--- a/src/HOL/Tools/ATP/atp_translate.ML Mon Jan 23 17:40:31 2012 +0100
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,2557 +0,0 @@
-(* Title: HOL/Tools/ATP/atp_translate.ML
- Author: Fabian Immler, TU Muenchen
- Author: Makarius
- Author: Jasmin Blanchette, TU Muenchen
-
-Translation of HOL to FOL for Metis and Sledgehammer.
-*)
-
-signature ATP_TRANSLATE =
-sig
- type ('a, 'b) ho_term = ('a, 'b) ATP_Problem.ho_term
- type connective = ATP_Problem.connective
- type ('a, 'b, 'c) formula = ('a, 'b, 'c) ATP_Problem.formula
- type atp_format = ATP_Problem.atp_format
- type formula_kind = ATP_Problem.formula_kind
- type 'a problem = 'a ATP_Problem.problem
-
- datatype locality =
- General | Helper | Induction | Intro | Elim | Simp | Local | Assum | Chained
-
- datatype polymorphism = Polymorphic | Raw_Monomorphic | Mangled_Monomorphic
- datatype strictness = Strict | Non_Strict
- datatype granularity = All_Vars | Positively_Naked_Vars | Ghost_Type_Arg_Vars
- datatype type_level =
- All_Types |
- Noninf_Nonmono_Types of strictness * granularity |
- Fin_Nonmono_Types of granularity |
- Const_Arg_Types |
- No_Types
- type type_enc
-
- val type_tag_idempotence : bool Config.T
- val type_tag_arguments : bool Config.T
- val no_lamsN : string
- val hide_lamsN : string
- val lam_liftingN : string
- val combinatorsN : string
- val hybrid_lamsN : string
- val keep_lamsN : string
- val schematic_var_prefix : string
- val fixed_var_prefix : string
- val tvar_prefix : string
- val tfree_prefix : string
- val const_prefix : string
- val type_const_prefix : string
- val class_prefix : string
- val lam_lifted_prefix : string
- val lam_lifted_mono_prefix : string
- val lam_lifted_poly_prefix : string
- val skolem_const_prefix : string
- val old_skolem_const_prefix : string
- val new_skolem_const_prefix : string
- val combinator_prefix : string
- val type_decl_prefix : string
- val sym_decl_prefix : string
- val guards_sym_formula_prefix : string
- val tags_sym_formula_prefix : string
- val fact_prefix : string
- val conjecture_prefix : string
- val helper_prefix : string
- val class_rel_clause_prefix : string
- val arity_clause_prefix : string
- val tfree_clause_prefix : string
- val lam_fact_prefix : string
- val typed_helper_suffix : string
- val untyped_helper_suffix : string
- val type_tag_idempotence_helper_name : string
- val predicator_name : string
- val app_op_name : string
- val type_guard_name : string
- val type_tag_name : string
- val simple_type_prefix : string
- val prefixed_predicator_name : string
- val prefixed_app_op_name : string
- val prefixed_type_tag_name : string
- val ascii_of : string -> string
- val unascii_of : string -> string
- val unprefix_and_unascii : string -> string -> string option
- val proxy_table : (string * (string * (thm * (string * string)))) list
- val proxify_const : string -> (string * string) option
- val invert_const : string -> string
- val unproxify_const : string -> string
- val new_skolem_var_name_from_const : string -> string
- val atp_irrelevant_consts : string list
- val atp_schematic_consts_of : term -> typ list Symtab.table
- val is_type_enc_higher_order : type_enc -> bool
- val polymorphism_of_type_enc : type_enc -> polymorphism
- val level_of_type_enc : type_enc -> type_level
- val is_type_enc_quasi_sound : type_enc -> bool
- val is_type_enc_fairly_sound : type_enc -> bool
- val type_enc_from_string : strictness -> string -> type_enc
- val adjust_type_enc : atp_format -> type_enc -> type_enc
- val mk_aconns :
- connective -> ('a, 'b, 'c) formula list -> ('a, 'b, 'c) formula
- val unmangled_const : string -> string * (string, 'b) ho_term list
- val unmangled_const_name : string -> string
- val helper_table : ((string * bool) * thm list) list
- val trans_lams_from_string :
- Proof.context -> type_enc -> string -> term list -> term list * term list
- val factsN : string
- val prepare_atp_problem :
- Proof.context -> atp_format -> formula_kind -> formula_kind -> type_enc
- -> bool -> string -> bool -> bool -> term list -> term
- -> ((string * locality) * term) list
- -> string problem * string Symtab.table * (string * locality) list vector
- * (string * term) list * int Symtab.table
- val atp_problem_weights : string problem -> (string * real) list
-end;
-
-structure ATP_Translate : ATP_TRANSLATE =
-struct
-
-open ATP_Util
-open ATP_Problem
-
-type name = string * string
-
-val type_tag_idempotence =
- Attrib.setup_config_bool @{binding atp_type_tag_idempotence} (K false)
-val type_tag_arguments =
- Attrib.setup_config_bool @{binding atp_type_tag_arguments} (K false)
-
-val no_lamsN = "no_lams" (* used internally; undocumented *)
-val hide_lamsN = "hide_lams"
-val lam_liftingN = "lam_lifting"
-val combinatorsN = "combinators"
-val hybrid_lamsN = "hybrid_lams"
-val keep_lamsN = "keep_lams"
-
-(* It's still unclear whether all TFF1 implementations will support type
- signatures such as "!>[A : $tType] : $o", with ghost type variables. *)
-val avoid_first_order_ghost_type_vars = false
-
-val bound_var_prefix = "B_"
-val all_bound_var_prefix = "BA_"
-val exist_bound_var_prefix = "BE_"
-val schematic_var_prefix = "V_"
-val fixed_var_prefix = "v_"
-val tvar_prefix = "T_"
-val tfree_prefix = "t_"
-val const_prefix = "c_"
-val type_const_prefix = "tc_"
-val simple_type_prefix = "s_"
-val class_prefix = "cl_"
-
-(* Freshness almost guaranteed! *)
-val atp_weak_prefix = "ATP:"
-
-val lam_lifted_prefix = atp_weak_prefix ^ "Lam"
-val lam_lifted_mono_prefix = lam_lifted_prefix ^ "m"
-val lam_lifted_poly_prefix = lam_lifted_prefix ^ "p"
-
-val skolem_const_prefix = "ATP" ^ Long_Name.separator ^ "Sko"
-val old_skolem_const_prefix = skolem_const_prefix ^ "o"
-val new_skolem_const_prefix = skolem_const_prefix ^ "n"
-
-val combinator_prefix = "COMB"
-
-val type_decl_prefix = "ty_"
-val sym_decl_prefix = "sy_"
-val guards_sym_formula_prefix = "gsy_"
-val tags_sym_formula_prefix = "tsy_"
-val fact_prefix = "fact_"
-val conjecture_prefix = "conj_"
-val helper_prefix = "help_"
-val class_rel_clause_prefix = "clar_"
-val arity_clause_prefix = "arity_"
-val tfree_clause_prefix = "tfree_"
-
-val lam_fact_prefix = "ATP.lambda_"
-val typed_helper_suffix = "_T"
-val untyped_helper_suffix = "_U"
-val type_tag_idempotence_helper_name = helper_prefix ^ "ti_idem"
-
-val predicator_name = "pp"
-val app_op_name = "aa"
-val type_guard_name = "gg"
-val type_tag_name = "tt"
-
-val prefixed_predicator_name = const_prefix ^ predicator_name
-val prefixed_app_op_name = const_prefix ^ app_op_name
-val prefixed_type_tag_name = const_prefix ^ type_tag_name
-
-(*Escaping of special characters.
- Alphanumeric characters are left unchanged.
- The character _ goes to __
- Characters in the range ASCII space to / go to _A to _P, respectively.
- Other characters go to _nnn where nnn is the decimal ASCII code.*)
-val upper_a_minus_space = Char.ord #"A" - Char.ord #" "
-
-fun stringN_of_int 0 _ = ""
- | stringN_of_int k n =
- stringN_of_int (k - 1) (n div 10) ^ string_of_int (n mod 10)
-
-fun ascii_of_char c =
- if Char.isAlphaNum c then
- String.str c
- else if c = #"_" then
- "__"
- else if #" " <= c andalso c <= #"/" then
- "_" ^ String.str (Char.chr (Char.ord c + upper_a_minus_space))
- else
- (* fixed width, in case more digits follow *)
- "_" ^ stringN_of_int 3 (Char.ord c)
-
-val ascii_of = String.translate ascii_of_char
-
-(** Remove ASCII armoring from names in proof files **)
-
-(* We don't raise error exceptions because this code can run inside a worker
- thread. Also, the errors are impossible. *)
-val unascii_of =
- let
- fun un rcs [] = String.implode(rev rcs)
- | un rcs [#"_"] = un (#"_" :: rcs) [] (* ERROR *)
- (* Three types of _ escapes: __, _A to _P, _nnn *)
- | un rcs (#"_" :: #"_" :: cs) = un (#"_" :: rcs) cs
- | un rcs (#"_" :: c :: cs) =
- if #"A" <= c andalso c<= #"P" then
- (* translation of #" " to #"/" *)
- un (Char.chr (Char.ord c - upper_a_minus_space) :: rcs) cs
- else
- let val digits = List.take (c :: cs, 3) handle General.Subscript => [] in
- case Int.fromString (String.implode digits) of
- SOME n => un (Char.chr n :: rcs) (List.drop (cs, 2))
- | NONE => un (c :: #"_" :: rcs) cs (* ERROR *)
- end
- | un rcs (c :: cs) = un (c :: rcs) cs
- in un [] o String.explode end
-
-(* If string s has the prefix s1, return the result of deleting it,
- un-ASCII'd. *)
-fun unprefix_and_unascii s1 s =
- if String.isPrefix s1 s then
- SOME (unascii_of (String.extract (s, size s1, NONE)))
- else
- NONE
-
-val proxy_table =
- [("c_False", (@{const_name False}, (@{thm fFalse_def},
- ("fFalse", @{const_name ATP.fFalse})))),
- ("c_True", (@{const_name True}, (@{thm fTrue_def},
- ("fTrue", @{const_name ATP.fTrue})))),
- ("c_Not", (@{const_name Not}, (@{thm fNot_def},
- ("fNot", @{const_name ATP.fNot})))),
- ("c_conj", (@{const_name conj}, (@{thm fconj_def},
- ("fconj", @{const_name ATP.fconj})))),
- ("c_disj", (@{const_name disj}, (@{thm fdisj_def},
- ("fdisj", @{const_name ATP.fdisj})))),
- ("c_implies", (@{const_name implies}, (@{thm fimplies_def},
- ("fimplies", @{const_name ATP.fimplies})))),
- ("equal", (@{const_name HOL.eq}, (@{thm fequal_def},
- ("fequal", @{const_name ATP.fequal})))),
- ("c_All", (@{const_name All}, (@{thm fAll_def},
- ("fAll", @{const_name ATP.fAll})))),
- ("c_Ex", (@{const_name Ex}, (@{thm fEx_def},
- ("fEx", @{const_name ATP.fEx}))))]
-
-val proxify_const = AList.lookup (op =) proxy_table #> Option.map (snd o snd)
-
-(* Readable names for the more common symbolic functions. Do not mess with the
- table unless you know what you are doing. *)
-val const_trans_table =
- [(@{type_name Product_Type.prod}, "prod"),
- (@{type_name Sum_Type.sum}, "sum"),
- (@{const_name False}, "False"),
- (@{const_name True}, "True"),
- (@{const_name Not}, "Not"),
- (@{const_name conj}, "conj"),
- (@{const_name disj}, "disj"),
- (@{const_name implies}, "implies"),
- (@{const_name HOL.eq}, "equal"),
- (@{const_name All}, "All"),
- (@{const_name Ex}, "Ex"),
- (@{const_name If}, "If"),
- (@{const_name Set.member}, "member"),
- (@{const_name Meson.COMBI}, combinator_prefix ^ "I"),
- (@{const_name Meson.COMBK}, combinator_prefix ^ "K"),
- (@{const_name Meson.COMBB}, combinator_prefix ^ "B"),
- (@{const_name Meson.COMBC}, combinator_prefix ^ "C"),
- (@{const_name Meson.COMBS}, combinator_prefix ^ "S")]
- |> Symtab.make
- |> fold (Symtab.update o swap o snd o snd o snd) proxy_table
-
-(* Invert the table of translations between Isabelle and ATPs. *)
-val const_trans_table_inv =
- const_trans_table |> Symtab.dest |> map swap |> Symtab.make
-val const_trans_table_unprox =
- Symtab.empty
- |> fold (fn (_, (isa, (_, (_, atp)))) => Symtab.update (atp, isa)) proxy_table
-
-val invert_const = perhaps (Symtab.lookup const_trans_table_inv)
-val unproxify_const = perhaps (Symtab.lookup const_trans_table_unprox)
-
-fun lookup_const c =
- case Symtab.lookup const_trans_table c of
- SOME c' => c'
- | NONE => ascii_of c
-
-fun ascii_of_indexname (v, 0) = ascii_of v
- | ascii_of_indexname (v, i) = ascii_of v ^ "_" ^ string_of_int i
-
-fun make_bound_var x = bound_var_prefix ^ ascii_of x
-fun make_all_bound_var x = all_bound_var_prefix ^ ascii_of x
-fun make_exist_bound_var x = exist_bound_var_prefix ^ ascii_of x
-fun make_schematic_var v = schematic_var_prefix ^ ascii_of_indexname v
-fun make_fixed_var x = fixed_var_prefix ^ ascii_of x
-
-fun make_schematic_type_var (x, i) =
- tvar_prefix ^ (ascii_of_indexname (unprefix "'" x, i))
-fun make_fixed_type_var x = tfree_prefix ^ (ascii_of (unprefix "'" x))
-
-(* "HOL.eq" and choice are mapped to the ATP's equivalents *)
-local
- val choice_const = (fst o dest_Const o HOLogic.choice_const) Term.dummyT
- fun default c = const_prefix ^ lookup_const c
-in
- fun make_fixed_const _ @{const_name HOL.eq} = tptp_old_equal
- | make_fixed_const (SOME (THF (_, _, THF_With_Choice))) c =
- if c = choice_const then tptp_choice else default c
- | make_fixed_const _ c = default c
-end
-
-fun make_fixed_type_const c = type_const_prefix ^ lookup_const c
-
-fun make_type_class clas = class_prefix ^ ascii_of clas
-
-fun new_skolem_var_name_from_const s =
- let val ss = s |> space_explode Long_Name.separator in
- nth ss (length ss - 2)
- end
-
-(* These are either simplified away by "Meson.presimplify" (most of the time) or
- handled specially via "fFalse", "fTrue", ..., "fequal". *)
-val atp_irrelevant_consts =
- [@{const_name False}, @{const_name True}, @{const_name Not},
- @{const_name conj}, @{const_name disj}, @{const_name implies},
- @{const_name HOL.eq}, @{const_name If}, @{const_name Let}]
-
-val atp_monomorph_bad_consts =
- atp_irrelevant_consts @
- (* These are ignored anyway by the relevance filter (unless they appear in
- higher-order places) but not by the monomorphizer. *)
- [@{const_name all}, @{const_name "==>"}, @{const_name "=="},
- @{const_name Trueprop}, @{const_name All}, @{const_name Ex},
- @{const_name Ex1}, @{const_name Ball}, @{const_name Bex}]
-
-fun add_schematic_const (x as (_, T)) =
- Monomorph.typ_has_tvars T ? Symtab.insert_list (op =) x
-val add_schematic_consts_of =
- Term.fold_aterms (fn Const (x as (s, _)) =>
- not (member (op =) atp_monomorph_bad_consts s)
- ? add_schematic_const x
- | _ => I)
-fun atp_schematic_consts_of t = add_schematic_consts_of t Symtab.empty
-
-(** Definitions and functions for FOL clauses and formulas for TPTP **)
-
-(** Isabelle arities **)
-
-type arity_atom = name * name * name list
-
-val type_class = the_single @{sort type}
-
-type arity_clause =
- {name : string,
- prem_atoms : arity_atom list,
- concl_atom : arity_atom}
-
-fun add_prem_atom tvar =
- fold (fn s => s <> type_class ? cons (`make_type_class s, `I tvar, []))
-
-(* Arity of type constructor "tcon :: (arg1, ..., argN) res" *)
-fun make_axiom_arity_clause (tcons, name, (cls, args)) =
- let
- val tvars = map (prefix tvar_prefix o string_of_int) (1 upto length args)
- val tvars_srts = ListPair.zip (tvars, args)
- in
- {name = name,
- prem_atoms = [] |> fold (uncurry add_prem_atom) tvars_srts,
- concl_atom = (`make_type_class cls, `make_fixed_type_const tcons,
- tvars ~~ tvars)}
- end
-
-fun arity_clause _ _ (_, []) = []
- | arity_clause seen n (tcons, ("HOL.type", _) :: ars) = (* ignore *)
- arity_clause seen n (tcons, ars)
- | arity_clause seen n (tcons, (ar as (class, _)) :: ars) =
- if member (op =) seen class then
- (* multiple arities for the same (tycon, class) pair *)
- make_axiom_arity_clause (tcons,
- lookup_const tcons ^ "___" ^ ascii_of class ^ "_" ^ string_of_int n,
- ar) ::
- arity_clause seen (n + 1) (tcons, ars)
- else
- make_axiom_arity_clause (tcons, lookup_const tcons ^ "___" ^
- ascii_of class, ar) ::
- arity_clause (class :: seen) n (tcons, ars)
-
-fun multi_arity_clause [] = []
- | multi_arity_clause ((tcons, ars) :: tc_arlists) =
- arity_clause [] 1 (tcons, ars) @ multi_arity_clause tc_arlists
-
-(* Generate all pairs (tycon, class, sorts) such that tycon belongs to class in
- theory thy provided its arguments have the corresponding sorts. *)
-fun type_class_pairs thy tycons classes =
- let
- val alg = Sign.classes_of thy
- fun domain_sorts tycon = Sorts.mg_domain alg tycon o single
- fun add_class tycon class =
- cons (class, domain_sorts tycon class)
- handle Sorts.CLASS_ERROR _ => I
- fun try_classes tycon = (tycon, fold (add_class tycon) classes [])
- in map try_classes tycons end
-
-(*Proving one (tycon, class) membership may require proving others, so iterate.*)
-fun iter_type_class_pairs _ _ [] = ([], [])
- | iter_type_class_pairs thy tycons classes =
- let
- fun maybe_insert_class s =
- (s <> type_class andalso not (member (op =) classes s))
- ? insert (op =) s
- val cpairs = type_class_pairs thy tycons classes
- val newclasses =
- [] |> fold (fold (fold (fold maybe_insert_class) o snd) o snd) cpairs
- val (classes', cpairs') = iter_type_class_pairs thy tycons newclasses
- in (classes' @ classes, union (op =) cpairs' cpairs) end
-
-fun make_arity_clauses thy tycons =
- iter_type_class_pairs thy tycons ##> multi_arity_clause
-
-
-(** Isabelle class relations **)
-
-type class_rel_clause =
- {name : string,
- subclass : name,
- superclass : name}
-
-(* Generate all pairs (sub, super) such that sub is a proper subclass of super
- in theory "thy". *)
-fun class_pairs _ [] _ = []
- | class_pairs thy subs supers =
- let
- val class_less = Sorts.class_less (Sign.classes_of thy)
- fun add_super sub super = class_less (sub, super) ? cons (sub, super)
- fun add_supers sub = fold (add_super sub) supers
- in fold add_supers subs [] end
-
-fun make_class_rel_clause (sub, super) =
- {name = sub ^ "_" ^ super, subclass = `make_type_class sub,
- superclass = `make_type_class super}
-
-fun make_class_rel_clauses thy subs supers =
- map make_class_rel_clause (class_pairs thy subs supers)
-
-(* intermediate terms *)
-datatype iterm =
- IConst of name * typ * typ list |
- IVar of name * typ |
- IApp of iterm * iterm |
- IAbs of (name * typ) * iterm
-
-fun ityp_of (IConst (_, T, _)) = T
- | ityp_of (IVar (_, T)) = T
- | ityp_of (IApp (t1, _)) = snd (dest_funT (ityp_of t1))
- | ityp_of (IAbs ((_, T), tm)) = T --> ityp_of tm
-
-(*gets the head of a combinator application, along with the list of arguments*)
-fun strip_iterm_comb u =
- let
- fun stripc (IApp (t, u), ts) = stripc (t, u :: ts)
- | stripc x = x
- in stripc (u, []) end
-
-fun atomic_types_of T = fold_atyps (insert (op =)) T []
-
-val tvar_a_str = "'a"
-val tvar_a = TVar ((tvar_a_str, 0), HOLogic.typeS)
-val tvar_a_name = (make_schematic_type_var (tvar_a_str, 0), tvar_a_str)
-val itself_name = `make_fixed_type_const @{type_name itself}
-val TYPE_name = `(make_fixed_const NONE) @{const_name TYPE}
-val tvar_a_atype = AType (tvar_a_name, [])
-val a_itself_atype = AType (itself_name, [tvar_a_atype])
-
-fun new_skolem_const_name s num_T_args =
- [new_skolem_const_prefix, s, string_of_int num_T_args]
- |> space_implode Long_Name.separator
-
-fun robust_const_type thy s =
- if s = app_op_name then
- Logic.varifyT_global @{typ "('a => 'b) => 'a => 'b"}
- else if String.isPrefix lam_lifted_prefix s then
- Logic.varifyT_global @{typ "'a => 'b"}
- else
- (* Old Skolems throw a "TYPE" exception here, which will be caught. *)
- s |> Sign.the_const_type thy
-
-(* This function only makes sense if "T" is as general as possible. *)
-fun robust_const_typargs thy (s, T) =
- if s = app_op_name then
- let val (T1, T2) = T |> domain_type |> dest_funT in [T1, T2] end
- else if String.isPrefix old_skolem_const_prefix s then
- [] |> Term.add_tvarsT T |> rev |> map TVar
- else if String.isPrefix lam_lifted_prefix s then
- if String.isPrefix lam_lifted_poly_prefix s then
- let val (T1, T2) = T |> dest_funT in [T1, T2] end
- else
- []
- else
- (s, T) |> Sign.const_typargs thy
-
-(* Converts an Isabelle/HOL term (with combinators) into an intermediate term.
- Also accumulates sort infomation. *)
-fun iterm_from_term thy format bs (P $ Q) =
- let
- val (P', P_atomics_Ts) = iterm_from_term thy format bs P
- val (Q', Q_atomics_Ts) = iterm_from_term thy format bs Q
- in (IApp (P', Q'), union (op =) P_atomics_Ts Q_atomics_Ts) end
- | iterm_from_term thy format _ (Const (c, T)) =
- (IConst (`(make_fixed_const (SOME format)) c, T,
- robust_const_typargs thy (c, T)),
- atomic_types_of T)
- | iterm_from_term _ _ _ (Free (s, T)) =
- (IConst (`make_fixed_var s, T, []), atomic_types_of T)
- | iterm_from_term _ format _ (Var (v as (s, _), T)) =
- (if String.isPrefix Meson_Clausify.new_skolem_var_prefix s then
- let
- val Ts = T |> strip_type |> swap |> op ::
- val s' = new_skolem_const_name s (length Ts)
- in IConst (`(make_fixed_const (SOME format)) s', T, Ts) end
- else
- IVar ((make_schematic_var v, s), T), atomic_types_of T)
- | iterm_from_term _ _ bs (Bound j) =
- nth bs j |> (fn (_, (name, T)) => (IConst (name, T, []), atomic_types_of T))
- | iterm_from_term thy format bs (Abs (s, T, t)) =
- let
- fun vary s = s |> AList.defined (op =) bs s ? vary o Symbol.bump_string
- val s = vary s
- val name = `make_bound_var s
- val (tm, atomic_Ts) = iterm_from_term thy format ((s, (name, T)) :: bs) t
- in (IAbs ((name, T), tm), union (op =) atomic_Ts (atomic_types_of T)) end
-
-datatype locality =
- General | Helper | Induction | Intro | Elim | Simp | Local | Assum | Chained
-
-datatype order = First_Order | Higher_Order
-datatype polymorphism = Polymorphic | Raw_Monomorphic | Mangled_Monomorphic
-datatype strictness = Strict | Non_Strict
-datatype granularity = All_Vars | Positively_Naked_Vars | Ghost_Type_Arg_Vars
-datatype type_level =
- All_Types |
- Noninf_Nonmono_Types of strictness * granularity |
- Fin_Nonmono_Types of granularity |
- Const_Arg_Types |
- No_Types
-
-datatype type_enc =
- Simple_Types of order * polymorphism * type_level |
- Guards of polymorphism * type_level |
- Tags of polymorphism * type_level
-
-fun is_type_enc_higher_order (Simple_Types (Higher_Order, _, _)) = true
- | is_type_enc_higher_order _ = false
-
-fun polymorphism_of_type_enc (Simple_Types (_, poly, _)) = poly
- | polymorphism_of_type_enc (Guards (poly, _)) = poly
- | polymorphism_of_type_enc (Tags (poly, _)) = poly
-
-fun level_of_type_enc (Simple_Types (_, _, level)) = level
- | level_of_type_enc (Guards (_, level)) = level
- | level_of_type_enc (Tags (_, level)) = level
-
-fun granularity_of_type_level (Noninf_Nonmono_Types (_, grain)) = grain
- | granularity_of_type_level (Fin_Nonmono_Types grain) = grain
- | granularity_of_type_level _ = All_Vars
-
-fun is_type_level_quasi_sound All_Types = true
- | is_type_level_quasi_sound (Noninf_Nonmono_Types _) = true
- | is_type_level_quasi_sound _ = false
-val is_type_enc_quasi_sound = is_type_level_quasi_sound o level_of_type_enc
-
-fun is_type_level_fairly_sound (Fin_Nonmono_Types _) = true
- | is_type_level_fairly_sound level = is_type_level_quasi_sound level
-val is_type_enc_fairly_sound = is_type_level_fairly_sound o level_of_type_enc
-
-fun is_type_level_monotonicity_based (Noninf_Nonmono_Types _) = true
- | is_type_level_monotonicity_based (Fin_Nonmono_Types _) = true
- | is_type_level_monotonicity_based _ = false
-
-(* "_query", "_bang", and "_at" are for the ASCII-challenged Metis and
- Mirabelle. *)
-val queries = ["?", "_query"]
-val bangs = ["!", "_bang"]
-val ats = ["@", "_at"]
-
-fun try_unsuffixes ss s =
- fold (fn s' => fn NONE => try (unsuffix s') s | some => some) ss NONE
-
-fun try_nonmono constr suffixes fallback s =
- case try_unsuffixes suffixes s of
- SOME s =>
- (case try_unsuffixes suffixes s of
- SOME s => (constr Positively_Naked_Vars, s)
- | NONE =>
- case try_unsuffixes ats s of
- SOME s => (constr Ghost_Type_Arg_Vars, s)
- | NONE => (constr All_Vars, s))
- | NONE => fallback s
-
-fun type_enc_from_string strictness s =
- (case try (unprefix "poly_") s of
- SOME s => (SOME Polymorphic, s)
- | NONE =>
- case try (unprefix "raw_mono_") s of
- SOME s => (SOME Raw_Monomorphic, s)
- | NONE =>
- case try (unprefix "mono_") s of
- SOME s => (SOME Mangled_Monomorphic, s)
- | NONE => (NONE, s))
- ||> (pair All_Types
- |> try_nonmono Fin_Nonmono_Types bangs
- |> try_nonmono (curry Noninf_Nonmono_Types strictness) queries)
- |> (fn (poly, (level, core)) =>
- case (core, (poly, level)) of
- ("simple", (SOME poly, _)) =>
- (case (poly, level) of
- (Polymorphic, All_Types) =>
- Simple_Types (First_Order, Polymorphic, All_Types)
- | (Mangled_Monomorphic, _) =>
- if granularity_of_type_level level = All_Vars then
- Simple_Types (First_Order, Mangled_Monomorphic, level)
- else
- raise Same.SAME
- | _ => raise Same.SAME)
- | ("simple_higher", (SOME poly, _)) =>
- (case (poly, level) of
- (Polymorphic, All_Types) =>
- Simple_Types (Higher_Order, Polymorphic, All_Types)
- | (_, Noninf_Nonmono_Types _) => raise Same.SAME
- | (Mangled_Monomorphic, _) =>
- if granularity_of_type_level level = All_Vars then
- Simple_Types (Higher_Order, Mangled_Monomorphic, level)
- else
- raise Same.SAME
- | _ => raise Same.SAME)
- | ("guards", (SOME poly, _)) =>
- if poly = Mangled_Monomorphic andalso
- granularity_of_type_level level = Ghost_Type_Arg_Vars then
- raise Same.SAME
- else
- Guards (poly, level)
- | ("tags", (SOME poly, _)) =>
- if granularity_of_type_level level = Ghost_Type_Arg_Vars then
- raise Same.SAME
- else
- Tags (poly, level)
- | ("args", (SOME poly, All_Types (* naja *))) =>
- Guards (poly, Const_Arg_Types)
- | ("erased", (NONE, All_Types (* naja *))) =>
- Guards (Polymorphic, No_Types)
- | _ => raise Same.SAME)
- handle Same.SAME => error ("Unknown type encoding: " ^ quote s ^ ".")
-
-fun adjust_type_enc (THF (TPTP_Monomorphic, _, _))
- (Simple_Types (order, _, level)) =
- Simple_Types (order, Mangled_Monomorphic, level)
- | adjust_type_enc (THF _) type_enc = type_enc
- | adjust_type_enc (TFF (TPTP_Monomorphic, _)) (Simple_Types (_, _, level)) =
- Simple_Types (First_Order, Mangled_Monomorphic, level)
- | adjust_type_enc (DFG DFG_Sorted) (Simple_Types (_, _, level)) =
- Simple_Types (First_Order, Mangled_Monomorphic, level)
- | adjust_type_enc (TFF _) (Simple_Types (_, poly, level)) =
- Simple_Types (First_Order, poly, level)
- | adjust_type_enc format (Simple_Types (_, poly, level)) =
- adjust_type_enc format (Guards (poly, level))
- | adjust_type_enc CNF_UEQ (type_enc as Guards stuff) =
- (if is_type_enc_fairly_sound type_enc then Tags else Guards) stuff
- | adjust_type_enc _ type_enc = type_enc
-
-fun constify_lifted (t $ u) = constify_lifted t $ constify_lifted u
- | constify_lifted (Abs (s, T, t)) = Abs (s, T, constify_lifted t)
- | constify_lifted (Free (x as (s, _))) =
- (if String.isPrefix lam_lifted_prefix s then Const else Free) x
- | constify_lifted t = t
-
-(* Requires bound variables not to clash with any schematic variables (as should
- be the case right after lambda-lifting). *)
-fun open_form (Const (@{const_name All}, _) $ Abs (s, T, t)) =
- let
- val names = Name.make_context (map fst (Term.add_var_names t []))
- val (s, _) = Name.variant s names
- in open_form (subst_bound (Var ((s, 0), T), t)) end
- | open_form t = t
-
-fun lift_lams_part_1 ctxt type_enc =
- map close_form #> rpair ctxt
- #-> Lambda_Lifting.lift_lambdas
- (SOME ((if polymorphism_of_type_enc type_enc = Polymorphic then
- lam_lifted_poly_prefix
- else
- lam_lifted_mono_prefix) ^ "_a"))
- Lambda_Lifting.is_quantifier
- #> fst
-val lift_lams_part_2 = pairself (map (open_form o constify_lifted))
-val lift_lams = lift_lams_part_2 ooo lift_lams_part_1
-
-fun intentionalize_def (Const (@{const_name All}, _) $ Abs (_, _, t)) =
- intentionalize_def t
- | intentionalize_def (Const (@{const_name HOL.eq}, _) $ t $ u) =
- let
- fun lam T t = Abs (Name.uu, T, t)
- val (head, args) = strip_comb t ||> rev
- val head_T = fastype_of head
- val n = length args
- val arg_Ts = head_T |> binder_types |> take n |> rev
- val u = u |> subst_atomic (args ~~ map Bound (0 upto n - 1))
- in HOLogic.eq_const head_T $ head $ fold lam arg_Ts u end
- | intentionalize_def t = t
-
-type translated_formula =
- {name : string,
- locality : locality,
- kind : formula_kind,
- iformula : (name, typ, iterm) formula,
- atomic_types : typ list}
-
-fun update_iformula f ({name, locality, kind, iformula, atomic_types}
- : translated_formula) =
- {name = name, locality = locality, kind = kind, iformula = f iformula,
- atomic_types = atomic_types} : translated_formula
-
-fun fact_lift f ({iformula, ...} : translated_formula) = f iformula
-
-fun insert_type ctxt get_T x xs =
- let val T = get_T x in
- if exists (type_instance ctxt T o get_T) xs then xs
- else x :: filter_out (type_generalization ctxt 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 (* infer_from_term_args *) |
- Mangled_Type_Args |
- No_Type_Args
-
-fun type_arg_policy monom_constrs type_enc s =
- let val poly = polymorphism_of_type_enc type_enc in
- if s = type_tag_name then
- if poly = Mangled_Monomorphic then Mangled_Type_Args
- else Explicit_Type_Args false
- else case type_enc of
- Simple_Types (_, Polymorphic, _) => Explicit_Type_Args false
- | Tags (_, All_Types) => No_Type_Args
- | _ =>
- let val level = level_of_type_enc type_enc in
- if level = No_Types orelse s = @{const_name HOL.eq} orelse
- (s = app_op_name andalso level = Const_Arg_Types) then
- No_Type_Args
- else if poly = Mangled_Monomorphic then
- Mangled_Type_Args
- else if member (op =) monom_constrs s andalso
- granularity_of_type_level level = Positively_Naked_Vars then
- No_Type_Args
- else
- Explicit_Type_Args
- (level = All_Types orelse
- granularity_of_type_level level = Ghost_Type_Arg_Vars)
- end
- end
-
-(* Make atoms for sorted type variables. *)
-fun generic_add_sorts_on_type (_, []) = I
- | generic_add_sorts_on_type ((x, i), s :: ss) =
- generic_add_sorts_on_type ((x, i), ss)
- #> (if s = the_single @{sort HOL.type} then
- I
- else if i = ~1 then
- insert (op =) (`make_type_class s, `make_fixed_type_var x)
- else
- insert (op =) (`make_type_class s,
- (make_schematic_type_var (x, i), x)))
-fun add_sorts_on_tfree (TFree (s, S)) = generic_add_sorts_on_type ((s, ~1), S)
- | add_sorts_on_tfree _ = I
-fun add_sorts_on_tvar (TVar z) = generic_add_sorts_on_type z
- | add_sorts_on_tvar _ = I
-
-fun type_class_formula type_enc class arg =
- AAtom (ATerm (class, arg ::
- (case type_enc of
- Simple_Types (First_Order, Polymorphic, _) =>
- if avoid_first_order_ghost_type_vars then [ATerm (TYPE_name, [arg])]
- else []
- | _ => [])))
-fun formulas_for_types type_enc add_sorts_on_typ Ts =
- [] |> level_of_type_enc type_enc <> No_Types ? fold add_sorts_on_typ Ts
- |> map (fn (class, name) =>
- type_class_formula type_enc class (ATerm (name, [])))
-
-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 add_term_vars phi =
- let
- fun add_formula_vars bounds (AQuant (_, xs, phi)) =
- add_formula_vars (map fst xs @ bounds) phi
- | add_formula_vars bounds (AConn (_, phis)) =
- fold (add_formula_vars bounds) phis
- | add_formula_vars bounds (AAtom tm) = add_term_vars bounds tm
- in mk_aquant AForall (add_formula_vars [] phi []) phi end
-
-fun add_term_vars bounds (ATerm (name as (s, _), tms)) =
- (if is_tptp_variable s andalso
- not (String.isPrefix tvar_prefix s) andalso
- not (member (op =) bounds name) then
- insert (op =) (name, NONE)
- else
- I)
- #> fold (add_term_vars bounds) tms
- | add_term_vars bounds (AAbs ((name, _), tm)) =
- add_term_vars (name :: bounds) tm
-fun close_formula_universally phi = close_universally add_term_vars phi
-
-fun add_iterm_vars bounds (IApp (tm1, tm2)) =
- fold (add_iterm_vars bounds) [tm1, tm2]
- | add_iterm_vars _ (IConst _) = I
- | add_iterm_vars bounds (IVar (name, T)) =
- not (member (op =) bounds name) ? insert (op =) (name, SOME T)
- | add_iterm_vars bounds (IAbs (_, tm)) = add_iterm_vars bounds tm
-fun close_iformula_universally phi = close_universally add_iterm_vars phi
-
-val fused_infinite_type_name = @{type_name ind} (* any infinite type *)
-val fused_infinite_type = Type (fused_infinite_type_name, [])
-
-fun tvar_name (x as (s, _)) = (make_schematic_type_var x, s)
-
-fun ho_term_from_typ format type_enc =
- let
- fun term (Type (s, Ts)) =
- ATerm (case (is_type_enc_higher_order type_enc, s) of
- (true, @{type_name bool}) => `I tptp_bool_type
- | (true, @{type_name fun}) => `I tptp_fun_type
- | _ => if s = fused_infinite_type_name andalso
- is_format_typed format 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, _)) = ATerm (tvar_name x, [])
- in term end
-
-fun ho_term_for_type_arg format type_enc T =
- if T = dummyT then NONE else SOME (ho_term_from_typ format type_enc T)
-
-(* 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)
- ^ ")"
- | generic_mangled_type_name _ _ = raise Fail "unexpected type abstraction"
-
-fun mangled_type format type_enc =
- generic_mangled_type_name fst o ho_term_from_typ format type_enc
-
-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
-
-fun ho_type_from_ho_term type_enc pred_sym ary =
- let
- fun to_mangled_atype ty =
- AType ((make_simple_type (generic_mangled_type_name fst ty),
- generic_mangled_type_name snd ty), [])
- fun to_poly_atype (ATerm (name, tys)) = AType (name, map to_poly_atype tys)
- | to_poly_atype _ = raise Fail "unexpected type abstraction"
- val to_atype =
- if polymorphism_of_type_enc type_enc = Polymorphic then to_poly_atype
- else to_mangled_atype
- 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
- | to_fo _ _ = raise Fail "unexpected type abstraction"
- 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
- | to_ho _ = raise Fail "unexpected type abstraction"
- in if is_type_enc_higher_order type_enc then to_ho else to_fo ary end
-
-fun ho_type_from_typ format type_enc pred_sym ary =
- ho_type_from_ho_term type_enc pred_sym ary
- o ho_term_from_typ format type_enc
-
-fun mangled_const_name format type_enc T_args (s, s') =
- let
- val ty_args = T_args |> map_filter (ho_term_for_type_arg format type_enc)
- 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_in_iterm type_enc =
- let
- fun tweak_ho_quant ho_quant T [IAbs _] = IConst (`I ho_quant, T, [])
- | tweak_ho_quant ho_quant (T as Type (_, [p_T as Type (_, [x_T, _]), _]))
- _ =
- (* Eta-expand "!!" and "??", to work around LEO-II 1.2.8 parser
- limitation. This works in conjuction with special code in
- "ATP_Problem" that uses the syntactic sugar "!" and "?" whenever
- possible. *)
- IAbs ((`I "P", p_T),
- IApp (IConst (`I ho_quant, T, []),
- IAbs ((`I "X", x_T),
- IApp (IConst (`I "P", p_T, []),
- IConst (`I "X", x_T, [])))))
- | tweak_ho_quant _ _ _ = raise Fail "unexpected type for quantifier"
- fun intro top_level args (IApp (tm1, tm2)) =
- IApp (intro top_level (tm2 :: args) tm1, intro false [] tm2)
- | intro top_level args (IConst (name as (s, _), T, T_args)) =
- (case proxify_const s of
- SOME proxy_base =>
- if top_level orelse is_type_enc_higher_order type_enc then
- case (top_level, s) of
- (_, "c_False") => IConst (`I tptp_false, T, [])
- | (_, "c_True") => IConst (`I tptp_true, T, [])
- | (false, "c_Not") => IConst (`I tptp_not, T, [])
- | (false, "c_conj") => IConst (`I tptp_and, T, [])
- | (false, "c_disj") => IConst (`I tptp_or, T, [])
- | (false, "c_implies") => IConst (`I tptp_implies, T, [])
- | (false, "c_All") => tweak_ho_quant tptp_ho_forall T args
- | (false, "c_Ex") => tweak_ho_quant tptp_ho_exists T args
- | (false, s) =>
- if is_tptp_equal s andalso length args = 2 then
- IConst (`I tptp_equal, T, [])
- else
- (* Use a proxy even for partially applied THF0 equality,
- because the LEO-II and Satallax parsers complain about not
- being able to infer the type of "=". *)
- IConst (proxy_base |>> prefix const_prefix, T, T_args)
- | _ => IConst (name, T, [])
- else
- IConst (proxy_base |>> prefix const_prefix, T, T_args)
- | NONE => if s = tptp_choice then tweak_ho_quant tptp_choice T args
- else IConst (name, T, T_args))
- | intro _ _ (IAbs (bound, tm)) = IAbs (bound, intro false [] tm)
- | intro _ _ tm = tm
- in intro true [] end
-
-fun mangle_type_args_in_iterm format type_enc =
- if polymorphism_of_type_enc type_enc = Mangled_Monomorphic then
- let
- fun mangle (IApp (tm1, tm2)) = IApp (mangle tm1, mangle tm2)
- | mangle (tm as IConst (_, _, [])) = tm
- | mangle (tm as IConst (name as (s, _), T, T_args)) =
- (case unprefix_and_unascii const_prefix s of
- NONE => tm
- | SOME s'' =>
- case type_arg_policy [] type_enc (invert_const s'') of
- Mangled_Type_Args =>
- IConst (mangled_const_name format type_enc T_args name, T, [])
- | _ => tm)
- | mangle (IAbs (bound, tm)) = IAbs (bound, mangle tm)
- | mangle tm = tm
- in mangle end
- else
- I
-
-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 _ T = ([], T)
-
-fun filter_const_type_args _ _ _ [] = []
- | filter_const_type_args thy s ary T_args =
- let
- val U = robust_const_type thy s
- val arg_U_vars = fold Term.add_tvarsT (U |> chop_fun ary |> fst) []
- val U_args = (s, U) |> robust_const_typargs thy
- in
- U_args ~~ T_args
- |> map (fn (U, T) =>
- if member (op =) arg_U_vars (dest_TVar U) then dummyT else T)
- end
- handle TYPE _ => T_args
-
-fun filter_type_args_in_iterm thy monom_constrs type_enc =
- let
- fun filt ary (IApp (tm1, tm2)) = IApp (filt (ary + 1) tm1, filt 0 tm2)
- | filt _ (tm as IConst (_, _, [])) = tm
- | filt ary (IConst (name as (s, _), T, T_args)) =
- (case unprefix_and_unascii const_prefix s of
- NONE =>
- (name,
- if level_of_type_enc type_enc = No_Types orelse s = tptp_choice then
- []
- else
- T_args)
- | SOME s'' =>
- let
- val s'' = invert_const s''
- fun filter_T_args false = T_args
- | filter_T_args true = filter_const_type_args thy s'' ary T_args
- in
- case type_arg_policy monom_constrs type_enc s'' of
- Explicit_Type_Args infer_from_term_args =>
- (name, filter_T_args infer_from_term_args)
- | No_Type_Args => (name, [])
- | Mangled_Type_Args => raise Fail "unexpected (un)mangled symbol"
- end)
- |> (fn (name, T_args) => IConst (name, T, T_args))
- | filt _ (IAbs (bound, tm)) = IAbs (bound, filt 0 tm)
- | filt _ tm = tm
- in filt 0 end
-
-fun iformula_from_prop ctxt format type_enc eq_as_iff =
- let
- val thy = Proof_Context.theory_of ctxt
- fun do_term bs t atomic_Ts =
- iterm_from_term thy format bs (Envir.eta_contract t)
- |>> (introduce_proxies_in_iterm type_enc
- #> mangle_type_args_in_iterm format type_enc
- #> AAtom)
- ||> union (op =) atomic_Ts
- fun do_quant bs q pos s T t' =
- let
- val s = singleton (Name.variant_list (map fst bs)) s
- val universal = Option.map (q = AExists ? not) pos
- val name =
- s |> `(case universal of
- SOME true => make_all_bound_var
- | SOME false => make_exist_bound_var
- | NONE => make_bound_var)
- in
- do_formula ((s, (name, T)) :: bs) pos t'
- #>> mk_aquant q [(name, SOME T)]
- ##> union (op =) (atomic_types_of T)
- end
- and do_conn bs c pos1 t1 pos2 t2 =
- do_formula bs pos1 t1 ##>> do_formula bs pos2 t2 #>> uncurry (mk_aconn c)
- and do_formula bs pos t =
- case t of
- @{const Trueprop} $ t1 => do_formula bs pos t1
- | @{const Not} $ t1 => do_formula bs (Option.map not pos) t1 #>> mk_anot
- | Const (@{const_name All}, _) $ Abs (s, T, t') =>
- do_quant bs AForall pos s T t'
- | (t0 as Const (@{const_name All}, _)) $ t1 =>
- do_formula bs pos (t0 $ eta_expand (map (snd o snd) bs) t1 1)
- | Const (@{const_name Ex}, _) $ Abs (s, T, t') =>
- do_quant bs AExists pos s T t'
- | (t0 as Const (@{const_name Ex}, _)) $ t1 =>
- do_formula bs pos (t0 $ eta_expand (map (snd o snd) bs) t1 1)
- | @{const HOL.conj} $ t1 $ t2 => do_conn bs AAnd pos t1 pos t2
- | @{const HOL.disj} $ t1 $ t2 => do_conn bs AOr pos t1 pos t2
- | @{const HOL.implies} $ t1 $ t2 =>
- do_conn bs AImplies (Option.map not pos) t1 pos t2
- | Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])) $ t1 $ t2 =>
- if eq_as_iff then do_conn bs AIff NONE t1 NONE t2 else do_term bs t
- | _ => do_term bs t
- in do_formula [] end
-
-fun presimplify_term ctxt t =
- t |> exists_Const (member (op =) Meson.presimplified_consts o fst) t
- ? (Skip_Proof.make_thm (Proof_Context.theory_of ctxt)
- #> Meson.presimplify
- #> prop_of)
-
-fun concealed_bound_name j = atp_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 is_fun_equality (@{const_name HOL.eq},
- Type (_, [Type (@{type_name fun}, _), _])) = true
- | is_fun_equality _ = false
-
-fun extensionalize_term ctxt t =
- if exists_Const is_fun_equality t then
- let val thy = Proof_Context.theory_of ctxt in
- t |> cterm_of thy |> Meson.extensionalize_conv ctxt
- |> prop_of |> Logic.dest_equals |> snd
- end
- else
- t
-
-fun simple_translate_lambdas do_lambdas ctxt t =
- let val thy = Proof_Context.theory_of ctxt in
- if Meson.is_fol_term thy t then
- t
- else
- let
- fun trans Ts t =
- case t of
- @{const Not} $ t1 => @{const Not} $ trans Ts t1
- | (t0 as Const (@{const_name All}, _)) $ Abs (s, T, t') =>
- t0 $ Abs (s, T, trans (T :: Ts) t')
- | (t0 as Const (@{const_name All}, _)) $ t1 =>
- trans Ts (t0 $ eta_expand Ts t1 1)
- | (t0 as Const (@{const_name Ex}, _)) $ Abs (s, T, t') =>
- t0 $ Abs (s, T, trans (T :: Ts) t')
- | (t0 as Const (@{const_name Ex}, _)) $ t1 =>
- trans Ts (t0 $ eta_expand Ts t1 1)
- | (t0 as @{const HOL.conj}) $ t1 $ t2 =>
- t0 $ trans Ts t1 $ trans Ts t2
- | (t0 as @{const HOL.disj}) $ t1 $ t2 =>
- t0 $ trans Ts t1 $ trans Ts t2
- | (t0 as @{const HOL.implies}) $ t1 $ t2 =>
- t0 $ trans Ts t1 $ trans Ts t2
- | (t0 as Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])))
- $ t1 $ t2 =>
- t0 $ trans Ts t1 $ trans Ts t2
- | _ =>
- if not (exists_subterm (fn Abs _ => true | _ => false) t) then t
- else t |> Envir.eta_contract |> do_lambdas ctxt Ts
- val (t, ctxt') = Variable.import_terms true [t] ctxt |>> the_single
- in t |> trans [] |> singleton (Variable.export_terms ctxt' ctxt) end
- end
-
-fun do_cheaply_conceal_lambdas Ts (t1 $ t2) =
- do_cheaply_conceal_lambdas Ts t1
- $ do_cheaply_conceal_lambdas Ts t2
- | do_cheaply_conceal_lambdas Ts (Abs (_, T, t)) =
- Const (lam_lifted_poly_prefix ^ serial_string (),
- T --> fastype_of1 (T :: Ts, t))
- | do_cheaply_conceal_lambdas _ t = t
-
-fun do_introduce_combinators ctxt Ts t =
- let val thy = Proof_Context.theory_of ctxt in
- t |> conceal_bounds Ts
- |> cterm_of thy
- |> Meson_Clausify.introduce_combinators_in_cterm
- |> prop_of |> Logic.dest_equals |> snd
- |> reveal_bounds Ts
- end
- (* A type variable of sort "{}" will make abstraction fail. *)
- handle THM _ => t |> do_cheaply_conceal_lambdas Ts
-val introduce_combinators = simple_translate_lambdas do_introduce_combinators
-
-fun preprocess_abstractions_in_terms trans_lams facts =
- let
- val (facts, lambda_ts) =
- facts |> map (snd o snd) |> trans_lams
- |>> map2 (fn (name, (kind, _)) => fn t => (name, (kind, t))) facts
- val lam_facts =
- map2 (fn t => fn j =>
- ((lam_fact_prefix ^ Int.toString j, Helper), (Axiom, t)))
- lambda_ts (1 upto length lambda_ts)
- in (facts, lam_facts) 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 freeze (t $ u) = freeze t $ freeze u
- | freeze (Abs (s, T, t)) = Abs (s, T, freeze t)
- | freeze (Var ((s, i), T)) =
- Free (atp_weak_prefix ^ s ^ "_" ^ string_of_int i, T)
- | freeze t = t
- in t |> exists_subterm is_Var t ? freeze end
-
-fun presimp_prop ctxt role 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})
- in
- t |> need_trueprop ? HOLogic.mk_Trueprop
- |> extensionalize_term ctxt
- |> presimplify_term ctxt
- |> HOLogic.dest_Trueprop
- end
- handle TERM _ => if role = Conjecture then @{term False} else @{term True})
- |> pair role
-
-fun make_formula ctxt format type_enc eq_as_iff name loc kind t =
- let
- val (iformula, atomic_Ts) =
- iformula_from_prop ctxt format type_enc eq_as_iff
- (SOME (kind <> Conjecture)) t []
- |>> close_iformula_universally
- in
- {name = name, locality = loc, kind = kind, iformula = iformula,
- atomic_types = atomic_Ts}
- end
-
-fun make_fact ctxt format type_enc eq_as_iff ((name, loc), t) =
- case t |> make_formula ctxt format type_enc (eq_as_iff andalso format <> CNF)
- name loc Axiom of
- formula as {iformula = AAtom (IConst ((s, _), _, _)), ...} =>
- if s = tptp_true then NONE else SOME formula
- | formula => SOME formula
-
-fun s_not_trueprop (@{const Trueprop} $ t) = @{const Trueprop} $ s_not t
- | s_not_trueprop t =
- if fastype_of t = @{typ bool} then s_not t else @{prop False} (* too meta *)
-
-fun make_conjecture ctxt format type_enc =
- map (fn ((name, loc), (kind, t)) =>
- t |> kind = Conjecture ? s_not_trueprop
- |> make_formula ctxt format type_enc (format <> CNF) name loc kind)
-
-(** Finite and infinite type inference **)
-
-fun tvar_footprint thy s ary =
- (case unprefix_and_unascii const_prefix s of
- SOME s =>
- s |> invert_const |> robust_const_type thy |> chop_fun ary |> fst
- |> map (fn T => Term.add_tvarsT T [] |> map fst)
- | NONE => [])
- handle TYPE _ => []
-
-fun ghost_type_args thy s ary =
- if is_tptp_equal s then
- 0 upto ary - 1
- else
- let
- val footprint = tvar_footprint thy s ary
- val eq = (s = @{const_name HOL.eq})
- fun ghosts _ [] = []
- | ghosts seen ((i, tvars) :: args) =
- ghosts (union (op =) seen tvars) args
- |> (eq orelse exists (fn tvar => not (member (op =) seen tvar)) tvars)
- ? cons i
- in
- if forall null footprint then
- []
- else
- 0 upto length footprint - 1 ~~ footprint
- |> sort (rev_order o list_ord Term_Ord.indexname_ord o pairself snd)
- |> ghosts []
- end
-
-type monotonicity_info =
- {maybe_finite_Ts : typ list,
- surely_finite_Ts : typ list,
- maybe_infinite_Ts : typ list,
- surely_infinite_Ts : typ list,
- maybe_nonmono_Ts : typ list}
-
-(* 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}, HOLogic.intT, HOLogic.realT, @{typ "nat => bool"}]
-
-fun is_type_kind_of_surely_infinite ctxt strictness cached_Ts T =
- strictness <> Strict andalso is_type_surely_infinite ctxt true cached_Ts T
-
-(* 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 _ (_ : monotonicity_info) All_Types _ = true
- | should_encode_type ctxt {maybe_finite_Ts, surely_infinite_Ts,
- maybe_nonmono_Ts, ...}
- (Noninf_Nonmono_Types (strictness, grain)) T =
- grain = Ghost_Type_Arg_Vars orelse
- (exists (type_intersect ctxt T) maybe_nonmono_Ts andalso
- not (exists (type_instance ctxt T) surely_infinite_Ts orelse
- (not (member (type_equiv ctxt) maybe_finite_Ts T) andalso
- is_type_kind_of_surely_infinite ctxt strictness surely_infinite_Ts
- T)))
- | should_encode_type ctxt {surely_finite_Ts, maybe_infinite_Ts,
- maybe_nonmono_Ts, ...}
- (Fin_Nonmono_Types grain) T =
- grain = Ghost_Type_Arg_Vars orelse
- (exists (type_intersect ctxt T) maybe_nonmono_Ts andalso
- (exists (type_generalization ctxt T) surely_finite_Ts orelse
- (not (member (type_equiv ctxt) maybe_infinite_Ts T) andalso
- is_type_surely_finite ctxt T)))
- | should_encode_type _ _ _ _ = false
-
-fun should_guard_type ctxt mono (Guards (_, level)) should_guard_var T =
- should_guard_var () andalso should_encode_type ctxt mono level T
- | should_guard_type _ _ _ _ _ = false
-
-fun is_maybe_universal_var (IConst ((s, _), _, _)) =
- String.isPrefix bound_var_prefix s orelse
- String.isPrefix all_bound_var_prefix s
- | is_maybe_universal_var (IVar _) = true
- | is_maybe_universal_var _ = false
-
-datatype site =
- Top_Level of bool option |
- Eq_Arg of bool option |
- Elsewhere
-
-fun should_tag_with_type _ _ _ (Top_Level _) _ _ = false
- | should_tag_with_type ctxt mono (Tags (_, level)) site u T =
- if granularity_of_type_level level = All_Vars then
- should_encode_type ctxt mono level T
- else
- (case (site, is_maybe_universal_var u) of
- (Eq_Arg _, true) => should_encode_type ctxt mono level T
- | _ => false)
- | should_tag_with_type _ _ _ _ _ _ = false
-
-fun fused_type ctxt mono level =
- let
- val should_encode = should_encode_type ctxt mono level
- fun fuse 0 T = if should_encode T then T else fused_infinite_type
- | fuse ary (Type (@{type_name fun}, [T1, T2])) =
- fuse 0 T1 --> fuse (ary - 1) T2
- | fuse _ _ = raise Fail "expected function type"
- in fuse end
-
-(** predicators and application operators **)
-
-type sym_info =
- {pred_sym : bool, min_ary : int, max_ary : int, types : typ list,
- in_conj : bool}
-
-fun default_sym_tab_entries type_enc =
- (make_fixed_const NONE @{const_name undefined},
- {pred_sym = false, min_ary = 0, max_ary = 0, types = [],
- in_conj = false}) ::
- ([tptp_false, tptp_true]
- |> map (rpair {pred_sym = true, min_ary = 0, max_ary = 0, types = [],
- in_conj = false})) @
- ([tptp_equal, tptp_old_equal]
- |> map (rpair {pred_sym = true, min_ary = 2, max_ary = 2, types = [],
- in_conj = false}))
- |> not (is_type_enc_higher_order type_enc)
- ? cons (prefixed_predicator_name,
- {pred_sym = true, min_ary = 1, max_ary = 1, types = [],
- in_conj = false})
-
-fun sym_table_for_facts ctxt type_enc explicit_apply conjs facts =
- let
- fun consider_var_ary const_T var_T max_ary =
- let
- fun iter ary T =
- if ary = max_ary orelse type_instance ctxt var_T T orelse
- type_instance ctxt T var_T then
- ary
- else
- iter (ary + 1) (range_type T)
- in iter 0 const_T end
- fun add_universal_var T (accum as ((bool_vars, fun_var_Ts), sym_tab)) =
- if explicit_apply = NONE andalso
- (can dest_funT T orelse T = @{typ bool}) then
- let
- val bool_vars' = bool_vars orelse body_type T = @{typ bool}
- fun repair_min_ary {pred_sym, min_ary, max_ary, types, in_conj} =
- {pred_sym = pred_sym andalso not bool_vars',
- min_ary = fold (fn T' => consider_var_ary T' T) types min_ary,
- max_ary = max_ary, types = types, in_conj = in_conj}
- val fun_var_Ts' =
- fun_var_Ts |> can dest_funT T ? insert_type ctxt I T
- in
- if bool_vars' = bool_vars andalso
- pointer_eq (fun_var_Ts', fun_var_Ts) then
- accum
- else
- ((bool_vars', fun_var_Ts'), Symtab.map (K repair_min_ary) sym_tab)
- end
- else
- accum
- fun add_fact_syms conj_fact =
- let
- fun add_iterm_syms top_level tm
- (accum as ((bool_vars, fun_var_Ts), sym_tab)) =
- let val (head, args) = strip_iterm_comb tm in
- (case head of
- IConst ((s, _), T, _) =>
- if String.isPrefix bound_var_prefix s orelse
- String.isPrefix all_bound_var_prefix s then
- add_universal_var T accum
- else if String.isPrefix exist_bound_var_prefix s then
- accum
- else
- let val ary = length args in
- ((bool_vars, fun_var_Ts),
- case Symtab.lookup sym_tab s of
- SOME {pred_sym, min_ary, max_ary, types, in_conj} =>
- let
- val pred_sym =
- pred_sym andalso top_level andalso not bool_vars
- val types' = types |> insert_type ctxt I T
- val in_conj = in_conj orelse conj_fact
- val min_ary =
- if is_some explicit_apply orelse
- pointer_eq (types', types) then
- min_ary
- else
- fold (consider_var_ary T) fun_var_Ts min_ary
- in
- Symtab.update (s, {pred_sym = pred_sym,
- min_ary = Int.min (ary, min_ary),
- max_ary = Int.max (ary, max_ary),
- types = types', in_conj = in_conj})
- sym_tab
- end
- | NONE =>
- let
- val pred_sym = top_level andalso not bool_vars
- val min_ary =
- case explicit_apply of
- SOME true => 0
- | SOME false => ary
- | NONE => fold (consider_var_ary T) fun_var_Ts ary
- in
- Symtab.update_new (s,
- {pred_sym = pred_sym, min_ary = min_ary,
- max_ary = ary, types = [T], in_conj = conj_fact})
- sym_tab
- end)
- end
- | IVar (_, T) => add_universal_var T accum
- | IAbs ((_, T), tm) =>
- accum |> add_universal_var T |> add_iterm_syms false tm
- | _ => accum)
- |> fold (add_iterm_syms false) args
- end
- in K (add_iterm_syms true) |> formula_fold NONE |> fact_lift end
- in
- ((false, []), Symtab.empty)
- |> fold (add_fact_syms true) conjs
- |> fold (add_fact_syms false) facts
- |> snd
- |> fold Symtab.update (default_sym_tab_entries type_enc)
- end
-
-fun min_ary_of sym_tab s =
- case Symtab.lookup sym_tab s of
- SOME ({min_ary, ...} : sym_info) => min_ary
- | NONE =>
- case unprefix_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_guard_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 app_op = `(make_fixed_const NONE) app_op_name
-val predicator_combconst =
- IConst (`(make_fixed_const NONE) predicator_name, @{typ "bool => bool"}, [])
-
-fun list_app head args = fold (curry (IApp o swap)) args head
-fun predicator tm = IApp (predicator_combconst, tm)
-
-fun firstorderize_fact thy monom_constrs format type_enc sym_tab =
- let
- fun do_app arg head =
- let
- val head_T = ityp_of head
- val (arg_T, res_T) = dest_funT head_T
- val app =
- IConst (app_op, head_T --> head_T, [arg_T, res_T])
- |> mangle_type_args_in_iterm format type_enc
- in list_app app [head, arg] end
- fun list_app_ops head args = fold do_app args head
- fun introduce_app_ops tm =
- case strip_iterm_comb tm of
- (head as IConst ((s, _), _, _), args) =>
- args |> map introduce_app_ops
- |> chop (min_ary_of sym_tab s)
- |>> list_app head
- |-> list_app_ops
- | (head, args) => list_app_ops head (map introduce_app_ops args)
- fun introduce_predicators tm =
- case strip_iterm_comb tm of
- (IConst ((s, _), _, _), _) =>
- if is_pred_sym sym_tab s then tm else predicator tm
- | _ => predicator tm
- val do_iterm =
- not (is_type_enc_higher_order type_enc)
- ? (introduce_app_ops #> introduce_predicators)
- #> filter_type_args_in_iterm thy monom_constrs type_enc
- in update_iformula (formula_map do_iterm) end
-
-(** Helper facts **)
-
-val not_ffalse = @{lemma "~ fFalse" by (unfold fFalse_def) fast}
-val ftrue = @{lemma "fTrue" by (unfold fTrue_def) fast}
-
-(* The Boolean indicates that a fairly sound type encoding is needed. *)
-val helper_table =
- [(("COMBI", false), @{thms Meson.COMBI_def}),
- (("COMBK", false), @{thms Meson.COMBK_def}),
- (("COMBB", false), @{thms Meson.COMBB_def}),
- (("COMBC", false), @{thms Meson.COMBC_def}),
- (("COMBS", false), @{thms Meson.COMBS_def}),
- ((predicator_name, false), [not_ffalse, ftrue]),
- (("fFalse", false), [not_ffalse]),
- (("fFalse", true), @{thms True_or_False}),
- (("fTrue", false), [ftrue]),
- (("fTrue", true), @{thms True_or_False}),
- (("fNot", false),
- @{thms fNot_def [THEN Meson.iff_to_disjD, THEN conjunct1]
- fNot_def [THEN Meson.iff_to_disjD, THEN conjunct2]}),
- (("fconj", false),
- @{lemma "~ P | ~ Q | fconj P Q" "~ fconj P Q | P" "~ fconj P Q | Q"
- by (unfold fconj_def) fast+}),
- (("fdisj", false),
- @{lemma "~ P | fdisj P Q" "~ Q | fdisj P Q" "~ fdisj P Q | P | Q"
- by (unfold fdisj_def) fast+}),
- (("fimplies", false),
- @{lemma "P | fimplies P Q" "~ Q | fimplies P Q" "~ fimplies P Q | ~ P | Q"
- by (unfold fimplies_def) fast+}),
- (("fequal", true),
- (* This is a lie: Higher-order equality doesn't need a sound type encoding.
- However, this is done so for backward compatibility: Including the
- equality helpers by default in Metis breaks a few existing proofs. *)
- @{thms fequal_def [THEN Meson.iff_to_disjD, THEN conjunct1]
- fequal_def [THEN Meson.iff_to_disjD, THEN conjunct2]}),
- (* Partial characterization of "fAll" and "fEx". A complete characterization
- would require the axiom of choice for replay with Metis. *)
- (("fAll", false), [@{lemma "~ fAll P | P x" by (auto simp: fAll_def)}]),
- (("fEx", false), [@{lemma "~ P x | fEx P" by (auto simp: fEx_def)}]),
- (("If", true), @{thms if_True if_False True_or_False})]
- |> map (apsnd (map zero_var_indexes))
-
-fun atype_of_type_vars (Simple_Types (_, Polymorphic, _)) = SOME atype_of_types
- | atype_of_type_vars _ = NONE
-
-fun bound_tvars type_enc sorts Ts =
- (sorts ? mk_ahorn (formulas_for_types type_enc add_sorts_on_tvar Ts))
- #> mk_aquant AForall
- (map_filter (fn TVar (x as (s, _), _) =>
- SOME ((make_schematic_type_var x, s),
- atype_of_type_vars type_enc)
- | _ => NONE) Ts)
-
-fun eq_formula type_enc atomic_Ts pred_sym tm1 tm2 =
- (if pred_sym then AConn (AIff, [AAtom tm1, AAtom tm2])
- else AAtom (ATerm (`I tptp_equal, [tm1, tm2])))
- |> close_formula_universally
- |> bound_tvars type_enc true atomic_Ts
-
-val type_tag = `(make_fixed_const NONE) type_tag_name
-
-fun type_tag_idempotence_fact format type_enc =
- let
- fun var s = ATerm (`I s, [])
- fun tag tm = ATerm (type_tag, [var "A", tm])
- val tagged_var = tag (var "X")
- in
- Formula (type_tag_idempotence_helper_name, Axiom,
- eq_formula type_enc [] false (tag tagged_var) tagged_var,
- isabelle_info format simpN, NONE)
- end
-
-fun should_specialize_helper type_enc t =
- polymorphism_of_type_enc type_enc <> Polymorphic andalso
- level_of_type_enc type_enc <> No_Types andalso
- not (null (Term.hidden_polymorphism t))
-
-fun helper_facts_for_sym ctxt format type_enc (s, {types, ...} : sym_info) =
- case unprefix_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 needs_fairly_sound j k =
- (unmangled_s ^ "_" ^ string_of_int j ^ "_" ^ string_of_int k ^
- (if mangled_s = unmangled_s then "" else "_" ^ ascii_of mangled_s) ^
- (if needs_fairly_sound then typed_helper_suffix
- else untyped_helper_suffix),
- Helper)
- fun dub_and_inst needs_fairly_sound (th, j) =
- let val t = prop_of th in
- if should_specialize_helper type_enc t then
- map (fn T => specialize_type thy (invert_const unmangled_s, T) t)
- types
- else
- [t]
- end
- |> map (fn (k, t) => (dub needs_fairly_sound j k, t)) o tag_list 1
- val make_facts = map_filter (make_fact ctxt format type_enc false)
- val fairly_sound = is_type_enc_fairly_sound type_enc
- in
- helper_table
- |> maps (fn ((helper_s, needs_fairly_sound), ths) =>
- if helper_s <> unmangled_s orelse
- (needs_fairly_sound andalso not fairly_sound) then
- []
- else
- ths ~~ (1 upto length ths)
- |> maps (dub_and_inst needs_fairly_sound)
- |> make_facts)
- end
- | NONE => []
-fun helper_facts_for_sym_table ctxt format type_enc sym_tab =
- Symtab.fold_rev (append o helper_facts_for_sym ctxt format type_enc) sym_tab
- []
-
-(***************************************************************)
-(* Type Classes Present in the Axiom or Conjecture Clauses *)
-(***************************************************************)
-
-fun set_insert (x, s) = Symtab.update (x, ()) s
-
-fun add_classes (sorts, cset) = List.foldl set_insert cset (flat sorts)
-
-(* Remove this trivial type class (FIXME: similar code elsewhere) *)
-fun delete_type cset = Symtab.delete_safe (the_single @{sort HOL.type}) cset
-
-fun classes_of_terms get_Ts =
- map (map snd o get_Ts)
- #> List.foldl add_classes Symtab.empty
- #> delete_type #> Symtab.keys
-
-val tfree_classes_of_terms = classes_of_terms Misc_Legacy.term_tfrees
-val tvar_classes_of_terms = classes_of_terms Misc_Legacy.term_tvars
-
-fun fold_type_constrs f (Type (s, Ts)) x =
- fold (fold_type_constrs f) Ts (f (s, x))
- | fold_type_constrs _ _ x = x
-
-(* Type constructors used to instantiate overloaded constants are the only ones
- needed. *)
-fun add_type_constrs_in_term thy =
- let
- fun add (Const (@{const_name Meson.skolem}, _) $ _) = I
- | add (t $ u) = add t #> add u
- | add (Const x) =
- x |> robust_const_typargs thy |> fold (fold_type_constrs set_insert)
- | add (Abs (_, _, u)) = add u
- | add _ = I
- in add end
-
-fun type_constrs_of_terms thy ts =
- Symtab.keys (fold (add_type_constrs_in_term thy) ts Symtab.empty)
-
-fun extract_lambda_def (Const (@{const_name HOL.eq}, _) $ t $ u) =
- let val (head, args) = strip_comb t in
- (head |> dest_Const |> fst,
- fold_rev (fn t as Var ((s, _), T) =>
- (fn u => Abs (s, T, abstract_over (t, u)))
- | _ => raise Fail "expected Var") args u)
- end
- | extract_lambda_def _ = raise Fail "malformed lifted lambda"
-
-fun trans_lams_from_string ctxt type_enc lam_trans =
- if lam_trans = no_lamsN then
- rpair []
- else if lam_trans = hide_lamsN then
- lift_lams ctxt type_enc ##> K []
- else if lam_trans = lam_liftingN then
- lift_lams ctxt type_enc
- else if lam_trans = combinatorsN then
- map (introduce_combinators ctxt) #> rpair []
- else if lam_trans = hybrid_lamsN then
- lift_lams_part_1 ctxt type_enc
- ##> maps (fn t => [t, introduce_combinators ctxt (intentionalize_def t)])
- #> lift_lams_part_2
- else if lam_trans = keep_lamsN then
- map (Envir.eta_contract) #> rpair []
- else
- error ("Unknown lambda translation scheme: " ^ quote lam_trans ^ ".")
-
-fun translate_formulas ctxt format prem_kind type_enc lam_trans presimp hyp_ts
- concl_t facts =
- let
- val thy = Proof_Context.theory_of ctxt
- val trans_lams = trans_lams_from_string ctxt type_enc lam_trans
- val fact_ts = facts |> map snd
- (* Remove existing facts from the conjecture, as this can dramatically
- boost an ATP's performance (for some reason). *)
- val hyp_ts =
- hyp_ts
- |> map (fn t => if member (op aconv) fact_ts t then @{prop True} else t)
- val facts = facts |> map (apsnd (pair Axiom))
- val conjs =
- map (pair prem_kind) hyp_ts @ [(Conjecture, s_not_trueprop concl_t)]
- |> map (apsnd freeze_term)
- |> map2 (pair o rpair Local o string_of_int) (0 upto length hyp_ts)
- val ((conjs, facts), lam_facts) =
- (conjs, facts)
- |> presimp ? pairself (map (apsnd (uncurry (presimp_prop ctxt))))
- |> (if lam_trans = no_lamsN then
- rpair []
- else
- op @
- #> preprocess_abstractions_in_terms trans_lams
- #>> chop (length conjs))
- val conjs = conjs |> make_conjecture ctxt format type_enc
- val (fact_names, facts) =
- facts
- |> map_filter (fn (name, (_, t)) =>
- make_fact ctxt format type_enc true (name, t)
- |> Option.map (pair name))
- |> ListPair.unzip
- val lifted = lam_facts |> map (extract_lambda_def o snd o snd)
- val lam_facts =
- lam_facts |> map_filter (make_fact ctxt format type_enc true o apsnd snd)
- val all_ts = concl_t :: hyp_ts @ fact_ts
- val subs = tfree_classes_of_terms all_ts
- val supers = tvar_classes_of_terms all_ts
- val tycons = type_constrs_of_terms thy all_ts
- val (supers, arity_clauses) =
- if level_of_type_enc type_enc = 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, union (op =) subs supers, conjs,
- facts @ lam_facts, class_rel_clauses, arity_clauses, lifted)
- end
-
-val type_guard = `(make_fixed_const NONE) type_guard_name
-
-fun type_guard_iterm format type_enc T tm =
- IApp (IConst (type_guard, T --> @{typ bool}, [T])
- |> mangle_type_args_in_iterm format type_enc, tm)
-
-fun is_var_positively_naked_in_term _ (SOME false) _ accum = accum
- | is_var_positively_naked_in_term name _ (ATerm ((s, _), tms)) accum =
- accum orelse (is_tptp_equal s andalso member (op =) tms (ATerm (name, [])))
- | is_var_positively_naked_in_term _ _ _ _ = true
-
-fun is_var_ghost_type_arg_in_term thy polym_constrs name pos tm accum =
- is_var_positively_naked_in_term name pos tm accum orelse
- let
- val var = ATerm (name, [])
- fun is_nasty_in_term (ATerm (_, [])) = false
- | is_nasty_in_term (ATerm ((s, _), tms)) =
- let
- val ary = length tms
- val polym_constr = member (op =) polym_constrs s
- val ghosts = ghost_type_args thy s ary
- in
- exists (fn (j, tm) =>
- if polym_constr then
- member (op =) ghosts j andalso
- (tm = var orelse is_nasty_in_term tm)
- else
- tm = var andalso member (op =) ghosts j)
- (0 upto ary - 1 ~~ tms)
- orelse (not polym_constr andalso exists is_nasty_in_term tms)
- end
- | is_nasty_in_term _ = true
- in is_nasty_in_term tm end
-
-fun should_guard_var_in_formula thy polym_constrs level pos phi (SOME true)
- name =
- (case granularity_of_type_level level of
- All_Vars => true
- | Positively_Naked_Vars =>
- formula_fold pos (is_var_positively_naked_in_term name) phi false
- | Ghost_Type_Arg_Vars =>
- formula_fold pos (is_var_ghost_type_arg_in_term thy polym_constrs name)
- phi false)
- | should_guard_var_in_formula _ _ _ _ _ _ _ = true
-
-fun always_guard_var_in_formula _ _ _ _ _ _ _ = true
-
-fun should_generate_tag_bound_decl _ _ _ (SOME true) _ = false
- | should_generate_tag_bound_decl ctxt mono (Tags (_, level)) _ T =
- granularity_of_type_level level <> All_Vars andalso
- should_encode_type ctxt mono level T
- | should_generate_tag_bound_decl _ _ _ _ _ = false
-
-fun mk_aterm format type_enc name T_args args =
- ATerm (name, map_filter (ho_term_for_type_arg format type_enc) T_args @ args)
-
-fun tag_with_type ctxt format mono type_enc pos T tm =
- IConst (type_tag, T --> T, [T])
- |> mangle_type_args_in_iterm format type_enc
- |> ho_term_from_iterm ctxt format mono type_enc pos
- |> (fn ATerm (s, tms) => ATerm (s, tms @ [tm])
- | _ => raise Fail "unexpected lambda-abstraction")
-and ho_term_from_iterm ctxt format mono type_enc =
- let
- fun term site u =
- let
- val (head, args) = strip_iterm_comb u
- val pos =
- case site of
- Top_Level pos => pos
- | Eq_Arg pos => pos
- | _ => NONE
- val t =
- case head of
- IConst (name as (s, _), _, T_args) =>
- let
- val arg_site = if is_tptp_equal s then Eq_Arg pos else Elsewhere
- in
- map (term arg_site) args |> mk_aterm format type_enc name T_args
- end
- | IVar (name, _) =>
- map (term Elsewhere) args |> mk_aterm format type_enc name []
- | IAbs ((name, T), tm) =>
- AAbs ((name, ho_type_from_typ format type_enc true 0 T),
- term Elsewhere tm)
- | IApp _ => raise Fail "impossible \"IApp\""
- val T = ityp_of u
- in
- if should_tag_with_type ctxt mono type_enc site u T then
- tag_with_type ctxt format mono type_enc pos T t
- else
- t
- end
- in term o Top_Level end
-and formula_from_iformula ctxt polym_constrs format mono type_enc
- should_guard_var =
- let
- val thy = Proof_Context.theory_of ctxt
- val level = level_of_type_enc type_enc
- val do_term = ho_term_from_iterm ctxt format mono type_enc
- val do_bound_type =
- case type_enc of
- Simple_Types _ => fused_type ctxt mono level 0
- #> ho_type_from_typ format type_enc false 0 #> SOME
- | _ => K NONE
- fun do_out_of_bound_type pos phi universal (name, T) =
- if should_guard_type ctxt mono type_enc
- (fn () => should_guard_var thy polym_constrs level pos phi
- universal name) T then
- IVar (name, T)
- |> type_guard_iterm format type_enc T
- |> do_term pos |> AAtom |> SOME
- else if should_generate_tag_bound_decl ctxt mono type_enc universal T then
- let
- val var = ATerm (name, [])
- val tagged_var = tag_with_type ctxt format mono type_enc pos T var
- in SOME (AAtom (ATerm (`I tptp_equal, [tagged_var, var]))) end
- 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 pos (AAtom tm) = AAtom (do_term pos tm)
- in do_formula end
-
-(* 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 polym_constrs format prefix encode freshen pos
- mono type_enc (j, {name, locality, kind, iformula, atomic_types}) =
- (prefix ^ (if freshen then string_of_int j ^ "_" else "") ^ encode name, kind,
- iformula
- |> formula_from_iformula ctxt polym_constrs format mono type_enc
- should_guard_var_in_formula (if pos then SOME true else NONE)
- |> close_formula_universally
- |> bound_tvars type_enc true atomic_types,
- NONE,
- case locality of
- Intro => isabelle_info format introN
- | Elim => isabelle_info format elimN
- | Simp => isabelle_info format simpN
- | _ => NONE)
- |> Formula
-
-fun formula_line_for_class_rel_clause format type_enc
- ({name, subclass, superclass, ...} : class_rel_clause) =
- let val ty_arg = ATerm (tvar_a_name, []) in
- Formula (class_rel_clause_prefix ^ ascii_of name, Axiom,
- AConn (AImplies,
- [type_class_formula type_enc subclass ty_arg,
- type_class_formula type_enc superclass ty_arg])
- |> mk_aquant AForall
- [(tvar_a_name, atype_of_type_vars type_enc)],
- isabelle_info format introN, NONE)
- end
-
-fun formula_from_arity_atom type_enc (class, t, args) =
- ATerm (t, map (fn arg => ATerm (arg, [])) args)
- |> type_class_formula type_enc class
-
-fun formula_line_for_arity_clause format type_enc
- ({name, prem_atoms, concl_atom} : arity_clause) =
- Formula (arity_clause_prefix ^ name, Axiom,
- mk_ahorn (map (formula_from_arity_atom type_enc) prem_atoms)
- (formula_from_arity_atom type_enc concl_atom)
- |> mk_aquant AForall
- (map (rpair (atype_of_type_vars type_enc)) (#3 concl_atom)),
- isabelle_info format introN, NONE)
-
-fun formula_line_for_conjecture ctxt polym_constrs format mono type_enc
- ({name, kind, iformula, atomic_types, ...} : translated_formula) =
- Formula (conjecture_prefix ^ name, kind,
- iformula
- |> formula_from_iformula ctxt polym_constrs format mono type_enc
- should_guard_var_in_formula (SOME false)
- |> close_formula_universally
- |> bound_tvars type_enc true atomic_types, NONE, NONE)
-
-fun formula_line_for_free_type j phi =
- Formula (tfree_clause_prefix ^ string_of_int j, Hypothesis, phi, NONE, NONE)
-fun formula_lines_for_free_types type_enc (facts : translated_formula list) =
- let
- val phis =
- fold (union (op =)) (map #atomic_types facts) []
- |> formulas_for_types type_enc add_sorts_on_tfree
- in map2 formula_line_for_free_type (0 upto length phis - 1) phis end
-
-(** Symbol declarations **)
-
-fun decl_line_for_class order s =
- let val name as (s, _) = `make_type_class s in
- Decl (sym_decl_prefix ^ s, name,
- if order = First_Order then
- ATyAbs ([tvar_a_name],
- if avoid_first_order_ghost_type_vars then
- AFun (a_itself_atype, bool_atype)
- else
- bool_atype)
- else
- AFun (atype_of_types, bool_atype))
- end
-
-fun decl_lines_for_classes type_enc classes =
- case type_enc of
- Simple_Types (order, Polymorphic, _) =>
- map (decl_line_for_class order) classes
- | _ => []
-
-fun sym_decl_table_for_facts ctxt format type_enc sym_tab (conjs, facts) =
- let
- fun add_iterm_syms tm =
- let val (head, args) = strip_iterm_comb tm in
- (case head of
- IConst ((s, s'), T, T_args) =>
- let
- val (pred_sym, in_conj) =
- case Symtab.lookup sym_tab s of
- SOME ({pred_sym, in_conj, ...} : sym_info) =>
- (pred_sym, in_conj)
- | NONE => (false, false)
- val decl_sym =
- (case type_enc of
- Guards _ => not pred_sym
- | _ => true) andalso
- is_tptp_user_symbol s
- in
- if decl_sym then
- Symtab.map_default (s, [])
- (insert_type ctxt #3 (s', T_args, T, pred_sym, length args,
- in_conj))
- else
- I
- end
- | IAbs (_, tm) => add_iterm_syms tm
- | _ => I)
- #> fold add_iterm_syms args
- end
- val add_fact_syms = K add_iterm_syms |> formula_fold NONE |> fact_lift
- fun add_formula_var_types (AQuant (_, xs, phi)) =
- fold (fn (_, SOME T) => insert_type ctxt I T | _ => I) xs
- #> add_formula_var_types phi
- | add_formula_var_types (AConn (_, phis)) =
- fold add_formula_var_types phis
- | add_formula_var_types _ = I
- fun var_types () =
- if polymorphism_of_type_enc type_enc = Polymorphic then [tvar_a]
- else fold (fact_lift add_formula_var_types) (conjs @ facts) []
- fun add_undefined_const T =
- let
- val (s, s') =
- `(make_fixed_const NONE) @{const_name undefined}
- |> (case type_arg_policy [] type_enc @{const_name undefined} of
- Mangled_Type_Args => mangled_const_name format type_enc [T]
- | _ => I)
- in
- Symtab.map_default (s, [])
- (insert_type ctxt #3 (s', [T], T, false, 0, false))
- end
- fun add_TYPE_const () =
- let val (s, s') = TYPE_name in
- Symtab.map_default (s, [])
- (insert_type ctxt #3
- (s', [tvar_a], @{typ "'a itself"}, false, 0, false))
- end
- in
- Symtab.empty
- |> is_type_enc_fairly_sound type_enc
- ? (fold (fold add_fact_syms) [conjs, facts]
- #> (case type_enc of
- Simple_Types (First_Order, Polymorphic, _) =>
- if avoid_first_order_ghost_type_vars then add_TYPE_const ()
- else I
- | Simple_Types _ => I
- | _ => fold add_undefined_const (var_types ())))
- end
-
-(* We add "bool" in case the helper "True_or_False" is included later. *)
-fun default_mono level =
- {maybe_finite_Ts = [@{typ bool}],
- surely_finite_Ts = [@{typ bool}],
- maybe_infinite_Ts = known_infinite_types,
- surely_infinite_Ts =
- case level of
- Noninf_Nonmono_Types (Strict, _) => []
- | _ => known_infinite_types,
- maybe_nonmono_Ts = [@{typ 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_iterm_mononotonicity_info _ _ (SOME false) _ mono = mono
- | add_iterm_mononotonicity_info ctxt level _
- (IApp (IApp (IConst ((s, _), Type (_, [T, _]), _), tm1), tm2))
- (mono as {maybe_finite_Ts, surely_finite_Ts, maybe_infinite_Ts,
- surely_infinite_Ts, maybe_nonmono_Ts}) =
- if is_tptp_equal s andalso exists is_maybe_universal_var [tm1, tm2] then
- case level of
- Noninf_Nonmono_Types (strictness, _) =>
- if exists (type_instance ctxt T) surely_infinite_Ts orelse
- member (type_equiv ctxt) maybe_finite_Ts T then
- mono
- else if is_type_kind_of_surely_infinite ctxt strictness
- surely_infinite_Ts T then
- {maybe_finite_Ts = maybe_finite_Ts,
- surely_finite_Ts = surely_finite_Ts,
- maybe_infinite_Ts = maybe_infinite_Ts,
- surely_infinite_Ts = surely_infinite_Ts |> insert_type ctxt I T,
- maybe_nonmono_Ts = maybe_nonmono_Ts}
- else
- {maybe_finite_Ts = maybe_finite_Ts |> insert (type_equiv ctxt) T,
- surely_finite_Ts = surely_finite_Ts,
- maybe_infinite_Ts = maybe_infinite_Ts,
- surely_infinite_Ts = surely_infinite_Ts,
- maybe_nonmono_Ts = maybe_nonmono_Ts |> insert_type ctxt I T}
- | Fin_Nonmono_Types _ =>
- if exists (type_instance ctxt T) surely_finite_Ts orelse
- member (type_equiv ctxt) maybe_infinite_Ts T then
- mono
- else if is_type_surely_finite ctxt T then
- {maybe_finite_Ts = maybe_finite_Ts,
- surely_finite_Ts = surely_finite_Ts |> insert_type ctxt I T,
- maybe_infinite_Ts = maybe_infinite_Ts,
- surely_infinite_Ts = surely_infinite_Ts,
- maybe_nonmono_Ts = maybe_nonmono_Ts |> insert_type ctxt I T}
- else
- {maybe_finite_Ts = maybe_finite_Ts,
- surely_finite_Ts = surely_finite_Ts,
- maybe_infinite_Ts = maybe_infinite_Ts |> insert (type_equiv ctxt) T,
- surely_infinite_Ts = surely_infinite_Ts,
- maybe_nonmono_Ts = maybe_nonmono_Ts}
- | _ => mono
- else
- mono
- | add_iterm_mononotonicity_info _ _ _ _ mono = mono
-fun add_fact_mononotonicity_info ctxt level
- ({kind, iformula, ...} : translated_formula) =
- formula_fold (SOME (kind <> Conjecture))
- (add_iterm_mononotonicity_info ctxt level) iformula
-fun mononotonicity_info_for_facts ctxt type_enc facts =
- let val level = level_of_type_enc type_enc in
- default_mono level
- |> is_type_level_monotonicity_based level
- ? fold (add_fact_mononotonicity_info ctxt level) facts
- end
-
-fun add_iformula_monotonic_types ctxt mono type_enc =
- let
- val level = level_of_type_enc type_enc
- val should_encode = should_encode_type ctxt mono level
- fun add_type T = not (should_encode T) ? insert_type ctxt I T
- fun add_args (IApp (tm1, tm2)) = add_args tm1 #> add_term tm2
- | add_args _ = I
- and add_term tm = add_type (ityp_of tm) #> add_args tm
- in formula_fold NONE (K add_term) end
-fun add_fact_monotonic_types ctxt mono type_enc =
- add_iformula_monotonic_types ctxt mono type_enc |> fact_lift
-fun monotonic_types_for_facts ctxt mono type_enc facts =
- let val level = level_of_type_enc type_enc in
- [] |> (polymorphism_of_type_enc type_enc = Polymorphic andalso
- is_type_level_monotonicity_based level andalso
- granularity_of_type_level level <> Ghost_Type_Arg_Vars)
- ? fold (add_fact_monotonic_types ctxt mono type_enc) facts
- end
-
-fun formula_line_for_guards_mono_type ctxt format mono type_enc T =
- Formula (guards_sym_formula_prefix ^
- ascii_of (mangled_type format type_enc T),
- Axiom,
- IConst (`make_bound_var "X", T, [])
- |> type_guard_iterm format type_enc T
- |> AAtom
- |> formula_from_iformula ctxt [] format mono type_enc
- always_guard_var_in_formula (SOME true)
- |> close_formula_universally
- |> bound_tvars type_enc true (atomic_types_of T),
- isabelle_info format introN, NONE)
-
-fun formula_line_for_tags_mono_type ctxt format mono type_enc T =
- let val x_var = ATerm (`make_bound_var "X", []) in
- Formula (tags_sym_formula_prefix ^
- ascii_of (mangled_type format type_enc T),
- Axiom,
- eq_formula type_enc (atomic_types_of T) false
- (tag_with_type ctxt format mono type_enc NONE T x_var) x_var,
- isabelle_info format simpN, NONE)
- end
-
-fun problem_lines_for_mono_types ctxt format mono type_enc Ts =
- case type_enc of
- Simple_Types _ => []
- | Guards _ =>
- map (formula_line_for_guards_mono_type ctxt format mono type_enc) Ts
- | Tags _ => map (formula_line_for_tags_mono_type ctxt format mono type_enc) Ts
-
-fun decl_line_for_sym ctxt format mono type_enc s
- (s', T_args, T, pred_sym, ary, _) =
- let
- val thy = Proof_Context.theory_of ctxt
- val (T, T_args) =
- if null T_args then
- (T, [])
- else case unprefix_and_unascii const_prefix s of
- SOME s' =>
- let
- val s' = s' |> invert_const
- val T = s' |> robust_const_type thy
- in (T, robust_const_typargs thy (s', T)) end
- | NONE => raise Fail "unexpected type arguments"
- in
- Decl (sym_decl_prefix ^ s, (s, s'),
- T |> fused_type ctxt mono (level_of_type_enc type_enc) ary
- |> ho_type_from_typ format type_enc pred_sym ary
- |> not (null T_args)
- ? curry ATyAbs (map (tvar_name o fst o dest_TVar) T_args))
- end
-
-fun formula_line_for_guards_sym_decl ctxt format conj_sym_kind mono type_enc n s
- j (s', T_args, T, _, ary, in_conj) =
- let
- val thy = Proof_Context.theory_of ctxt
- 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 ary |> map (`I o make_bound_var o string_of_int)
- val bounds =
- bound_names ~~ arg_Ts |> map (fn (name, T) => IConst (name, T, []))
- val bound_Ts =
- if exists (curry (op =) dummyT) T_args then
- case level_of_type_enc type_enc of
- All_Types => map SOME arg_Ts
- | level =>
- if granularity_of_type_level level = Ghost_Type_Arg_Vars then
- let val ghosts = ghost_type_args thy s ary in
- map2 (fn j => if member (op =) ghosts j then SOME else K NONE)
- (0 upto ary - 1) arg_Ts
- end
- else
- replicate ary NONE
- else
- replicate ary NONE
- in
- Formula (guards_sym_formula_prefix ^ s ^
- (if n > 1 then "_" ^ string_of_int j else ""), kind,
- IConst ((s, s'), T, T_args)
- |> fold (curry (IApp o swap)) bounds
- |> type_guard_iterm format type_enc res_T
- |> AAtom |> mk_aquant AForall (bound_names ~~ bound_Ts)
- |> formula_from_iformula ctxt [] format mono type_enc
- always_guard_var_in_formula (SOME true)
- |> close_formula_universally
- |> bound_tvars type_enc (n > 1) (atomic_types_of T)
- |> maybe_negate,
- isabelle_info format introN, NONE)
- end
-
-fun formula_lines_for_tags_sym_decl ctxt format conj_sym_kind mono type_enc n s
- (j, (s', T_args, T, pred_sym, ary, in_conj)) =
- let
- val thy = Proof_Context.theory_of ctxt
- val level = level_of_type_enc type_enc
- val grain = granularity_of_type_level level
- val ident_base =
- tags_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 ary |> map (`I o make_bound_var o string_of_int)
- val bounds = bound_names |> map (fn name => ATerm (name, []))
- val cst = mk_aterm format type_enc (s, s') T_args
- val eq = maybe_negate oo eq_formula type_enc (atomic_types_of T) pred_sym
- val should_encode = should_encode_type ctxt mono level
- val tag_with = tag_with_type ctxt format mono type_enc NONE
- val add_formula_for_res =
- if should_encode res_T then
- let
- val tagged_bounds =
- if grain = Ghost_Type_Arg_Vars then
- let val ghosts = ghost_type_args thy s ary in
- map2 (fn (j, arg_T) => member (op =) ghosts j ? tag_with arg_T)
- (0 upto ary - 1 ~~ arg_Ts) bounds
- end
- else
- bounds
- in
- cons (Formula (ident_base ^ "_res", kind,
- eq (tag_with res_T (cst bounds)) (cst tagged_bounds),
- isabelle_info format simpN, NONE))
- end
- 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),
- isabelle_info format simpN, NONE))
- | _ => raise Fail "expected nonempty tail"
- else
- I
- end
- in
- [] |> not pred_sym ? add_formula_for_res
- |> (Config.get ctxt type_tag_arguments andalso
- grain = Positively_Naked_Vars)
- ? fold add_formula_for_arg (ary - 1 downto 0)
- end
-
-fun result_type_of_decl (_, _, T, _, ary, _) = chop_fun ary T |> snd
-
-fun rationalize_decls ctxt (decls as decl :: (decls' as _ :: _)) =
- let
- val T = result_type_of_decl decl
- |> map_type_tvar (fn (z, _) => TVar (z, HOLogic.typeS))
- in
- if forall (type_generalization ctxt T o result_type_of_decl) decls' then
- [decl]
- else
- decls
- end
- | rationalize_decls _ decls = decls
-
-fun problem_lines_for_sym_decls ctxt format conj_sym_kind mono type_enc
- (s, decls) =
- case type_enc of
- Simple_Types _ => [decl_line_for_sym ctxt format mono type_enc s (hd decls)]
- | Guards (_, level) =>
- let
- val decls = decls |> rationalize_decls ctxt
- val n = length decls
- val decls =
- decls |> filter (should_encode_type ctxt mono level
- o result_type_of_decl)
- in
- (0 upto length decls - 1, decls)
- |-> map2 (formula_line_for_guards_sym_decl ctxt format conj_sym_kind mono
- type_enc n s)
- end
- | Tags (_, level) =>
- if granularity_of_type_level level = All_Vars then
- []
- else
- let val n = length decls in
- (0 upto n - 1 ~~ decls)
- |> maps (formula_lines_for_tags_sym_decl ctxt format conj_sym_kind mono
- type_enc n s)
- end
-
-fun problem_lines_for_sym_decl_table ctxt format conj_sym_kind mono type_enc
- mono_Ts sym_decl_tab =
- let
- val syms = sym_decl_tab |> Symtab.dest |> sort_wrt fst
- val mono_lines =
- problem_lines_for_mono_types ctxt format mono type_enc mono_Ts
- val decl_lines =
- fold_rev (append o problem_lines_for_sym_decls ctxt format conj_sym_kind
- mono type_enc)
- syms []
- in mono_lines @ decl_lines end
-
-fun needs_type_tag_idempotence ctxt (Tags (poly, level)) =
- Config.get ctxt type_tag_idempotence andalso
- is_type_level_monotonicity_based level andalso
- poly <> Mangled_Monomorphic
- | needs_type_tag_idempotence _ _ = false
-
-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"
-
-(* TFF allows implicit declarations of types, function symbols, and predicate
- symbols (with "$i" as the type of individuals), but some provers (e.g.,
- SNARK) require explicit declarations. The situation is similar for THF. *)
-
-fun default_type type_enc pred_sym s =
- let
- val ind =
- case type_enc of
- Simple_Types _ =>
- if String.isPrefix type_const_prefix s then atype_of_types
- else individual_atype
- | _ => individual_atype
- fun typ 0 = if pred_sym then bool_atype else ind
- | typ ary = AFun (ind, typ (ary - 1))
- in typ end
-
-fun nary_type_constr_type n =
- funpow n (curry AFun atype_of_types) atype_of_types
-
-fun undeclared_syms_in_problem type_enc problem =
- let
- val declared = declared_syms_in_problem problem
- fun do_sym name ty =
- if member (op =) declared name then I else AList.default (op =) (name, ty)
- fun do_type (AType (name as (s, _), tys)) =
- is_tptp_user_symbol s
- ? do_sym name (fn () => nary_type_constr_type (length tys))
- #> fold do_type tys
- | do_type (AFun (ty1, ty2)) = do_type ty1 #> do_type ty2
- | do_type (ATyAbs (_, ty)) = do_type ty
- fun do_term pred_sym (ATerm (name as (s, _), tms)) =
- is_tptp_user_symbol s
- ? do_sym name (fn _ => default_type type_enc pred_sym s (length tms))
- #> fold (do_term false) tms
- | do_term _ (AAbs ((_, ty), tm)) = do_type ty #> do_term false tm
- fun do_formula (AQuant (_, xs, phi)) =
- fold do_type (map_filter snd xs) #> do_formula phi
- | do_formula (AConn (_, phis)) = fold do_formula phis
- | do_formula (AAtom tm) = do_term true tm
- fun do_problem_line (Decl (_, _, ty)) = do_type ty
- | do_problem_line (Formula (_, _, phi, _, _)) = do_formula phi
- in
- fold (fold do_problem_line o snd) problem []
- |> filter_out (is_built_in_tptp_symbol o fst o fst)
- end
-
-fun declare_undeclared_syms_in_atp_problem type_enc problem =
- let
- val decls =
- problem
- |> undeclared_syms_in_problem type_enc
- |> sort_wrt (fst o fst)
- |> map (fn (x as (s, _), ty) => Decl (type_decl_prefix ^ s, x, ty ()))
- in (implicit_declsN, decls) :: problem end
-
-fun exists_subdtype P =
- let
- fun ex U = P U orelse
- (case U of Datatype.DtType (_, Us) => exists ex Us | _ => false)
- in ex end
-
-fun is_poly_constr (_, Us) =
- exists (exists_subdtype (fn Datatype.DtTFree _ => true | _ => false)) Us
-
-fun all_constrs_of_polymorphic_datatypes thy =
- Symtab.fold (snd
- #> #descr
- #> maps (snd #> #3)
- #> (fn cs => exists is_poly_constr cs ? append cs))
- (Datatype.get_all thy) []
- |> List.partition is_poly_constr
- |> pairself (map fst)
-
-(* Forcing explicit applications is expensive for polymorphic encodings, because
- it takes only one existential variable ranging over "'a => 'b" to ruin
- everything. Hence we do it only if there are few facts (is normally the case
- for "metis" and the minimizer. *)
-val explicit_apply_threshold = 50
-
-fun prepare_atp_problem ctxt format conj_sym_kind prem_kind type_enc exporter
- lam_trans readable_names preproc hyp_ts concl_t facts =
- let
- val thy = Proof_Context.theory_of ctxt
- val type_enc = type_enc |> adjust_type_enc format
- val explicit_apply =
- if polymorphism_of_type_enc type_enc <> Polymorphic orelse
- length facts <= explicit_apply_threshold then
- NONE
- else
- SOME false
- val lam_trans =
- if lam_trans = keep_lamsN andalso
- not (is_type_enc_higher_order type_enc) then
- error ("Lambda translation scheme incompatible with first-order \
- \encoding.")
- else
- lam_trans
- val (fact_names, classes, conjs, facts, class_rel_clauses, arity_clauses,
- lifted) =
- translate_formulas ctxt format prem_kind type_enc lam_trans preproc hyp_ts
- concl_t facts
- val sym_tab = sym_table_for_facts ctxt type_enc explicit_apply conjs facts
- val mono = conjs @ facts |> mononotonicity_info_for_facts ctxt type_enc
- val (polym_constrs, monom_constrs) =
- all_constrs_of_polymorphic_datatypes thy
- |>> map (make_fixed_const (SOME format))
- val firstorderize =
- firstorderize_fact thy monom_constrs format type_enc sym_tab
- val (conjs, facts) = (conjs, facts) |> pairself (map firstorderize)
- val sym_tab = sym_table_for_facts ctxt type_enc (SOME false) conjs facts
- val helpers =
- sym_tab |> helper_facts_for_sym_table ctxt format type_enc
- |> map firstorderize
- val mono_Ts =
- helpers @ conjs @ facts |> monotonic_types_for_facts ctxt mono type_enc
- val class_decl_lines = decl_lines_for_classes type_enc classes
- val sym_decl_lines =
- (conjs, helpers @ facts)
- |> sym_decl_table_for_facts ctxt format type_enc sym_tab
- |> problem_lines_for_sym_decl_table ctxt format conj_sym_kind mono
- type_enc mono_Ts
- val helper_lines =
- 0 upto length helpers - 1 ~~ helpers
- |> map (formula_line_for_fact ctxt polym_constrs format helper_prefix I
- false true mono type_enc)
- |> (if needs_type_tag_idempotence ctxt type_enc then
- cons (type_tag_idempotence_fact format type_enc)
- else
- I)
- (* Reordering these might confuse the proof reconstruction code or the SPASS
- FLOTTER hack. *)
- val problem =
- [(explicit_declsN, class_decl_lines @ sym_decl_lines),
- (factsN,
- map (formula_line_for_fact ctxt polym_constrs format fact_prefix
- ascii_of (not exporter) (not exporter) mono type_enc)
- (0 upto length facts - 1 ~~ facts)),
- (class_relsN,
- map (formula_line_for_class_rel_clause format type_enc)
- class_rel_clauses),
- (aritiesN,
- map (formula_line_for_arity_clause format type_enc) arity_clauses),
- (helpersN, helper_lines),
- (conjsN,
- map (formula_line_for_conjecture ctxt polym_constrs format mono
- type_enc) conjs),
- (free_typesN, formula_lines_for_free_types type_enc (facts @ conjs))]
- val problem =
- problem
- |> (case format of
- CNF => ensure_cnf_problem
- | CNF_UEQ => filter_cnf_ueq_problem
- | FOF => I
- | TFF (_, TPTP_Implicit) => I
- | THF (_, TPTP_Implicit, _) => I
- | _ => declare_undeclared_syms_in_atp_problem type_enc)
- val (problem, pool) = problem |> nice_atp_problem readable_names format
- fun add_sym_ary (s, {min_ary, ...} : sym_info) =
- min_ary > 0 ? Symtab.insert (op =) (s, min_ary)
- in
- (problem,
- case pool of SOME the_pool => snd the_pool | NONE => Symtab.empty,
- fact_names |> Vector.fromList,
- lifted,
- Symtab.empty |> Symtab.fold add_sym_ary 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
- | add_term_weights weight (AAbs (_, tm)) = add_term_weights weight tm
-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;