src/HOL/Tools/Sledgehammer/sledgehammer_reconstruct.ML
author blanchet
Tue Sep 14 20:07:18 2010 +0200 (2010-09-14)
changeset 39372 2fd8a9a7080d
parent 39370 f8292d3020db
child 39373 fe95c860434c
permissions -rw-r--r--
first step in generalizing to nonnumeric proof step names (e.g. remote Vampire 0.6)
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(*  Title:      HOL/Tools/Sledgehammer/sledgehammer_reconstruct.ML
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    Author:     Lawrence C. Paulson, Cambridge University Computer Laboratory
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    Author:     Claire Quigley, Cambridge University Computer Laboratory
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    Author:     Jasmin Blanchette, TU Muenchen
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Transfer of proofs from external provers.
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*)
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signature SLEDGEHAMMER_RECONSTRUCT =
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sig
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  type locality = Sledgehammer_Filter.locality
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  type minimize_command = string list -> string
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  type metis_params =
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    string * bool * minimize_command * string * (string * locality) list vector
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    * thm * int
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  type isar_params =
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    string Symtab.table * bool * int * Proof.context * int list list
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  type text_result = string * (string * locality) list
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  val metis_proof_text : metis_params -> text_result
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  val isar_proof_text : isar_params -> metis_params -> text_result
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  val proof_text : bool -> isar_params -> metis_params -> text_result
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end;
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structure Sledgehammer_Reconstruct : SLEDGEHAMMER_RECONSTRUCT =
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struct
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open ATP_Problem
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open Metis_Clauses
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open Sledgehammer_Util
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open Sledgehammer_Filter
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open Sledgehammer_Translate
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type minimize_command = string list -> string
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type metis_params =
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  string * bool * minimize_command * string * (string * locality) list vector
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  * thm * int
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type isar_params =
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  string Symtab.table * bool * int * Proof.context * int list list
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type text_result = string * (string * locality) list
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(* Simple simplifications to ensure that sort annotations don't leave a trail of
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   spurious "True"s. *)
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fun s_not @{const False} = @{const True}
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  | s_not @{const True} = @{const False}
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  | s_not (@{const Not} $ t) = t
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  | s_not t = @{const Not} $ t
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fun s_conj (@{const True}, t2) = t2
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  | s_conj (t1, @{const True}) = t1
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  | s_conj p = HOLogic.mk_conj p
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fun s_disj (@{const False}, t2) = t2
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  | s_disj (t1, @{const False}) = t1
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  | s_disj p = HOLogic.mk_disj p
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fun s_imp (@{const True}, t2) = t2
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  | s_imp (t1, @{const False}) = s_not t1
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  | s_imp p = HOLogic.mk_imp p
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fun s_iff (@{const True}, t2) = t2
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  | s_iff (t1, @{const True}) = t1
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  | s_iff (t1, t2) = HOLogic.eq_const HOLogic.boolT $ t1 $ t2
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fun mk_anot (AConn (ANot, [phi])) = phi
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  | mk_anot phi = AConn (ANot, [phi])
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fun mk_aconn c (phi1, phi2) = AConn (c, [phi1, phi2])
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datatype raw_step_name = Str of string * string | Num of string
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fun raw_step_name_num (Str (num, _)) = num
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  | raw_step_name_num (Num num) = num
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fun raw_step_name_ord p =
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  let val q = pairself raw_step_name_num p in
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    case pairself Int.fromString q of
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      (NONE, NONE) => string_ord q
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    | (NONE, SOME _) => LESS
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    | (SOME _, NONE) => GREATER
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    | (SOME i, SOME j) => int_ord (i, j)
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  end
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fun index_in_shape x = find_index (exists (curry (op =) x))
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fun resolve_axiom axiom_names (Str (_, str)) =
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    (case find_first_in_list_vector axiom_names str of
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       SOME x => [(str, x)]
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     | NONE => [])
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  | resolve_axiom axiom_names (Num num) =
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    case Int.fromString num of
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      SOME j =>
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      if j > 0 andalso j <= Vector.length axiom_names then
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        Vector.sub (axiom_names, j - 1)
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      else
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        []
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    | NONE => []
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val is_axiom = not o null oo resolve_axiom
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fun resolve_conjecture conjecture_shape (Str (num, s)) =
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    let
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      val j = try (unprefix conjecture_prefix) s |> the_default num
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              |> Int.fromString |> the_default ~1
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      val k = index_in_shape j conjecture_shape
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    in if k >= 0 then [k] else [] end
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  | resolve_conjecture conjecture_shape (Num num) =
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    resolve_conjecture conjecture_shape (Str (num, "")) (* HACK *)
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val is_conjecture = not o null oo resolve_conjecture
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fun negate_term (Const (@{const_name All}, T) $ Abs (s, T', t')) =
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    Const (@{const_name Ex}, T) $ Abs (s, T', negate_term t')
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  | negate_term (Const (@{const_name Ex}, T) $ Abs (s, T', t')) =
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    Const (@{const_name All}, T) $ Abs (s, T', negate_term t')
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  | negate_term (@{const HOL.implies} $ t1 $ t2) =
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    @{const HOL.conj} $ t1 $ negate_term t2
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  | negate_term (@{const HOL.conj} $ t1 $ t2) =
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    @{const HOL.disj} $ negate_term t1 $ negate_term t2
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  | negate_term (@{const HOL.disj} $ t1 $ t2) =
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    @{const HOL.conj} $ negate_term t1 $ negate_term t2
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  | negate_term (@{const Not} $ t) = t
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  | negate_term t = @{const Not} $ t
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datatype ('a, 'b, 'c) raw_step =
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  Definition of raw_step_name * 'a * 'b |
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  Inference of raw_step_name * 'c * raw_step_name list
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(**** PARSING OF TSTP FORMAT ****)
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(*Strings enclosed in single quotes, e.g. filenames*)
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val scan_general_id =
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  $$ "'" |-- Scan.repeat (~$$ "'") --| $$ "'" >> implode
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  || Scan.repeat ($$ "$") -- Scan.many1 Symbol.is_letdig
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     >> (fn (ss1, ss2) => implode ss1 ^ implode ss2)
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fun repair_name _ "$true" = "c_True"
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  | repair_name _ "$false" = "c_False"
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  | repair_name _ "$$e" = "c_equal" (* seen in Vampire proofs *)
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  | repair_name _ "equal" = "c_equal" (* needed by SPASS? *)
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  | repair_name pool s =
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    case Symtab.lookup pool s of
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      SOME s' => s'
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    | NONE =>
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      if String.isPrefix "sQ" s andalso String.isSuffix "_eqProxy" s then
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        "c_equal" (* seen in Vampire proofs *)
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      else
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        s
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(* Generalized first-order terms, which include file names, numbers, etc. *)
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fun parse_annotation strict x =
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  ((scan_general_id ::: Scan.repeat ($$ " " |-- scan_general_id)
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      >> (strict ? filter (is_some o Int.fromString)))
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   -- Scan.optional (parse_annotation strict) [] >> uncurry (union (op =))
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   || $$ "(" |-- parse_annotations strict --| $$ ")"
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   || $$ "[" |-- parse_annotations strict --| $$ "]") x
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and parse_annotations strict x =
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  (Scan.optional (parse_annotation strict
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                  ::: Scan.repeat ($$ "," |-- parse_annotation strict)) []
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   >> (fn numss => fold (union (op =)) numss [])) x
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(* Vampire proof lines sometimes contain needless information such as "(0:3)",
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   which can be hard to disambiguate from function application in an LL(1)
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   parser. As a workaround, we extend the TPTP term syntax with such detritus
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   and ignore it. *)
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fun parse_vampire_detritus x =
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  (scan_general_id |-- $$ ":" --| scan_general_id >> K []) x
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fun parse_term pool x =
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  ((scan_general_id >> repair_name pool)
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    -- Scan.optional ($$ "(" |-- (parse_vampire_detritus || parse_terms pool)
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                      --| $$ ")") []
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    --| Scan.optional ($$ "(" |-- parse_vampire_detritus --| $$ ")") []
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   >> ATerm) x
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and parse_terms pool x =
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  (parse_term pool ::: Scan.repeat ($$ "," |-- parse_term pool)) x
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fun parse_atom pool =
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  parse_term pool -- Scan.option (Scan.option ($$ "!") --| $$ "="
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                                  -- parse_term pool)
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  >> (fn (u1, NONE) => AAtom u1
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       | (u1, SOME (NONE, u2)) => AAtom (ATerm ("c_equal", [u1, u2]))
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       | (u1, SOME (SOME _, u2)) =>
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         mk_anot (AAtom (ATerm ("c_equal", [u1, u2]))))
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fun fo_term_head (ATerm (s, _)) = s
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(* TPTP formulas are fully parenthesized, so we don't need to worry about
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   operator precedence. *)
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fun parse_formula pool x =
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  (($$ "(" |-- parse_formula pool --| $$ ")"
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    || ($$ "!" >> K AForall || $$ "?" >> K AExists)
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       --| $$ "[" -- parse_terms pool --| $$ "]" --| $$ ":"
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       -- parse_formula pool
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       >> (fn ((q, ts), phi) => AQuant (q, map fo_term_head ts, phi))
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    || $$ "~" |-- parse_formula pool >> mk_anot
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    || parse_atom pool)
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   -- Scan.option ((Scan.this_string "=>" >> K AImplies
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                    || Scan.this_string "<=>" >> K AIff
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                    || Scan.this_string "<~>" >> K ANotIff
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                    || Scan.this_string "<=" >> K AIf
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                    || $$ "|" >> K AOr || $$ "&" >> K AAnd)
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                   -- parse_formula pool)
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   >> (fn (phi1, NONE) => phi1
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        | (phi1, SOME (c, phi2)) => mk_aconn c (phi1, phi2))) x
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val parse_tstp_extra_arguments =
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  Scan.optional ($$ "," |-- parse_annotation false
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                 --| Scan.option ($$ "," |-- parse_annotations false)) []
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(* Syntax: (fof|cnf)\(<num>, <formula_role>, <formula> <extra_arguments>\).
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   The <num> could be an identifier, but we assume integers. *)
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 fun parse_tstp_line pool =
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   ((Scan.this_string "fof" || Scan.this_string "cnf") -- $$ "(")
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     |-- scan_general_id --| $$ "," -- Symbol.scan_id --| $$ ","
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     -- parse_formula pool -- parse_tstp_extra_arguments --| $$ ")" --| $$ "."
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    >> (fn (((num, role), phi), deps) =>
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           case role of
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             "definition" =>
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             (case phi of
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                AConn (AIff, [phi1 as AAtom _, phi2]) =>
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                Definition (Num num, phi1, phi2)
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              | AAtom (ATerm ("c_equal", _)) =>
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                (* Vampire's equality proxy axiom *)
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                Inference (Num num, phi, map Num deps)
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              | _ => raise Fail "malformed definition")
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           | _ => Inference (Num num, phi, map Num deps))
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(**** PARSING OF VAMPIRE OUTPUT ****)
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(* Syntax: <num>. <formula> <annotation> *)
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fun parse_vampire_line pool =
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  scan_general_id --| $$ "." -- parse_formula pool -- parse_annotation true
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  >> (fn ((num, phi), deps) => Inference (Num num, phi, map Num deps))
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(**** PARSING OF SPASS OUTPUT ****)
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(* SPASS returns clause references of the form "x.y". We ignore "y", whose role
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   is not clear anyway. *)
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val parse_dot_name = scan_general_id --| $$ "." --| scan_general_id
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val parse_spass_annotations =
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  Scan.optional ($$ ":" |-- Scan.repeat (parse_dot_name
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                                         --| Scan.option ($$ ","))) []
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(* It is not clear why some literals are followed by sequences of stars and/or
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   pluses. We ignore them. *)
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fun parse_decorated_atom pool =
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  parse_atom pool --| Scan.repeat ($$ "*" || $$ "+" || $$ " ")
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fun mk_horn ([], []) = AAtom (ATerm ("c_False", []))
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  | mk_horn ([], pos_lits) = foldr1 (mk_aconn AOr) pos_lits
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  | mk_horn (neg_lits, []) = mk_anot (foldr1 (mk_aconn AAnd) neg_lits)
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  | mk_horn (neg_lits, pos_lits) =
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    mk_aconn AImplies (foldr1 (mk_aconn AAnd) neg_lits,
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                       foldr1 (mk_aconn AOr) pos_lits)
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fun parse_horn_clause pool =
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  Scan.repeat (parse_decorated_atom pool) --| $$ "|" --| $$ "|"
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    -- Scan.repeat (parse_decorated_atom pool) --| $$ "-" --| $$ ">"
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    -- Scan.repeat (parse_decorated_atom pool)
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  >> (mk_horn o apfst (op @))
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(* Syntax: <num>[0:<inference><annotations>]
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   <atoms> || <atoms> -> <atoms>. *)
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fun parse_spass_line pool =
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  scan_general_id --| $$ "[" --| $$ "0" --| $$ ":" --| Symbol.scan_id
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    -- parse_spass_annotations --| $$ "]" -- parse_horn_clause pool --| $$ "."
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  >> (fn ((num, deps), u) => Inference (Num num, u, map Num deps))
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fun parse_line pool =
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  parse_tstp_line pool || parse_vampire_line pool || parse_spass_line pool
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fun parse_lines pool = Scan.repeat1 (parse_line pool)
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fun parse_proof pool =
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  fst o Scan.finite Symbol.stopper
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            (Scan.error (!! (fn _ => raise Fail "unrecognized ATP output")
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                            (parse_lines pool)))
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  o explode o strip_spaces_except_between_ident_chars
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(**** INTERPRETATION OF TSTP SYNTAX TREES ****)
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exception FO_TERM of string fo_term list
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exception FORMULA of (string, string fo_term) formula list
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exception SAME of unit
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(* Type variables are given the basic sort "HOL.type". Some will later be
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   constrained by information from type literals, or by type inference. *)
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fun type_from_fo_term tfrees (u as ATerm (a, us)) =
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  let val Ts = map (type_from_fo_term tfrees) us in
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    case strip_prefix_and_unascii type_const_prefix a of
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      SOME b => Type (invert_const b, Ts)
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    | NONE =>
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      if not (null us) then
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        raise FO_TERM [u]  (* only "tconst"s have type arguments *)
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      else case strip_prefix_and_unascii tfree_prefix a of
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        SOME b =>
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        let val s = "'" ^ b in
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          TFree (s, AList.lookup (op =) tfrees s |> the_default HOLogic.typeS)
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        end
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      | NONE =>
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        case strip_prefix_and_unascii tvar_prefix a of
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          SOME b => TVar (("'" ^ b, 0), HOLogic.typeS)
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        | NONE =>
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          (* Variable from the ATP, say "X1" *)
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          Type_Infer.param 0 (a, HOLogic.typeS)
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  end
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(* Type class literal applied to a type. Returns triple of polarity, class,
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   type. *)
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fun type_constraint_from_term pos tfrees (u as ATerm (a, us)) =
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  case (strip_prefix_and_unascii class_prefix a,
blanchet@38014
   303
        map (type_from_fo_term tfrees) us) of
blanchet@38014
   304
    (SOME b, [T]) => (pos, b, T)
blanchet@38014
   305
  | _ => raise FO_TERM [u]
blanchet@38014
   306
blanchet@38085
   307
(** Accumulate type constraints in a formula: negative type literals **)
blanchet@38014
   308
fun add_var (key, z)  = Vartab.map_default (key, []) (cons z)
blanchet@38014
   309
fun add_type_constraint (false, cl, TFree (a ,_)) = add_var ((a, ~1), cl)
blanchet@38014
   310
  | add_type_constraint (false, cl, TVar (ix, _)) = add_var (ix, cl)
blanchet@38014
   311
  | add_type_constraint _ = I
blanchet@38014
   312
blanchet@38490
   313
fun repair_atp_variable_name f s =
blanchet@36486
   314
  let
blanchet@36486
   315
    fun subscript_name s n = s ^ nat_subscript n
blanchet@38488
   316
    val s = String.map f s
blanchet@36486
   317
  in
blanchet@36486
   318
    case space_explode "_" s of
blanchet@36486
   319
      [_] => (case take_suffix Char.isDigit (String.explode s) of
blanchet@36486
   320
                (cs1 as _ :: _, cs2 as _ :: _) =>
blanchet@36486
   321
                subscript_name (String.implode cs1)
blanchet@36486
   322
                               (the (Int.fromString (String.implode cs2)))
blanchet@36486
   323
              | (_, _) => s)
blanchet@36486
   324
    | [s1, s2] => (case Int.fromString s2 of
blanchet@36486
   325
                     SOME n => subscript_name s1 n
blanchet@36486
   326
                   | NONE => s)
blanchet@36486
   327
    | _ => s
blanchet@36486
   328
  end
blanchet@36486
   329
blanchet@36909
   330
(* First-order translation. No types are known for variables. "HOLogic.typeT"
blanchet@38014
   331
   should allow them to be inferred. *)
blanchet@38014
   332
fun raw_term_from_pred thy full_types tfrees =
blanchet@36909
   333
  let
blanchet@37643
   334
    fun aux opt_T extra_us u =
blanchet@36909
   335
      case u of
blanchet@37991
   336
        ATerm ("hBOOL", [u1]) => aux (SOME @{typ bool}) [] u1
blanchet@37991
   337
      | ATerm ("hAPP", [u1, u2]) => aux opt_T (u2 :: extra_us) u1
blanchet@37991
   338
      | ATerm (a, us) =>
blanchet@36909
   339
        if a = type_wrapper_name then
blanchet@36909
   340
          case us of
blanchet@37643
   341
            [typ_u, term_u] =>
blanchet@37991
   342
            aux (SOME (type_from_fo_term tfrees typ_u)) extra_us term_u
blanchet@37991
   343
          | _ => raise FO_TERM us
blanchet@38748
   344
        else case strip_prefix_and_unascii const_prefix a of
blanchet@36909
   345
          SOME "equal" =>
blanchet@39106
   346
          let val ts = map (aux NONE []) us in
blanchet@39106
   347
            if length ts = 2 andalso hd ts aconv List.last ts then
blanchet@39106
   348
              (* Vampire is keen on producing these. *)
blanchet@39106
   349
              @{const True}
blanchet@39106
   350
            else
blanchet@39106
   351
              list_comb (Const (@{const_name HOL.eq}, HOLogic.typeT), ts)
blanchet@39106
   352
          end
blanchet@36909
   353
        | SOME b =>
blanchet@36909
   354
          let
blanchet@36909
   355
            val c = invert_const b
blanchet@36909
   356
            val num_type_args = num_type_args thy c
blanchet@37643
   357
            val (type_us, term_us) =
blanchet@37643
   358
              chop (if full_types then 0 else num_type_args) us
blanchet@37643
   359
            (* Extra args from "hAPP" come after any arguments given directly to
blanchet@37643
   360
               the constant. *)
blanchet@37643
   361
            val term_ts = map (aux NONE []) term_us
blanchet@37643
   362
            val extra_ts = map (aux NONE []) extra_us
blanchet@36909
   363
            val t =
blanchet@36909
   364
              Const (c, if full_types then
blanchet@36909
   365
                          case opt_T of
blanchet@37643
   366
                            SOME T => map fastype_of term_ts ---> T
blanchet@36909
   367
                          | NONE =>
blanchet@36909
   368
                            if num_type_args = 0 then
blanchet@36909
   369
                              Sign.const_instance thy (c, [])
blanchet@36909
   370
                            else
blanchet@36909
   371
                              raise Fail ("no type information for " ^ quote c)
blanchet@36909
   372
                        else
blanchet@37998
   373
                          Sign.const_instance thy (c,
blanchet@37998
   374
                              map (type_from_fo_term tfrees) type_us))
blanchet@37643
   375
          in list_comb (t, term_ts @ extra_ts) end
blanchet@36909
   376
        | NONE => (* a free or schematic variable *)
blanchet@36909
   377
          let
blanchet@37643
   378
            val ts = map (aux NONE []) (us @ extra_us)
blanchet@36909
   379
            val T = map fastype_of ts ---> HOLogic.typeT
blanchet@36909
   380
            val t =
blanchet@38748
   381
              case strip_prefix_and_unascii fixed_var_prefix a of
blanchet@36909
   382
                SOME b => Free (b, T)
blanchet@36909
   383
              | NONE =>
blanchet@38748
   384
                case strip_prefix_and_unascii schematic_var_prefix a of
blanchet@36967
   385
                  SOME b => Var ((b, 0), T)
blanchet@36909
   386
                | NONE =>
blanchet@38017
   387
                  if is_tptp_variable a then
blanchet@38490
   388
                    Var ((repair_atp_variable_name Char.toLower a, 0), T)
blanchet@38017
   389
                  else
blanchet@38488
   390
                    (* Skolem constants? *)
blanchet@38490
   391
                    Var ((repair_atp_variable_name Char.toUpper a, 0), T)
blanchet@36909
   392
          in list_comb (t, ts) end
blanchet@38014
   393
  in aux (SOME HOLogic.boolT) [] end
paulson@21978
   394
blanchet@38014
   395
fun term_from_pred thy full_types tfrees pos (u as ATerm (s, _)) =
blanchet@38014
   396
  if String.isPrefix class_prefix s then
blanchet@38014
   397
    add_type_constraint (type_constraint_from_term pos tfrees u)
blanchet@38014
   398
    #> pair @{const True}
blanchet@38014
   399
  else
blanchet@38014
   400
    pair (raw_term_from_pred thy full_types tfrees u)
blanchet@36402
   401
blanchet@36555
   402
val combinator_table =
blanchet@36555
   403
  [(@{const_name COMBI}, @{thm COMBI_def_raw}),
blanchet@36555
   404
   (@{const_name COMBK}, @{thm COMBK_def_raw}),
blanchet@36555
   405
   (@{const_name COMBB}, @{thm COMBB_def_raw}),
blanchet@36555
   406
   (@{const_name COMBC}, @{thm COMBC_def_raw}),
blanchet@36555
   407
   (@{const_name COMBS}, @{thm COMBS_def_raw})]
blanchet@36555
   408
blanchet@36555
   409
fun uncombine_term (t1 $ t2) = betapply (pairself uncombine_term (t1, t2))
blanchet@36555
   410
  | uncombine_term (Abs (s, T, t')) = Abs (s, T, uncombine_term t')
blanchet@36555
   411
  | uncombine_term (t as Const (x as (s, _))) =
blanchet@36555
   412
    (case AList.lookup (op =) combinator_table s of
blanchet@36555
   413
       SOME thm => thm |> prop_of |> specialize_type @{theory} x |> Logic.dest_equals |> snd
blanchet@36555
   414
     | NONE => t)
blanchet@36555
   415
  | uncombine_term t = t
blanchet@36555
   416
blanchet@37991
   417
(* Update schematic type variables with detected sort constraints. It's not
blanchet@37991
   418
   totally clear when this code is necessary. *)
blanchet@38014
   419
fun repair_tvar_sorts (t, tvar_tab) =
blanchet@36909
   420
  let
blanchet@37991
   421
    fun do_type (Type (a, Ts)) = Type (a, map do_type Ts)
blanchet@37991
   422
      | do_type (TVar (xi, s)) =
blanchet@37991
   423
        TVar (xi, the_default s (Vartab.lookup tvar_tab xi))
blanchet@37991
   424
      | do_type (TFree z) = TFree z
blanchet@37991
   425
    fun do_term (Const (a, T)) = Const (a, do_type T)
blanchet@37991
   426
      | do_term (Free (a, T)) = Free (a, do_type T)
blanchet@37991
   427
      | do_term (Var (xi, T)) = Var (xi, do_type T)
blanchet@37991
   428
      | do_term (t as Bound _) = t
blanchet@37991
   429
      | do_term (Abs (a, T, t)) = Abs (a, do_type T, do_term t)
blanchet@37991
   430
      | do_term (t1 $ t2) = do_term t1 $ do_term t2
blanchet@37991
   431
  in t |> not (Vartab.is_empty tvar_tab) ? do_term end
blanchet@37991
   432
blanchet@39370
   433
(* ### TODO: looks broken; see forall_of below *)
blanchet@37991
   434
fun quantify_over_free quant_s free_s body_t =
blanchet@37991
   435
  case Term.add_frees body_t [] |> filter (curry (op =) free_s o fst) of
blanchet@37991
   436
    [] => body_t
blanchet@37991
   437
  | frees as (_, free_T) :: _ =>
blanchet@37991
   438
    Abs (free_s, free_T, fold (curry abstract_over) (map Free frees) body_t)
blanchet@37991
   439
blanchet@38085
   440
(* Interpret an ATP formula as a HOL term, extracting sort constraints as they
blanchet@38085
   441
   appear in the formula. *)
blanchet@38014
   442
fun prop_from_formula thy full_types tfrees phi =
blanchet@38014
   443
  let
blanchet@38014
   444
    fun do_formula pos phi =
blanchet@37991
   445
      case phi of
blanchet@38014
   446
        AQuant (_, [], phi) => do_formula pos phi
blanchet@37991
   447
      | AQuant (q, x :: xs, phi') =>
blanchet@38014
   448
        do_formula pos (AQuant (q, xs, phi'))
blanchet@38014
   449
        #>> quantify_over_free (case q of
blanchet@38014
   450
                                  AForall => @{const_name All}
blanchet@38490
   451
                                | AExists => @{const_name Ex})
blanchet@38490
   452
                               (repair_atp_variable_name Char.toLower x)
blanchet@38014
   453
      | AConn (ANot, [phi']) => do_formula (not pos) phi' #>> s_not
blanchet@37991
   454
      | AConn (c, [phi1, phi2]) =>
blanchet@38014
   455
        do_formula (pos |> c = AImplies ? not) phi1
blanchet@38014
   456
        ##>> do_formula pos phi2
blanchet@38014
   457
        #>> (case c of
blanchet@38014
   458
               AAnd => s_conj
blanchet@38014
   459
             | AOr => s_disj
blanchet@38014
   460
             | AImplies => s_imp
blanchet@38038
   461
             | AIf => s_imp o swap
blanchet@38038
   462
             | AIff => s_iff
blanchet@38038
   463
             | ANotIff => s_not o s_iff)
blanchet@38034
   464
      | AAtom tm => term_from_pred thy full_types tfrees pos tm
blanchet@37991
   465
      | _ => raise FORMULA [phi]
blanchet@38014
   466
  in repair_tvar_sorts (do_formula true phi Vartab.empty) end
blanchet@37991
   467
blanchet@36556
   468
fun check_formula ctxt =
wenzelm@39288
   469
  Type.constraint HOLogic.boolT
blanchet@36486
   470
  #> Syntax.check_term (ProofContext.set_mode ProofContext.mode_schematic ctxt)
paulson@21978
   471
paulson@21978
   472
paulson@21978
   473
(**** Translation of TSTP files to Isar Proofs ****)
paulson@21978
   474
blanchet@36486
   475
fun unvarify_term (Var ((s, 0), T)) = Free (s, T)
blanchet@36486
   476
  | unvarify_term t = raise TERM ("unvarify_term: non-Var", [t])
paulson@21978
   477
blanchet@39368
   478
fun decode_line full_types tfrees (Definition (name, phi1, phi2)) ctxt =
blanchet@36486
   479
    let
blanchet@37991
   480
      val thy = ProofContext.theory_of ctxt
blanchet@37991
   481
      val t1 = prop_from_formula thy full_types tfrees phi1
blanchet@36551
   482
      val vars = snd (strip_comb t1)
blanchet@36486
   483
      val frees = map unvarify_term vars
blanchet@36486
   484
      val unvarify_args = subst_atomic (vars ~~ frees)
blanchet@37991
   485
      val t2 = prop_from_formula thy full_types tfrees phi2
blanchet@36551
   486
      val (t1, t2) =
blanchet@36551
   487
        HOLogic.eq_const HOLogic.typeT $ t1 $ t2
blanchet@36556
   488
        |> unvarify_args |> uncombine_term |> check_formula ctxt
blanchet@36555
   489
        |> HOLogic.dest_eq
blanchet@36486
   490
    in
blanchet@39368
   491
      (Definition (name, t1, t2),
blanchet@36551
   492
       fold Variable.declare_term (maps OldTerm.term_frees [t1, t2]) ctxt)
blanchet@36486
   493
    end
blanchet@39368
   494
  | decode_line full_types tfrees (Inference (name, u, deps)) ctxt =
blanchet@36551
   495
    let
blanchet@37991
   496
      val thy = ProofContext.theory_of ctxt
blanchet@37991
   497
      val t = u |> prop_from_formula thy full_types tfrees
blanchet@37998
   498
                |> uncombine_term |> check_formula ctxt
blanchet@36551
   499
    in
blanchet@39368
   500
      (Inference (name, t, deps),
blanchet@36551
   501
       fold Variable.declare_term (OldTerm.term_frees t) ctxt)
blanchet@36486
   502
    end
blanchet@36967
   503
fun decode_lines ctxt full_types tfrees lines =
blanchet@36967
   504
  fst (fold_map (decode_line full_types tfrees) lines ctxt)
paulson@21978
   505
blanchet@38035
   506
fun is_same_inference _ (Definition _) = false
blanchet@38035
   507
  | is_same_inference t (Inference (_, t', _)) = t aconv t'
blanchet@36486
   508
blanchet@36486
   509
(* No "real" literals means only type information (tfree_tcs, clsrel, or
blanchet@36486
   510
   clsarity). *)
blanchet@36486
   511
val is_only_type_information = curry (op aconv) HOLogic.true_const
blanchet@36486
   512
blanchet@36486
   513
fun replace_one_dep (old, new) dep = if dep = old then new else [dep]
blanchet@36486
   514
fun replace_deps_in_line _ (line as Definition _) = line
blanchet@39368
   515
  | replace_deps_in_line p (Inference (name, t, deps)) =
blanchet@39368
   516
    Inference (name, t, fold (union (op =) o replace_one_dep p) deps [])
paulson@21978
   517
blanchet@38085
   518
(* Discard axioms; consolidate adjacent lines that prove the same formula, since
blanchet@38085
   519
   they differ only in type information.*)
blanchet@36551
   520
fun add_line _ _ (line as Definition _) lines = line :: lines
blanchet@39368
   521
  | add_line conjecture_shape axiom_names (Inference (name, t, [])) lines =
blanchet@38085
   522
    (* No dependencies: axiom, conjecture, or (for Vampire) internal axioms or
blanchet@38085
   523
       definitions. *)
blanchet@39370
   524
    if is_axiom axiom_names name then
blanchet@36486
   525
      (* Axioms are not proof lines. *)
blanchet@36486
   526
      if is_only_type_information t then
blanchet@39368
   527
        map (replace_deps_in_line (name, [])) lines
blanchet@36486
   528
      (* Is there a repetition? If so, replace later line by earlier one. *)
blanchet@38035
   529
      else case take_prefix (not o is_same_inference t) lines of
blanchet@36486
   530
        (_, []) => lines (*no repetition of proof line*)
blanchet@39368
   531
      | (pre, Inference (name', _, _) :: post) =>
blanchet@39368
   532
        pre @ map (replace_deps_in_line (name', [name])) post
blanchet@39370
   533
    else if is_conjecture conjecture_shape name then
blanchet@39368
   534
      Inference (name, negate_term t, []) :: lines
blanchet@36551
   535
    else
blanchet@39368
   536
      map (replace_deps_in_line (name, [])) lines
blanchet@39368
   537
  | add_line _ _ (Inference (name, t, deps)) lines =
blanchet@36486
   538
    (* Type information will be deleted later; skip repetition test. *)
blanchet@36486
   539
    if is_only_type_information t then
blanchet@39368
   540
      Inference (name, t, deps) :: lines
blanchet@36486
   541
    (* Is there a repetition? If so, replace later line by earlier one. *)
blanchet@38035
   542
    else case take_prefix (not o is_same_inference t) lines of
blanchet@36486
   543
      (* FIXME: Doesn't this code risk conflating proofs involving different
blanchet@38035
   544
         types? *)
blanchet@39368
   545
       (_, []) => Inference (name, t, deps) :: lines
blanchet@39368
   546
     | (pre, Inference (name', t', _) :: post) =>
blanchet@39368
   547
       Inference (name, t', deps) ::
blanchet@39368
   548
       pre @ map (replace_deps_in_line (name', [name])) post
paulson@22044
   549
blanchet@36486
   550
(* Recursively delete empty lines (type information) from the proof. *)
blanchet@39368
   551
fun add_nontrivial_line (Inference (name, t, [])) lines =
blanchet@39368
   552
    if is_only_type_information t then delete_dep name lines
blanchet@39368
   553
    else Inference (name, t, []) :: lines
blanchet@36486
   554
  | add_nontrivial_line line lines = line :: lines
blanchet@39368
   555
and delete_dep name lines =
blanchet@39368
   556
  fold_rev add_nontrivial_line (map (replace_deps_in_line (name, [])) lines) []
blanchet@36486
   557
blanchet@37323
   558
(* ATPs sometimes reuse free variable names in the strangest ways. Removing
blanchet@37323
   559
   offending lines often does the trick. *)
blanchet@36560
   560
fun is_bad_free frees (Free x) = not (member (op =) frees x)
blanchet@36560
   561
  | is_bad_free _ _ = false
paulson@22470
   562
blanchet@39368
   563
fun add_desired_line _ _ _ _ (line as Definition (name, _, _)) (j, lines) =
blanchet@39368
   564
    (j, line :: map (replace_deps_in_line (name, [])) lines)
blanchet@38282
   565
  | add_desired_line isar_shrink_factor conjecture_shape axiom_names frees
blanchet@39368
   566
                     (Inference (name, t, deps)) (j, lines) =
blanchet@36402
   567
    (j + 1,
blanchet@39370
   568
     if is_axiom axiom_names name orelse
blanchet@39370
   569
        is_conjecture conjecture_shape name orelse
blanchet@36570
   570
        (not (is_only_type_information t) andalso
blanchet@36570
   571
         null (Term.add_tvars t []) andalso
blanchet@36570
   572
         not (exists_subterm (is_bad_free frees) t) andalso
blanchet@36570
   573
         (null lines orelse (* last line must be kept *)
blanchet@36924
   574
          (length deps >= 2 andalso j mod isar_shrink_factor = 0))) then
blanchet@39368
   575
       Inference (name, t, deps) :: lines  (* keep line *)
blanchet@36402
   576
     else
blanchet@39368
   577
       map (replace_deps_in_line (name, deps)) lines)  (* drop line *)
paulson@21978
   578
blanchet@36402
   579
(** EXTRACTING LEMMAS **)
paulson@21979
   580
blanchet@38599
   581
(* Like "split_line", but ignores "\n" that follow a comma (as in SNARK's
blanchet@38599
   582
   output). *)
blanchet@38599
   583
val split_proof_lines =
blanchet@38599
   584
  let
blanchet@38599
   585
    fun aux [] [] = []
blanchet@38599
   586
      | aux line [] = [implode (rev line)]
blanchet@38599
   587
      | aux line ("," :: "\n" :: rest) = aux ("," :: line) rest
blanchet@38599
   588
      | aux line ("\n" :: rest) = aux line [] @ aux [] rest
blanchet@38599
   589
      | aux line (s :: rest) = aux (s :: line) rest
blanchet@38599
   590
  in aux [] o explode end
blanchet@38599
   591
blanchet@37991
   592
(* A list consisting of the first number in each line is returned. For TSTP,
blanchet@37991
   593
   interesting lines have the form "fof(108, axiom, ...)", where the number
blanchet@37991
   594
   (108) is extracted. For SPASS, lines have the form "108[0:Inp] ...", where
blanchet@38033
   595
   the first number (108) is extracted. For Vampire, we look for
blanchet@38033
   596
   "108. ... [input]". *)
blanchet@38282
   597
fun used_facts_in_atp_proof axiom_names atp_proof =
blanchet@35865
   598
  let
blanchet@38039
   599
    val tokens_of =
blanchet@38039
   600
      String.tokens (fn c => not (Char.isAlphaNum c) andalso c <> #"_")
blanchet@38599
   601
    fun do_line (tag :: num :: "axiom" :: (rest as _ :: _)) =
blanchet@38599
   602
        if tag = "cnf" orelse tag = "fof" then
blanchet@38748
   603
          (case strip_prefix_and_unascii axiom_prefix (List.last rest) of
blanchet@38599
   604
             SOME name =>
blanchet@38698
   605
             if member (op =) rest "file" then
blanchet@38818
   606
               ([(name, name |> find_first_in_list_vector axiom_names |> the)]
blanchet@38818
   607
                handle Option.Option =>
blanchet@38818
   608
                       error ("No such fact: " ^ quote name ^ "."))
blanchet@38698
   609
             else
blanchet@39370
   610
               resolve_axiom axiom_names (Num num)
blanchet@39370
   611
           | NONE => resolve_axiom axiom_names (Num num))
blanchet@38599
   612
        else
blanchet@38818
   613
          []
blanchet@39370
   614
      | do_line (num :: "0" :: "Inp" :: _) = resolve_axiom axiom_names (Num num)
blanchet@38039
   615
      | do_line (num :: rest) =
blanchet@39370
   616
        (case List.last rest of
blanchet@39370
   617
           "input" => resolve_axiom axiom_names (Num num)
blanchet@39370
   618
         | _ => [])
blanchet@38818
   619
      | do_line _ = []
blanchet@38818
   620
  in atp_proof |> split_proof_lines |> maps (do_line o tokens_of) end
blanchet@37399
   621
blanchet@37399
   622
val indent_size = 2
blanchet@37399
   623
val no_label = ("", ~1)
blanchet@37399
   624
blanchet@37399
   625
val raw_prefix = "X"
blanchet@37399
   626
val assum_prefix = "A"
blanchet@37399
   627
val fact_prefix = "F"
blanchet@37399
   628
blanchet@37399
   629
fun string_for_label (s, num) = s ^ string_of_int num
blanchet@37399
   630
blanchet@39370
   631
fun raw_label_for_name conjecture_shape name =
blanchet@39370
   632
  case resolve_conjecture conjecture_shape name of
blanchet@39370
   633
    [j] => (conjecture_prefix, j)
blanchet@39372
   634
  | _ => case Int.fromString (raw_step_name_num name) of
blanchet@39370
   635
           SOME j => (raw_prefix, j)
blanchet@39372
   636
         | NONE => (raw_prefix ^ raw_step_name_num name, 0)
blanchet@39368
   637
blanchet@37399
   638
fun metis_using [] = ""
blanchet@37399
   639
  | metis_using ls =
blanchet@37399
   640
    "using " ^ space_implode " " (map string_for_label ls) ^ " "
blanchet@37399
   641
fun metis_apply _ 1 = "by "
blanchet@37399
   642
  | metis_apply 1 _ = "apply "
blanchet@37399
   643
  | metis_apply i _ = "prefer " ^ string_of_int i ^ " apply "
blanchet@37479
   644
fun metis_name full_types = if full_types then "metisFT" else "metis"
blanchet@37479
   645
fun metis_call full_types [] = metis_name full_types
blanchet@37479
   646
  | metis_call full_types ss =
blanchet@37479
   647
    "(" ^ metis_name full_types ^ " " ^ space_implode " " ss ^ ")"
blanchet@37479
   648
fun metis_command full_types i n (ls, ss) =
blanchet@37479
   649
  metis_using ls ^ metis_apply i n ^ metis_call full_types ss
blanchet@39327
   650
fun metis_line banner full_types i n ss =
blanchet@39327
   651
  banner ^ ": " ^
blanchet@38597
   652
  Markup.markup Markup.sendback (metis_command full_types i n ([], ss)) ^ "."
blanchet@36281
   653
fun minimize_line _ [] = ""
blanchet@38696
   654
  | minimize_line minimize_command ss =
blanchet@38696
   655
    case minimize_command ss of
blanchet@36281
   656
      "" => ""
blanchet@36281
   657
    | command =>
blanchet@38597
   658
      "\nTo minimize the number of lemmas, try this: " ^
blanchet@38597
   659
      Markup.markup Markup.sendback command ^ "."
immler@31840
   660
blanchet@38282
   661
fun used_facts axiom_names =
blanchet@38282
   662
  used_facts_in_atp_proof axiom_names
blanchet@38752
   663
  #> List.partition (curry (op =) Chained o snd)
blanchet@38752
   664
  #> pairself (sort_distinct (string_ord o pairself fst))
blanchet@38015
   665
blanchet@39327
   666
fun metis_proof_text (banner, full_types, minimize_command, atp_proof,
blanchet@39327
   667
                      axiom_names, goal, i) =
blanchet@36063
   668
  let
blanchet@38282
   669
    val (chained_lemmas, other_lemmas) = used_facts axiom_names atp_proof
blanchet@36063
   670
    val n = Logic.count_prems (prop_of goal)
blanchet@37171
   671
  in
blanchet@39327
   672
    (metis_line banner full_types i n (map fst other_lemmas) ^
blanchet@38752
   673
     minimize_line minimize_command (map fst (other_lemmas @ chained_lemmas)),
blanchet@38752
   674
     other_lemmas @ chained_lemmas)
blanchet@37171
   675
  end
immler@31037
   676
blanchet@36486
   677
(** Isar proof construction and manipulation **)
blanchet@36486
   678
blanchet@36486
   679
fun merge_fact_sets (ls1, ss1) (ls2, ss2) =
blanchet@36486
   680
  (union (op =) ls1 ls2, union (op =) ss1 ss2)
blanchet@36402
   681
blanchet@36402
   682
type label = string * int
blanchet@36402
   683
type facts = label list * string list
blanchet@36402
   684
blanchet@36402
   685
datatype qualifier = Show | Then | Moreover | Ultimately
blanchet@36291
   686
blanchet@36402
   687
datatype step =
blanchet@36478
   688
  Fix of (string * typ) list |
blanchet@36486
   689
  Let of term * term |
blanchet@36402
   690
  Assume of label * term |
blanchet@36402
   691
  Have of qualifier list * label * term * byline
blanchet@36402
   692
and byline =
blanchet@36564
   693
  ByMetis of facts |
blanchet@36402
   694
  CaseSplit of step list list * facts
blanchet@36402
   695
blanchet@36574
   696
fun smart_case_split [] facts = ByMetis facts
blanchet@36574
   697
  | smart_case_split proofs facts = CaseSplit (proofs, facts)
blanchet@36574
   698
blanchet@39370
   699
fun add_fact_from_dep conjecture_shape axiom_names name =
blanchet@39370
   700
  if is_axiom axiom_names name then
blanchet@39368
   701
    apsnd (union (op =) (map fst (resolve_axiom axiom_names name)))
blanchet@36475
   702
  else
blanchet@39370
   703
    apfst (insert (op =) (raw_label_for_name conjecture_shape name))
blanchet@36402
   704
blanchet@37998
   705
fun forall_of v t = HOLogic.all_const (fastype_of v) $ lambda v t
blanchet@36491
   706
fun forall_vars t = fold_rev forall_of (map Var (Term.add_vars t [])) t
blanchet@36491
   707
blanchet@39370
   708
fun step_for_line _ _ _ (Definition (_, t1, t2)) = Let (t1, t2)
blanchet@39370
   709
  | step_for_line conjecture_shape _ _ (Inference (name, t, [])) =
blanchet@39370
   710
    Assume (raw_label_for_name conjecture_shape name, t)
blanchet@39370
   711
  | step_for_line conjecture_shape axiom_names j (Inference (name, t, deps)) =
blanchet@39370
   712
    Have (if j = 1 then [Show] else [],
blanchet@39370
   713
          raw_label_for_name conjecture_shape name, forall_vars t,
blanchet@39370
   714
          ByMetis (fold (add_fact_from_dep conjecture_shape axiom_names) deps
blanchet@39370
   715
                        ([], [])))
blanchet@36291
   716
blanchet@39372
   717
fun raw_step_name (Definition (name, _, _)) = name
blanchet@39372
   718
  | raw_step_name (Inference (name, _, _)) = name
blanchet@39372
   719
blanchet@36967
   720
fun proof_from_atp_proof pool ctxt full_types tfrees isar_shrink_factor
blanchet@38282
   721
                         atp_proof conjecture_shape axiom_names params frees =
blanchet@36402
   722
  let
blanchet@36486
   723
    val lines =
blanchet@38035
   724
      atp_proof ^ "$" (* the $ sign acts as a sentinel (FIXME: needed?) *)
blanchet@36548
   725
      |> parse_proof pool
blanchet@39372
   726
      |> sort (raw_step_name_ord o pairself raw_step_name)
blanchet@36967
   727
      |> decode_lines ctxt full_types tfrees
blanchet@38282
   728
      |> rpair [] |-> fold_rev (add_line conjecture_shape axiom_names)
blanchet@36486
   729
      |> rpair [] |-> fold_rev add_nontrivial_line
blanchet@37498
   730
      |> rpair (0, []) |-> fold_rev (add_desired_line isar_shrink_factor
blanchet@38282
   731
                                             conjecture_shape axiom_names frees)
blanchet@36486
   732
      |> snd
blanchet@36402
   733
  in
blanchet@36909
   734
    (if null params then [] else [Fix params]) @
blanchet@39370
   735
    map2 (step_for_line conjecture_shape axiom_names) (length lines downto 1)
blanchet@39370
   736
         lines
blanchet@36402
   737
  end
blanchet@36402
   738
blanchet@36402
   739
(* When redirecting proofs, we keep information about the labels seen so far in
blanchet@36402
   740
   the "backpatches" data structure. The first component indicates which facts
blanchet@36402
   741
   should be associated with forthcoming proof steps. The second component is a
blanchet@37322
   742
   pair ("assum_ls", "drop_ls"), where "assum_ls" are the labels that should
blanchet@37322
   743
   become assumptions and "drop_ls" are the labels that should be dropped in a
blanchet@37322
   744
   case split. *)
blanchet@36402
   745
type backpatches = (label * facts) list * (label list * label list)
blanchet@36402
   746
blanchet@36556
   747
fun used_labels_of_step (Have (_, _, _, by)) =
blanchet@36402
   748
    (case by of
blanchet@36564
   749
       ByMetis (ls, _) => ls
blanchet@36556
   750
     | CaseSplit (proofs, (ls, _)) =>
blanchet@36556
   751
       fold (union (op =) o used_labels_of) proofs ls)
blanchet@36556
   752
  | used_labels_of_step _ = []
blanchet@36556
   753
and used_labels_of proof = fold (union (op =) o used_labels_of_step) proof []
blanchet@36402
   754
blanchet@36402
   755
fun new_labels_of_step (Fix _) = []
blanchet@36486
   756
  | new_labels_of_step (Let _) = []
blanchet@36402
   757
  | new_labels_of_step (Assume (l, _)) = [l]
blanchet@36402
   758
  | new_labels_of_step (Have (_, l, _, _)) = [l]
blanchet@36402
   759
val new_labels_of = maps new_labels_of_step
blanchet@36402
   760
blanchet@36402
   761
val join_proofs =
blanchet@36402
   762
  let
blanchet@36402
   763
    fun aux _ [] = NONE
blanchet@36402
   764
      | aux proof_tail (proofs as (proof1 :: _)) =
blanchet@36402
   765
        if exists null proofs then
blanchet@36402
   766
          NONE
blanchet@36402
   767
        else if forall (curry (op =) (hd proof1) o hd) (tl proofs) then
blanchet@36402
   768
          aux (hd proof1 :: proof_tail) (map tl proofs)
blanchet@36402
   769
        else case hd proof1 of
blanchet@37498
   770
          Have ([], l, t, _) => (* FIXME: should we really ignore the "by"? *)
blanchet@36402
   771
          if forall (fn Have ([], l', t', _) :: _ => (l, t) = (l', t')
blanchet@36402
   772
                      | _ => false) (tl proofs) andalso
blanchet@36402
   773
             not (exists (member (op =) (maps new_labels_of proofs))
blanchet@36556
   774
                         (used_labels_of proof_tail)) then
blanchet@36402
   775
            SOME (l, t, map rev proofs, proof_tail)
blanchet@36402
   776
          else
blanchet@36402
   777
            NONE
blanchet@36402
   778
        | _ => NONE
blanchet@36402
   779
  in aux [] o map rev end
blanchet@36402
   780
blanchet@36402
   781
fun case_split_qualifiers proofs =
blanchet@36402
   782
  case length proofs of
blanchet@36402
   783
    0 => []
blanchet@36402
   784
  | 1 => [Then]
blanchet@36402
   785
  | _ => [Ultimately]
blanchet@36402
   786
blanchet@39372
   787
fun redirect_proof hyp_ts concl_t proof =
wenzelm@33310
   788
  let
blanchet@37324
   789
    (* The first pass outputs those steps that are independent of the negated
blanchet@37324
   790
       conjecture. The second pass flips the proof by contradiction to obtain a
blanchet@37324
   791
       direct proof, introducing case splits when an inference depends on
blanchet@37324
   792
       several facts that depend on the negated conjecture. *)
blanchet@39372
   793
     val concl_l = (conjecture_prefix, length hyp_ts)
blanchet@38040
   794
     fun first_pass ([], contra) = ([], contra)
blanchet@38040
   795
       | first_pass ((step as Fix _) :: proof, contra) =
blanchet@38040
   796
         first_pass (proof, contra) |>> cons step
blanchet@38040
   797
       | first_pass ((step as Let _) :: proof, contra) =
blanchet@38040
   798
         first_pass (proof, contra) |>> cons step
blanchet@39370
   799
       | first_pass ((step as Assume (l as (_, j), _)) :: proof, contra) =
blanchet@39372
   800
         if l = concl_l then first_pass (proof, contra ||> cons step)
blanchet@39372
   801
         else first_pass (proof, contra) |>> cons (Assume (l, nth hyp_ts j))
blanchet@38040
   802
       | first_pass (Have (qs, l, t, ByMetis (ls, ss)) :: proof, contra) =
blanchet@39372
   803
         let val step = Have (qs, l, t, ByMetis (ls, ss)) in
blanchet@38040
   804
           if exists (member (op =) (fst contra)) ls then
blanchet@38040
   805
             first_pass (proof, contra |>> cons l ||> cons step)
blanchet@38040
   806
           else
blanchet@38040
   807
             first_pass (proof, contra) |>> cons step
blanchet@38040
   808
         end
blanchet@38040
   809
       | first_pass _ = raise Fail "malformed proof"
blanchet@36402
   810
    val (proof_top, (contra_ls, contra_proof)) =
blanchet@39372
   811
      first_pass (proof, ([concl_l], []))
blanchet@36402
   812
    val backpatch_label = the_default ([], []) oo AList.lookup (op =) o fst
blanchet@36402
   813
    fun backpatch_labels patches ls =
blanchet@36402
   814
      fold merge_fact_sets (map (backpatch_label patches) ls) ([], [])
blanchet@36402
   815
    fun second_pass end_qs ([], assums, patches) =
blanchet@37324
   816
        ([Have (end_qs, no_label, concl_t,
blanchet@36564
   817
                ByMetis (backpatch_labels patches (map snd assums)))], patches)
blanchet@36402
   818
      | second_pass end_qs (Assume (l, t) :: proof, assums, patches) =
blanchet@36402
   819
        second_pass end_qs (proof, (t, l) :: assums, patches)
blanchet@36564
   820
      | second_pass end_qs (Have (qs, l, t, ByMetis (ls, ss)) :: proof, assums,
blanchet@36402
   821
                            patches) =
blanchet@36402
   822
        if member (op =) (snd (snd patches)) l andalso
blanchet@37322
   823
           not (member (op =) (fst (snd patches)) l) andalso
blanchet@36402
   824
           not (AList.defined (op =) (fst patches) l) then
blanchet@36402
   825
          second_pass end_qs (proof, assums, patches ||> apsnd (append ls))
blanchet@36402
   826
        else
blanchet@36402
   827
          (case List.partition (member (op =) contra_ls) ls of
blanchet@36402
   828
             ([contra_l], co_ls) =>
blanchet@37322
   829
             if member (op =) qs Show then
blanchet@37322
   830
               second_pass end_qs (proof, assums,
blanchet@37322
   831
                                   patches |>> cons (contra_l, (co_ls, ss)))
blanchet@37322
   832
             else
blanchet@36402
   833
               second_pass end_qs
blanchet@36402
   834
                           (proof, assums,
blanchet@36402
   835
                            patches |>> cons (contra_l, (l :: co_ls, ss)))
blanchet@36402
   836
               |>> cons (if member (op =) (fst (snd patches)) l then
blanchet@37991
   837
                           Assume (l, negate_term t)
blanchet@36402
   838
                         else
blanchet@37991
   839
                           Have (qs, l, negate_term t,
blanchet@36564
   840
                                 ByMetis (backpatch_label patches l)))
blanchet@36402
   841
           | (contra_ls as _ :: _, co_ls) =>
blanchet@36402
   842
             let
blanchet@36402
   843
               val proofs =
blanchet@36402
   844
                 map_filter
blanchet@36402
   845
                     (fn l =>
blanchet@39372
   846
                         if l = concl_l then
blanchet@36402
   847
                           NONE
blanchet@36402
   848
                         else
blanchet@36402
   849
                           let
blanchet@36402
   850
                             val drop_ls = filter (curry (op <>) l) contra_ls
blanchet@36402
   851
                           in
blanchet@36402
   852
                             second_pass []
blanchet@36402
   853
                                 (proof, assums,
blanchet@36402
   854
                                  patches ||> apfst (insert (op =) l)
blanchet@36402
   855
                                          ||> apsnd (union (op =) drop_ls))
blanchet@36402
   856
                             |> fst |> SOME
blanchet@36402
   857
                           end) contra_ls
blanchet@37324
   858
               val (assumes, facts) =
blanchet@37324
   859
                 if member (op =) (fst (snd patches)) l then
blanchet@37991
   860
                   ([Assume (l, negate_term t)], (l :: co_ls, ss))
blanchet@37324
   861
                 else
blanchet@37324
   862
                   ([], (co_ls, ss))
blanchet@36402
   863
             in
blanchet@36402
   864
               (case join_proofs proofs of
blanchet@36402
   865
                  SOME (l, t, proofs, proof_tail) =>
blanchet@36402
   866
                  Have (case_split_qualifiers proofs @
blanchet@36402
   867
                        (if null proof_tail then end_qs else []), l, t,
blanchet@36574
   868
                        smart_case_split proofs facts) :: proof_tail
blanchet@36402
   869
                | NONE =>
blanchet@36402
   870
                  [Have (case_split_qualifiers proofs @ end_qs, no_label,
blanchet@36574
   871
                         concl_t, smart_case_split proofs facts)],
blanchet@36402
   872
                patches)
blanchet@37324
   873
               |>> append assumes
blanchet@36402
   874
             end
blanchet@36402
   875
           | _ => raise Fail "malformed proof")
blanchet@36402
   876
       | second_pass _ _ = raise Fail "malformed proof"
blanchet@36486
   877
    val proof_bottom =
blanchet@36486
   878
      second_pass [Show] (contra_proof, [], ([], ([], []))) |> fst
blanchet@36402
   879
  in proof_top @ proof_bottom end
blanchet@36402
   880
blanchet@38490
   881
(* FIXME: Still needed? Probably not. *)
blanchet@36402
   882
val kill_duplicate_assumptions_in_proof =
blanchet@36402
   883
  let
blanchet@36402
   884
    fun relabel_facts subst =
blanchet@36402
   885
      apfst (map (fn l => AList.lookup (op =) subst l |> the_default l))
blanchet@36491
   886
    fun do_step (step as Assume (l, t)) (proof, subst, assums) =
blanchet@36402
   887
        (case AList.lookup (op aconv) assums t of
blanchet@36967
   888
           SOME l' => (proof, (l, l') :: subst, assums)
blanchet@36491
   889
         | NONE => (step :: proof, subst, (t, l) :: assums))
blanchet@36402
   890
      | do_step (Have (qs, l, t, by)) (proof, subst, assums) =
blanchet@36402
   891
        (Have (qs, l, t,
blanchet@36402
   892
               case by of
blanchet@36564
   893
                 ByMetis facts => ByMetis (relabel_facts subst facts)
blanchet@36402
   894
               | CaseSplit (proofs, facts) =>
blanchet@36402
   895
                 CaseSplit (map do_proof proofs, relabel_facts subst facts)) ::
blanchet@36402
   896
         proof, subst, assums)
blanchet@36491
   897
      | do_step step (proof, subst, assums) = (step :: proof, subst, assums)
blanchet@36402
   898
    and do_proof proof = fold do_step proof ([], [], []) |> #1 |> rev
blanchet@36402
   899
  in do_proof end
blanchet@36402
   900
blanchet@36402
   901
val then_chain_proof =
blanchet@36402
   902
  let
blanchet@36402
   903
    fun aux _ [] = []
blanchet@36491
   904
      | aux _ ((step as Assume (l, _)) :: proof) = step :: aux l proof
blanchet@36402
   905
      | aux l' (Have (qs, l, t, by) :: proof) =
blanchet@36402
   906
        (case by of
blanchet@36564
   907
           ByMetis (ls, ss) =>
blanchet@36402
   908
           Have (if member (op =) ls l' then
blanchet@36402
   909
                   (Then :: qs, l, t,
blanchet@36564
   910
                    ByMetis (filter_out (curry (op =) l') ls, ss))
blanchet@36402
   911
                 else
blanchet@36564
   912
                   (qs, l, t, ByMetis (ls, ss)))
blanchet@36402
   913
         | CaseSplit (proofs, facts) =>
blanchet@36402
   914
           Have (qs, l, t, CaseSplit (map (aux no_label) proofs, facts))) ::
blanchet@36402
   915
        aux l proof
blanchet@36491
   916
      | aux _ (step :: proof) = step :: aux no_label proof
blanchet@36402
   917
  in aux no_label end
blanchet@36402
   918
blanchet@36402
   919
fun kill_useless_labels_in_proof proof =
blanchet@36402
   920
  let
blanchet@36556
   921
    val used_ls = used_labels_of proof
blanchet@36402
   922
    fun do_label l = if member (op =) used_ls l then l else no_label
blanchet@36556
   923
    fun do_step (Assume (l, t)) = Assume (do_label l, t)
blanchet@36556
   924
      | do_step (Have (qs, l, t, by)) =
blanchet@36402
   925
        Have (qs, do_label l, t,
blanchet@36402
   926
              case by of
blanchet@36402
   927
                CaseSplit (proofs, facts) =>
blanchet@36556
   928
                CaseSplit (map (map do_step) proofs, facts)
blanchet@36402
   929
              | _ => by)
blanchet@36556
   930
      | do_step step = step
blanchet@36556
   931
  in map do_step proof end
blanchet@36402
   932
blanchet@36402
   933
fun prefix_for_depth n = replicate_string (n + 1)
blanchet@36402
   934
blanchet@36402
   935
val relabel_proof =
blanchet@36402
   936
  let
blanchet@36402
   937
    fun aux _ _ _ [] = []
blanchet@36402
   938
      | aux subst depth (next_assum, next_fact) (Assume (l, t) :: proof) =
blanchet@36402
   939
        if l = no_label then
blanchet@36402
   940
          Assume (l, t) :: aux subst depth (next_assum, next_fact) proof
blanchet@36402
   941
        else
blanchet@36402
   942
          let val l' = (prefix_for_depth depth assum_prefix, next_assum) in
blanchet@36402
   943
            Assume (l', t) ::
blanchet@36402
   944
            aux ((l, l') :: subst) depth (next_assum + 1, next_fact) proof
blanchet@36402
   945
          end
blanchet@36402
   946
      | aux subst depth (next_assum, next_fact) (Have (qs, l, t, by) :: proof) =
blanchet@36402
   947
        let
blanchet@36402
   948
          val (l', subst, next_fact) =
blanchet@36402
   949
            if l = no_label then
blanchet@36402
   950
              (l, subst, next_fact)
blanchet@36402
   951
            else
blanchet@36402
   952
              let
blanchet@36402
   953
                val l' = (prefix_for_depth depth fact_prefix, next_fact)
blanchet@36402
   954
              in (l', (l, l') :: subst, next_fact + 1) end
blanchet@36570
   955
          val relabel_facts =
blanchet@39370
   956
            apfst (maps (the_list o AList.lookup (op =) subst))
blanchet@36402
   957
          val by =
blanchet@36402
   958
            case by of
blanchet@36564
   959
              ByMetis facts => ByMetis (relabel_facts facts)
blanchet@36402
   960
            | CaseSplit (proofs, facts) =>
blanchet@36402
   961
              CaseSplit (map (aux subst (depth + 1) (1, 1)) proofs,
blanchet@36402
   962
                         relabel_facts facts)
blanchet@36402
   963
        in
blanchet@36402
   964
          Have (qs, l', t, by) ::
blanchet@36402
   965
          aux subst depth (next_assum, next_fact) proof
blanchet@36402
   966
        end
blanchet@36491
   967
      | aux subst depth nextp (step :: proof) =
blanchet@36491
   968
        step :: aux subst depth nextp proof
blanchet@36402
   969
  in aux [] 0 (1, 1) end
blanchet@36402
   970
wenzelm@39115
   971
fun string_for_proof ctxt0 full_types i n =
blanchet@36402
   972
  let
wenzelm@39134
   973
    val ctxt = ctxt0
wenzelm@39134
   974
      |> Config.put show_free_types false
wenzelm@39134
   975
      |> Config.put show_types true
blanchet@37319
   976
    fun fix_print_mode f x =
wenzelm@39134
   977
      Print_Mode.setmp (filter (curry (op =) Symbol.xsymbolsN)
wenzelm@39134
   978
                               (print_mode_value ())) f x
blanchet@36402
   979
    fun do_indent ind = replicate_string (ind * indent_size) " "
blanchet@36478
   980
    fun do_free (s, T) =
blanchet@36478
   981
      maybe_quote s ^ " :: " ^
blanchet@36478
   982
      maybe_quote (fix_print_mode (Syntax.string_of_typ ctxt) T)
blanchet@36570
   983
    fun do_label l = if l = no_label then "" else string_for_label l ^ ": "
blanchet@36402
   984
    fun do_have qs =
blanchet@36402
   985
      (if member (op =) qs Moreover then "moreover " else "") ^
blanchet@36402
   986
      (if member (op =) qs Ultimately then "ultimately " else "") ^
blanchet@36402
   987
      (if member (op =) qs Then then
blanchet@36402
   988
         if member (op =) qs Show then "thus" else "hence"
blanchet@36402
   989
       else
blanchet@36402
   990
         if member (op =) qs Show then "show" else "have")
blanchet@36478
   991
    val do_term = maybe_quote o fix_print_mode (Syntax.string_of_term ctxt)
blanchet@36570
   992
    fun do_facts (ls, ss) =
blanchet@38698
   993
      metis_command full_types 1 1
blanchet@38698
   994
                    (ls |> sort_distinct (prod_ord string_ord int_ord),
blanchet@38698
   995
                     ss |> sort_distinct string_ord)
blanchet@36478
   996
    and do_step ind (Fix xs) =
blanchet@36478
   997
        do_indent ind ^ "fix " ^ space_implode " and " (map do_free xs) ^ "\n"
blanchet@36486
   998
      | do_step ind (Let (t1, t2)) =
blanchet@36486
   999
        do_indent ind ^ "let " ^ do_term t1 ^ " = " ^ do_term t2 ^ "\n"
blanchet@36402
  1000
      | do_step ind (Assume (l, t)) =
blanchet@36402
  1001
        do_indent ind ^ "assume " ^ do_label l ^ do_term t ^ "\n"
blanchet@36564
  1002
      | do_step ind (Have (qs, l, t, ByMetis facts)) =
blanchet@36402
  1003
        do_indent ind ^ do_have qs ^ " " ^
blanchet@36479
  1004
        do_label l ^ do_term t ^ " " ^ do_facts facts ^ "\n"
blanchet@36402
  1005
      | do_step ind (Have (qs, l, t, CaseSplit (proofs, facts))) =
blanchet@36402
  1006
        space_implode (do_indent ind ^ "moreover\n")
blanchet@36402
  1007
                      (map (do_block ind) proofs) ^
blanchet@36479
  1008
        do_indent ind ^ do_have qs ^ " " ^ do_label l ^ do_term t ^ " " ^
blanchet@36478
  1009
        do_facts facts ^ "\n"
blanchet@36402
  1010
    and do_steps prefix suffix ind steps =
blanchet@36402
  1011
      let val s = implode (map (do_step ind) steps) in
blanchet@36402
  1012
        replicate_string (ind * indent_size - size prefix) " " ^ prefix ^
blanchet@36402
  1013
        String.extract (s, ind * indent_size,
blanchet@36402
  1014
                        SOME (size s - ind * indent_size - 1)) ^
blanchet@36402
  1015
        suffix ^ "\n"
blanchet@36402
  1016
      end
blanchet@36402
  1017
    and do_block ind proof = do_steps "{ " " }" (ind + 1) proof
blanchet@36564
  1018
    (* One-step proofs are pointless; better use the Metis one-liner
blanchet@36564
  1019
       directly. *)
blanchet@36564
  1020
    and do_proof [Have (_, _, _, ByMetis _)] = ""
blanchet@36564
  1021
      | do_proof proof =
blanchet@36480
  1022
        (if i <> 1 then "prefer " ^ string_of_int i ^ "\n" else "") ^
blanchet@36480
  1023
        do_indent 0 ^ "proof -\n" ^
blanchet@36480
  1024
        do_steps "" "" 1 proof ^
blanchet@38599
  1025
        do_indent 0 ^ (if n <> 1 then "next" else "qed")
blanchet@36488
  1026
  in do_proof end
blanchet@36402
  1027
blanchet@37479
  1028
fun isar_proof_text (pool, debug, isar_shrink_factor, ctxt, conjecture_shape)
blanchet@39327
  1029
                    (other_params as (_, full_types, _, atp_proof, axiom_names,
blanchet@38282
  1030
                                      goal, i)) =
blanchet@36402
  1031
  let
blanchet@36909
  1032
    val (params, hyp_ts, concl_t) = strip_subgoal goal i
blanchet@36909
  1033
    val frees = fold Term.add_frees (concl_t :: hyp_ts) []
blanchet@36967
  1034
    val tfrees = fold Term.add_tfrees (concl_t :: hyp_ts) []
blanchet@36402
  1035
    val n = Logic.count_prems (prop_of goal)
blanchet@37479
  1036
    val (one_line_proof, lemma_names) = metis_proof_text other_params
blanchet@36283
  1037
    fun isar_proof_for () =
blanchet@36967
  1038
      case proof_from_atp_proof pool ctxt full_types tfrees isar_shrink_factor
blanchet@38282
  1039
                                atp_proof conjecture_shape axiom_names params
blanchet@36924
  1040
                                frees
blanchet@39372
  1041
           |> redirect_proof hyp_ts concl_t
blanchet@36402
  1042
           |> kill_duplicate_assumptions_in_proof
blanchet@36402
  1043
           |> then_chain_proof
blanchet@36402
  1044
           |> kill_useless_labels_in_proof
blanchet@36402
  1045
           |> relabel_proof
blanchet@37479
  1046
           |> string_for_proof ctxt full_types i n of
blanchet@38599
  1047
        "" => "\nNo structured proof available."
blanchet@38599
  1048
      | proof => "\n\nStructured proof:\n" ^ Markup.markup Markup.sendback proof
blanchet@35868
  1049
    val isar_proof =
blanchet@36402
  1050
      if debug then
blanchet@36283
  1051
        isar_proof_for ()
blanchet@36283
  1052
      else
blanchet@36283
  1053
        try isar_proof_for ()
blanchet@38599
  1054
        |> the_default "\nWarning: The Isar proof construction failed."
blanchet@36283
  1055
  in (one_line_proof ^ isar_proof, lemma_names) end
paulson@21978
  1056
blanchet@36557
  1057
fun proof_text isar_proof isar_params other_params =
blanchet@36557
  1058
  (if isar_proof then isar_proof_text isar_params else metis_proof_text)
blanchet@36557
  1059
      other_params
blanchet@36223
  1060
immler@31038
  1061
end;