author | wenzelm |
Wed, 08 Jun 2011 17:49:01 +0200 | |
changeset 43283 | 446e6621762d |
parent 43171 | 37e1431cc213 |
child 43423 | 717880e98e6b |
permissions | -rw-r--r-- |
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(* Title: HOL/Tools/ATP/atp_util.ML |
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Author: Jasmin Blanchette, TU Muenchen |
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General-purpose functions used by the ATP module. |
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*) |
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signature ATP_UTIL = |
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sig |
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val timestamp : unit -> string |
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val hashw : word * word -> word |
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val hashw_string : string * word -> word |
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val strip_spaces : bool -> (char -> bool) -> string -> string |
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val nat_subscript : int -> string |
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val unyxml : string -> string |
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val maybe_quote : string -> string |
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val string_from_ext_time : bool * Time.time -> string |
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val string_from_time : Time.time -> string |
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val varify_type : Proof.context -> typ -> typ |
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val instantiate_type : theory -> typ -> typ -> typ -> typ |
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val varify_and_instantiate_type : Proof.context -> typ -> typ -> typ -> typ |
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val typ_of_dtyp : |
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Datatype_Aux.descr -> (Datatype_Aux.dtyp * typ) list -> Datatype_Aux.dtyp |
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-> typ |
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val is_type_surely_finite : Proof.context -> typ -> bool |
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val is_type_surely_infinite : Proof.context -> typ list -> typ -> bool |
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val monomorphic_term : Type.tyenv -> term -> term |
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val eta_expand : typ list -> term -> int -> term |
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val transform_elim_prop : term -> term |
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val specialize_type : theory -> (string * typ) -> term -> term |
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val strip_subgoal : |
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Proof.context -> thm -> int -> (string * typ) list * term list * term |
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end; |
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structure ATP_Util : ATP_UTIL = |
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struct |
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val timestamp = Date.fmt "%Y-%m-%d %H:%M:%S" o Date.fromTimeLocal o Time.now |
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(* This hash function is recommended in "Compilers: Principles, Techniques, and |
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Tools" by Aho, Sethi, and Ullman. The "hashpjw" function, which they |
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particularly recommend, triggers a bug in versions of Poly/ML up to 4.2.0. *) |
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fun hashw (u, w) = Word.+ (u, Word.* (0w65599, w)) |
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fun hashw_char (c, w) = hashw (Word.fromInt (Char.ord c), w) |
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fun hashw_string (s : string, w) = CharVector.foldl hashw_char w s |
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fun strip_c_style_comment _ [] = [] |
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| strip_c_style_comment is_evil (#"*" :: #"/" :: cs) = |
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strip_spaces_in_list true is_evil cs |
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| strip_c_style_comment is_evil (_ :: cs) = strip_c_style_comment is_evil cs |
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and strip_spaces_in_list _ _ [] = [] |
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| strip_spaces_in_list true is_evil (#"%" :: cs) = |
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strip_spaces_in_list true is_evil |
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(cs |> chop_while (not_equal #"\n") |> snd) |
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| strip_spaces_in_list true is_evil (#"/" :: #"*" :: cs) = |
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strip_c_style_comment is_evil cs |
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| strip_spaces_in_list _ _ [c1] = if Char.isSpace c1 then [] else [str c1] |
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| strip_spaces_in_list skip_comments is_evil [c1, c2] = |
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strip_spaces_in_list skip_comments is_evil [c1] @ |
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strip_spaces_in_list skip_comments is_evil [c2] |
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| strip_spaces_in_list skip_comments is_evil (c1 :: c2 :: c3 :: cs) = |
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if Char.isSpace c1 then |
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strip_spaces_in_list skip_comments is_evil (c2 :: c3 :: cs) |
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else if Char.isSpace c2 then |
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if Char.isSpace c3 then |
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strip_spaces_in_list skip_comments is_evil (c1 :: c3 :: cs) |
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else |
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str c1 :: (if forall is_evil [c1, c3] then [" "] else []) @ |
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strip_spaces_in_list skip_comments is_evil (c3 :: cs) |
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else |
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str c1 :: strip_spaces_in_list skip_comments is_evil (c2 :: c3 :: cs) |
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fun strip_spaces skip_comments is_evil = |
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implode o strip_spaces_in_list skip_comments is_evil o String.explode |
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val subscript = implode o map (prefix "\<^isub>") o raw_explode (* FIXME Symbol.explode (?) *) |
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fun nat_subscript n = |
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n |> string_of_int |> print_mode_active Symbol.xsymbolsN ? subscript |
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val unyxml = XML.content_of o YXML.parse_body |
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val is_long_identifier = forall Lexicon.is_identifier o space_explode "." |
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fun maybe_quote y = |
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let val s = unyxml y in |
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y |> ((not (is_long_identifier (perhaps (try (unprefix "'")) s)) andalso |
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not (is_long_identifier (perhaps (try (unprefix "?")) s))) orelse |
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Keyword.is_keyword s) ? quote |
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end |
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fun string_from_ext_time (plus, time) = |
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let val ms = Time.toMilliseconds time in |
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(if plus then "> " else "") ^ |
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(if plus andalso ms mod 1000 = 0 then |
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signed_string_of_int (ms div 1000) ^ " s" |
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else if ms < 1000 then |
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signed_string_of_int ms ^ " ms" |
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else |
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string_of_real (0.01 * Real.fromInt (ms div 10)) ^ " s") |
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end |
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val string_from_time = string_from_ext_time o pair false |
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fun varify_type ctxt T = |
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Variable.polymorphic_types ctxt [Const (@{const_name undefined}, T)] |
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|> snd |> the_single |> dest_Const |> snd |
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(* TODO: use "Term_Subst.instantiateT" instead? *) |
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fun instantiate_type thy T1 T1' T2 = |
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Same.commit (Envir.subst_type_same |
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(Sign.typ_match thy (T1, T1') Vartab.empty)) T2 |
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handle Type.TYPE_MATCH => raise TYPE ("instantiate_type", [T1, T1'], []) |
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fun varify_and_instantiate_type ctxt T1 T1' T2 = |
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let val thy = Proof_Context.theory_of ctxt in |
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instantiate_type thy (varify_type ctxt T1) T1' (varify_type ctxt T2) |
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end |
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fun typ_of_dtyp _ typ_assoc (Datatype_Aux.DtTFree a) = |
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the (AList.lookup (op =) typ_assoc (Datatype_Aux.DtTFree a)) |
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| typ_of_dtyp descr typ_assoc (Datatype_Aux.DtType (s, Us)) = |
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Type (s, map (typ_of_dtyp descr typ_assoc) Us) |
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| typ_of_dtyp descr typ_assoc (Datatype_Aux.DtRec i) = |
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let val (s, ds, _) = the (AList.lookup (op =) descr i) in |
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Type (s, map (typ_of_dtyp descr typ_assoc) ds) |
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end |
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fun datatype_constrs thy (T as Type (s, Ts)) = |
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(case Datatype.get_info thy s of |
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SOME {index, descr, ...} => |
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let val (_, dtyps, constrs) = AList.lookup (op =) descr index |> the in |
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map (apsnd (fn Us => map (typ_of_dtyp descr (dtyps ~~ Ts)) Us ---> T)) |
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130 |
constrs |
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131 |
end |
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132 |
| NONE => []) |
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133 |
| datatype_constrs _ _ = [] |
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134 |
|
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135 |
(* Similar to "Nitpick_HOL.bounded_exact_card_of_type". |
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0 means infinite type, 1 means singleton type (e.g., "unit"), and 2 means |
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cardinality 2 or more. The specified default cardinality is returned if the |
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cardinality of the type can't be determined. *) |
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139 |
fun tiny_card_of_type ctxt default_card assigns T = |
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140 |
let |
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141 |
val thy = Proof_Context.theory_of ctxt |
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val max = 2 (* 1 would be too small for the "fun" case *) |
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fun aux slack avoid T = |
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if member (op =) avoid T then |
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145 |
0 |
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else case AList.lookup (Sign.typ_instance thy o swap) assigns T of |
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SOME k => k |
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| NONE => |
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149 |
case T of |
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Type (@{type_name fun}, [T1, T2]) => |
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(case (aux slack avoid T1, aux slack avoid T2) of |
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(k, 1) => if slack andalso k = 0 then 0 else 1 |
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| (0, _) => 0 |
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154 |
| (_, 0) => 0 |
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155 |
| (k1, k2) => |
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if k1 >= max orelse k2 >= max then max |
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else Int.min (max, Integer.pow k2 k1)) |
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158 |
| @{typ prop} => 2 |
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| @{typ bool} => 2 (* optimization *) |
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| @{typ nat} => 0 (* optimization *) |
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| Type ("Int.int", []) => 0 (* optimization *) |
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| Type (s, _) => |
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(case datatype_constrs thy T of |
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constrs as _ :: _ => |
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165 |
let |
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166 |
val constr_cards = |
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map (Integer.prod o map (aux slack (T :: avoid)) o binder_types |
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o snd) constrs |
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169 |
in |
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if exists (curry (op =) 0) constr_cards then 0 |
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else Int.min (max, Integer.sum constr_cards) |
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172 |
end |
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173 |
| [] => |
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case Typedef.get_info ctxt s of |
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({abs_type, rep_type, ...}, _) :: _ => |
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176 |
(* We cheat here by assuming that typedef types are infinite if |
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177 |
their underlying type is infinite. This is unsound in general |
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178 |
but it's hard to think of a realistic example where this would |
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not be the case. We are also slack with representation types: |
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If a representation type has the form "sigma => tau", we |
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181 |
consider it enough to check "sigma" for infiniteness. (Look |
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182 |
for "slack" in this function.) *) |
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183 |
(case varify_and_instantiate_type ctxt |
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184 |
(Logic.varifyT_global abs_type) T |
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185 |
(Logic.varifyT_global rep_type) |
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186 |
|> aux true avoid of |
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187 |
0 => 0 |
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188 |
| 1 => 1 |
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189 |
| _ => default_card) |
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190 |
| [] => default_card) |
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191 |
(* Very slightly unsound: Type variables are assumed not to be |
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192 |
constrained to cardinality 1. (In practice, the user would most |
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193 |
likely have used "unit" directly anyway.) *) |
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194 |
| TFree _ => if default_card = 1 then 2 else default_card |
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195 |
(* Schematic type variables that contain only unproblematic sorts |
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196 |
(with no finiteness axiom) can safely be considered infinite. *) |
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197 |
| TVar _ => default_card |
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198 |
in Int.min (max, aux false [] T) end |
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199 |
|
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fun is_type_surely_finite ctxt T = tiny_card_of_type ctxt 0 [] T <> 0 |
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201 |
fun is_type_surely_infinite ctxt infinite_Ts T = |
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202 |
tiny_card_of_type ctxt 1 (map (rpair 0) infinite_Ts) T = 0 |
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203 |
|
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204 |
fun monomorphic_term subst = |
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205 |
map_types (map_type_tvar (fn v => |
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206 |
case Type.lookup subst v of |
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207 |
SOME typ => typ |
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208 |
| NONE => TVar v)) |
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209 |
|
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210 |
fun eta_expand _ t 0 = t |
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211 |
| eta_expand Ts (Abs (s, T, t')) n = |
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212 |
Abs (s, T, eta_expand (T :: Ts) t' (n - 1)) |
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213 |
| eta_expand Ts t n = |
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214 |
fold_rev (fn T => fn t' => Abs ("x" ^ nat_subscript n, T, t')) |
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(List.take (binder_types (fastype_of1 (Ts, t)), n)) |
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(list_comb (incr_boundvars n t, map Bound (n - 1 downto 0))) |
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217 |
|
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218 |
(* Converts an elim-rule into an equivalent theorem that does not have the |
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219 |
predicate variable. Leaves other theorems unchanged. We simply instantiate |
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the conclusion variable to False. (Cf. "transform_elim_theorem" in |
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221 |
"Meson_Clausify".) *) |
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222 |
fun transform_elim_prop t = |
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223 |
case Logic.strip_imp_concl t of |
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@{const Trueprop} $ Var (z, @{typ bool}) => |
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subst_Vars [(z, @{const False})] t |
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| Var (z, @{typ prop}) => subst_Vars [(z, @{prop False})] t |
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227 |
| _ => t |
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228 |
|
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229 |
fun specialize_type thy (s, T) t = |
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230 |
let |
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231 |
fun subst_for (Const (s', T')) = |
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232 |
if s = s' then |
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SOME (Sign.typ_match thy (T', T) Vartab.empty) |
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234 |
handle Type.TYPE_MATCH => NONE |
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235 |
else |
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236 |
NONE |
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237 |
| subst_for (t1 $ t2) = |
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(case subst_for t1 of SOME x => SOME x | NONE => subst_for t2) |
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239 |
| subst_for (Abs (_, _, t')) = subst_for t' |
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240 |
| subst_for _ = NONE |
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241 |
in |
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242 |
case subst_for t of |
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243 |
SOME subst => monomorphic_term subst t |
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244 |
| NONE => raise Type.TYPE_MATCH |
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245 |
end |
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246 |
|
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247 |
fun strip_subgoal ctxt goal i = |
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248 |
let |
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249 |
val (t, (frees, params)) = |
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250 |
Logic.goal_params (prop_of goal) i |
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||> (map dest_Free #> Variable.variant_frees ctxt [] #> `(map Free)) |
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val hyp_ts = t |> Logic.strip_assums_hyp |> map (curry subst_bounds frees) |
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val concl_t = t |> Logic.strip_assums_concl |> curry subst_bounds frees |
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in (rev params, hyp_ts, concl_t) end |
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first step in sharing more code between ATP and Metis translation
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255 |
|
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first step in sharing more code between ATP and Metis translation
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changeset
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256 |
end; |