> filter is_line_negated in if length conjs = 1 andalso conjs <> lines then problem else [] end) (** Symbol declarations **) fun add_declared_in_line (Class_Decl (_, cl, _)) = apfst (apfst (cons cl)) | add_declared_in_line (Type_Decl (_, ty, _)) = apfst (apsnd (cons ty)) | add_declared_in_line (Sym_Decl (_, sym, _)) = apsnd (cons sym) | add_declared_in_line _ = I fun declared_in_atp_problem problem = fold (fold add_declared_in_line o snd) problem (([], []), []) (** Nice names **) val no_qualifiers = let fun skip [] = [] | skip (#"." :: cs) = skip cs | skip (c :: cs) = if Char.isAlphaNum c then skip cs else c :: keep cs and keep [] = [] | keep (#"." :: cs) = skip cs | keep (c :: cs) = c :: keep cs in String.explode #> rev #> keep #> rev #> String.implode end (* Long names can slow down the ATPs. *) val max_readable_name_size = 20 (* "equal" is reserved by some ATPs. "op" is also reserved, to avoid the unreadable "op_1", "op_2", etc., in the problem files. "eq" is reserved to ensure that "HOL.eq" is correctly mapped to equality (not clear whether this is still necessary). *) val reserved_nice_names = [tptp_old_equal, "op", "eq"] (* hack to get the same hashing across Mirabelle runs (see "mirabelle.pl") *) fun cleanup_mirabelle_name s = let val mirabelle_infix = "_Mirabelle_" val random_suffix_len = 10 val (s1, s2) = Substring.position mirabelle_infix (Substring.full s) in if Substring.isEmpty s2 then s else Substring.string s1 ^ Substring.string (Substring.triml (size mirabelle_infix + random_suffix_len) s2) end fun readable_name protect full_name s = (if s = full_name then s else s |> no_qualifiers |> unquote_tvar |> Name.desymbolize (SOME (Char.isUpper (String.sub (full_name, 0)))) |> (fn s => if size s > max_readable_name_size then String.substring (s, 0, max_readable_name_size div 2 - 4) ^ string_of_int (hash_string (cleanup_mirabelle_name full_name)) ^ String.extract (s, size s - max_readable_name_size div 2 + 4, NONE) else s) |> (fn s => if member (op =) reserved_nice_names s then full_name else s)) |> protect fun nice_name _ (full_name, _) NONE = (full_name, NONE) | nice_name protect (full_name, desired_name) (SOME the_pool) = if is_built_in_tptp_symbol full_name then (full_name, SOME the_pool) else (case Symtab.lookup (fst the_pool) full_name of SOME nice_name => (nice_name, SOME the_pool) | NONE => let val nice_prefix = readable_name protect full_name desired_name fun add j = let val nice_name = nice_prefix ^ (if j = 1 then "" else string_of_int j) in (case Symtab.lookup (snd the_pool) nice_name of SOME full_name' => if full_name = full_name' then (nice_name, the_pool) else add (j + 1) | NONE => (nice_name, (Symtab.update_new (full_name, nice_name) (fst the_pool), Symtab.update_new (nice_name, full_name) (snd the_pool)))) end in add 1 |> apsnd SOME end) fun avoid_clash_with_dfg_keywords s = let val n = String.size s in if n < 2 orelse (n = 2 andalso String.sub (s, 0) = String.sub (s, 1)) orelse String.isSubstring "_" s then s else if is_tptp_variable s then s ^ "_" else String.substring (s, 0, n - 1) ^ String.str (Char.toUpper (String.sub (s, n - 1))) end fun nice_atp_problem readable_names format problem = let val empty_pool = if readable_names then SOME (Symtab.empty, Symtab.empty) else NONE val avoid_clash = (case format of DFG _ => avoid_clash_with_dfg_keywords | _ => I) val nice_name = nice_name avoid_clash fun nice_bound_tvars xs = fold_map (nice_name o fst) xs ##>> fold_map (fold_map nice_name o snd) xs #>> op ~~ fun nice_type (AType ((name, clss), tys)) = nice_name name ##>> fold_map nice_name clss ##>> fold_map nice_type tys #>> AType | nice_type (AFun (ty1, ty2)) = nice_type ty1 ##>> nice_type ty2 #>> AFun | nice_type (APi (names, ty)) = fold_map nice_name names ##>> nice_type ty #>> APi fun nice_term (ATerm ((name, tys), ts)) = nice_name name ##>> fold_map nice_type tys ##>> fold_map nice_term ts #>> ATerm | nice_term (AAbs (((name, ty), tm), args)) = nice_name name ##>> nice_type ty ##>> nice_term tm ##>> fold_map nice_term args #>> AAbs fun nice_formula (ATyQuant (q, xs, phi)) = fold_map (nice_type o fst) xs ##>> fold_map (fold_map nice_name o snd) xs ##>> nice_formula phi #>> (fn ((tys, cls), phi) => ATyQuant (q, tys ~~ cls, phi)) | nice_formula (AQuant (q, xs, phi)) = fold_map (nice_name o fst) xs ##>> fold_map (fn (_, NONE) => pair NONE | (_, SOME ty) => nice_type ty #>> SOME) xs ##>> nice_formula phi #>> (fn ((ss, ts), phi) => AQuant (q, ss ~~ ts, phi)) | nice_formula (AConn (c, phis)) = fold_map nice_formula phis #>> curry AConn c | nice_formula (AAtom tm) = nice_term tm #>> AAtom fun nice_line (Class_Decl (ident, cl, cls)) = nice_name cl ##>> fold_map nice_name cls #>> (fn (cl, cls) => Class_Decl (ident, cl, cls)) | nice_line (Type_Decl (ident, ty, ary)) = nice_name ty #>> (fn ty => Type_Decl (ident, ty, ary)) | nice_line (Sym_Decl (ident, sym, ty)) = nice_name sym ##>> nice_type ty #>> (fn (sym, ty) => Sym_Decl (ident, sym, ty)) | nice_line (Datatype_Decl (ident, xs, ty, tms, exhaust)) = nice_bound_tvars xs ##>> nice_type ty ##>> fold_map nice_term tms #>> (fn ((xs, ty), tms) => Datatype_Decl (ident, xs, ty, tms, exhaust)) | nice_line (Class_Memb (ident, xs, ty, cl)) = nice_bound_tvars xs ##>> nice_type ty ##>> nice_name cl #>> (fn ((xs, ty), cl) => Class_Memb (ident, xs, ty, cl)) | nice_line (Formula (ident, kind, phi, source, info)) = nice_formula phi #>> (fn phi => Formula (ident, kind, phi, source, info)) fun nice_problem problem = fold_map (fn (heading, lines) => fold_map nice_line lines #>> pair heading) problem in nice_problem problem empty_pool end end;