(* Title: HOL/Tools/ATP/atp_util.ML
Author: Jasmin Blanchette, TU Muenchen
General-purpose functions used by the ATP module.
*)
signature ATP_UTIL =
sig
val timestamp : unit -> string
val hash_string : string -> int
val hash_term : term -> int
val chunk_list : int -> 'a list -> 'a list list
val stringN_of_int : int -> int -> string
val strip_spaces : bool -> (char -> bool) -> string -> string
val strip_spaces_except_between_idents : string -> string
val elide_string : int -> string -> string
val nat_subscript : int -> string
val unyxml : string -> string
val maybe_quote : string -> string
val string_from_ext_time : bool * Time.time -> string
val string_from_time : Time.time -> string
val type_instance : theory -> typ -> typ -> bool
val type_generalization : theory -> typ -> typ -> bool
val type_intersect : theory -> typ -> typ -> bool
val type_equiv : theory -> typ * typ -> bool
val varify_type : Proof.context -> typ -> typ
val instantiate_type : theory -> typ -> typ -> typ -> typ
val varify_and_instantiate_type : Proof.context -> typ -> typ -> typ -> typ
val typ_of_dtyp : Datatype.descr -> (Datatype.dtyp * typ) list -> Datatype.dtyp -> typ
val is_type_surely_finite : Proof.context -> typ -> bool
val is_type_surely_infinite : Proof.context -> bool -> typ list -> typ -> bool
val s_not : term -> term
val s_conj : term * term -> term
val s_disj : term * term -> term
val s_imp : term * term -> term
val s_iff : term * term -> term
val close_form : term -> term
val hol_close_form_prefix : string
val hol_close_form : term -> term
val hol_open_form : (string -> string) -> term -> term
val monomorphic_term : Type.tyenv -> term -> term
val eta_expand : typ list -> term -> int -> term
val cong_extensionalize_term : theory -> term -> term
val abs_extensionalize_term : Proof.context -> term -> term
val unextensionalize_def : term -> term
val is_legitimate_tptp_def : term -> bool
val transform_elim_prop : term -> term
val specialize_type : theory -> (string * typ) -> term -> term
val strip_subgoal :
Proof.context -> thm -> int -> (string * typ) list * term list * term
end;
structure ATP_Util : ATP_UTIL =
struct
val timestamp = Date.fmt "%Y-%m-%d %H:%M:%S" o Date.fromTimeLocal o Time.now
(* This hash function is recommended in "Compilers: Principles, Techniques, and
Tools" by Aho, Sethi, and Ullman. The "hashpjw" function, which they
particularly recommend, triggers a bug in versions of Poly/ML up to 4.2.0. *)
fun hashw (u, w) = Word.+ (u, Word.* (0w65599, w))
fun hashw_char (c, w) = hashw (Word.fromInt (Char.ord c), w)
fun hashw_string (s : string, w) = CharVector.foldl hashw_char w s
fun hashw_term (t1 $ t2) = hashw (hashw_term t1, hashw_term t2)
| hashw_term (Const (s, _)) = hashw_string (s, 0w0)
| hashw_term (Free (s, _)) = hashw_string (s, 0w0)
| hashw_term _ = 0w0
fun hash_string s = Word.toInt (hashw_string (s, 0w0))
val hash_term = Word.toInt o hashw_term
fun chunk_list _ [] = []
| chunk_list k xs =
let val (xs1, xs2) = chop k xs in xs1 :: chunk_list k xs2 end
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 strip_spaces skip_comments is_evil =
let
fun strip_c_style_comment [] accum = accum
| strip_c_style_comment (#"*" :: #"/" :: cs) accum =
strip_spaces_in_list true cs accum
| strip_c_style_comment (_ :: cs) accum = strip_c_style_comment cs accum
and strip_spaces_in_list _ [] accum = accum
| strip_spaces_in_list true (#"%" :: cs) accum =
strip_spaces_in_list true (cs |> take_prefix (not_equal #"\n") |> snd)
accum
| strip_spaces_in_list true (#"/" :: #"*" :: cs) accum =
strip_c_style_comment cs accum
| strip_spaces_in_list _ [c1] accum =
accum |> not (Char.isSpace c1) ? cons c1
| strip_spaces_in_list skip_comments (cs as [_, _]) accum =
accum |> fold (strip_spaces_in_list skip_comments o single) cs
| strip_spaces_in_list skip_comments (c1 :: c2 :: c3 :: cs) accum =
if Char.isSpace c1 then
strip_spaces_in_list skip_comments (c2 :: c3 :: cs) accum
else if Char.isSpace c2 then
if Char.isSpace c3 then
strip_spaces_in_list skip_comments (c1 :: c3 :: cs) accum
else
strip_spaces_in_list skip_comments (c3 :: cs)
(c1 :: accum |> forall is_evil [c1, c3] ? cons #" ")
else
strip_spaces_in_list skip_comments (c2 :: c3 :: cs) (cons c1 accum)
in
String.explode
#> rpair [] #-> strip_spaces_in_list skip_comments
#> rev #> String.implode
end
fun is_ident_char c = Char.isAlphaNum c orelse c = #"_"
val strip_spaces_except_between_idents = strip_spaces true is_ident_char
fun elide_string threshold s =
if size s > threshold then
String.extract (s, 0, SOME (threshold div 2 - 5)) ^ " ...... " ^
String.extract (s, size s - (threshold + 1) div 2 + 6, NONE)
else
s
val subscript = implode o map (prefix "\<^isub>") o raw_explode (* FIXME Symbol.explode (?) *)
fun nat_subscript n =
n |> string_of_int |> print_mode_active Symbol.xsymbolsN ? subscript
val unyxml = XML.content_of o YXML.parse_body
val is_long_identifier = forall Symbol_Pos.is_identifier o Long_Name.explode
fun maybe_quote y =
let val s = unyxml y in
y |> ((not (is_long_identifier (perhaps (try (unprefix "'")) s)) andalso
not (is_long_identifier (perhaps (try (unprefix "?")) s))) orelse
Keyword.is_keyword s) ? quote
end
fun string_from_ext_time (plus, time) =
let val ms = Time.toMilliseconds time in
(if plus then "> " else "") ^
(if plus andalso ms mod 1000 = 0 then
signed_string_of_int (ms div 1000) ^ " s"
else if ms < 1000 then
signed_string_of_int ms ^ " ms"
else
string_of_real (0.01 * Real.fromInt (ms div 10)) ^ " s")
end
val string_from_time = string_from_ext_time o pair false
fun type_instance thy T T' = Sign.typ_instance thy (T, T')
fun type_generalization thy T T' = Sign.typ_instance thy (T', T)
fun type_intersect _ (TVar _) _ = true
| type_intersect _ _ (TVar _) = true
| type_intersect thy T T' =
let
val tvars = Term.add_tvar_namesT T []
val tvars' = Term.add_tvar_namesT T' []
val T =
if exists (member (op =) tvars') tvars then
T |> Logic.incr_tvar (maxidx_of_typ T' + 1)
else
T
in can (Sign.typ_unify thy (T, T')) (Vartab.empty, 0) end
val type_equiv = Sign.typ_equiv
fun varify_type ctxt T =
Variable.polymorphic_types ctxt [Const (@{const_name undefined}, T)]
|> snd |> the_single |> dest_Const |> snd
(* TODO: use "Term_Subst.instantiateT" instead? *)
fun instantiate_type thy T1 T1' T2 =
Same.commit (Envir.subst_type_same
(Sign.typ_match thy (T1, T1') Vartab.empty)) T2
handle Type.TYPE_MATCH => raise TYPE ("instantiate_type", [T1, T1'], [])
fun varify_and_instantiate_type ctxt T1 T1' T2 =
let val thy = Proof_Context.theory_of ctxt in
instantiate_type thy (varify_type ctxt T1) T1' (varify_type ctxt T2)
end
fun typ_of_dtyp _ typ_assoc (Datatype.DtTFree a) =
the (AList.lookup (op =) typ_assoc (Datatype.DtTFree a))
| typ_of_dtyp descr typ_assoc (Datatype.DtType (s, Us)) =
Type (s, map (typ_of_dtyp descr typ_assoc) Us)
| typ_of_dtyp descr typ_assoc (Datatype.DtRec i) =
let val (s, ds, _) = the (AList.lookup (op =) descr i) in
Type (s, map (typ_of_dtyp descr typ_assoc) ds)
end
fun datatype_constrs thy (T as Type (s, Ts)) =
(case Datatype.get_info thy s of
SOME {index, descr, ...} =>
let val (_, dtyps, constrs) = AList.lookup (op =) descr index |> the in
map (apsnd (fn Us => map (typ_of_dtyp descr (dtyps ~~ Ts)) Us ---> T))
constrs
end
| NONE => [])
| datatype_constrs _ _ = []
(* Similar to "Nitpick_HOL.bounded_exact_card_of_type".
0 means infinite type, 1 means singleton type (e.g., "unit"), and 2 means
cardinality 2 or more. The specified default cardinality is returned if the
cardinality of the type can't be determined. *)
fun tiny_card_of_type ctxt sound assigns default_card T =
let
val thy = Proof_Context.theory_of ctxt
val max = 2 (* 1 would be too small for the "fun" case *)
fun aux slack avoid T =
if member (op =) avoid T then
0
else case AList.lookup (type_equiv thy) assigns T of
SOME k => k
| NONE =>
case T of
Type (@{type_name fun}, [T1, T2]) =>
(case (aux slack avoid T1, aux slack avoid T2) of
(k, 1) => if slack andalso k = 0 then 0 else 1
| (0, _) => 0
| (_, 0) => 0
| (k1, k2) =>
if k1 >= max orelse k2 >= max then max
else Int.min (max, Integer.pow k2 k1))
| Type (@{type_name set}, [T']) => aux slack avoid (T' --> @{typ bool})
| @{typ prop} => 2
| @{typ bool} => 2 (* optimization *)
| @{typ nat} => 0 (* optimization *)
| Type ("Int.int", []) => 0 (* optimization *)
| Type (s, _) =>
(case datatype_constrs thy T of
constrs as _ :: _ =>
let
val constr_cards =
map (Integer.prod o map (aux slack (T :: avoid)) o binder_types
o snd) constrs
in
if exists (curry (op =) 0) constr_cards then 0
else Int.min (max, Integer.sum constr_cards)
end
| [] =>
case Typedef.get_info ctxt s of
({abs_type, rep_type, ...}, _) :: _ =>
if not sound then
(* We cheat here by assuming that typedef types are infinite if
their underlying type is infinite. This is unsound in
general but it's hard to think of a realistic example where
this would not be the case. We are also slack with
representation types: If a representation type has the form
"sigma => tau", we consider it enough to check "sigma" for
infiniteness. *)
(case varify_and_instantiate_type ctxt
(Logic.varifyT_global abs_type) T
(Logic.varifyT_global rep_type)
|> aux true avoid of
0 => 0
| 1 => 1
| _ => default_card)
else
default_card
| [] => default_card)
(* Very slightly unsound: Type variables are assumed not to be
constrained to cardinality 1. (In practice, the user would most
likely have used "unit" directly anyway.) *)
| TFree _ =>
if not sound andalso default_card = 1 then 2 else default_card
| TVar _ => default_card
in Int.min (max, aux false [] T) end
fun is_type_surely_finite ctxt T = tiny_card_of_type ctxt true [] 0 T <> 0
fun is_type_surely_infinite ctxt sound infinite_Ts T =
tiny_card_of_type ctxt sound (map (rpair 0) infinite_Ts) 1 T = 0
(* Simple simplifications to ensure that sort annotations don't leave a trail of
spurious "True"s. *)
fun s_not (Const (@{const_name All}, T) $ Abs (s, T', t')) =
Const (@{const_name Ex}, T) $ Abs (s, T', s_not t')
| s_not (Const (@{const_name Ex}, T) $ Abs (s, T', t')) =
Const (@{const_name All}, T) $ Abs (s, T', s_not t')
| s_not (@{const HOL.implies} $ t1 $ t2) = @{const HOL.conj} $ t1 $ s_not t2
| s_not (@{const HOL.conj} $ t1 $ t2) =
@{const HOL.disj} $ s_not t1 $ s_not t2
| s_not (@{const HOL.disj} $ t1 $ t2) =
@{const HOL.conj} $ s_not t1 $ s_not t2
| s_not (@{const False}) = @{const True}
| s_not (@{const True}) = @{const False}
| s_not (@{const Not} $ t) = t
| s_not t = @{const Not} $ t
fun s_conj (@{const True}, t2) = t2
| s_conj (t1, @{const True}) = t1
| s_conj p = HOLogic.mk_conj p
fun s_disj (@{const False}, t2) = t2
| s_disj (t1, @{const False}) = t1
| s_disj p = HOLogic.mk_disj p
fun s_imp (@{const True}, t2) = t2
| s_imp (t1, @{const False}) = s_not t1
| s_imp p = HOLogic.mk_imp p
fun s_iff (@{const True}, t2) = t2
| s_iff (t1, @{const True}) = t1
| s_iff (t1, t2) = HOLogic.eq_const HOLogic.boolT $ t1 $ t2
(* cf. "close_form" in "refute.ML" *)
fun close_form t =
fold (fn ((s, i), T) => fn t' =>
Logic.all_const T $ Abs (s, T, abstract_over (Var ((s, i), T), t')))
(Term.add_vars t []) t
val hol_close_form_prefix = "ATP.close_form."
fun hol_close_form t =
fold (fn ((s, i), T) => fn t' =>
HOLogic.all_const T
$ Abs (hol_close_form_prefix ^ s, T,
abstract_over (Var ((s, i), T), t')))
(Term.add_vars t []) t
fun hol_open_form unprefix
(t as Const (@{const_name All}, _) $ Abs (s, T, t')) =
(case try unprefix s of
SOME s =>
let
val names = Name.make_context (map fst (Term.add_var_names t' []))
val (s, _) = Name.variant s names
in hol_open_form unprefix (subst_bound (Var ((s, 0), T), t')) end
| NONE => t)
| hol_open_form _ t = t
fun monomorphic_term subst =
map_types (map_type_tvar (fn v =>
case Type.lookup subst v of
SOME typ => typ
| NONE => TVar v))
fun eta_expand _ t 0 = t
| eta_expand Ts (Abs (s, T, t')) n =
Abs (s, T, eta_expand (T :: Ts) t' (n - 1))
| eta_expand Ts t n =
fold_rev (fn T => fn t' => Abs ("x" ^ nat_subscript n, T, t'))
(List.take (binder_types (fastype_of1 (Ts, t)), n))
(list_comb (incr_boundvars n t, map Bound (n - 1 downto 0)))
fun cong_extensionalize_term thy t =
if exists_Const (fn (s, _) => s = @{const_name Not}) t then
t |> Skip_Proof.make_thm thy
|> Meson.cong_extensionalize_thm thy
|> prop_of
else
t
fun is_fun_equality (@{const_name HOL.eq},
Type (_, [Type (@{type_name fun}, _), _])) = true
| is_fun_equality _ = false
fun abs_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.abs_extensionalize_conv ctxt
|> prop_of |> Logic.dest_equals |> snd
end
else
t
fun unextensionalize_def t =
case t of
@{const Trueprop} $ (Const (@{const_name HOL.eq}, _) $ lhs $ rhs) =>
(case strip_comb lhs of
(c as Const (_, T), args) =>
if forall is_Var args andalso not (has_duplicates (op =) args) then
@{const Trueprop}
$ (Const (@{const_name HOL.eq}, T --> T --> @{typ bool})
$ c $ fold_rev lambda args rhs)
else
t
| _ => t)
| _ => t
fun is_legitimate_tptp_def (@{const Trueprop} $ t) = is_legitimate_tptp_def t
| is_legitimate_tptp_def (Const (@{const_name HOL.eq}, _) $ t $ u) =
(is_Const t orelse is_Free t) andalso
not (exists_subterm (curry (op =) t) u)
| is_legitimate_tptp_def _ = false
(* Converts an elim-rule into an equivalent theorem that does not have the
predicate variable. Leaves other theorems unchanged. We simply instantiate
the conclusion variable to "False". (Cf. "transform_elim_theorem" in
"Meson_Clausify".) *)
fun transform_elim_prop t =
case Logic.strip_imp_concl t of
@{const Trueprop} $ Var (z, @{typ bool}) =>
subst_Vars [(z, @{const False})] t
| Var (z, @{typ prop}) => subst_Vars [(z, @{prop False})] t
| _ => t
fun specialize_type thy (s, T) t =
let
fun subst_for (Const (s', T')) =
if s = s' then
SOME (Sign.typ_match thy (T', T) Vartab.empty)
handle Type.TYPE_MATCH => NONE
else
NONE
| subst_for (t1 $ t2) =
(case subst_for t1 of SOME x => SOME x | NONE => subst_for t2)
| subst_for (Abs (_, _, t')) = subst_for t'
| subst_for _ = NONE
in
case subst_for t of
SOME subst => monomorphic_term subst t
| NONE => raise Type.TYPE_MATCH
end
fun strip_subgoal ctxt goal i =
let
val (t, (frees, params)) =
Logic.goal_params (prop_of goal) i
||> (map dest_Free #> Variable.variant_frees ctxt [] #> `(map Free))
val hyp_ts = t |> Logic.strip_assums_hyp |> map (curry subst_bounds frees)
val concl_t = t |> Logic.strip_assums_concl |> curry subst_bounds frees
in (rev params, hyp_ts, concl_t) end
end;