--- a/src/HOL/Tools/Sledgehammer/sledgehammer_atp_translate.ML Tue May 31 11:21:47 2011 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,1389 +0,0 @@
-(* Title: HOL/Tools/Sledgehammer/sledgehammer_atp_translate.ML
- Author: Fabian Immler, TU Muenchen
- Author: Makarius
- Author: Jasmin Blanchette, TU Muenchen
-
-Translation of HOL to FOL for Sledgehammer.
-*)
-
-signature SLEDGEHAMMER_ATP_TRANSLATE =
-sig
- type 'a fo_term = 'a ATP_Problem.fo_term
- type format = ATP_Problem.format
- type formula_kind = ATP_Problem.formula_kind
- type 'a problem = 'a ATP_Problem.problem
- type locality = Sledgehammer_Filter.locality
-
- datatype polymorphism = Polymorphic | Monomorphic | Mangled_Monomorphic
- datatype type_level =
- All_Types | Nonmonotonic_Types | Finite_Types | Const_Arg_Types | No_Types
- datatype type_heaviness = Heavy | Light
-
- datatype type_system =
- Simple_Types of type_level |
- Preds of polymorphism * type_level * type_heaviness |
- Tags of polymorphism * type_level * type_heaviness
-
- type translated_formula
-
- val readable_names : bool Config.T
- val fact_prefix : string
- val conjecture_prefix : string
- val helper_prefix : string
- val typed_helper_suffix : string
- val predicator_name : string
- val app_op_name : string
- val type_pred_name : string
- val simple_type_prefix : string
- val type_sys_from_string : string -> type_system
- val polymorphism_of_type_sys : type_system -> polymorphism
- val level_of_type_sys : type_system -> type_level
- val is_type_sys_virtually_sound : type_system -> bool
- val is_type_sys_fairly_sound : type_system -> bool
- val unmangled_const : string -> string * string fo_term list
- val translate_atp_fact :
- Proof.context -> format -> type_system -> bool -> (string * locality) * thm
- -> translated_formula option * ((string * locality) * thm)
- val prepare_atp_problem :
- Proof.context -> format -> formula_kind -> formula_kind -> type_system
- -> bool option -> term list -> term
- -> (translated_formula option * ((string * 'a) * thm)) list
- -> string problem * string Symtab.table * int * int
- * (string * 'a) list vector * int list * int Symtab.table
- val atp_problem_weights : string problem -> (string * real) list
-end;
-
-structure Sledgehammer_ATP_Translate : SLEDGEHAMMER_ATP_TRANSLATE =
-struct
-
-open ATP_Problem
-open Metis_Translate
-open Sledgehammer_Util
-open Sledgehammer_Filter
-
-(* experimental *)
-val generate_useful_info = false
-
-fun useful_isabelle_info s =
- if generate_useful_info then
- SOME (ATerm ("[]", [ATerm ("isabelle_" ^ s, [])]))
- else
- NONE
-
-val intro_info = useful_isabelle_info "intro"
-val elim_info = useful_isabelle_info "elim"
-val simp_info = useful_isabelle_info "simp"
-
-(* Readable names are often much shorter, especially if types are mangled in
- names. Also, the logic for generating legal SNARK sort names is only
- implemented for readable names. Finally, readable names are, well, more
- readable. For these reason, they are enabled by default. *)
-val readable_names =
- Attrib.setup_config_bool @{binding sledgehammer_atp_readable_names} (K true)
-
-val type_decl_prefix = "ty_"
-val sym_decl_prefix = "sy_"
-val sym_formula_prefix = "sym_"
-val fact_prefix = "fact_"
-val conjecture_prefix = "conj_"
-val helper_prefix = "help_"
-val class_rel_clause_prefix = "crel_";
-val arity_clause_prefix = "arity_"
-val tfree_prefix = "tfree_"
-
-val typed_helper_suffix = "_T"
-val untyped_helper_suffix = "_U"
-
-val predicator_name = "hBOOL"
-val app_op_name = "hAPP"
-val type_pred_name = "is"
-val simple_type_prefix = "ty_"
-
-fun make_simple_type s =
- if s = tptp_bool_type orelse s = tptp_fun_type orelse
- s = tptp_individual_type then
- s
- else
- simple_type_prefix ^ ascii_of s
-
-(* Freshness almost guaranteed! *)
-val sledgehammer_weak_prefix = "Sledgehammer:"
-
-datatype polymorphism = Polymorphic | Monomorphic | Mangled_Monomorphic
-datatype type_level =
- All_Types | Nonmonotonic_Types | Finite_Types | Const_Arg_Types | No_Types
-datatype type_heaviness = Heavy | Light
-
-datatype type_system =
- Simple_Types of type_level |
- Preds of polymorphism * type_level * type_heaviness |
- Tags of polymorphism * type_level * type_heaviness
-
-fun try_unsuffixes ss s =
- fold (fn s' => fn NONE => try (unsuffix s') s | some => some) ss NONE
-
-fun type_sys_from_string s =
- (case try (unprefix "poly_") s of
- SOME s => (SOME Polymorphic, s)
- | NONE =>
- case try (unprefix "mono_") s of
- SOME s => (SOME Monomorphic, s)
- | NONE =>
- case try (unprefix "mangled_") s of
- SOME s => (SOME Mangled_Monomorphic, s)
- | NONE => (NONE, s))
- ||> (fn s =>
- (* "_query" and "_bang" are for the ASCII-challenged Mirabelle. *)
- case try_unsuffixes ["?", "_query"] s of
- SOME s => (Nonmonotonic_Types, s)
- | NONE =>
- case try_unsuffixes ["!", "_bang"] s of
- SOME s => (Finite_Types, s)
- | NONE => (All_Types, s))
- ||> apsnd (fn s =>
- case try (unsuffix "_heavy") s of
- SOME s => (Heavy, s)
- | NONE => (Light, s))
- |> (fn (poly, (level, (heaviness, core))) =>
- case (core, (poly, level, heaviness)) of
- ("simple", (NONE, _, Light)) => Simple_Types level
- | ("preds", (SOME poly, _, _)) => Preds (poly, level, heaviness)
- | ("tags", (SOME Polymorphic, All_Types, _)) =>
- Tags (Polymorphic, All_Types, heaviness)
- | ("tags", (SOME Polymorphic, _, _)) =>
- (* The actual light encoding is very unsound. *)
- Tags (Polymorphic, level, Heavy)
- | ("tags", (SOME poly, _, _)) => Tags (poly, level, heaviness)
- | ("args", (SOME poly, All_Types (* naja *), Light)) =>
- Preds (poly, Const_Arg_Types, Light)
- | ("erased", (NONE, All_Types (* naja *), Light)) =>
- Preds (Polymorphic, No_Types, Light)
- | _ => raise Same.SAME)
- handle Same.SAME => error ("Unknown type system: " ^ quote s ^ ".")
-
-fun polymorphism_of_type_sys (Simple_Types _) = Mangled_Monomorphic
- | polymorphism_of_type_sys (Preds (poly, _, _)) = poly
- | polymorphism_of_type_sys (Tags (poly, _, _)) = poly
-
-fun level_of_type_sys (Simple_Types level) = level
- | level_of_type_sys (Preds (_, level, _)) = level
- | level_of_type_sys (Tags (_, level, _)) = level
-
-fun heaviness_of_type_sys (Simple_Types _) = Heavy
- | heaviness_of_type_sys (Preds (_, _, heaviness)) = heaviness
- | heaviness_of_type_sys (Tags (_, _, heaviness)) = heaviness
-
-fun is_type_level_virtually_sound level =
- level = All_Types orelse level = Nonmonotonic_Types
-val is_type_sys_virtually_sound =
- is_type_level_virtually_sound o level_of_type_sys
-
-fun is_type_level_fairly_sound level =
- is_type_level_virtually_sound level orelse level = Finite_Types
-val is_type_sys_fairly_sound = is_type_level_fairly_sound o level_of_type_sys
-
-fun is_setting_higher_order THF (Simple_Types _) = true
- | is_setting_higher_order _ _ = false
-
-type translated_formula =
- {name: string,
- locality: locality,
- kind: formula_kind,
- combformula: (name, typ, combterm) formula,
- atomic_types: typ list}
-
-fun update_combformula f ({name, locality, kind, combformula, atomic_types}
- : translated_formula) =
- {name = name, locality = locality, kind = kind, combformula = f combformula,
- atomic_types = atomic_types} : translated_formula
-
-fun fact_lift f ({combformula, ...} : translated_formula) = f combformula
-
-val type_instance = Sign.typ_instance o Proof_Context.theory_of
-
-fun insert_type ctxt get_T x xs =
- let val T = get_T x in
- if exists (curry (type_instance ctxt) T o get_T) xs then xs
- else x :: filter_out (curry (type_instance ctxt o swap) T o get_T) xs
- end
-
-(* The Booleans indicate whether all type arguments should be kept. *)
-datatype type_arg_policy =
- Explicit_Type_Args of bool |
- Mangled_Type_Args of bool |
- No_Type_Args
-
-fun should_drop_arg_type_args (Simple_Types _) =
- false (* since TFF doesn't support overloading *)
- | should_drop_arg_type_args type_sys =
- level_of_type_sys type_sys = All_Types andalso
- heaviness_of_type_sys type_sys = Heavy
-
-fun general_type_arg_policy type_sys =
- if level_of_type_sys type_sys = No_Types then
- No_Type_Args
- else if polymorphism_of_type_sys type_sys = Mangled_Monomorphic then
- Mangled_Type_Args (should_drop_arg_type_args type_sys)
- else
- Explicit_Type_Args (should_drop_arg_type_args type_sys)
-
-fun type_arg_policy type_sys s =
- if s = @{const_name HOL.eq} orelse
- (s = app_op_name andalso level_of_type_sys type_sys = Const_Arg_Types) then
- No_Type_Args
- else
- general_type_arg_policy type_sys
-
-fun atp_type_literals_for_types format type_sys kind Ts =
- if level_of_type_sys type_sys = No_Types orelse format = CNF_UEQ then
- []
- else
- Ts |> type_literals_for_types
- |> filter (fn TyLitVar _ => kind <> Conjecture
- | TyLitFree _ => kind = Conjecture)
-
-fun mk_aconns c phis =
- let val (phis', phi') = split_last phis in
- fold_rev (mk_aconn c) phis' phi'
- end
-fun mk_ahorn [] phi = phi
- | mk_ahorn phis psi = AConn (AImplies, [mk_aconns AAnd phis, psi])
-fun mk_aquant _ [] phi = phi
- | mk_aquant q xs (phi as AQuant (q', xs', phi')) =
- if q = q' then AQuant (q, xs @ xs', phi') else AQuant (q, xs, phi)
- | mk_aquant q xs phi = AQuant (q, xs, phi)
-
-fun close_universally atom_vars phi =
- let
- fun formula_vars bounds (AQuant (_, xs, phi)) =
- formula_vars (map fst xs @ bounds) phi
- | formula_vars bounds (AConn (_, phis)) = fold (formula_vars bounds) phis
- | formula_vars bounds (AAtom tm) =
- union (op =) (atom_vars tm []
- |> filter_out (member (op =) bounds o fst))
- in mk_aquant AForall (formula_vars [] phi []) phi end
-
-fun combterm_vars (CombApp (tm1, tm2)) = fold combterm_vars [tm1, tm2]
- | combterm_vars (CombConst _) = I
- | combterm_vars (CombVar (name, T)) = insert (op =) (name, SOME T)
-fun close_combformula_universally phi = close_universally combterm_vars phi
-
-fun term_vars (ATerm (name as (s, _), tms)) =
- is_tptp_variable s ? insert (op =) (name, NONE) #> fold term_vars tms
-fun close_formula_universally phi = close_universally term_vars phi
-
-val homo_infinite_type_name = @{type_name ind} (* any infinite type *)
-val homo_infinite_type = Type (homo_infinite_type_name, [])
-
-fun fo_term_from_typ higher_order =
- let
- fun term (Type (s, Ts)) =
- ATerm (case (higher_order, s) of
- (true, @{type_name bool}) => `I tptp_bool_type
- | (true, @{type_name fun}) => `I tptp_fun_type
- | _ => if s = homo_infinite_type_name then `I tptp_individual_type
- else `make_fixed_type_const s,
- map term Ts)
- | term (TFree (s, _)) = ATerm (`make_fixed_type_var s, [])
- | term (TVar ((x as (s, _)), _)) =
- ATerm ((make_schematic_type_var x, s), [])
- in term end
-
-(* This shouldn't clash with anything else. *)
-val mangled_type_sep = "\000"
-
-fun generic_mangled_type_name f (ATerm (name, [])) = f name
- | generic_mangled_type_name f (ATerm (name, tys)) =
- f name ^ "(" ^ space_implode "," (map (generic_mangled_type_name f) tys)
- ^ ")"
-
-val bool_atype = AType (`I tptp_bool_type)
-
-fun ho_type_from_fo_term higher_order pred_sym ary =
- let
- fun to_atype ty =
- AType ((make_simple_type (generic_mangled_type_name fst ty),
- generic_mangled_type_name snd ty))
- fun to_afun f1 f2 tys = AFun (f1 (hd tys), f2 (nth tys 1))
- fun to_fo 0 ty = if pred_sym then bool_atype else to_atype ty
- | to_fo ary (ATerm (_, tys)) = to_afun to_atype (to_fo (ary - 1)) tys
- fun to_ho (ty as ATerm ((s, _), tys)) =
- if s = tptp_fun_type then to_afun to_ho to_ho tys else to_atype ty
- in if higher_order then to_ho else to_fo ary end
-
-fun mangled_type higher_order pred_sym ary =
- ho_type_from_fo_term higher_order pred_sym ary o fo_term_from_typ higher_order
-
-fun mangled_const_name T_args (s, s') =
- let
- val ty_args = map (fo_term_from_typ false) T_args
- fun type_suffix f g =
- fold_rev (curry (op ^) o g o prefix mangled_type_sep
- o generic_mangled_type_name f) ty_args ""
- in (s ^ type_suffix fst ascii_of, s' ^ type_suffix snd I) end
-
-val parse_mangled_ident =
- Scan.many1 (not o member (op =) ["(", ")", ","]) >> implode
-
-fun parse_mangled_type x =
- (parse_mangled_ident
- -- Scan.optional ($$ "(" |-- Scan.optional parse_mangled_types [] --| $$ ")")
- [] >> ATerm) x
-and parse_mangled_types x =
- (parse_mangled_type ::: Scan.repeat ($$ "," |-- parse_mangled_type)) x
-
-fun unmangled_type s =
- s |> suffix ")" |> raw_explode
- |> Scan.finite Symbol.stopper
- (Scan.error (!! (fn _ => raise Fail ("unrecognized mangled type " ^
- quote s)) parse_mangled_type))
- |> fst
-
-val unmangled_const_name = space_explode mangled_type_sep #> hd
-fun unmangled_const s =
- let val ss = space_explode mangled_type_sep s in
- (hd ss, map unmangled_type (tl ss))
- end
-
-fun introduce_proxies format type_sys =
- let
- fun intro top_level (CombApp (tm1, tm2)) =
- CombApp (intro top_level tm1, intro false tm2)
- | intro top_level (CombConst (name as (s, _), T, T_args)) =
- (case proxify_const s of
- SOME (_, proxy_base) =>
- if top_level orelse is_setting_higher_order format type_sys then
- case (top_level, s) of
- (_, "c_False") => (`I tptp_false, [])
- | (_, "c_True") => (`I tptp_true, [])
- | (false, "c_Not") => (`I tptp_not, [])
- | (false, "c_conj") => (`I tptp_and, [])
- | (false, "c_disj") => (`I tptp_or, [])
- | (false, "c_implies") => (`I tptp_implies, [])
- | (false, s) =>
- if is_tptp_equal s then (`I tptp_equal, [])
- else (proxy_base |>> prefix const_prefix, T_args)
- | _ => (name, [])
- else
- (proxy_base |>> prefix const_prefix, T_args)
- | NONE => (name, T_args))
- |> (fn (name, T_args) => CombConst (name, T, T_args))
- | intro _ tm = tm
- in intro true end
-
-fun combformula_from_prop thy format type_sys eq_as_iff =
- let
- fun do_term bs t atomic_types =
- combterm_from_term thy bs (Envir.eta_contract t)
- |>> (introduce_proxies format type_sys #> AAtom)
- ||> union (op =) atomic_types
- fun do_quant bs q s T t' =
- let val s = Name.variant (map fst bs) s in
- do_formula ((s, T) :: bs) t'
- #>> mk_aquant q [(`make_bound_var s, SOME T)]
- end
- and do_conn bs c t1 t2 =
- do_formula bs t1 ##>> do_formula bs t2
- #>> uncurry (mk_aconn c)
- and do_formula bs t =
- case t of
- @{const Not} $ t1 => do_formula bs t1 #>> mk_anot
- | Const (@{const_name All}, _) $ Abs (s, T, t') =>
- do_quant bs AForall s T t'
- | Const (@{const_name Ex}, _) $ Abs (s, T, t') =>
- do_quant bs AExists s T t'
- | @{const HOL.conj} $ t1 $ t2 => do_conn bs AAnd t1 t2
- | @{const HOL.disj} $ t1 $ t2 => do_conn bs AOr t1 t2
- | @{const HOL.implies} $ t1 $ t2 => do_conn bs AImplies t1 t2
- | Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])) $ t1 $ t2 =>
- if eq_as_iff then do_conn bs AIff t1 t2 else do_term bs t
- | _ => do_term bs t
- in do_formula [] end
-
-fun presimplify_term ctxt =
- Skip_Proof.make_thm (Proof_Context.theory_of ctxt)
- #> Meson.presimplify ctxt
- #> prop_of
-
-fun concealed_bound_name j = sledgehammer_weak_prefix ^ string_of_int j
-fun conceal_bounds Ts t =
- subst_bounds (map (Free o apfst concealed_bound_name)
- (0 upto length Ts - 1 ~~ Ts), t)
-fun reveal_bounds Ts =
- subst_atomic (map (fn (j, T) => (Free (concealed_bound_name j, T), Bound j))
- (0 upto length Ts - 1 ~~ Ts))
-
-fun extensionalize_term ctxt t =
- let val thy = Proof_Context.theory_of ctxt in
- t |> cterm_of thy |> Meson.extensionalize_conv ctxt
- |> prop_of |> Logic.dest_equals |> snd
- end
-
-fun introduce_combinators_in_term ctxt kind t =
- let val thy = Proof_Context.theory_of ctxt in
- if Meson.is_fol_term thy t then
- t
- else
- let
- fun aux Ts t =
- case t of
- @{const Not} $ t1 => @{const Not} $ aux Ts t1
- | (t0 as Const (@{const_name All}, _)) $ Abs (s, T, t') =>
- t0 $ Abs (s, T, aux (T :: Ts) t')
- | (t0 as Const (@{const_name All}, _)) $ t1 =>
- aux Ts (t0 $ eta_expand Ts t1 1)
- | (t0 as Const (@{const_name Ex}, _)) $ Abs (s, T, t') =>
- t0 $ Abs (s, T, aux (T :: Ts) t')
- | (t0 as Const (@{const_name Ex}, _)) $ t1 =>
- aux Ts (t0 $ eta_expand Ts t1 1)
- | (t0 as @{const HOL.conj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
- | (t0 as @{const HOL.disj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
- | (t0 as @{const HOL.implies}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
- | (t0 as Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])))
- $ t1 $ t2 =>
- t0 $ aux Ts t1 $ aux Ts t2
- | _ => if not (exists_subterm (fn Abs _ => true | _ => false) t) then
- t
- else
- t |> conceal_bounds Ts
- |> Envir.eta_contract
- |> cterm_of thy
- |> Meson_Clausify.introduce_combinators_in_cterm
- |> prop_of |> Logic.dest_equals |> snd
- |> reveal_bounds Ts
- val (t, ctxt') = Variable.import_terms true [t] ctxt |>> the_single
- in t |> aux [] |> singleton (Variable.export_terms ctxt' ctxt) end
- handle THM _ =>
- (* A type variable of sort "{}" will make abstraction fail. *)
- if kind = Conjecture then HOLogic.false_const
- else HOLogic.true_const
- end
-
-(* Metis's use of "resolve_tac" freezes the schematic variables. We simulate the
- same in Sledgehammer to prevent the discovery of unreplayable proofs. *)
-fun freeze_term t =
- let
- fun aux (t $ u) = aux t $ aux u
- | aux (Abs (s, T, t)) = Abs (s, T, aux t)
- | aux (Var ((s, i), T)) =
- Free (sledgehammer_weak_prefix ^ s ^ "_" ^ string_of_int i, T)
- | aux t = t
- in t |> exists_subterm is_Var t ? aux end
-
-(* making fact and conjecture formulas *)
-fun make_formula ctxt format type_sys eq_as_iff presimp name loc kind t =
- let
- val thy = Proof_Context.theory_of ctxt
- val t = t |> Envir.beta_eta_contract
- |> transform_elim_prop
- |> Object_Logic.atomize_term thy
- val need_trueprop = (fastype_of t = @{typ bool})
- val t = t |> need_trueprop ? HOLogic.mk_Trueprop
- |> Raw_Simplifier.rewrite_term thy
- (Meson.unfold_set_const_simps ctxt) []
- |> extensionalize_term ctxt
- |> presimp ? presimplify_term ctxt
- |> perhaps (try (HOLogic.dest_Trueprop))
- |> introduce_combinators_in_term ctxt kind
- |> kind <> Axiom ? freeze_term
- val (combformula, atomic_types) =
- combformula_from_prop thy format type_sys eq_as_iff t []
- in
- {name = name, locality = loc, kind = kind, combformula = combformula,
- atomic_types = atomic_types}
- end
-
-fun make_fact ctxt format type_sys keep_trivial eq_as_iff presimp
- ((name, loc), t) =
- case (keep_trivial,
- make_formula ctxt format type_sys eq_as_iff presimp name loc Axiom t) of
- (false, formula as {combformula = AAtom (CombConst ((s, _), _, _)), ...}) =>
- if s = tptp_true then NONE else SOME formula
- | (_, formula) => SOME formula
-
-fun make_conjecture ctxt format prem_kind type_sys ts =
- let val last = length ts - 1 in
- map2 (fn j => fn t =>
- let
- val (kind, maybe_negate) =
- if j = last then
- (Conjecture, I)
- else
- (prem_kind,
- if prem_kind = Conjecture then update_combformula mk_anot
- else I)
- in
- t |> make_formula ctxt format type_sys true true
- (string_of_int j) General kind
- |> maybe_negate
- end)
- (0 upto last) ts
- end
-
-(** Finite and infinite type inference **)
-
-fun deep_freeze_atyp (TVar (_, S)) = TFree ("v", S)
- | deep_freeze_atyp T = T
-val deep_freeze_type = map_atyps deep_freeze_atyp
-
-(* Finite types such as "unit", "bool", "bool * bool", and "bool => bool" are
- dangerous because their "exhaust" properties can easily lead to unsound ATP
- proofs. On the other hand, all HOL infinite types can be given the same
- models in first-order logic (via Löwenheim-Skolem). *)
-
-fun should_encode_type ctxt (nonmono_Ts as _ :: _) _ T =
- exists (curry (type_instance ctxt) (deep_freeze_type T)) nonmono_Ts
- | should_encode_type _ _ All_Types _ = true
- | should_encode_type ctxt _ Finite_Types T = is_type_surely_finite ctxt T
- | should_encode_type _ _ _ _ = false
-
-fun should_predicate_on_type ctxt nonmono_Ts (Preds (_, level, heaviness))
- should_predicate_on_var T =
- (heaviness = Heavy orelse should_predicate_on_var ()) andalso
- should_encode_type ctxt nonmono_Ts level T
- | should_predicate_on_type _ _ _ _ _ = false
-
-fun is_var_or_bound_var (CombConst ((s, _), _, _)) =
- String.isPrefix bound_var_prefix s
- | is_var_or_bound_var (CombVar _) = true
- | is_var_or_bound_var _ = false
-
-datatype tag_site = Top_Level | Eq_Arg | Elsewhere
-
-fun should_tag_with_type _ _ _ Top_Level _ _ = false
- | should_tag_with_type ctxt nonmono_Ts (Tags (_, level, heaviness)) site u T =
- (case heaviness of
- Heavy => should_encode_type ctxt nonmono_Ts level T
- | Light =>
- case (site, is_var_or_bound_var u) of
- (Eq_Arg, true) => should_encode_type ctxt nonmono_Ts level T
- | _ => false)
- | should_tag_with_type _ _ _ _ _ _ = false
-
-fun homogenized_type ctxt nonmono_Ts level =
- let
- val should_encode = should_encode_type ctxt nonmono_Ts level
- fun homo 0 T = if should_encode T then T else homo_infinite_type
- | homo ary (Type (@{type_name fun}, [T1, T2])) =
- homo 0 T1 --> homo (ary - 1) T2
- | homo _ _ = raise Fail "expected function type"
- in homo end
-
-(** "hBOOL" and "hAPP" **)
-
-type sym_info =
- {pred_sym : bool, min_ary : int, max_ary : int, types : typ list}
-
-fun add_combterm_syms_to_table ctxt explicit_apply =
- let
- fun consider_var_arity const_T var_T max_ary =
- let
- fun iter ary T =
- if ary = max_ary orelse type_instance ctxt (var_T, T) then ary
- else iter (ary + 1) (range_type T)
- in iter 0 const_T end
- fun add top_level tm (accum as (ho_var_Ts, sym_tab)) =
- let val (head, args) = strip_combterm_comb tm in
- (case head of
- CombConst ((s, _), T, _) =>
- if String.isPrefix bound_var_prefix s then
- if explicit_apply = NONE andalso can dest_funT T then
- let
- fun repair_min_arity {pred_sym, min_ary, max_ary, types} =
- {pred_sym = pred_sym,
- min_ary =
- fold (fn T' => consider_var_arity T' T) types min_ary,
- max_ary = max_ary, types = types}
- val ho_var_Ts' = ho_var_Ts |> insert_type ctxt I T
- in
- if pointer_eq (ho_var_Ts', ho_var_Ts) then accum
- else (ho_var_Ts', Symtab.map (K repair_min_arity) sym_tab)
- end
- else
- accum
- else
- let
- val ary = length args
- in
- (ho_var_Ts,
- case Symtab.lookup sym_tab s of
- SOME {pred_sym, min_ary, max_ary, types} =>
- let
- val types' = types |> insert_type ctxt I T
- val min_ary =
- if is_some explicit_apply orelse
- pointer_eq (types', types) then
- min_ary
- else
- fold (consider_var_arity T) ho_var_Ts min_ary
- in
- Symtab.update (s, {pred_sym = pred_sym andalso top_level,
- min_ary = Int.min (ary, min_ary),
- max_ary = Int.max (ary, max_ary),
- types = types'})
- sym_tab
- end
- | NONE =>
- let
- val min_ary =
- case explicit_apply of
- SOME true => 0
- | SOME false => ary
- | NONE => fold (consider_var_arity T) ho_var_Ts ary
- in
- Symtab.update_new (s, {pred_sym = top_level,
- min_ary = min_ary, max_ary = ary,
- types = [T]})
- sym_tab
- end)
- end
- | _ => accum)
- |> fold (add false) args
- end
- in add true end
-fun add_fact_syms_to_table ctxt explicit_apply =
- fact_lift (formula_fold NONE
- (K (add_combterm_syms_to_table ctxt explicit_apply)))
-
-val default_sym_table_entries : (string * sym_info) list =
- [(tptp_equal, {pred_sym = true, min_ary = 2, max_ary = 2, types = []}),
- (tptp_old_equal, {pred_sym = true, min_ary = 2, max_ary = 2, types = []}),
- (make_fixed_const predicator_name,
- {pred_sym = true, min_ary = 1, max_ary = 1, types = []})] @
- ([tptp_false, tptp_true]
- |> map (rpair {pred_sym = true, min_ary = 0, max_ary = 0, types = []}))
-
-fun sym_table_for_facts ctxt explicit_apply facts =
- Symtab.empty
- |> fold Symtab.default default_sym_table_entries
- |> pair [] |> fold (add_fact_syms_to_table ctxt explicit_apply) facts |> snd
-
-fun min_arity_of sym_tab s =
- case Symtab.lookup sym_tab s of
- SOME ({min_ary, ...} : sym_info) => min_ary
- | NONE =>
- case strip_prefix_and_unascii const_prefix s of
- SOME s =>
- let val s = s |> unmangled_const_name |> invert_const in
- if s = predicator_name then 1
- else if s = app_op_name then 2
- else if s = type_pred_name then 1
- else 0
- end
- | NONE => 0
-
-(* True if the constant ever appears outside of the top-level position in
- literals, or if it appears with different arities (e.g., because of different
- type instantiations). If false, the constant always receives all of its
- arguments and is used as a predicate. *)
-fun is_pred_sym sym_tab s =
- case Symtab.lookup sym_tab s of
- SOME ({pred_sym, min_ary, max_ary, ...} : sym_info) =>
- pred_sym andalso min_ary = max_ary
- | NONE => false
-
-val predicator_combconst =
- CombConst (`make_fixed_const predicator_name, @{typ "bool => bool"}, [])
-fun predicator tm = CombApp (predicator_combconst, tm)
-
-fun introduce_predicators_in_combterm sym_tab tm =
- case strip_combterm_comb tm of
- (CombConst ((s, _), _, _), _) =>
- if is_pred_sym sym_tab s then tm else predicator tm
- | _ => predicator tm
-
-fun list_app head args = fold (curry (CombApp o swap)) args head
-
-fun explicit_app arg head =
- let
- val head_T = combtyp_of head
- val (arg_T, res_T) = dest_funT head_T
- val explicit_app =
- CombConst (`make_fixed_const app_op_name, head_T --> head_T,
- [arg_T, res_T])
- in list_app explicit_app [head, arg] end
-fun list_explicit_app head args = fold explicit_app args head
-
-fun introduce_explicit_apps_in_combterm sym_tab =
- let
- fun aux tm =
- case strip_combterm_comb tm of
- (head as CombConst ((s, _), _, _), args) =>
- args |> map aux
- |> chop (min_arity_of sym_tab s)
- |>> list_app head
- |-> list_explicit_app
- | (head, args) => list_explicit_app head (map aux args)
- in aux end
-
-fun chop_fun 0 T = ([], T)
- | chop_fun n (Type (@{type_name fun}, [dom_T, ran_T])) =
- chop_fun (n - 1) ran_T |>> cons dom_T
- | chop_fun _ _ = raise Fail "unexpected non-function"
-
-fun filter_type_args _ _ _ [] = []
- | filter_type_args thy s arity T_args =
- let
- (* will throw "TYPE" for pseudo-constants *)
- val U = if s = app_op_name then
- @{typ "('a => 'b) => 'a => 'b"} |> Logic.varifyT_global
- else
- s |> Sign.the_const_type thy
- in
- case Term.add_tvarsT (U |> chop_fun arity |> snd) [] of
- [] => []
- | res_U_vars =>
- let val U_args = (s, U) |> Sign.const_typargs thy in
- U_args ~~ T_args
- |> map_filter (fn (U, T) =>
- if member (op =) res_U_vars (dest_TVar U) then
- SOME T
- else
- NONE)
- end
- end
- handle TYPE _ => T_args
-
-fun enforce_type_arg_policy_in_combterm ctxt nonmono_Ts type_sys =
- let
- val thy = Proof_Context.theory_of ctxt
- fun aux arity (CombApp (tm1, tm2)) =
- CombApp (aux (arity + 1) tm1, aux 0 tm2)
- | aux arity (CombConst (name as (s, _), T, T_args)) =
- let
- val level = level_of_type_sys type_sys
- val (T, T_args) =
- (* Aggressively merge most "hAPPs" if the type system is unsound
- anyway, by distinguishing overloads only on the homogenized
- result type. Don't do it for lightweight type systems, though,
- since it leads to too many unsound proofs. *)
- if s = const_prefix ^ app_op_name andalso
- length T_args = 2 andalso
- not (is_type_sys_virtually_sound type_sys) andalso
- heaviness_of_type_sys type_sys = Heavy then
- T_args |> map (homogenized_type ctxt nonmono_Ts level 0)
- |> (fn Ts => let val T = hd Ts --> nth Ts 1 in
- (T --> T, tl Ts)
- end)
- else
- (T, T_args)
- in
- (case strip_prefix_and_unascii const_prefix s of
- NONE => (name, T_args)
- | SOME s'' =>
- let
- val s'' = invert_const s''
- fun filtered_T_args false = T_args
- | filtered_T_args true = filter_type_args thy s'' arity T_args
- in
- case type_arg_policy type_sys s'' of
- Explicit_Type_Args drop_args =>
- (name, filtered_T_args drop_args)
- | Mangled_Type_Args drop_args =>
- (mangled_const_name (filtered_T_args drop_args) name, [])
- | No_Type_Args => (name, [])
- end)
- |> (fn (name, T_args) => CombConst (name, T, T_args))
- end
- | aux _ tm = tm
- in aux 0 end
-
-fun repair_combterm ctxt format nonmono_Ts type_sys sym_tab =
- not (is_setting_higher_order format type_sys)
- ? (introduce_explicit_apps_in_combterm sym_tab
- #> introduce_predicators_in_combterm sym_tab)
- #> enforce_type_arg_policy_in_combterm ctxt nonmono_Ts type_sys
-fun repair_fact ctxt format nonmono_Ts type_sys sym_tab =
- update_combformula (formula_map
- (repair_combterm ctxt format nonmono_Ts type_sys sym_tab))
-
-(** Helper facts **)
-
-fun ti_ti_helper_fact () =
- let
- fun var s = ATerm (`I s, [])
- fun tag tm = ATerm (`make_fixed_const type_tag_name, [var "X", tm])
- in
- Formula (helper_prefix ^ "ti_ti", Axiom,
- AAtom (ATerm (`I tptp_equal, [tag (tag (var "Y")), tag (var "Y")]))
- |> close_formula_universally, simp_info, NONE)
- end
-
-fun helper_facts_for_sym ctxt format type_sys (s, {types, ...} : sym_info) =
- case strip_prefix_and_unascii const_prefix s of
- SOME mangled_s =>
- let
- val thy = Proof_Context.theory_of ctxt
- val unmangled_s = mangled_s |> unmangled_const_name
- fun dub_and_inst c needs_fairly_sound (th, j) =
- ((c ^ "_" ^ string_of_int j ^
- (if needs_fairly_sound then typed_helper_suffix
- else untyped_helper_suffix),
- General),
- let val t = th |> prop_of in
- t |> ((case general_type_arg_policy type_sys of
- Mangled_Type_Args _ => true
- | _ => false) andalso
- not (null (Term.hidden_polymorphism t)))
- ? (case types of
- [T] => specialize_type thy (invert_const unmangled_s, T)
- | _ => I)
- end)
- fun make_facts eq_as_iff =
- map_filter (make_fact ctxt format type_sys false eq_as_iff false)
- val fairly_sound = is_type_sys_fairly_sound type_sys
- in
- metis_helpers
- |> maps (fn (metis_s, (needs_fairly_sound, ths)) =>
- if metis_s <> unmangled_s orelse
- (needs_fairly_sound andalso not fairly_sound) then
- []
- else
- ths ~~ (1 upto length ths)
- |> map (dub_and_inst mangled_s needs_fairly_sound)
- |> make_facts (not needs_fairly_sound))
- end
- | NONE => []
-fun helper_facts_for_sym_table ctxt format type_sys sym_tab =
- Symtab.fold_rev (append o helper_facts_for_sym ctxt format type_sys) sym_tab
- []
-
-fun translate_atp_fact ctxt format type_sys keep_trivial =
- `(make_fact ctxt format type_sys keep_trivial true true o apsnd prop_of)
-
-fun translate_formulas ctxt format prem_kind type_sys hyp_ts concl_t
- rich_facts =
- let
- val thy = Proof_Context.theory_of ctxt
- val fact_ts = map (prop_of o snd o snd) rich_facts
- val (facts, fact_names) =
- rich_facts
- |> map_filter (fn (NONE, _) => NONE
- | (SOME fact, (name, _)) => SOME (fact, name))
- |> ListPair.unzip
- (* Remove existing facts from the conjecture, as this can dramatically
- boost an ATP's performance (for some reason). *)
- val hyp_ts = hyp_ts |> filter_out (member (op aconv) fact_ts)
- val goal_t = Logic.list_implies (hyp_ts, concl_t)
- val all_ts = goal_t :: fact_ts
- val subs = tfree_classes_of_terms all_ts
- val supers = tvar_classes_of_terms all_ts
- val tycons = type_consts_of_terms thy all_ts
- val conjs =
- hyp_ts @ [concl_t] |> make_conjecture ctxt format prem_kind type_sys
- val (supers', arity_clauses) =
- if level_of_type_sys type_sys = No_Types then ([], [])
- else make_arity_clauses thy tycons supers
- val class_rel_clauses = make_class_rel_clauses thy subs supers'
- in
- (fact_names |> map single, (conjs, facts, class_rel_clauses, arity_clauses))
- end
-
-fun fo_literal_from_type_literal (TyLitVar (class, name)) =
- (true, ATerm (class, [ATerm (name, [])]))
- | fo_literal_from_type_literal (TyLitFree (class, name)) =
- (true, ATerm (class, [ATerm (name, [])]))
-
-fun formula_from_fo_literal (pos, t) = AAtom t |> not pos ? mk_anot
-
-fun type_pred_combterm ctxt nonmono_Ts type_sys T tm =
- CombApp (CombConst (`make_fixed_const type_pred_name, T --> @{typ bool}, [T])
- |> enforce_type_arg_policy_in_combterm ctxt nonmono_Ts type_sys,
- tm)
-
-fun var_occurs_positively_naked_in_term _ (SOME false) _ accum = accum
- | var_occurs_positively_naked_in_term name _ (ATerm ((s, _), tms)) accum =
- accum orelse (is_tptp_equal s andalso member (op =) tms (ATerm (name, [])))
-fun is_var_nonmonotonic_in_formula _ _ (SOME false) _ = false
- | is_var_nonmonotonic_in_formula pos phi _ name =
- formula_fold pos (var_occurs_positively_naked_in_term name) phi false
-
-fun mk_const_aterm x T_args args =
- ATerm (x, map (fo_term_from_typ false) T_args @ args)
-
-fun tag_with_type ctxt format nonmono_Ts type_sys T tm =
- CombConst (`make_fixed_const type_tag_name, T --> T, [T])
- |> enforce_type_arg_policy_in_combterm ctxt nonmono_Ts type_sys
- |> term_from_combterm ctxt format nonmono_Ts type_sys Top_Level
- |> (fn ATerm (s, tms) => ATerm (s, tms @ [tm]))
-and term_from_combterm ctxt format nonmono_Ts type_sys =
- let
- fun aux site u =
- let
- val (head, args) = strip_combterm_comb u
- val (x as (s, _), T_args) =
- case head of
- CombConst (name, _, T_args) => (name, T_args)
- | CombVar (name, _) => (name, [])
- | CombApp _ => raise Fail "impossible \"CombApp\""
- val arg_site = if site = Top_Level andalso is_tptp_equal s then Eq_Arg
- else Elsewhere
- val t = mk_const_aterm x T_args (map (aux arg_site) args)
- val T = combtyp_of u
- in
- t |> (if should_tag_with_type ctxt nonmono_Ts type_sys site u T then
- tag_with_type ctxt format nonmono_Ts type_sys T
- else
- I)
- end
- in aux end
-and formula_from_combformula ctxt format nonmono_Ts type_sys
- should_predicate_on_var =
- let
- val higher_order = is_setting_higher_order format type_sys
- val do_term = term_from_combterm ctxt format nonmono_Ts type_sys Top_Level
- val do_bound_type =
- case type_sys of
- Simple_Types level =>
- homogenized_type ctxt nonmono_Ts level 0
- #> mangled_type higher_order false 0 #> SOME
- | _ => K NONE
- fun do_out_of_bound_type pos phi universal (name, T) =
- if should_predicate_on_type ctxt nonmono_Ts type_sys
- (fn () => should_predicate_on_var pos phi universal name) T then
- CombVar (name, T)
- |> type_pred_combterm ctxt nonmono_Ts type_sys T
- |> do_term |> AAtom |> SOME
- else
- NONE
- fun do_formula pos (AQuant (q, xs, phi)) =
- let
- val phi = phi |> do_formula pos
- val universal = Option.map (q = AExists ? not) pos
- in
- AQuant (q, xs |> map (apsnd (fn NONE => NONE
- | SOME T => do_bound_type T)),
- (if q = AForall then mk_ahorn else fold_rev (mk_aconn AAnd))
- (map_filter
- (fn (_, NONE) => NONE
- | (s, SOME T) =>
- do_out_of_bound_type pos phi universal (s, T))
- xs)
- phi)
- end
- | do_formula pos (AConn conn) = aconn_map pos do_formula conn
- | do_formula _ (AAtom tm) = AAtom (do_term tm)
- in do_formula o SOME end
-
-fun bound_atomic_types format type_sys Ts =
- mk_ahorn (map (formula_from_fo_literal o fo_literal_from_type_literal)
- (atp_type_literals_for_types format type_sys Axiom Ts))
-
-fun formula_for_fact ctxt format nonmono_Ts type_sys
- ({combformula, atomic_types, ...} : translated_formula) =
- combformula
- |> close_combformula_universally
- |> formula_from_combformula ctxt format nonmono_Ts type_sys
- is_var_nonmonotonic_in_formula true
- |> bound_atomic_types format type_sys atomic_types
- |> close_formula_universally
-
-(* Each fact is given a unique fact number to avoid name clashes (e.g., because
- of monomorphization). The TPTP explicitly forbids name clashes, and some of
- the remote provers might care. *)
-fun formula_line_for_fact ctxt format prefix nonmono_Ts type_sys
- (j, formula as {name, locality, kind, ...}) =
- Formula (prefix ^ (if polymorphism_of_type_sys type_sys = Polymorphic then ""
- else string_of_int j ^ "_") ^
- ascii_of name,
- kind, formula_for_fact ctxt format nonmono_Ts type_sys formula, NONE,
- case locality of
- Intro => intro_info
- | Elim => elim_info
- | Simp => simp_info
- | _ => NONE)
-
-fun formula_line_for_class_rel_clause
- (ClassRelClause {name, subclass, superclass, ...}) =
- let val ty_arg = ATerm (`I "T", []) in
- Formula (class_rel_clause_prefix ^ ascii_of name, Axiom,
- AConn (AImplies, [AAtom (ATerm (subclass, [ty_arg])),
- AAtom (ATerm (superclass, [ty_arg]))])
- |> close_formula_universally, intro_info, NONE)
- end
-
-fun fo_literal_from_arity_literal (TConsLit (c, t, args)) =
- (true, ATerm (c, [ATerm (t, map (fn arg => ATerm (arg, [])) args)]))
- | fo_literal_from_arity_literal (TVarLit (c, sort)) =
- (false, ATerm (c, [ATerm (sort, [])]))
-
-fun formula_line_for_arity_clause
- (ArityClause {name, prem_lits, concl_lits, ...}) =
- Formula (arity_clause_prefix ^ ascii_of name, Axiom,
- mk_ahorn (map (formula_from_fo_literal o apfst not
- o fo_literal_from_arity_literal) prem_lits)
- (formula_from_fo_literal
- (fo_literal_from_arity_literal concl_lits))
- |> close_formula_universally, intro_info, NONE)
-
-fun formula_line_for_conjecture ctxt format nonmono_Ts type_sys
- ({name, kind, combformula, ...} : translated_formula) =
- Formula (conjecture_prefix ^ name, kind,
- formula_from_combformula ctxt format nonmono_Ts type_sys
- is_var_nonmonotonic_in_formula false
- (close_combformula_universally combformula)
- |> close_formula_universally, NONE, NONE)
-
-fun free_type_literals format type_sys
- ({atomic_types, ...} : translated_formula) =
- atomic_types |> atp_type_literals_for_types format type_sys Conjecture
- |> map fo_literal_from_type_literal
-
-fun formula_line_for_free_type j lit =
- Formula (tfree_prefix ^ string_of_int j, Hypothesis,
- formula_from_fo_literal lit, NONE, NONE)
-fun formula_lines_for_free_types format type_sys facts =
- let
- val litss = map (free_type_literals format type_sys) facts
- val lits = fold (union (op =)) litss []
- in map2 formula_line_for_free_type (0 upto length lits - 1) lits end
-
-(** Symbol declarations **)
-
-fun should_declare_sym type_sys pred_sym s =
- is_tptp_user_symbol s andalso not (String.isPrefix bound_var_prefix s) andalso
- (case type_sys of
- Simple_Types _ => true
- | Tags (_, _, Light) => true
- | _ => not pred_sym)
-
-fun sym_decl_table_for_facts ctxt type_sys repaired_sym_tab (conjs, facts) =
- let
- fun add_combterm in_conj tm =
- let val (head, args) = strip_combterm_comb tm in
- (case head of
- CombConst ((s, s'), T, T_args) =>
- let val pred_sym = is_pred_sym repaired_sym_tab s in
- if should_declare_sym type_sys pred_sym s then
- Symtab.map_default (s, [])
- (insert_type ctxt #3 (s', T_args, T, pred_sym, length args,
- in_conj))
- else
- I
- end
- | _ => I)
- #> fold (add_combterm in_conj) args
- end
- fun add_fact in_conj =
- fact_lift (formula_fold NONE (K (add_combterm in_conj)))
- in
- Symtab.empty
- |> is_type_sys_fairly_sound type_sys
- ? (fold (add_fact true) conjs #> fold (add_fact false) facts)
- end
-
-(* These types witness that the type classes they belong to allow infinite
- models and hence that any types with these type classes is monotonic. *)
-val known_infinite_types = [@{typ nat}, @{typ int}, @{typ "nat => bool"}]
-
-(* This inference is described in section 2.3 of Claessen et al.'s "Sorting it
- out with monotonicity" paper presented at CADE 2011. *)
-fun add_combterm_nonmonotonic_types _ _ (SOME false) _ = I
- | add_combterm_nonmonotonic_types ctxt level _
- (CombApp (CombApp (CombConst ((s, _), Type (_, [T, _]), _), tm1), tm2)) =
- (is_tptp_equal s andalso exists is_var_or_bound_var [tm1, tm2] andalso
- (case level of
- Nonmonotonic_Types =>
- not (is_type_surely_infinite ctxt known_infinite_types T)
- | Finite_Types => is_type_surely_finite ctxt T
- | _ => true)) ? insert_type ctxt I (deep_freeze_type T)
- | add_combterm_nonmonotonic_types _ _ _ _ = I
-fun add_fact_nonmonotonic_types ctxt level ({kind, combformula, ...}
- : translated_formula) =
- formula_fold (SOME (kind <> Conjecture))
- (add_combterm_nonmonotonic_types ctxt level) combformula
-fun nonmonotonic_types_for_facts ctxt type_sys facts =
- let val level = level_of_type_sys type_sys in
- if level = Nonmonotonic_Types orelse level = Finite_Types then
- [] |> fold (add_fact_nonmonotonic_types ctxt level) facts
- (* We must add "bool" in case the helper "True_or_False" is added
- later. In addition, several places in the code rely on the list of
- nonmonotonic types not being empty. *)
- |> insert_type ctxt I @{typ bool}
- else
- []
- end
-
-fun decl_line_for_sym ctxt format nonmono_Ts type_sys s
- (s', T_args, T, pred_sym, ary, _) =
- let
- val (higher_order, T_arg_Ts, level) =
- case type_sys of
- Simple_Types level => (format = THF, [], level)
- | _ => (false, replicate (length T_args) homo_infinite_type, No_Types)
- in
- Decl (sym_decl_prefix ^ s, (s, s'),
- (T_arg_Ts ---> (T |> homogenized_type ctxt nonmono_Ts level ary))
- |> mangled_type higher_order pred_sym (length T_arg_Ts + ary))
- end
-
-fun is_polymorphic_type T = fold_atyps (fn TVar _ => K true | _ => I) T false
-
-fun formula_line_for_pred_sym_decl ctxt format conj_sym_kind nonmono_Ts type_sys
- n s j (s', T_args, T, _, ary, in_conj) =
- let
- val (kind, maybe_negate) =
- if in_conj then (conj_sym_kind, conj_sym_kind = Conjecture ? mk_anot)
- else (Axiom, I)
- val (arg_Ts, res_T) = chop_fun ary T
- val bound_names =
- 1 upto length arg_Ts |> map (`I o make_bound_var o string_of_int)
- val bounds =
- bound_names ~~ arg_Ts |> map (fn (name, T) => CombConst (name, T, []))
- val bound_Ts =
- arg_Ts |> map (fn T => if n > 1 orelse is_polymorphic_type T then SOME T
- else NONE)
- in
- Formula (sym_formula_prefix ^ s ^
- (if n > 1 then "_" ^ string_of_int j else ""), kind,
- CombConst ((s, s'), T, T_args)
- |> fold (curry (CombApp o swap)) bounds
- |> type_pred_combterm ctxt nonmono_Ts type_sys res_T
- |> AAtom |> mk_aquant AForall (bound_names ~~ bound_Ts)
- |> formula_from_combformula ctxt format nonmono_Ts type_sys
- (K (K (K (K true)))) true
- |> n > 1 ? bound_atomic_types format type_sys (atyps_of T)
- |> close_formula_universally
- |> maybe_negate,
- intro_info, NONE)
- end
-
-fun formula_lines_for_tag_sym_decl ctxt format conj_sym_kind nonmono_Ts type_sys
- n s (j, (s', T_args, T, pred_sym, ary, in_conj)) =
- let
- val ident_base =
- sym_formula_prefix ^ s ^ (if n > 1 then "_" ^ string_of_int j else "")
- val (kind, maybe_negate) =
- if in_conj then (conj_sym_kind, conj_sym_kind = Conjecture ? mk_anot)
- else (Axiom, I)
- val (arg_Ts, res_T) = chop_fun ary T
- val bound_names =
- 1 upto length arg_Ts |> map (`I o make_bound_var o string_of_int)
- val bounds = bound_names |> map (fn name => ATerm (name, []))
- val cst = mk_const_aterm (s, s') T_args
- val atomic_Ts = atyps_of T
- fun eq tms =
- (if pred_sym then AConn (AIff, map AAtom tms)
- else AAtom (ATerm (`I tptp_equal, tms)))
- |> bound_atomic_types format type_sys atomic_Ts
- |> close_formula_universally
- |> maybe_negate
- val should_encode = should_encode_type ctxt nonmono_Ts All_Types
- val tag_with = tag_with_type ctxt format nonmono_Ts type_sys
- val add_formula_for_res =
- if should_encode res_T then
- cons (Formula (ident_base ^ "_res", kind,
- eq [tag_with res_T (cst bounds), cst bounds],
- simp_info, NONE))
- else
- I
- fun add_formula_for_arg k =
- let val arg_T = nth arg_Ts k in
- if should_encode arg_T then
- case chop k bounds of
- (bounds1, bound :: bounds2) =>
- cons (Formula (ident_base ^ "_arg" ^ string_of_int (k + 1), kind,
- eq [cst (bounds1 @ tag_with arg_T bound :: bounds2),
- cst bounds],
- simp_info, NONE))
- | _ => raise Fail "expected nonempty tail"
- else
- I
- end
- in
- [] |> not pred_sym ? add_formula_for_res
- |> fold add_formula_for_arg (ary - 1 downto 0)
- end
-
-fun result_type_of_decl (_, _, T, _, ary, _) = chop_fun ary T |> snd
-
-fun problem_lines_for_sym_decls ctxt format conj_sym_kind nonmono_Ts type_sys
- (s, decls) =
- case type_sys of
- Simple_Types _ =>
- decls |> map (decl_line_for_sym ctxt format nonmono_Ts type_sys s)
- | Preds _ =>
- let
- val decls =
- case decls of
- decl :: (decls' as _ :: _) =>
- let val T = result_type_of_decl decl in
- if forall (curry (type_instance ctxt o swap) T
- o result_type_of_decl) decls' then
- [decl]
- else
- decls
- end
- | _ => decls
- val n = length decls
- val decls =
- decls
- |> filter (should_predicate_on_type ctxt nonmono_Ts type_sys (K true)
- o result_type_of_decl)
- in
- (0 upto length decls - 1, decls)
- |-> map2 (formula_line_for_pred_sym_decl ctxt format conj_sym_kind
- nonmono_Ts type_sys n s)
- end
- | Tags (_, _, heaviness) =>
- (case heaviness of
- Heavy => []
- | Light =>
- let val n = length decls in
- (0 upto n - 1 ~~ decls)
- |> maps (formula_lines_for_tag_sym_decl ctxt format conj_sym_kind
- nonmono_Ts type_sys n s)
- end)
-
-fun problem_lines_for_sym_decl_table ctxt format conj_sym_kind nonmono_Ts
- type_sys sym_decl_tab =
- sym_decl_tab
- |> Symtab.dest
- |> sort_wrt fst
- |> rpair []
- |-> fold_rev (append o problem_lines_for_sym_decls ctxt format conj_sym_kind
- nonmono_Ts type_sys)
-
-fun should_add_ti_ti_helper (Tags (Polymorphic, level, Heavy)) =
- level = Nonmonotonic_Types orelse level = Finite_Types
- | should_add_ti_ti_helper _ = false
-
-fun offset_of_heading_in_problem _ [] j = j
- | offset_of_heading_in_problem needle ((heading, lines) :: problem) j =
- if heading = needle then j
- else offset_of_heading_in_problem needle problem (j + length lines)
-
-val implicit_declsN = "Should-be-implicit typings"
-val explicit_declsN = "Explicit typings"
-val factsN = "Relevant facts"
-val class_relsN = "Class relationships"
-val aritiesN = "Arities"
-val helpersN = "Helper facts"
-val conjsN = "Conjectures"
-val free_typesN = "Type variables"
-
-fun prepare_atp_problem ctxt format conj_sym_kind prem_kind type_sys
- explicit_apply hyp_ts concl_t facts =
- let
- val (fact_names, (conjs, facts, class_rel_clauses, arity_clauses)) =
- translate_formulas ctxt format prem_kind type_sys hyp_ts concl_t facts
- val sym_tab = conjs @ facts |> sym_table_for_facts ctxt explicit_apply
- val nonmono_Ts = conjs @ facts |> nonmonotonic_types_for_facts ctxt type_sys
- val repair = repair_fact ctxt format nonmono_Ts type_sys sym_tab
- val (conjs, facts) = (conjs, facts) |> pairself (map repair)
- val repaired_sym_tab =
- conjs @ facts |> sym_table_for_facts ctxt (SOME false)
- val helpers =
- repaired_sym_tab |> helper_facts_for_sym_table ctxt format type_sys
- |> map repair
- val lavish_nonmono_Ts =
- if null nonmono_Ts orelse
- polymorphism_of_type_sys type_sys <> Polymorphic then
- nonmono_Ts
- else
- [TVar (("'a", 0), HOLogic.typeS)]
- val sym_decl_lines =
- (conjs, helpers @ facts)
- |> sym_decl_table_for_facts ctxt type_sys repaired_sym_tab
- |> problem_lines_for_sym_decl_table ctxt format conj_sym_kind
- lavish_nonmono_Ts type_sys
- val helper_lines =
- 0 upto length helpers - 1 ~~ helpers
- |> map (formula_line_for_fact ctxt format helper_prefix lavish_nonmono_Ts
- type_sys)
- |> (if should_add_ti_ti_helper type_sys then cons (ti_ti_helper_fact ())
- else I)
- (* Reordering these might confuse the proof reconstruction code or the SPASS
- FLOTTER hack. *)
- val problem =
- [(explicit_declsN, sym_decl_lines),
- (factsN,
- map (formula_line_for_fact ctxt format fact_prefix nonmono_Ts type_sys)
- (0 upto length facts - 1 ~~ facts)),
- (class_relsN, map formula_line_for_class_rel_clause class_rel_clauses),
- (aritiesN, map formula_line_for_arity_clause arity_clauses),
- (helpersN, helper_lines),
- (conjsN,
- map (formula_line_for_conjecture ctxt format nonmono_Ts type_sys)
- conjs),
- (free_typesN,
- formula_lines_for_free_types format type_sys (facts @ conjs))]
- val problem =
- problem
- |> (if format = CNF_UEQ then filter_cnf_ueq_problem else I)
- |> (if is_format_typed format then
- declare_undeclared_syms_in_atp_problem type_decl_prefix
- implicit_declsN
- else
- I)
- val (problem, pool) =
- problem |> nice_atp_problem (Config.get ctxt readable_names)
- val helpers_offset = offset_of_heading_in_problem helpersN problem 0
- val typed_helpers =
- map_filter (fn (j, {name, ...}) =>
- if String.isSuffix typed_helper_suffix name then SOME j
- else NONE)
- ((helpers_offset + 1 upto helpers_offset + length helpers)
- ~~ helpers)
- fun add_sym_arity (s, {min_ary, ...} : sym_info) =
- if min_ary > 0 then
- case strip_prefix_and_unascii const_prefix s of
- SOME s => Symtab.insert (op =) (s, min_ary)
- | NONE => I
- else
- I
- in
- (problem,
- case pool of SOME the_pool => snd the_pool | NONE => Symtab.empty,
- offset_of_heading_in_problem conjsN problem 0,
- offset_of_heading_in_problem factsN problem 0,
- fact_names |> Vector.fromList,
- typed_helpers,
- Symtab.empty |> Symtab.fold add_sym_arity sym_tab)
- end
-
-(* FUDGE *)
-val conj_weight = 0.0
-val hyp_weight = 0.1
-val fact_min_weight = 0.2
-val fact_max_weight = 1.0
-val type_info_default_weight = 0.8
-
-fun add_term_weights weight (ATerm (s, tms)) =
- is_tptp_user_symbol s ? Symtab.default (s, weight)
- #> fold (add_term_weights weight) tms
-fun add_problem_line_weights weight (Formula (_, _, phi, _, _)) =
- formula_fold NONE (K (add_term_weights weight)) phi
- | add_problem_line_weights _ _ = I
-
-fun add_conjectures_weights [] = I
- | add_conjectures_weights conjs =
- let val (hyps, conj) = split_last conjs in
- add_problem_line_weights conj_weight conj
- #> fold (add_problem_line_weights hyp_weight) hyps
- end
-
-fun add_facts_weights facts =
- let
- val num_facts = length facts
- fun weight_of j =
- fact_min_weight + (fact_max_weight - fact_min_weight) * Real.fromInt j
- / Real.fromInt num_facts
- in
- map weight_of (0 upto num_facts - 1) ~~ facts
- |> fold (uncurry add_problem_line_weights)
- end
-
-(* Weights are from 0.0 (most important) to 1.0 (least important). *)
-fun atp_problem_weights problem =
- let val get = these o AList.lookup (op =) problem in
- Symtab.empty
- |> add_conjectures_weights (get free_typesN @ get conjsN)
- |> add_facts_weights (get factsN)
- |> fold (fold (add_problem_line_weights type_info_default_weight) o get)
- [explicit_declsN, class_relsN, aritiesN]
- |> Symtab.dest
- |> sort (prod_ord Real.compare string_ord o pairself swap)
- end
-
-end;