renamed "Sledgehammer_Fact_Preprocessor" to "Clausifier";
the new name reflects that it's not used only by Sledgehammer (but also by "meson" and "metis") and that it doesn't only clausify facts (but also goals)
(* Title: HOL/Tools/Sledgehammer/sledgehammer_hol_clause.ML
Author: Jia Meng, NICTA
Author: Jasmin Blanchette, TU Muenchen
FOL clauses translated from HOL formulas.
*)
signature SLEDGEHAMMER_HOL_CLAUSE =
sig
type cnf_thm = Clausifier.cnf_thm
type name = Sledgehammer_FOL_Clause.name
type name_pool = Sledgehammer_FOL_Clause.name_pool
type kind = Sledgehammer_FOL_Clause.kind
type classrel_clause = Sledgehammer_FOL_Clause.classrel_clause
type arity_clause = Sledgehammer_FOL_Clause.arity_clause
type polarity = bool
datatype combtyp =
TyVar of name |
TyFree of name |
TyConstr of name * combtyp list
datatype combterm =
CombConst of name * combtyp * combtyp list (* Const and Free *) |
CombVar of name * combtyp |
CombApp of combterm * combterm
datatype literal = Literal of polarity * combterm
datatype hol_clause =
HOLClause of {clause_id: int, axiom_name: string, th: thm, kind: kind,
literals: literal list, ctypes_sorts: typ list}
exception TRIVIAL of unit
val type_of_combterm : combterm -> combtyp
val strip_combterm_comb : combterm -> combterm * combterm list
val literals_of_term : theory -> term -> literal list * typ list
val conceal_skolem_somes :
int -> (string * term) list -> term -> (string * term) list * term
val is_quasi_fol_theorem : theory -> thm -> bool
val make_clause_table : (thm * 'a) list -> (thm * 'a) Termtab.table
val tfree_classes_of_terms : term list -> string list
val tvar_classes_of_terms : term list -> string list
val type_consts_of_terms : theory -> term list -> string list
val prepare_clauses :
bool -> thm list -> cnf_thm list -> cnf_thm list -> theory
-> string vector
* (hol_clause list * hol_clause list * hol_clause list * hol_clause list
* classrel_clause list * arity_clause list)
end
structure Sledgehammer_HOL_Clause : SLEDGEHAMMER_HOL_CLAUSE =
struct
open Clausifier
open Sledgehammer_Util
open Sledgehammer_FOL_Clause
(******************************************************)
(* data types for typed combinator expressions *)
(******************************************************)
type polarity = bool
datatype combtyp =
TyVar of name |
TyFree of name |
TyConstr of name * combtyp list
datatype combterm =
CombConst of name * combtyp * combtyp list (* Const and Free *) |
CombVar of name * combtyp |
CombApp of combterm * combterm
datatype literal = Literal of polarity * combterm;
datatype hol_clause =
HOLClause of {clause_id: int, axiom_name: string, th: thm, kind: kind,
literals: literal list, ctypes_sorts: typ list}
(*********************************************************************)
(* convert a clause with type Term.term to a clause with type clause *)
(*********************************************************************)
(*Result of a function type; no need to check that the argument type matches.*)
fun result_type (TyConstr (_, [_, tp2])) = tp2
| result_type _ = raise Fail "non-function type"
fun type_of_combterm (CombConst (_, tp, _)) = tp
| type_of_combterm (CombVar (_, tp)) = tp
| type_of_combterm (CombApp (t1, _)) = result_type (type_of_combterm t1)
(*gets the head of a combinator application, along with the list of arguments*)
fun strip_combterm_comb u =
let fun stripc (CombApp(t,u), ts) = stripc (t, u::ts)
| stripc x = x
in stripc(u,[]) end
fun isFalse (Literal (pol, CombConst ((c, _), _, _))) =
(pol andalso c = "c_False") orelse (not pol andalso c = "c_True")
| isFalse _ = false;
fun isTrue (Literal (pol, CombConst ((c, _), _, _))) =
(pol andalso c = "c_True") orelse
(not pol andalso c = "c_False")
| isTrue _ = false;
fun isTaut (HOLClause {literals,...}) = exists isTrue literals;
fun type_of (Type (a, Ts)) =
let val (folTypes,ts) = types_of Ts in
(TyConstr (`make_fixed_type_const a, folTypes), ts)
end
| type_of (tp as TFree (a, _)) = (TyFree (`make_fixed_type_var a), [tp])
| type_of (tp as TVar (x, _)) =
(TyVar (make_schematic_type_var x, string_of_indexname x), [tp])
and types_of Ts =
let val (folTyps, ts) = ListPair.unzip (map type_of Ts) in
(folTyps, union_all ts)
end
(* same as above, but no gathering of sort information *)
fun simp_type_of (Type (a, Ts)) =
TyConstr (`make_fixed_type_const a, map simp_type_of Ts)
| simp_type_of (TFree (a, _)) = TyFree (`make_fixed_type_var a)
| simp_type_of (TVar (x, _)) =
TyVar (make_schematic_type_var x, string_of_indexname x)
(* convert a Term.term (with combinators) into a combterm, also accummulate sort info *)
fun combterm_of thy (Const (c, T)) =
let
val (tp, ts) = type_of T
val tvar_list =
(if String.isPrefix skolem_theory_name c then
[] |> Term.add_tvarsT T |> map TVar
else
(c, T) |> Sign.const_typargs thy)
|> map simp_type_of
val c' = CombConst (`make_fixed_const c, tp, tvar_list)
in (c',ts) end
| combterm_of _ (Free(v, T)) =
let val (tp,ts) = type_of T
val v' = CombConst (`make_fixed_var v, tp, [])
in (v',ts) end
| combterm_of _ (Var(v, T)) =
let val (tp,ts) = type_of T
val v' = CombVar ((make_schematic_var v, string_of_indexname v), tp)
in (v',ts) end
| combterm_of thy (P $ Q) =
let val (P', tsP) = combterm_of thy P
val (Q', tsQ) = combterm_of thy Q
in (CombApp (P', Q'), union (op =) tsP tsQ) end
| combterm_of _ (t as Abs _) = raise Fail "HOL clause: Abs"
fun predicate_of thy ((@{const Not} $ P), polarity) =
predicate_of thy (P, not polarity)
| predicate_of thy (t, polarity) =
(combterm_of thy (Envir.eta_contract t), polarity)
fun literals_of_term1 args thy (@{const Trueprop} $ P) =
literals_of_term1 args thy P
| literals_of_term1 args thy (@{const "op |"} $ P $ Q) =
literals_of_term1 (literals_of_term1 args thy P) thy Q
| literals_of_term1 (lits, ts) thy P =
let val ((pred, ts'), pol) = predicate_of thy (P, true) in
(Literal (pol, pred) :: lits, union (op =) ts ts')
end
val literals_of_term = literals_of_term1 ([], [])
fun skolem_name i j num_T_args =
skolem_prefix ^ (space_implode "_" (map Int.toString [i, j, num_T_args])) ^
skolem_infix ^ "g"
fun conceal_skolem_somes i skolem_somes t =
if exists_Const (curry (op =) @{const_name skolem_id} o fst) t then
let
fun aux skolem_somes
(t as (Const (@{const_name skolem_id}, Type (_, [_, T])) $ _)) =
let
val (skolem_somes, s) =
if i = ~1 then
(skolem_somes, @{const_name undefined})
else case AList.find (op aconv) skolem_somes t of
s :: _ => (skolem_somes, s)
| [] =>
let
val s = skolem_theory_name ^ "." ^
skolem_name i (length skolem_somes)
(length (Term.add_tvarsT T []))
in ((s, t) :: skolem_somes, s) end
in (skolem_somes, Const (s, T)) end
| aux skolem_somes (t1 $ t2) =
let
val (skolem_somes, t1) = aux skolem_somes t1
val (skolem_somes, t2) = aux skolem_somes t2
in (skolem_somes, t1 $ t2) end
| aux skolem_somes (Abs (s, T, t')) =
let val (skolem_somes, t') = aux skolem_somes t' in
(skolem_somes, Abs (s, T, t'))
end
| aux skolem_somes t = (skolem_somes, t)
in aux skolem_somes t end
else
(skolem_somes, t)
fun is_quasi_fol_theorem thy =
Meson.is_fol_term thy o snd o conceal_skolem_somes ~1 [] o prop_of
(* Trivial problem, which resolution cannot handle (empty clause) *)
exception TRIVIAL of unit
(* making axiom and conjecture clauses *)
fun make_clause thy (clause_id, axiom_name, kind, th) skolem_somes =
let
val (skolem_somes, t) =
th |> prop_of |> conceal_skolem_somes clause_id skolem_somes
val (lits, ctypes_sorts) = literals_of_term thy t
in
if forall isFalse lits then
raise TRIVIAL ()
else
(skolem_somes,
HOLClause {clause_id = clause_id, axiom_name = axiom_name, th = th,
kind = kind, literals = lits, ctypes_sorts = ctypes_sorts})
end
fun add_axiom_clause thy (th, ((name, id), _ : thm)) (skolem_somes, clss) =
let
val (skolem_somes, cls) = make_clause thy (id, name, Axiom, th) skolem_somes
in (skolem_somes, clss |> not (isTaut cls) ? cons (name, cls)) end
fun make_axiom_clauses thy clauses =
([], []) |> fold_rev (add_axiom_clause thy) clauses |> snd
fun make_conjecture_clauses thy =
let
fun aux _ _ [] = []
| aux n skolem_somes (th :: ths) =
let
val (skolem_somes, cls) =
make_clause thy (n, "conjecture", Conjecture, th) skolem_somes
in cls :: aux (n + 1) skolem_somes ths end
in aux 0 [] end
(** Helper clauses **)
fun count_combterm (CombConst ((c, _), _, _)) =
Symtab.map_entry c (Integer.add 1)
| count_combterm (CombVar _) = I
| count_combterm (CombApp (t1, t2)) = count_combterm t1 #> count_combterm t2
fun count_literal (Literal (_, t)) = count_combterm t
fun count_clause (HOLClause {literals, ...}) = fold count_literal literals
fun raw_cnf_rules_pairs ps = map (fn (name, thm) => (thm, ((name, 0), thm))) ps
fun cnf_helper_thms thy raw =
map (`Thm.get_name_hint)
#> (if raw then raw_cnf_rules_pairs else cnf_rules_pairs thy)
val optional_helpers =
[(["c_COMBI", "c_COMBK"], (false, @{thms COMBI_def COMBK_def})),
(["c_COMBB", "c_COMBC"], (false, @{thms COMBB_def COMBC_def})),
(["c_COMBS"], (false, @{thms COMBS_def}))]
val optional_typed_helpers =
[(["c_True", "c_False"], (true, @{thms True_or_False})),
(["c_If"], (true, @{thms if_True if_False True_or_False}))]
val mandatory_helpers = @{thms fequal_imp_equal equal_imp_fequal}
val init_counters =
Symtab.make (maps (maps (map (rpair 0) o fst))
[optional_helpers, optional_typed_helpers])
fun get_helper_clauses thy is_FO full_types conjectures axcls =
let
val axclauses = map snd (make_axiom_clauses thy axcls)
val ct = fold (fold count_clause) [conjectures, axclauses] init_counters
fun is_needed c = the (Symtab.lookup ct c) > 0
val cnfs =
(optional_helpers
|> full_types ? append optional_typed_helpers
|> maps (fn (ss, (raw, ths)) =>
if exists is_needed ss then cnf_helper_thms thy raw ths
else []))
@ (if is_FO then [] else cnf_helper_thms thy false mandatory_helpers)
in map snd (make_axiom_clauses thy cnfs) end
fun make_clause_table xs =
fold (Termtab.update o `(prop_of o fst)) xs Termtab.empty
(***************************************************************)
(* 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*)
fun delete_type cset = Symtab.delete_safe (the_single @{sort HOL.type}) cset;
fun tfree_classes_of_terms ts =
let val sorts_list = map (map #2 o OldTerm.term_tfrees) ts
in Symtab.keys (delete_type (List.foldl add_classes Symtab.empty sorts_list)) end;
fun tvar_classes_of_terms ts =
let val sorts_list = map (map #2 o OldTerm.term_tvars) ts
in Symtab.keys (delete_type (List.foldl add_classes Symtab.empty sorts_list)) end;
(*fold type constructors*)
fun fold_type_consts f (Type (a, Ts)) x = fold (fold_type_consts f) Ts (f (a,x))
| fold_type_consts _ _ x = x;
(*Type constructors used to instantiate overloaded constants are the only ones needed.*)
fun add_type_consts_in_term thy =
let
val const_typargs = Sign.const_typargs thy
fun aux (Const x) = fold (fold_type_consts set_insert) (const_typargs x)
| aux (Abs (_, _, u)) = aux u
| aux (Const (@{const_name skolem_id}, _) $ _) = I
| aux (t $ u) = aux t #> aux u
| aux _ = I
in aux end
fun type_consts_of_terms thy ts =
Symtab.keys (fold (add_type_consts_in_term thy) ts Symtab.empty);
(* Remove existing axiom clauses from the conjecture clauses, as this can
dramatically boost an ATP's performance (for some reason). *)
fun subtract_cls ax_clauses =
filter_out (Termtab.defined (make_clause_table ax_clauses) o prop_of)
(* prepare for passing to writer,
create additional clauses based on the information from extra_cls *)
fun prepare_clauses full_types goal_cls axcls extra_cls thy =
let
val is_FO = forall (Meson.is_fol_term thy o prop_of) goal_cls
val ccls = subtract_cls extra_cls goal_cls
val _ = app (fn th => trace_msg (fn _ => Display.string_of_thm_global thy th)) ccls
val ccltms = map prop_of ccls
and axtms = map (prop_of o #1) extra_cls
val subs = tfree_classes_of_terms ccltms
and supers = tvar_classes_of_terms axtms
and tycons = type_consts_of_terms thy (ccltms @ axtms)
(*TFrees in conjecture clauses; TVars in axiom clauses*)
val conjectures = make_conjecture_clauses thy ccls
val (_, extra_clauses) = ListPair.unzip (make_axiom_clauses thy extra_cls)
val (clnames, axiom_clauses) = ListPair.unzip (make_axiom_clauses thy axcls)
val helper_clauses =
get_helper_clauses thy is_FO full_types conjectures extra_cls
val (supers', arity_clauses) = make_arity_clauses thy tycons supers
val classrel_clauses = make_classrel_clauses thy subs supers'
in
(Vector.fromList clnames,
(conjectures, axiom_clauses, extra_clauses, helper_clauses, classrel_clauses, arity_clauses))
end
end;