correctly handle TFrees that occur in (local) facts -- Metis did the right thing here but Sledgehammer was incorrectly generating spurious preconditions such as "dense_linorder(t_a)"
(* Title: HOL/Tools/Sledgehammer/sledgehammer_atp_translate.ML
Author: Fabian Immler, TU Muenchen
Author: Makarius
Author: Jasmin Blanchette, TU Muenchen
Translation of HOL to FOL for Sledgehammer.
*)
signature SLEDGEHAMMER_ATP_TRANSLATE =
sig
type 'a fo_term = 'a ATP_Problem.fo_term
type 'a problem = 'a ATP_Problem.problem
type translated_formula
datatype type_system =
Tags of bool |
Args |
Mangled |
No_Types
val precise_overloaded_args : bool Unsynchronized.ref
val fact_prefix : string
val conjecture_prefix : string
val types_dangerous_types : type_system -> bool
val num_atp_type_args : theory -> type_system -> string -> int
val translate_atp_fact :
Proof.context -> bool -> (string * 'a) * thm
-> translated_formula option * ((string * 'a) * thm)
val unmangled_const : string -> string * string fo_term list
val prepare_atp_problem :
Proof.context -> bool -> bool -> type_system -> bool -> term list -> term
-> (translated_formula option * ((string * 'a) * thm)) list
-> string problem * string Symtab.table * int * (string * 'a) list vector
val atp_problem_weights : string problem -> (string * real) list
end;
structure Sledgehammer_ATP_Translate : SLEDGEHAMMER_ATP_TRANSLATE =
struct
open ATP_Problem
open Metis_Translate
open Sledgehammer_Util
(* FIXME: Remove references once appropriate defaults have been determined
empirically. *)
val precise_overloaded_args = Unsynchronized.ref false
val fact_prefix = "fact_"
val conjecture_prefix = "conj_"
val helper_prefix = "help_"
val class_rel_clause_prefix = "clrel_";
val arity_clause_prefix = "arity_"
val tfree_prefix = "tfree_"
(* Freshness almost guaranteed! *)
val sledgehammer_weak_prefix = "Sledgehammer:"
type translated_formula =
{name: string,
kind: kind,
combformula: (name, combterm) formula,
ctypes_sorts: typ list}
datatype type_system =
Tags of bool |
Args |
Mangled |
No_Types
fun types_dangerous_types (Tags _) = true
| types_dangerous_types _ = false
(* This is an approximation. If it returns "true" for a constant that isn't
overloaded (i.e., that has one uniform definition), needless clutter is
generated; if it returns "false" for an overloaded constant, the ATP gets a
license to do unsound reasoning if the type system is "overloaded_args". *)
fun is_overloaded thy s =
not (s = @{const_name HOL.eq}) andalso
not (s = @{const_name Metis.fequal}) andalso
(not (!precise_overloaded_args) orelse s = @{const_name finite} orelse
length (Defs.specifications_of (Theory.defs_of thy) s) > 1)
fun needs_type_args thy type_sys s =
case type_sys of
Tags full_types => not full_types andalso is_overloaded thy s
| Args => is_overloaded thy s
| Mangled => true
| No_Types => false
datatype type_arg_policy = No_Type_Args | Explicit_Type_Args | Mangled_Types
fun type_arg_policy thy type_sys s =
if needs_type_args thy type_sys s then
if type_sys = Mangled then Mangled_Types else Explicit_Type_Args
else
No_Type_Args
fun num_atp_type_args thy type_sys s =
if type_arg_policy thy type_sys s = Explicit_Type_Args then
num_type_args thy s
else
0
fun atp_type_literals_for_types type_sys kind Ts =
if type_sys = No_Types then
[]
else
Ts |> type_literals_for_types
|> filter (fn TyLitVar _ => kind <> Conjecture
| TyLitFree _ => kind = Conjecture)
fun mk_anot phi = AConn (ANot, [phi])
fun mk_aconn c phi1 phi2 = AConn (c, [phi1, phi2])
fun mk_ahorn [] phi = phi
| mk_ahorn (phi :: phis) psi =
AConn (AImplies, [fold (mk_aconn AAnd) phis phi, psi])
fun close_universally phi =
let
fun term_vars bounds (ATerm (name as (s, _), tms)) =
(is_atp_variable s andalso not (member (op =) bounds name))
? insert (op =) name
#> fold (term_vars bounds) tms
fun formula_vars bounds (AQuant (_, xs, phi)) =
formula_vars (xs @ bounds) phi
| formula_vars bounds (AConn (_, phis)) = fold (formula_vars bounds) phis
| formula_vars bounds (AAtom tm) = term_vars bounds tm
in
case formula_vars [] phi [] of [] => phi | xs => AQuant (AForall, xs, phi)
end
fun combformula_for_prop thy eq_as_iff =
let
fun do_term bs t ts =
combterm_from_term thy bs (Envir.eta_contract t)
|>> AAtom ||> union (op =) ts
fun do_quant bs q s T t' =
let val s = Name.variant (map fst bs) s in
do_formula ((s, T) :: bs) t'
#>> (fn phi => AQuant (q, [`make_bound_var s], phi))
end
and do_conn bs c t1 t2 =
do_formula bs t1 ##>> do_formula bs t2
#>> (fn (phi1, phi2) => AConn (c, [phi1, phi2]))
and do_formula bs t =
case t of
@{const Not} $ t1 =>
do_formula bs t1 #>> (fn phi => AConn (ANot, [phi]))
| Const (@{const_name All}, _) $ Abs (s, T, t') =>
do_quant bs AForall s T t'
| Const (@{const_name Ex}, _) $ Abs (s, T, t') =>
do_quant bs AExists s T t'
| @{const HOL.conj} $ t1 $ t2 => do_conn bs AAnd t1 t2
| @{const HOL.disj} $ t1 $ t2 => do_conn bs AOr t1 t2
| @{const HOL.implies} $ t1 $ t2 => do_conn bs AImplies t1 t2
| Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])) $ t1 $ t2 =>
if eq_as_iff then do_conn bs AIff t1 t2 else do_term bs t
| _ => do_term bs t
in do_formula [] end
val presimplify_term = prop_of o Meson.presimplify oo Skip_Proof.make_thm
fun concealed_bound_name j = sledgehammer_weak_prefix ^ string_of_int j
fun conceal_bounds Ts t =
subst_bounds (map (Free o apfst concealed_bound_name)
(0 upto length Ts - 1 ~~ Ts), t)
fun reveal_bounds Ts =
subst_atomic (map (fn (j, T) => (Free (concealed_bound_name j, T), Bound j))
(0 upto length Ts - 1 ~~ Ts))
(* Removes the lambdas from an equation of the form "t = (%x. u)".
(Cf. "extensionalize_theorem" in "Meson_Clausify".) *)
fun extensionalize_term t =
let
fun aux j (@{const Trueprop} $ t') = @{const Trueprop} $ aux j t'
| aux j (t as Const (s, Type (_, [Type (_, [_, T']),
Type (_, [_, res_T])]))
$ t2 $ Abs (var_s, var_T, t')) =
if s = @{const_name HOL.eq} orelse s = @{const_name "=="} then
let val var_t = Var ((var_s, j), var_T) in
Const (s, T' --> T' --> res_T)
$ betapply (t2, var_t) $ subst_bound (var_t, t')
|> aux (j + 1)
end
else
t
| aux _ t = t
in aux (maxidx_of_term t + 1) t end
fun introduce_combinators_in_term ctxt kind t =
let val thy = ProofContext.theory_of ctxt in
if Meson.is_fol_term thy t then
t
else
let
fun aux Ts t =
case t of
@{const Not} $ t1 => @{const Not} $ aux Ts t1
| (t0 as Const (@{const_name All}, _)) $ Abs (s, T, t') =>
t0 $ Abs (s, T, aux (T :: Ts) t')
| (t0 as Const (@{const_name All}, _)) $ t1 =>
aux Ts (t0 $ eta_expand Ts t1 1)
| (t0 as Const (@{const_name Ex}, _)) $ Abs (s, T, t') =>
t0 $ Abs (s, T, aux (T :: Ts) t')
| (t0 as Const (@{const_name Ex}, _)) $ t1 =>
aux Ts (t0 $ eta_expand Ts t1 1)
| (t0 as @{const HOL.conj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
| (t0 as @{const HOL.disj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
| (t0 as @{const HOL.implies}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2
| (t0 as Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])))
$ t1 $ t2 =>
t0 $ aux Ts t1 $ aux Ts t2
| _ => if not (exists_subterm (fn Abs _ => true | _ => false) t) then
t
else
t |> conceal_bounds Ts
|> Envir.eta_contract
|> cterm_of thy
|> Meson_Clausify.introduce_combinators_in_cterm
|> prop_of |> Logic.dest_equals |> snd
|> reveal_bounds Ts
val (t, ctxt') = Variable.import_terms true [t] ctxt |>> the_single
in t |> aux [] |> singleton (Variable.export_terms ctxt' ctxt) end
handle THM _ =>
(* A type variable of sort "{}" will make abstraction fail. *)
if kind = Conjecture then HOLogic.false_const
else HOLogic.true_const
end
(* Metis's use of "resolve_tac" freezes the schematic variables. We simulate the
same in Sledgehammer to prevent the discovery of unreplayable proofs. *)
fun freeze_term t =
let
fun aux (t $ u) = aux t $ aux u
| aux (Abs (s, T, t)) = Abs (s, T, aux t)
| aux (Var ((s, i), T)) =
Free (sledgehammer_weak_prefix ^ s ^ "_" ^ string_of_int i, T)
| aux t = t
in t |> exists_subterm is_Var t ? aux end
(* making fact and conjecture formulas *)
fun make_formula ctxt eq_as_iff presimp name kind t =
let
val thy = ProofContext.theory_of ctxt
val t = t |> Envir.beta_eta_contract
|> transform_elim_term
|> Object_Logic.atomize_term thy
val need_trueprop = (fastype_of t = HOLogic.boolT)
val t = t |> need_trueprop ? HOLogic.mk_Trueprop
|> extensionalize_term
|> presimp ? presimplify_term thy
|> perhaps (try (HOLogic.dest_Trueprop))
|> introduce_combinators_in_term ctxt kind
|> kind <> Axiom ? freeze_term
val (combformula, ctypes_sorts) = combformula_for_prop thy eq_as_iff t []
in
{name = name, combformula = combformula, kind = kind,
ctypes_sorts = ctypes_sorts}
end
fun make_fact ctxt keep_trivial eq_as_iff presimp ((name, _), th) =
case (keep_trivial,
make_formula ctxt eq_as_iff presimp name Axiom (prop_of th)) of
(false, {combformula = AAtom (CombConst (("c_True", _), _, _)), ...}) =>
NONE
| (_, formula) => SOME formula
fun make_conjecture ctxt ts =
let val last = length ts - 1 in
map2 (fn j => make_formula ctxt true true (string_of_int j)
(if j = last then Conjecture else Hypothesis))
(0 upto last) ts
end
(** Helper facts **)
fun fold_formula f (AQuant (_, _, phi)) = fold_formula f phi
| fold_formula f (AConn (_, phis)) = fold (fold_formula f) phis
| fold_formula f (AAtom tm) = f tm
fun count_term (ATerm ((s, _), tms)) =
(if is_atp_variable s then I
else Symtab.map_entry s (Integer.add 1))
#> fold count_term tms
fun count_formula x = fold_formula count_term x
val init_counters =
metis_helpers |> map fst |> sort_distinct string_ord |> map (rpair 0)
|> Symtab.make
fun get_helper_facts ctxt explicit_forall type_sys formulas =
let
val no_dangerous_types = types_dangerous_types type_sys
val ct = init_counters |> fold count_formula formulas
fun is_used s = the (Symtab.lookup ct s) > 0
fun dub c needs_full_types (th, j) =
((c ^ "_" ^ string_of_int j ^ (if needs_full_types then "ft" else ""),
false), th)
fun make_facts eq_as_iff = map_filter (make_fact ctxt false eq_as_iff false)
in
(metis_helpers
|> filter (is_used o fst)
|> maps (fn (c, (needs_full_types, ths)) =>
if needs_full_types andalso not no_dangerous_types then
[]
else
ths ~~ (1 upto length ths)
|> map (dub c needs_full_types)
|> make_facts (not needs_full_types)),
if type_sys = Tags false then
let
fun var s = ATerm (`I s, [])
fun tag tm = ATerm (`I type_tag_name, [var "X", tm])
in
[Fof (helper_prefix ^ ascii_of "ti_ti", Axiom,
AAtom (ATerm (`I "equal", [tag (tag (var "Y")), tag (var "Y")]))
|> explicit_forall ? close_universally, NONE)]
end
else
[])
end
fun translate_atp_fact ctxt keep_trivial =
`(make_fact ctxt keep_trivial true true)
fun translate_formulas ctxt type_sys hyp_ts concl_t rich_facts =
let
val thy = ProofContext.theory_of ctxt
val fact_ts = map (prop_of o snd o snd) rich_facts
val (facts, fact_names) =
rich_facts
|> map_filter (fn (NONE, _) => NONE
| (SOME fact, (name, _)) => SOME (fact, name))
|> ListPair.unzip
(* Remove existing facts from the conjecture, as this can dramatically
boost an ATP's performance (for some reason). *)
val hyp_ts = hyp_ts |> filter_out (member (op aconv) fact_ts)
val goal_t = Logic.list_implies (hyp_ts, concl_t)
val all_ts = goal_t :: fact_ts
val subs = tfree_classes_of_terms all_ts
val supers = tvar_classes_of_terms all_ts
val tycons = type_consts_of_terms thy all_ts
val conjs = make_conjecture ctxt (hyp_ts @ [concl_t])
val (supers', arity_clauses) =
if type_sys = No_Types then ([], [])
else make_arity_clauses thy tycons supers
val class_rel_clauses = make_class_rel_clauses thy subs supers'
in
(fact_names |> map single, (conjs, facts, class_rel_clauses, arity_clauses))
end
fun tag_with_type ty t = ATerm (`I type_tag_name, [ty, t])
fun fo_term_for_combtyp (CombTVar name) = ATerm (name, [])
| fo_term_for_combtyp (CombTFree name) = ATerm (name, [])
| fo_term_for_combtyp (CombType (name, tys)) =
ATerm (name, map fo_term_for_combtyp tys)
fun fo_literal_for_type_literal (TyLitVar (class, name)) =
(true, ATerm (class, [ATerm (name, [])]))
| fo_literal_for_type_literal (TyLitFree (class, name)) =
(true, ATerm (class, [ATerm (name, [])]))
fun formula_for_fo_literal (pos, t) = AAtom t |> not pos ? mk_anot
(* Finite types such as "unit", "bool", "bool * bool", and "bool => bool" are
considered dangerous because their "exhaust" properties can easily lead to
unsound ATP proofs. The checks below are an (unsound) approximation of
finiteness. *)
fun is_dtyp_dangerous _ (Datatype_Aux.DtTFree _) = true
| is_dtyp_dangerous ctxt (Datatype_Aux.DtType (s, Us)) =
is_type_constr_dangerous ctxt s andalso forall (is_dtyp_dangerous ctxt) Us
| is_dtyp_dangerous _ (Datatype_Aux.DtRec _) = false
and is_type_dangerous ctxt (Type (s, Ts)) =
is_type_constr_dangerous ctxt s andalso forall (is_type_dangerous ctxt) Ts
| is_type_dangerous _ _ = false
and is_type_constr_dangerous ctxt s =
let val thy = ProofContext.theory_of ctxt in
case Datatype_Data.get_info thy s of
SOME {descr, ...} =>
forall (fn (_, (_, _, constrs)) =>
forall (forall (is_dtyp_dangerous ctxt) o snd) constrs) descr
| NONE =>
case Typedef.get_info ctxt s of
({rep_type, ...}, _) :: _ => is_type_dangerous ctxt rep_type
| [] => true
end
fun is_combtyp_dangerous ctxt (CombType ((s, _), tys)) =
(case strip_prefix_and_unascii type_const_prefix s of
SOME s' => forall (is_combtyp_dangerous ctxt) tys andalso
is_type_constr_dangerous ctxt (invert_const s')
| NONE => false)
| is_combtyp_dangerous _ _ = false
fun should_tag_with_type ctxt (Tags full_types) ty =
full_types orelse is_combtyp_dangerous ctxt ty
| should_tag_with_type _ _ _ = false
val fname_table =
[("c_False", (0, ("c_fFalse", @{const_name Metis.fFalse}))),
("c_True", (0, ("c_fTrue", @{const_name Metis.fTrue}))),
("c_Not", (1, ("c_fNot", @{const_name Metis.fNot}))),
("c_conj", (2, ("c_fconj", @{const_name Metis.fconj}))),
("c_disj", (2, ("c_fdisj", @{const_name Metis.fdisj}))),
("c_implies", (2, ("c_fimplies", @{const_name Metis.fimplies}))),
("equal", (2, ("c_fequal", @{const_name Metis.fequal})))]
(* We are crossing our fingers that it doesn't clash with anything else. *)
val mangled_type_sep = "\000"
fun mangled_combtyp f (CombTFree name) = f name
| mangled_combtyp f (CombTVar name) =
f name (* FIXME: shouldn't happen *)
(* raise Fail "impossible schematic type variable" *)
| mangled_combtyp f (CombType (name, tys)) =
"(" ^ commas (map (mangled_combtyp f) tys) ^ ")" ^ f name
fun mangled_type_suffix f g tys =
fold_rev (curry (op ^) o g o prefix mangled_type_sep o mangled_combtyp f)
tys ""
val parse_mangled_ident =
Scan.many1 (not o member (op =) ["(", ")", ","]) >> implode
fun parse_mangled_type x =
($$ "(" |-- Scan.optional parse_mangled_types [] --| $$ ")"
-- parse_mangled_ident >> (ATerm o swap)
|| parse_mangled_ident >> (ATerm o rpair [])) 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
fun unmangled_const s =
let val ss = space_explode mangled_type_sep s in
(hd ss, map unmangled_type (tl ss))
end
fun fo_term_for_combterm ctxt type_sys =
let
val thy = ProofContext.theory_of ctxt
fun aux top_level u =
let
val (head, args) = strip_combterm_comb u
val (x, ty_args) =
case head of
CombConst (name as (s, s'), _, ty_args) =>
(case AList.lookup (op =) fname_table s of
SOME (n, fname) =>
(if top_level andalso length args = n then
case s of
"c_False" => ("$false", s')
| "c_True" => ("$true", s')
| _ => name
else
fname, [])
| NONE =>
case strip_prefix_and_unascii const_prefix s of
NONE => (name, ty_args)
| SOME s'' =>
let val s'' = invert_const s'' in
case type_arg_policy thy type_sys s'' of
No_Type_Args => (name, [])
| Explicit_Type_Args => (name, ty_args)
| Mangled_Types =>
((s ^ mangled_type_suffix fst ascii_of ty_args,
s' ^ mangled_type_suffix snd I ty_args), [])
end)
| CombVar (name, _) => (name, [])
| CombApp _ => raise Fail "impossible \"CombApp\""
val t =
ATerm (x, map fo_term_for_combtyp ty_args @ map (aux false) args)
val ty = combtyp_of u
in
t |> (if should_tag_with_type ctxt type_sys ty then
tag_with_type (fo_term_for_combtyp ty)
else
I)
end
in aux true end
fun formula_for_combformula ctxt type_sys =
let
fun aux (AQuant (q, xs, phi)) = AQuant (q, xs, aux phi)
| aux (AConn (c, phis)) = AConn (c, map aux phis)
| aux (AAtom tm) = AAtom (fo_term_for_combterm ctxt type_sys tm)
in aux end
fun formula_for_fact ctxt type_sys
({combformula, ctypes_sorts, ...} : translated_formula) =
mk_ahorn (map (formula_for_fo_literal o fo_literal_for_type_literal)
(atp_type_literals_for_types type_sys Axiom ctypes_sorts))
(formula_for_combformula ctxt type_sys combformula)
(* 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 problem_line_for_fact ctxt prefix type_sys
(j, formula as {name, kind, ...}) =
Fof (prefix ^ string_of_int j ^ "_" ^ ascii_of name, kind,
formula_for_fact ctxt type_sys formula, NONE)
fun problem_line_for_class_rel_clause (ClassRelClause {name, subclass,
superclass, ...}) =
let val ty_arg = ATerm (("T", "T"), []) in
Fof (class_rel_clause_prefix ^ ascii_of name, Axiom,
AConn (AImplies, [AAtom (ATerm (subclass, [ty_arg])),
AAtom (ATerm (superclass, [ty_arg]))]), NONE)
end
fun fo_literal_for_arity_literal (TConsLit (c, t, args)) =
(true, ATerm (c, [ATerm (t, map (fn arg => ATerm (arg, [])) args)]))
| fo_literal_for_arity_literal (TVarLit (c, sort)) =
(false, ATerm (c, [ATerm (sort, [])]))
fun problem_line_for_arity_clause (ArityClause {name, conclLit, premLits,
...}) =
Fof (arity_clause_prefix ^ ascii_of name, Axiom,
mk_ahorn (map (formula_for_fo_literal o apfst not
o fo_literal_for_arity_literal) premLits)
(formula_for_fo_literal
(fo_literal_for_arity_literal conclLit)), NONE)
fun problem_line_for_conjecture ctxt type_sys
({name, kind, combformula, ...} : translated_formula) =
Fof (conjecture_prefix ^ name, kind,
formula_for_combformula ctxt type_sys combformula, NONE)
fun free_type_literals type_sys ({ctypes_sorts, ...} : translated_formula) =
ctypes_sorts |> atp_type_literals_for_types type_sys Conjecture
|> map fo_literal_for_type_literal
fun problem_line_for_free_type j lit =
Fof (tfree_prefix ^ string_of_int j, Hypothesis, formula_for_fo_literal lit,
NONE)
fun problem_lines_for_free_types type_sys facts =
let
val litss = map (free_type_literals type_sys) facts
val lits = fold (union (op =)) litss []
in map2 problem_line_for_free_type (0 upto length lits - 1) lits end
(** "hBOOL" and "hAPP" **)
type const_info = {min_arity: int, max_arity: int, sub_level: bool}
fun consider_term top_level (ATerm ((s, _), ts)) =
(if is_atp_variable s then
I
else
let val n = length ts in
Symtab.map_default
(s, {min_arity = n, max_arity = 0, sub_level = false})
(fn {min_arity, max_arity, sub_level} =>
{min_arity = Int.min (n, min_arity),
max_arity = Int.max (n, max_arity),
sub_level = sub_level orelse not top_level})
end)
#> fold (consider_term (top_level andalso s = type_tag_name)) ts
fun consider_formula (AQuant (_, _, phi)) = consider_formula phi
| consider_formula (AConn (_, phis)) = fold consider_formula phis
| consider_formula (AAtom tm) = consider_term true tm
fun consider_problem_line (Fof (_, _, phi, _)) = consider_formula phi
fun consider_problem problem = fold (fold consider_problem_line o snd) problem
(* needed for helper facts if the problem otherwise does not involve equality *)
val equal_entry = ("equal", {min_arity = 2, max_arity = 2, sub_level = false})
fun const_table_for_problem explicit_apply problem =
if explicit_apply then
NONE
else
SOME (Symtab.empty |> Symtab.default equal_entry |> consider_problem problem)
fun min_arity_of thy type_sys NONE s =
(if s = "equal" orelse s = type_tag_name orelse
String.isPrefix type_const_prefix s orelse
String.isPrefix class_prefix s then
16383 (* large number *)
else case strip_prefix_and_unascii const_prefix s of
SOME s' =>
s' |> unmangled_const |> fst |> invert_const
|> num_atp_type_args thy type_sys
| NONE => 0)
| min_arity_of _ _ (SOME the_const_tab) s =
case Symtab.lookup the_const_tab s of
SOME ({min_arity, ...} : const_info) => min_arity
| NONE => 0
fun full_type_of (ATerm ((s, _), [ty, _])) =
if s = type_tag_name then SOME ty else NONE
| full_type_of _ = NONE
fun list_hAPP_rev _ t1 [] = t1
| list_hAPP_rev NONE t1 (t2 :: ts2) =
ATerm (`I "hAPP", [list_hAPP_rev NONE t1 ts2, t2])
| list_hAPP_rev (SOME ty) t1 (t2 :: ts2) =
case full_type_of t2 of
SOME ty2 =>
let val ty' = ATerm (`make_fixed_type_const @{type_name fun},
[ty2, ty]) in
ATerm (`I "hAPP",
[tag_with_type ty' (list_hAPP_rev (SOME ty') t1 ts2), t2])
end
| NONE => list_hAPP_rev NONE t1 (t2 :: ts2)
fun repair_applications_in_term thy type_sys const_tab =
let
fun aux opt_ty (ATerm (name as (s, _), ts)) =
if s = type_tag_name then
case ts of
[t1, t2] => ATerm (name, [aux NONE t1, aux (SOME t1) t2])
| _ => raise Fail "malformed type tag"
else
let
val ts = map (aux NONE) ts
val (ts1, ts2) = chop (min_arity_of thy type_sys const_tab s) ts
in list_hAPP_rev opt_ty (ATerm (name, ts1)) (rev ts2) end
in aux NONE end
fun boolify t = ATerm (`I "hBOOL", [t])
(* 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_predicate NONE s =
s = "equal" orelse s = "$false" orelse s = "$true" orelse
String.isPrefix type_const_prefix s orelse String.isPrefix class_prefix s
| is_predicate (SOME the_const_tab) s =
case Symtab.lookup the_const_tab s of
SOME {min_arity, max_arity, sub_level} =>
not sub_level andalso min_arity = max_arity
| NONE => false
fun repair_predicates_in_term pred_const_tab (t as ATerm ((s, _), ts)) =
if s = type_tag_name then
case ts of
[_, t' as ATerm ((s', _), _)] =>
if is_predicate pred_const_tab s' then t' else boolify t
| _ => raise Fail "malformed type tag"
else
t |> not (is_predicate pred_const_tab s) ? boolify
fun repair_formula thy explicit_forall type_sys const_tab =
let
val pred_const_tab = case type_sys of Tags _ => NONE | _ => const_tab
fun aux (AQuant (q, xs, phi)) = AQuant (q, xs, aux phi)
| aux (AConn (c, phis)) = AConn (c, map aux phis)
| aux (AAtom tm) =
AAtom (tm |> repair_applications_in_term thy type_sys const_tab
|> repair_predicates_in_term pred_const_tab)
in aux #> explicit_forall ? close_universally end
fun repair_problem_line thy explicit_forall type_sys const_tab
(Fof (ident, kind, phi, source)) =
Fof (ident, kind, repair_formula thy explicit_forall type_sys const_tab phi,
source)
fun repair_problem thy = map o apsnd o map ooo repair_problem_line thy
fun dest_Fof (Fof z) = z
val factsN = "Relevant facts"
val class_relsN = "Class relationships"
val aritiesN = "Arity declarations"
val helpersN = "Helper facts"
val conjsN = "Conjectures"
val free_typesN = "Type variables"
fun offset_of_heading_in_problem _ [] j = j
| offset_of_heading_in_problem needle ((heading, lines) :: problem) j =
if heading = needle then j
else offset_of_heading_in_problem needle problem (j + length lines)
fun prepare_atp_problem ctxt readable_names explicit_forall type_sys
explicit_apply hyp_ts concl_t facts =
let
val thy = ProofContext.theory_of ctxt
val (fact_names, (conjs, facts, class_rel_clauses, arity_clauses)) =
translate_formulas ctxt type_sys hyp_ts concl_t facts
(* Reordering these might or might not confuse the proof reconstruction
code or the SPASS Flotter hack. *)
val problem =
[(factsN, map (problem_line_for_fact ctxt fact_prefix type_sys)
(0 upto length facts - 1 ~~ facts)),
(class_relsN, map problem_line_for_class_rel_clause class_rel_clauses),
(aritiesN, map problem_line_for_arity_clause arity_clauses),
(helpersN, []),
(conjsN, map (problem_line_for_conjecture ctxt type_sys) conjs),
(free_typesN, problem_lines_for_free_types type_sys (facts @ conjs))]
val const_tab = const_table_for_problem explicit_apply problem
val problem =
problem |> repair_problem thy explicit_forall type_sys const_tab
val helper_lines =
get_helper_facts ctxt explicit_forall type_sys
(maps (map (#3 o dest_Fof) o snd) problem)
|>> map (pair 0
#> problem_line_for_fact ctxt helper_prefix type_sys
#> repair_problem_line thy explicit_forall type_sys const_tab)
|> op @
val (problem, pool) =
problem |> AList.update (op =) (helpersN, helper_lines)
|> nice_atp_problem readable_names
in
(problem,
case pool of SOME the_pool => snd the_pool | NONE => Symtab.empty,
offset_of_heading_in_problem conjsN problem 0,
fact_names |> Vector.fromList)
end
(* FUDGE *)
val conj_weight = 0.0
val hyp_weight = 0.1
val fact_min_weight = 0.2
val fact_max_weight = 1.0
fun add_term_weights weight (ATerm (s, tms)) =
(not (is_atp_variable s) andalso s <> "equal") ? Symtab.default (s, weight)
#> fold (add_term_weights weight) tms
fun add_problem_line_weights weight (Fof (_, _, phi, _)) =
fold_formula (add_term_weights weight) phi
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 =
Symtab.empty
|> add_conjectures_weights (these (AList.lookup (op =) problem conjsN))
|> add_facts_weights (these (AList.lookup (op =) problem factsN))
|> Symtab.dest
|> sort (prod_ord Real.compare string_ord o pairself swap)
end;