removed Sledgehammer's support for the DFG syntax;
this removes 350 buggy lines from Sledgehammer. SPASS 3.5 and above support the TPTP syntax.
(* Title: HOL/Tools/Sledgehammer/sledgehammer_hol_clause.ML
Author: Jia Meng, NICTA
Author: Jasmin Blanchette, TU Muenchen
FOL clauses translated from HOL formulae.
*)
signature SLEDGEHAMMER_HOL_CLAUSE =
sig
type name = Sledgehammer_FOL_Clause.name
type name_pool = Sledgehammer_FOL_Clause.name_pool
type kind = Sledgehammer_FOL_Clause.kind
type fol_type = Sledgehammer_FOL_Clause.fol_type
type classrel_clause = Sledgehammer_FOL_Clause.classrel_clause
type arity_clause = Sledgehammer_FOL_Clause.arity_clause
type axiom_name = string
type polarity = bool
type hol_clause_id = int
datatype combterm =
CombConst of name * fol_type * fol_type list (* Const and Free *) |
CombVar of name * fol_type |
CombApp of combterm * combterm
datatype literal = Literal of polarity * combterm
datatype hol_clause =
HOLClause of {clause_id: hol_clause_id, axiom_name: axiom_name, th: thm,
kind: kind, literals: literal list, ctypes_sorts: typ list}
val type_of_combterm : combterm -> fol_type
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
exception TRIVIAL
val make_conjecture_clauses : theory -> thm list -> hol_clause list
val make_axiom_clauses :
theory -> (thm * (axiom_name * hol_clause_id)) list
-> (axiom_name * hol_clause) list
val type_wrapper_name : string
val get_helper_clauses :
theory -> bool -> bool -> hol_clause list
-> (thm * (axiom_name * hol_clause_id)) list -> hol_clause list
val write_tptp_file : bool -> bool -> bool -> Path.T ->
hol_clause list * hol_clause list * hol_clause list * hol_clause list *
classrel_clause list * arity_clause list -> name_pool option * int
end
structure Sledgehammer_HOL_Clause : SLEDGEHAMMER_HOL_CLAUSE =
struct
open Sledgehammer_Util
open Sledgehammer_FOL_Clause
open Sledgehammer_Fact_Preprocessor
fun min_arity_of const_min_arity c =
the_default 0 (Symtab.lookup const_min_arity c)
(*True if the constant ever appears outside of the top-level position in literals.
If false, the constant always receives all of its arguments and is used as a predicate.*)
fun needs_hBOOL explicit_apply const_needs_hBOOL c =
explicit_apply orelse the_default false (Symtab.lookup const_needs_hBOOL c)
(******************************************************)
(* data types for typed combinator expressions *)
(******************************************************)
type axiom_name = string;
type polarity = bool;
type hol_clause_id = int;
datatype combterm =
CombConst of name * fol_type * fol_type list (* Const and Free *) |
CombVar of name * fol_type |
CombApp of combterm * combterm
datatype literal = Literal of polarity * combterm;
datatype hol_clause =
HOLClause of {clause_id: hol_clause_id, axiom_name: axiom_name, th: thm,
kind: kind, literals: literal list, ctypes_sorts: typ list};
(*********************************************************************)
(* convert a clause with type Term.term to a clause with type clause *)
(*********************************************************************)
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 CLAUSE ("HOL clause", t)
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 t = Envir.beta_eta_contract t
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)
(* Trivial problem, which resolution cannot handle (empty clause) *)
exception TRIVIAL;
(* 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)) (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 (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
(**********************************************************************)
(* convert clause into TPTP format *)
(**********************************************************************)
(*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;
val type_wrapper_name = "ti"
fun head_needs_hBOOL explicit_apply const_needs_hBOOL
(CombConst ((c, _), _, _)) =
needs_hBOOL explicit_apply const_needs_hBOOL c
| head_needs_hBOOL _ _ _ = true
fun wrap_type full_types (s, ty) pool =
if full_types then
let val (s', pool) = string_of_fol_type ty pool in
(type_wrapper_name ^ paren_pack [s, s'], pool)
end
else
(s, pool)
fun wrap_type_if full_types explicit_apply cnh (head, s, tp) =
if head_needs_hBOOL explicit_apply cnh head then
wrap_type full_types (s, tp)
else
pair s
fun apply ss = "hAPP" ^ paren_pack ss;
fun rev_apply (v, []) = v
| rev_apply (v, arg::args) = apply [rev_apply (v, args), arg];
fun string_apply (v, args) = rev_apply (v, rev args);
(* Apply an operator to the argument strings, using either the "apply" operator
or direct function application. *)
fun string_of_application full_types cma (CombConst ((s, s'), _, tvars), args)
pool =
let
val s = if s = "equal" then "c_fequal" else s
val nargs = min_arity_of cma s
val args1 = List.take (args, nargs)
handle Subscript =>
raise Fail (quote s ^ " has arity " ^ Int.toString nargs ^
" but is applied to " ^ commas (map quote args))
val args2 = List.drop (args, nargs)
val (targs, pool) = if full_types then ([], pool)
else pool_map string_of_fol_type tvars pool
val (s, pool) = nice_name (s, s') pool
in (string_apply (s ^ paren_pack (args1 @ targs), args2), pool) end
| string_of_application _ _ (CombVar (name, _), args) pool =
nice_name name pool |>> (fn s => string_apply (s, args))
fun string_of_combterm (params as (full_types, explicit_apply, cma, cnh)) t
pool =
let
val (head, args) = strip_combterm_comb t
val (ss, pool) = pool_map (string_of_combterm params) args pool
val (s, pool) = string_of_application full_types cma (head, ss) pool
in
wrap_type_if full_types explicit_apply cnh (head, s, type_of_combterm t)
pool
end
(*Boolean-valued terms are here converted to literals.*)
fun boolify params c =
string_of_combterm params c #>> prefix "hBOOL" o paren_pack o single
fun string_of_predicate (params as (_, explicit_apply, _, cnh)) t =
case #1 (strip_combterm_comb t) of
CombConst ((s, _), _, _) =>
(if needs_hBOOL explicit_apply cnh s then boolify else string_of_combterm)
params t
| _ => boolify params t
(*** TPTP format ***)
fun tptp_of_equality params pos (t1, t2) =
pool_map (string_of_combterm params) [t1, t2]
#>> space_implode (if pos then " = " else " != ")
fun tptp_literal params
(Literal (pos, CombApp (CombApp (CombConst (("equal", _), _, _), t1),
t2))) =
tptp_of_equality params pos (t1, t2)
| tptp_literal params (Literal (pos, pred)) =
string_of_predicate params pred #>> tptp_sign pos
(* Given a clause, returns its literals paired with a list of literals
concerning TFrees; the latter should only occur in conjecture clauses. *)
fun tptp_type_literals params pos (HOLClause {literals, ctypes_sorts, ...})
pool =
let
val (lits, pool) = pool_map (tptp_literal params) literals pool
val (tylits, pool) = pool_map (tptp_of_type_literal pos)
(type_literals_for_types ctypes_sorts) pool
in ((lits, tylits), pool) end
fun tptp_clause params (cls as HOLClause {axiom_name, clause_id, kind, ...})
pool =
let
val ((lits, tylits), pool) =
tptp_type_literals params (kind = Conjecture) cls pool
in
((gen_tptp_cls (clause_id, axiom_name, kind, lits, tylits), tylits), pool)
end
(**********************************************************************)
(* write clauses to files *)
(**********************************************************************)
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
val raw_cnf_rules_pairs = map (fn (name, thm) => (thm, (name, 0)))
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
(*Find the minimal arity of each function mentioned in the term. Also, note which uses
are not at top level, to see if hBOOL is needed.*)
fun count_constants_term toplev t (const_min_arity, const_needs_hBOOL) =
let val (head, args) = strip_combterm_comb t
val n = length args
val (const_min_arity, const_needs_hBOOL) =
(const_min_arity, const_needs_hBOOL)
|> fold (count_constants_term false) args
in
case head of
CombConst ((a, _),_,_) => (*predicate or function version of "equal"?*)
let val a = if a="equal" andalso not toplev then "c_fequal" else a
in
(const_min_arity |> Symtab.map_default (a, n) (Integer.min n),
const_needs_hBOOL |> not toplev ? Symtab.update (a, true))
end
| _ => (const_min_arity, const_needs_hBOOL)
end;
(*A literal is a top-level term*)
fun count_constants_lit (Literal (_,t)) (const_min_arity, const_needs_hBOOL) =
count_constants_term true t (const_min_arity, const_needs_hBOOL);
fun count_constants_clause (HOLClause {literals, ...})
(const_min_arity, const_needs_hBOOL) =
fold count_constants_lit literals (const_min_arity, const_needs_hBOOL);
fun display_arity explicit_apply const_needs_hBOOL (c, n) =
trace_msg (fn () => "Constant: " ^ c ^
" arity:\t" ^ Int.toString n ^
(if needs_hBOOL explicit_apply const_needs_hBOOL c then
" needs hBOOL"
else
""))
fun count_constants explicit_apply
(conjectures, _, extra_clauses, helper_clauses, _, _) =
if not explicit_apply then
let val (const_min_arity, const_needs_hBOOL) =
fold count_constants_clause conjectures (Symtab.empty, Symtab.empty)
|> fold count_constants_clause extra_clauses
|> fold count_constants_clause helper_clauses
val _ = app (display_arity explicit_apply const_needs_hBOOL)
(Symtab.dest (const_min_arity))
in (const_min_arity, const_needs_hBOOL) end
else (Symtab.empty, Symtab.empty);
(* TPTP format *)
fun write_tptp_file readable_names full_types explicit_apply file clauses =
let
fun section _ [] = []
| section name ss =
"\n% " ^ name ^ plural_s (length ss) ^ " (" ^ Int.toString (length ss) ^
")\n" :: ss
val pool = empty_name_pool readable_names
val (conjectures, axclauses, _, helper_clauses,
classrel_clauses, arity_clauses) = clauses
val (cma, cnh) = count_constants explicit_apply clauses
val params = (full_types, explicit_apply, cma, cnh)
val ((conjecture_clss, tfree_litss), pool) =
pool_map (tptp_clause params) conjectures pool |>> ListPair.unzip
val tfree_clss = map tptp_tfree_clause (fold (union (op =)) tfree_litss [])
val (ax_clss, pool) = pool_map (apfst fst oo tptp_clause params) axclauses
pool
val classrel_clss = map tptp_classrel_clause classrel_clauses
val arity_clss = map tptp_arity_clause arity_clauses
val (helper_clss, pool) = pool_map (apfst fst oo tptp_clause params)
helper_clauses pool
val conjecture_offset =
length ax_clss + length classrel_clss + length arity_clss
+ length helper_clss
val _ =
File.write_list file
("% This file was generated by Isabelle (most likely Sledgehammer)\n\
\% " ^ timestamp () ^ "\n" ::
section "Relevant fact" ax_clss @
section "Class relationship" classrel_clss @
section "Arity declaration" arity_clss @
section "Helper fact" helper_clss @
section "Conjecture" conjecture_clss @
section "Type variable" tfree_clss)
in (pool, conjecture_offset) end
end;