src/HOL/Tools/Sledgehammer/sledgehammer_proof_reconstruct.ML
author blanchet
Mon Jun 21 12:31:41 2010 +0200 (2010-06-21)
changeset 37479 f6b1ee5b420b
parent 37410 2bf7e6136047
child 37498 b426cbdb5a23
permissions -rw-r--r--
try to improve Sledgehammer/Metis's behavior in full_types mode, e.g. by handing True, False, and If better
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(*  Title:      HOL/Tools/Sledgehammer/sledgehammer_proof_reconstruct.ML
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    Author:     Lawrence C Paulson and 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_PROOF_RECONSTRUCT =
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sig
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  type minimize_command = string list -> string
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  type name_pool = Sledgehammer_FOL_Clause.name_pool
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  val invert_const: string -> string
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  val invert_type_const: string -> string
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  val num_type_args: theory -> string -> int
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  val strip_prefix: string -> string -> string option
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  val metis_line: bool -> int -> int -> string list -> string
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  val metis_proof_text:
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    bool * minimize_command * string * string vector * thm * int
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    -> string * string list
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  val isar_proof_text:
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    name_pool option * bool * int * Proof.context * int list list
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    -> bool * minimize_command * string * string vector * thm * int
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    -> string * string list
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  val proof_text:
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    bool -> name_pool option * bool * int * Proof.context * int list list
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    -> bool * minimize_command * string * string vector * thm * int
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    -> string * string list
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end;
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structure Sledgehammer_Proof_Reconstruct : SLEDGEHAMMER_PROOF_RECONSTRUCT =
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struct
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open Sledgehammer_Util
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open Sledgehammer_FOL_Clause
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open Sledgehammer_HOL_Clause
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open Sledgehammer_Fact_Preprocessor
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type minimize_command = string list -> string
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fun is_ident_char c = Char.isAlphaNum c orelse c = #"_"
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fun is_head_digit s = Char.isDigit (String.sub (s, 0))
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val index_in_shape : int -> int list list -> int =
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  find_index o exists o curry (op =)
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fun is_axiom_clause_number thm_names num = num <= Vector.length thm_names
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fun is_conjecture_clause_number conjecture_shape num =
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  index_in_shape num conjecture_shape >= 0
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fun ugly_name NONE s = s
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  | ugly_name (SOME the_pool) s =
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    case Symtab.lookup (snd the_pool) s of
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      SOME s' => s'
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    | NONE => s
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fun smart_lambda v t =
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  Abs (case v of
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         Const (s, _) =>
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         List.last (space_explode skolem_infix (Long_Name.base_name s))
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       | Var ((s, _), _) => s
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       | Free (s, _) => s
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       | _ => "", fastype_of v, abstract_over (v, t))
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fun forall_of v t = HOLogic.all_const (fastype_of v) $ smart_lambda v t
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datatype ('a, 'b, 'c, 'd, 'e) raw_step =
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  Definition of 'a * 'b * 'c |
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  Inference of 'a * 'd * 'e list
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(**** PARSING OF TSTP FORMAT ****)
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fun strip_spaces_in_list [] = ""
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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 [c1, c2] =
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    strip_spaces_in_list [c1] ^ strip_spaces_in_list [c2]
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  | strip_spaces_in_list (c1 :: c2 :: c3 :: cs) =
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    if Char.isSpace c1 then
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      strip_spaces_in_list (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 (c1 :: c3 :: cs)
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      else
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        str c1 ^ (if forall is_ident_char [c1, c3] then " " else "") ^
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        strip_spaces_in_list (c3 :: cs)
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    else
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      str c1 ^ strip_spaces_in_list (c2 :: c3 :: cs)
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val strip_spaces = strip_spaces_in_list o String.explode
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(* Syntax trees, either term list or formulae *)
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datatype node = IntLeaf of int | StrNode of string * node list
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fun str_leaf s = StrNode (s, [])
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fun scons (x, y) = StrNode ("cons", [x, y])
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val slist_of = List.foldl scons (str_leaf "nil")
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(*Strings enclosed in single quotes, e.g. filenames*)
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val parse_quoted = $$ "'" |-- Scan.repeat (~$$ "'") --| $$ "'" >> implode;
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(*Integer constants, typically proof line numbers*)
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val parse_integer = Scan.many1 is_head_digit >> (the o Int.fromString o implode)
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val parse_dollar_name =
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  Scan.repeat ($$ "$") -- Symbol.scan_id >> (fn (ss, s) => implode ss ^ s)
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(* needed for SPASS's output format *)
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fun repair_name _ "$true" = "c_True"
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  | repair_name _ "$false" = "c_False"
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  | repair_name _ "$$e" = "c_equal" (* seen in Vampire 11 proofs *)
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  | repair_name _ "equal" = "c_equal" (* probably not needed *)
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  | repair_name pool s = ugly_name pool s
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(* Generalized first-order terms, which include file names, numbers, etc. *)
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(* The "x" argument is not strictly necessary, but without it Poly/ML loops
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   forever at compile time. *)
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fun parse_term pool x =
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     (parse_quoted >> str_leaf
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   || parse_integer >> IntLeaf
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   || (parse_dollar_name >> repair_name pool)
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      -- Scan.optional ($$ "(" |-- parse_terms pool --| $$ ")") [] >> StrNode
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   || $$ "(" |-- parse_term pool --| $$ ")"
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   || $$ "[" |-- Scan.optional (parse_terms pool) [] --| $$ "]" >> slist_of) x
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and parse_terms pool x =
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  (parse_term pool ::: Scan.repeat ($$ "," |-- parse_term pool)) x
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fun negate_node u = StrNode ("c_Not", [u])
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fun equate_nodes u1 u2 = StrNode ("c_equal", [u1, u2])
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(* Apply equal or not-equal to a term. *)
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fun repair_predicate_term (u, NONE) = u
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  | repair_predicate_term (u1, SOME (NONE, u2)) = equate_nodes u1 u2
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  | repair_predicate_term (u1, SOME (SOME _, u2)) =
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    negate_node (equate_nodes u1 u2)
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fun parse_predicate_term pool =
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  parse_term pool -- Scan.option (Scan.option ($$ "!") --| $$ "="
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                                  -- parse_term pool)
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  >> repair_predicate_term
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fun parse_literal pool x =
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  ($$ "~" |-- parse_literal pool >> negate_node || parse_predicate_term pool) x
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fun parse_literals pool =
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  parse_literal pool ::: Scan.repeat ($$ "|" |-- parse_literal pool)
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fun parse_parenthesized_literals pool =
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  $$ "(" |-- parse_literals pool --| $$ ")" || parse_literals pool
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fun parse_clause pool =
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  parse_parenthesized_literals pool
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    ::: Scan.repeat ($$ "|" |-- parse_parenthesized_literals pool)
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  >> List.concat
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fun ints_of_node (IntLeaf n) = cons n
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  | ints_of_node (StrNode (_, us)) = fold ints_of_node us
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val parse_tstp_annotations =
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  Scan.optional ($$ "," |-- parse_term NONE
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                   --| Scan.option ($$ "," |-- parse_terms NONE)
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                 >> (fn source => ints_of_node source [])) []
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fun parse_definition pool =
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  $$ "(" |-- parse_literal NONE --| Scan.this_string "<=>"
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  -- parse_clause pool --| $$ ")"
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(* Syntax: cnf(<num>, <formula_role>, <cnf_formula> <annotations>).
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   The <num> could be an identifier, but we assume integers. *)
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fun finish_tstp_definition_line (num, (u, us)) = Definition (num, u, us)
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fun finish_tstp_inference_line ((num, us), deps) = Inference (num, us, deps)
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fun parse_tstp_line pool =
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     ((Scan.this_string "fof" -- $$ "(") |-- parse_integer --| $$ ","
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       --| Scan.this_string "definition" --| $$ "," -- parse_definition pool
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       --| parse_tstp_annotations --| $$ ")" --| $$ "."
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      >> finish_tstp_definition_line)
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  || ((Scan.this_string "cnf" -- $$ "(") |-- parse_integer --| $$ ","
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       --| Symbol.scan_id --| $$ "," -- parse_clause pool
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       -- parse_tstp_annotations --| $$ ")" --| $$ "."
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      >> finish_tstp_inference_line)
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(**** PARSING OF SPASS OUTPUT ****)
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(* SPASS returns clause references of the form "x.y". We ignore "y", whose role
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   is not clear anyway. *)
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val parse_dot_name = parse_integer --| $$ "." --| parse_integer
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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_predicate_term pool =
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  parse_predicate_term pool --| Scan.repeat ($$ "*" || $$ "+" || $$ " ")
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fun parse_horn_clause pool =
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  Scan.repeat (parse_decorated_predicate_term pool) --| $$ "|" --| $$ "|"
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    -- Scan.repeat (parse_decorated_predicate_term pool) --| $$ "-" --| $$ ">"
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    -- Scan.repeat (parse_decorated_predicate_term pool)
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  >> (fn (([], []), []) => [str_leaf "c_False"]
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       | ((clauses1, clauses2), clauses3) =>
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         map negate_node (clauses1 @ clauses2) @ clauses3)
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(* Syntax: <num>[0:<inference><annotations>]
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   <cnf_formulas> || <cnf_formulas> -> <cnf_formulas>. *)
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fun finish_spass_line ((num, deps), us) = Inference (num, us, deps)
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fun parse_spass_line pool =
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  parse_integer --| $$ "[" --| $$ "0" --| $$ ":" --| Symbol.scan_id
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  -- parse_spass_annotations --| $$ "]" -- parse_horn_clause pool --| $$ "."
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  >> finish_spass_line
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fun parse_line pool = parse_tstp_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
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(**** INTERPRETATION OF TSTP SYNTAX TREES ****)
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exception NODE of node list
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(*If string s has the prefix s1, return the result of deleting it.*)
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fun strip_prefix s1 s =
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  if String.isPrefix s1 s
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  then SOME (undo_ascii_of (String.extract (s, size s1, NONE)))
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  else NONE;
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(*Invert the table of translations between Isabelle and ATPs*)
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val type_const_trans_table_inv =
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      Symtab.make (map swap (Symtab.dest type_const_trans_table));
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fun invert_type_const c =
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    case Symtab.lookup type_const_trans_table_inv c of
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        SOME c' => c'
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      | NONE => c;
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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_node _ (u as IntLeaf _) = raise NODE [u]
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  | type_from_node tfrees (u as StrNode (a, us)) =
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    let val Ts = map (type_from_node tfrees) us in
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      case strip_prefix tconst_prefix a of
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        SOME b => Type (invert_type_const b, Ts)
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      | NONE =>
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        if not (null us) then
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          raise NODE [u]  (* only "tconst"s have type arguments *)
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        else case strip_prefix 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 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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(*Invert the table of translations between Isabelle and ATPs*)
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val const_trans_table_inv =
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  Symtab.update ("fequal", @{const_name "op ="})
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                (Symtab.make (map swap (Symtab.dest const_trans_table)))
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fun invert_const c = c |> Symtab.lookup const_trans_table_inv |> the_default c
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(* The number of type arguments of a constant, zero if it's monomorphic. For
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   (instances of) Skolem pseudoconstants, this information is encoded in the
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   constant name. *)
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fun num_type_args thy s =
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  if String.isPrefix skolem_theory_name s then
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    s |> unprefix skolem_theory_name
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      |> space_explode skolem_infix |> hd
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      |> space_explode "_" |> List.last |> Int.fromString |> the
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  else
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    (s, Sign.the_const_type thy s) |> Sign.const_typargs thy |> length
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fun fix_atp_variable_name s =
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  let
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    fun subscript_name s n = s ^ nat_subscript n
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    val s = String.map Char.toLower s
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  in
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    case space_explode "_" s of
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      [_] => (case take_suffix Char.isDigit (String.explode s) of
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                (cs1 as _ :: _, cs2 as _ :: _) =>
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                subscript_name (String.implode cs1)
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                               (the (Int.fromString (String.implode cs2)))
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              | (_, _) => s)
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    | [s1, s2] => (case Int.fromString s2 of
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                     SOME n => subscript_name s1 n
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                   | NONE => s)
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    | _ => s
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  end
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(* First-order translation. No types are known for variables. "HOLogic.typeT"
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   should allow them to be inferred.*)
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fun term_from_node thy full_types tfrees =
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  let
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    fun aux opt_T args u =
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      case u of
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        IntLeaf _ => raise NODE [u]
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      | StrNode ("hBOOL", [u1]) => aux (SOME @{typ bool}) [] u1
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      | StrNode ("hAPP", [u1, u2]) => aux opt_T (u2 :: args) u1
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      | StrNode ("c_Not", [u1]) => @{const Not} $ aux (SOME @{typ bool}) [] u1
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      | StrNode (a, us) =>
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        if a = type_wrapper_name then
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          case us of
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            [term_u, typ_u] =>
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            aux (SOME (type_from_node tfrees typ_u)) args term_u
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          | _ => raise NODE us
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        else case strip_prefix const_prefix a of
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          SOME "equal" =>
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          list_comb (Const (@{const_name "op ="}, HOLogic.typeT),
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                     map (aux NONE []) us)
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        | SOME b =>
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   309
          let
blanchet@36909
   310
            val c = invert_const b
blanchet@36909
   311
            val num_type_args = num_type_args thy c
blanchet@36909
   312
            val actual_num_type_args = if full_types then 0 else num_type_args
blanchet@36909
   313
            val num_term_args = length us - actual_num_type_args
blanchet@36909
   314
            val ts = map (aux NONE []) (take num_term_args us @ args)
blanchet@36909
   315
            val t =
blanchet@36909
   316
              Const (c, if full_types then
blanchet@36909
   317
                          case opt_T of
blanchet@36909
   318
                            SOME T => map fastype_of ts ---> T
blanchet@36909
   319
                          | NONE =>
blanchet@36909
   320
                            if num_type_args = 0 then
blanchet@36909
   321
                              Sign.const_instance thy (c, [])
blanchet@36909
   322
                            else
blanchet@36909
   323
                              raise Fail ("no type information for " ^ quote c)
blanchet@36909
   324
                        else
blanchet@36909
   325
                          (* Extra args from "hAPP" come after any arguments
blanchet@36909
   326
                             given directly to the constant. *)
blanchet@37410
   327
                          if String.isPrefix skolem_theory_name c then
blanchet@37399
   328
                            map fastype_of ts ---> HOLogic.typeT
blanchet@37399
   329
                          else
blanchet@37399
   330
                            Sign.const_instance thy (c,
blanchet@37399
   331
                                map (type_from_node tfrees)
blanchet@37399
   332
                                    (drop num_term_args us)))
blanchet@36909
   333
          in list_comb (t, ts) end
blanchet@36909
   334
        | NONE => (* a free or schematic variable *)
blanchet@36909
   335
          let
blanchet@36909
   336
            val ts = map (aux NONE []) (us @ args)
blanchet@36909
   337
            val T = map fastype_of ts ---> HOLogic.typeT
blanchet@36909
   338
            val t =
blanchet@36909
   339
              case strip_prefix fixed_var_prefix a of
blanchet@36909
   340
                SOME b => Free (b, T)
blanchet@36909
   341
              | NONE =>
blanchet@36909
   342
                case strip_prefix schematic_var_prefix a of
blanchet@36967
   343
                  SOME b => Var ((b, 0), T)
blanchet@36909
   344
                | NONE =>
blanchet@36909
   345
                  (* Variable from the ATP, say "X1" *)
blanchet@36967
   346
                  Var ((fix_atp_variable_name a, 0), T)
blanchet@36909
   347
          in list_comb (t, ts) end
blanchet@36909
   348
  in aux end
paulson@21978
   349
blanchet@36392
   350
(* Type class literal applied to a type. Returns triple of polarity, class,
blanchet@36392
   351
   type. *)
blanchet@36967
   352
fun type_constraint_from_node pos tfrees (StrNode ("c_Not", [u])) =
blanchet@36967
   353
    type_constraint_from_node (not pos) tfrees u
blanchet@36967
   354
  | type_constraint_from_node pos tfrees u = case u of
blanchet@36909
   355
        IntLeaf _ => raise NODE [u]
blanchet@36486
   356
      | StrNode (a, us) =>
blanchet@36967
   357
            (case (strip_prefix class_prefix a,
blanchet@36967
   358
                   map (type_from_node tfrees) us) of
blanchet@36486
   359
                 (SOME b, [T]) => (pos, b, T)
blanchet@36909
   360
               | _ => raise NODE [u])
paulson@21978
   361
paulson@21978
   362
(** Accumulate type constraints in a clause: negative type literals **)
paulson@21978
   363
blanchet@36485
   364
fun add_var (key, z)  = Vartab.map_default (key, []) (cons z)
paulson@21978
   365
blanchet@36909
   366
fun add_type_constraint (false, cl, TFree (a ,_)) = add_var ((a, ~1), cl)
blanchet@36909
   367
  | add_type_constraint (false, cl, TVar (ix, _)) = add_var (ix, cl)
blanchet@36909
   368
  | add_type_constraint _ = I
paulson@21978
   369
blanchet@36491
   370
fun is_positive_literal (@{const Not} $ _) = false
blanchet@36402
   371
  | is_positive_literal t = true
blanchet@36402
   372
blanchet@36485
   373
fun negate_term thy (Const (@{const_name All}, T) $ Abs (s, T', t')) =
blanchet@36402
   374
    Const (@{const_name Ex}, T) $ Abs (s, T', negate_term thy t')
blanchet@36402
   375
  | negate_term thy (Const (@{const_name Ex}, T) $ Abs (s, T', t')) =
blanchet@36402
   376
    Const (@{const_name All}, T) $ Abs (s, T', negate_term thy t')
blanchet@36402
   377
  | negate_term thy (@{const "op -->"} $ t1 $ t2) =
blanchet@36402
   378
    @{const "op &"} $ t1 $ negate_term thy t2
blanchet@36402
   379
  | negate_term thy (@{const "op &"} $ t1 $ t2) =
blanchet@36402
   380
    @{const "op |"} $ negate_term thy t1 $ negate_term thy t2
blanchet@36402
   381
  | negate_term thy (@{const "op |"} $ t1 $ t2) =
blanchet@36402
   382
    @{const "op &"} $ negate_term thy t1 $ negate_term thy t2
blanchet@36486
   383
  | negate_term _ (@{const Not} $ t) = t
blanchet@36486
   384
  | negate_term _ t = @{const Not} $ t
blanchet@36402
   385
blanchet@36402
   386
fun clause_for_literals _ [] = HOLogic.false_const
blanchet@36402
   387
  | clause_for_literals _ [lit] = lit
blanchet@36402
   388
  | clause_for_literals thy lits =
blanchet@36402
   389
    case List.partition is_positive_literal lits of
blanchet@36402
   390
      (pos_lits as _ :: _, neg_lits as _ :: _) =>
blanchet@36402
   391
      @{const "op -->"}
blanchet@36402
   392
          $ foldr1 HOLogic.mk_conj (map (negate_term thy) neg_lits)
blanchet@36402
   393
          $ foldr1 HOLogic.mk_disj pos_lits
blanchet@36402
   394
    | _ => foldr1 HOLogic.mk_disj lits
blanchet@36402
   395
blanchet@36402
   396
(* Final treatment of the list of "real" literals from a clause.
blanchet@36402
   397
   No "real" literals means only type information. *)
blanchet@36402
   398
fun finish_clause _ [] = HOLogic.true_const
blanchet@36402
   399
  | finish_clause thy lits =
blanchet@36402
   400
    lits |> filter_out (curry (op =) HOLogic.false_const) |> rev
blanchet@36402
   401
         |> clause_for_literals thy
paulson@22491
   402
paulson@21978
   403
(*Accumulate sort constraints in vt, with "real" literals in lits.*)
blanchet@36967
   404
fun lits_of_nodes thy full_types tfrees =
blanchet@36967
   405
  let
blanchet@36967
   406
    fun aux (vt, lits) [] = (vt, finish_clause thy lits)
blanchet@36967
   407
      | aux (vt, lits) (u :: us) =
blanchet@36967
   408
        aux (add_type_constraint
blanchet@36967
   409
                 (type_constraint_from_node true tfrees u) vt, lits) us
blanchet@36967
   410
        handle NODE _ =>
blanchet@36967
   411
               aux (vt, term_from_node thy full_types tfrees (SOME @{typ bool})
blanchet@36967
   412
                                       [] u :: lits) us
blanchet@36967
   413
  in aux end
paulson@21978
   414
blanchet@36967
   415
(* Update TVars with detected sort constraints. It's not totally clear when
blanchet@36967
   416
   this code is necessary. *)
blanchet@36967
   417
fun repair_tvar_sorts vt =
blanchet@36556
   418
  let
blanchet@36556
   419
    fun do_type (Type (a, Ts)) = Type (a, map do_type Ts)
blanchet@36556
   420
      | do_type (TVar (xi, s)) = TVar (xi, the_default s (Vartab.lookup vt xi))
blanchet@36967
   421
      | do_type (TFree z) = TFree z
blanchet@36556
   422
    fun do_term (Const (a, T)) = Const (a, do_type T)
blanchet@36556
   423
      | do_term (Free (a, T)) = Free (a, do_type T)
blanchet@36556
   424
      | do_term (Var (xi, T)) = Var (xi, do_type T)
blanchet@36556
   425
      | do_term (t as Bound _) = t
blanchet@36556
   426
      | do_term (Abs (a, T, t)) = Abs (a, do_type T, do_term t)
blanchet@36556
   427
      | do_term (t1 $ t2) = do_term t1 $ do_term t2
blanchet@36556
   428
  in not (Vartab.is_empty vt) ? do_term end
blanchet@36551
   429
blanchet@36551
   430
fun unskolemize_term t =
blanchet@36909
   431
  Term.add_consts t []
blanchet@36909
   432
  |> filter (is_skolem_const_name o fst) |> map Const
blanchet@36909
   433
  |> rpair t |-> fold forall_of
paulson@21978
   434
blanchet@36555
   435
val combinator_table =
blanchet@36555
   436
  [(@{const_name COMBI}, @{thm COMBI_def_raw}),
blanchet@36555
   437
   (@{const_name COMBK}, @{thm COMBK_def_raw}),
blanchet@36555
   438
   (@{const_name COMBB}, @{thm COMBB_def_raw}),
blanchet@36555
   439
   (@{const_name COMBC}, @{thm COMBC_def_raw}),
blanchet@36555
   440
   (@{const_name COMBS}, @{thm COMBS_def_raw})]
blanchet@36555
   441
blanchet@36555
   442
fun uncombine_term (t1 $ t2) = betapply (pairself uncombine_term (t1, t2))
blanchet@36555
   443
  | uncombine_term (Abs (s, T, t')) = Abs (s, T, uncombine_term t')
blanchet@36555
   444
  | uncombine_term (t as Const (x as (s, _))) =
blanchet@36555
   445
    (case AList.lookup (op =) combinator_table s of
blanchet@36555
   446
       SOME thm => thm |> prop_of |> specialize_type @{theory} x |> Logic.dest_equals |> snd
blanchet@36555
   447
     | NONE => t)
blanchet@36555
   448
  | uncombine_term t = t
blanchet@36555
   449
blanchet@36486
   450
(* Interpret a list of syntax trees as a clause, given by "real" literals and
blanchet@36486
   451
   sort constraints. "vt" holds the initial sort constraints, from the
blanchet@36486
   452
   conjecture clauses. *)
blanchet@36967
   453
fun clause_of_nodes ctxt full_types tfrees us =
blanchet@36909
   454
  let
blanchet@36909
   455
    val thy = ProofContext.theory_of ctxt
blanchet@36967
   456
    val (vt, t) = lits_of_nodes thy full_types tfrees (Vartab.empty, []) us
blanchet@36967
   457
  in repair_tvar_sorts vt t end
blanchet@36556
   458
fun check_formula ctxt =
wenzelm@37145
   459
  Type_Infer.constrain @{typ bool}
blanchet@36486
   460
  #> Syntax.check_term (ProofContext.set_mode ProofContext.mode_schematic ctxt)
paulson@21978
   461
paulson@21978
   462
paulson@21978
   463
(**** Translation of TSTP files to Isar Proofs ****)
paulson@21978
   464
blanchet@36486
   465
fun unvarify_term (Var ((s, 0), T)) = Free (s, T)
blanchet@36486
   466
  | unvarify_term t = raise TERM ("unvarify_term: non-Var", [t])
paulson@21978
   467
blanchet@36967
   468
fun decode_line full_types tfrees (Definition (num, u, us)) ctxt =
blanchet@36486
   469
    let
blanchet@36967
   470
      val t1 = clause_of_nodes ctxt full_types tfrees [u]
blanchet@36551
   471
      val vars = snd (strip_comb t1)
blanchet@36486
   472
      val frees = map unvarify_term vars
blanchet@36486
   473
      val unvarify_args = subst_atomic (vars ~~ frees)
blanchet@36967
   474
      val t2 = clause_of_nodes ctxt full_types tfrees us
blanchet@36551
   475
      val (t1, t2) =
blanchet@36551
   476
        HOLogic.eq_const HOLogic.typeT $ t1 $ t2
blanchet@36556
   477
        |> unvarify_args |> uncombine_term |> check_formula ctxt
blanchet@36555
   478
        |> HOLogic.dest_eq
blanchet@36486
   479
    in
blanchet@36551
   480
      (Definition (num, t1, t2),
blanchet@36551
   481
       fold Variable.declare_term (maps OldTerm.term_frees [t1, t2]) ctxt)
blanchet@36486
   482
    end
blanchet@36967
   483
  | decode_line full_types tfrees (Inference (num, us, deps)) ctxt =
blanchet@36551
   484
    let
blanchet@36967
   485
      val t = us |> clause_of_nodes ctxt full_types tfrees
blanchet@36556
   486
                 |> unskolemize_term |> uncombine_term |> check_formula ctxt
blanchet@36551
   487
    in
blanchet@36551
   488
      (Inference (num, t, deps),
blanchet@36551
   489
       fold Variable.declare_term (OldTerm.term_frees t) ctxt)
blanchet@36486
   490
    end
blanchet@36967
   491
fun decode_lines ctxt full_types tfrees lines =
blanchet@36967
   492
  fst (fold_map (decode_line full_types tfrees) lines ctxt)
paulson@21978
   493
blanchet@37323
   494
fun aint_actual_inference _ (Definition _) = true
blanchet@37323
   495
  | aint_actual_inference t (Inference (_, t', _)) = not (t aconv t')
blanchet@36486
   496
blanchet@36486
   497
(* No "real" literals means only type information (tfree_tcs, clsrel, or
blanchet@36486
   498
   clsarity). *)
blanchet@36486
   499
val is_only_type_information = curry (op aconv) HOLogic.true_const
blanchet@36486
   500
blanchet@36486
   501
fun replace_one_dep (old, new) dep = if dep = old then new else [dep]
blanchet@36486
   502
fun replace_deps_in_line _ (line as Definition _) = line
blanchet@36486
   503
  | replace_deps_in_line p (Inference (num, t, deps)) =
blanchet@36486
   504
    Inference (num, t, fold (union (op =) o replace_one_dep p) deps [])
paulson@21978
   505
paulson@22491
   506
(*Discard axioms; consolidate adjacent lines that prove the same clause, since they differ
paulson@22491
   507
  only in type information.*)
blanchet@36551
   508
fun add_line _ _ (line as Definition _) lines = line :: lines
blanchet@36551
   509
  | add_line conjecture_shape thm_names (Inference (num, t, [])) lines =
blanchet@36570
   510
    (* No dependencies: axiom, conjecture clause, or internal axioms or
blanchet@36570
   511
       definitions (Vampire). *)
blanchet@36486
   512
    if is_axiom_clause_number thm_names num then
blanchet@36486
   513
      (* Axioms are not proof lines. *)
blanchet@36486
   514
      if is_only_type_information t then
blanchet@36486
   515
        map (replace_deps_in_line (num, [])) lines
blanchet@36486
   516
      (* Is there a repetition? If so, replace later line by earlier one. *)
blanchet@37323
   517
      else case take_prefix (aint_actual_inference t) lines of
blanchet@36486
   518
        (_, []) => lines (*no repetition of proof line*)
blanchet@36486
   519
      | (pre, Inference (num', _, _) :: post) =>
blanchet@36486
   520
        pre @ map (replace_deps_in_line (num', [num])) post
blanchet@36570
   521
    else if is_conjecture_clause_number conjecture_shape num then
blanchet@36486
   522
      Inference (num, t, []) :: lines
blanchet@36551
   523
    else
blanchet@36570
   524
      map (replace_deps_in_line (num, [])) lines
blanchet@36551
   525
  | add_line _ _ (Inference (num, t, deps)) lines =
blanchet@36486
   526
    (* Type information will be deleted later; skip repetition test. *)
blanchet@36486
   527
    if is_only_type_information t then
blanchet@36486
   528
      Inference (num, t, deps) :: lines
blanchet@36486
   529
    (* Is there a repetition? If so, replace later line by earlier one. *)
blanchet@37323
   530
    else case take_prefix (aint_actual_inference t) lines of
blanchet@36486
   531
      (* FIXME: Doesn't this code risk conflating proofs involving different
blanchet@36486
   532
         types?? *)
blanchet@36486
   533
       (_, []) => Inference (num, t, deps) :: lines
blanchet@36486
   534
     | (pre, Inference (num', t', _) :: post) =>
blanchet@36486
   535
       Inference (num, t', deps) ::
blanchet@36486
   536
       pre @ map (replace_deps_in_line (num', [num])) post
paulson@22044
   537
blanchet@36486
   538
(* Recursively delete empty lines (type information) from the proof. *)
blanchet@36486
   539
fun add_nontrivial_line (Inference (num, t, [])) lines =
blanchet@36486
   540
    if is_only_type_information t then delete_dep num lines
blanchet@36486
   541
    else Inference (num, t, []) :: lines
blanchet@36486
   542
  | add_nontrivial_line line lines = line :: lines
blanchet@36395
   543
and delete_dep num lines =
blanchet@36486
   544
  fold_rev add_nontrivial_line (map (replace_deps_in_line (num, [])) lines) []
blanchet@36486
   545
blanchet@37323
   546
(* ATPs sometimes reuse free variable names in the strangest ways. Removing
blanchet@37323
   547
   offending lines often does the trick. *)
blanchet@36560
   548
fun is_bad_free frees (Free x) = not (member (op =) frees x)
blanchet@36560
   549
  | is_bad_free _ _ = false
paulson@22470
   550
blanchet@36570
   551
(* Vampire is keen on producing these. *)
blanchet@36570
   552
fun is_trivial_formula (@{const Not} $ (Const (@{const_name "op ="}, _)
blanchet@36570
   553
                                        $ t1 $ t2)) = (t1 aconv t2)
blanchet@36570
   554
  | is_trivial_formula t = false
blanchet@36570
   555
blanchet@37323
   556
fun add_desired_line _ _ _ _ _ (line as Definition (num, _, _)) (j, lines) =
blanchet@37323
   557
    (j, line :: map (replace_deps_in_line (num, [])) lines)
blanchet@36924
   558
  | add_desired_line ctxt isar_shrink_factor conjecture_shape thm_names frees
blanchet@36570
   559
                     (Inference (num, t, deps)) (j, lines) =
blanchet@36402
   560
    (j + 1,
blanchet@36570
   561
     if is_axiom_clause_number thm_names num orelse
blanchet@36570
   562
        is_conjecture_clause_number conjecture_shape num orelse
blanchet@36570
   563
        (not (is_only_type_information t) andalso
blanchet@36570
   564
         null (Term.add_tvars t []) andalso
blanchet@36570
   565
         not (exists_subterm (is_bad_free frees) t) andalso
blanchet@36570
   566
         not (is_trivial_formula t) andalso
blanchet@36570
   567
         (null lines orelse (* last line must be kept *)
blanchet@36924
   568
          (length deps >= 2 andalso j mod isar_shrink_factor = 0))) then
blanchet@36570
   569
       Inference (num, t, deps) :: lines  (* keep line *)
blanchet@36402
   570
     else
blanchet@36570
   571
       map (replace_deps_in_line (num, deps)) lines)  (* drop line *)
paulson@21978
   572
blanchet@36402
   573
(** EXTRACTING LEMMAS **)
paulson@21979
   574
blanchet@36223
   575
(* A list consisting of the first number in each line is returned.
blanchet@36395
   576
   TSTP: Interesting lines have the form "cnf(108, axiom, ...)", where the
blanchet@36223
   577
   number (108) is extracted.
blanchet@36395
   578
   SPASS: Lines have the form "108[0:Inp] ...", where the first number (108) is
blanchet@36223
   579
   extracted. *)
blanchet@36402
   580
fun extract_clause_numbers_in_atp_proof atp_proof =
blanchet@35865
   581
  let
blanchet@36395
   582
    val tokens_of = String.tokens (not o is_ident_char)
blanchet@36402
   583
    fun extract_num ("cnf" :: num :: "axiom" :: _) = Int.fromString num
blanchet@36395
   584
      | extract_num (num :: "0" :: "Inp" :: _) = Int.fromString num
blanchet@36395
   585
      | extract_num _ = NONE
blanchet@36402
   586
  in atp_proof |> split_lines |> map_filter (extract_num o tokens_of) end
blanchet@37399
   587
blanchet@37399
   588
val indent_size = 2
blanchet@37399
   589
val no_label = ("", ~1)
blanchet@37399
   590
blanchet@37399
   591
val raw_prefix = "X"
blanchet@37399
   592
val assum_prefix = "A"
blanchet@37399
   593
val fact_prefix = "F"
blanchet@37399
   594
blanchet@37399
   595
fun string_for_label (s, num) = s ^ string_of_int num
blanchet@37399
   596
blanchet@37399
   597
fun metis_using [] = ""
blanchet@37399
   598
  | metis_using ls =
blanchet@37399
   599
    "using " ^ space_implode " " (map string_for_label ls) ^ " "
blanchet@37399
   600
fun metis_apply _ 1 = "by "
blanchet@37399
   601
  | metis_apply 1 _ = "apply "
blanchet@37399
   602
  | metis_apply i _ = "prefer " ^ string_of_int i ^ " apply "
blanchet@37479
   603
fun metis_name full_types = if full_types then "metisFT" else "metis"
blanchet@37479
   604
fun metis_call full_types [] = metis_name full_types
blanchet@37479
   605
  | metis_call full_types ss =
blanchet@37479
   606
    "(" ^ metis_name full_types ^ " " ^ space_implode " " ss ^ ")"
blanchet@37479
   607
fun metis_command full_types i n (ls, ss) =
blanchet@37479
   608
  metis_using ls ^ metis_apply i n ^ metis_call full_types ss
blanchet@37479
   609
fun metis_line full_types i n ss =
blanchet@36063
   610
  "Try this command: " ^
blanchet@37479
   611
  Markup.markup Markup.sendback (metis_command full_types i n ([], ss)) ^ ".\n"
blanchet@36281
   612
fun minimize_line _ [] = ""
blanchet@36281
   613
  | minimize_line minimize_command facts =
blanchet@36281
   614
    case minimize_command facts of
blanchet@36281
   615
      "" => ""
blanchet@36281
   616
    | command =>
blanchet@36065
   617
      "To minimize the number of lemmas, try this command: " ^
blanchet@36281
   618
      Markup.markup Markup.sendback command ^ ".\n"
immler@31840
   619
blanchet@37171
   620
val unprefix_chained = perhaps (try (unprefix chained_prefix))
blanchet@37171
   621
blanchet@37479
   622
fun metis_proof_text (full_types, minimize_command, atp_proof, thm_names, goal,
blanchet@37479
   623
                      i) =
blanchet@36063
   624
  let
blanchet@37171
   625
    val raw_lemmas =
blanchet@36402
   626
      atp_proof |> extract_clause_numbers_in_atp_proof
blanchet@36402
   627
                |> filter (is_axiom_clause_number thm_names)
blanchet@36402
   628
                |> map (fn i => Vector.sub (thm_names, i - 1))
blanchet@37171
   629
    val (chained_lemmas, other_lemmas) =
blanchet@37171
   630
      raw_lemmas |> List.partition (String.isPrefix chained_prefix)
blanchet@37171
   631
                 |>> map (unprefix chained_prefix)
blanchet@37171
   632
                 |> pairself (sort_distinct string_ord)
blanchet@37171
   633
    val lemmas = other_lemmas @ chained_lemmas
blanchet@36063
   634
    val n = Logic.count_prems (prop_of goal)
blanchet@37171
   635
  in
blanchet@37479
   636
    (metis_line full_types i n other_lemmas ^
blanchet@37479
   637
     minimize_line minimize_command lemmas, lemmas)
blanchet@37171
   638
  end
immler@31037
   639
blanchet@36486
   640
(** Isar proof construction and manipulation **)
blanchet@36486
   641
blanchet@36486
   642
fun merge_fact_sets (ls1, ss1) (ls2, ss2) =
blanchet@36486
   643
  (union (op =) ls1 ls2, union (op =) ss1 ss2)
blanchet@36402
   644
blanchet@36402
   645
type label = string * int
blanchet@36402
   646
type facts = label list * string list
blanchet@36402
   647
blanchet@36402
   648
datatype qualifier = Show | Then | Moreover | Ultimately
blanchet@36291
   649
blanchet@36402
   650
datatype step =
blanchet@36478
   651
  Fix of (string * typ) list |
blanchet@36486
   652
  Let of term * term |
blanchet@36402
   653
  Assume of label * term |
blanchet@36402
   654
  Have of qualifier list * label * term * byline
blanchet@36402
   655
and byline =
blanchet@36564
   656
  ByMetis of facts |
blanchet@36402
   657
  CaseSplit of step list list * facts
blanchet@36402
   658
blanchet@36574
   659
fun smart_case_split [] facts = ByMetis facts
blanchet@36574
   660
  | smart_case_split proofs facts = CaseSplit (proofs, facts)
blanchet@36574
   661
blanchet@36475
   662
fun add_fact_from_dep thm_names num =
blanchet@36475
   663
  if is_axiom_clause_number thm_names num then
blanchet@36480
   664
    apsnd (insert (op =) (Vector.sub (thm_names, num - 1)))
blanchet@36475
   665
  else
blanchet@36480
   666
    apfst (insert (op =) (raw_prefix, num))
blanchet@36402
   667
blanchet@36491
   668
fun forall_vars t = fold_rev forall_of (map Var (Term.add_vars t [])) t
blanchet@36491
   669
blanchet@36486
   670
fun step_for_line _ _ (Definition (num, t1, t2)) = Let (t1, t2)
blanchet@36486
   671
  | step_for_line _ _ (Inference (num, t, [])) = Assume ((raw_prefix, num), t)
blanchet@36486
   672
  | step_for_line thm_names j (Inference (num, t, deps)) =
blanchet@36486
   673
    Have (if j = 1 then [Show] else [], (raw_prefix, num),
blanchet@36491
   674
          forall_vars t,
blanchet@36564
   675
          ByMetis (fold (add_fact_from_dep thm_names) deps ([], [])))
blanchet@36291
   676
blanchet@36967
   677
fun proof_from_atp_proof pool ctxt full_types tfrees isar_shrink_factor
blanchet@36967
   678
                         atp_proof conjecture_shape thm_names params frees =
blanchet@36402
   679
  let
blanchet@36486
   680
    val lines =
blanchet@36574
   681
      atp_proof ^ "$" (* the $ sign acts as a sentinel *)
blanchet@36548
   682
      |> parse_proof pool
blanchet@36967
   683
      |> decode_lines ctxt full_types tfrees
blanchet@36551
   684
      |> rpair [] |-> fold_rev (add_line conjecture_shape thm_names)
blanchet@36486
   685
      |> rpair [] |-> fold_rev add_nontrivial_line
blanchet@36924
   686
      |> rpair (0, []) |-> fold_rev (add_desired_line ctxt isar_shrink_factor
blanchet@36570
   687
                                               conjecture_shape thm_names frees)
blanchet@36486
   688
      |> snd
blanchet@36402
   689
  in
blanchet@36909
   690
    (if null params then [] else [Fix params]) @
blanchet@36486
   691
    map2 (step_for_line thm_names) (length lines downto 1) lines
blanchet@36402
   692
  end
blanchet@36402
   693
blanchet@36402
   694
(* When redirecting proofs, we keep information about the labels seen so far in
blanchet@36402
   695
   the "backpatches" data structure. The first component indicates which facts
blanchet@36402
   696
   should be associated with forthcoming proof steps. The second component is a
blanchet@37322
   697
   pair ("assum_ls", "drop_ls"), where "assum_ls" are the labels that should
blanchet@37322
   698
   become assumptions and "drop_ls" are the labels that should be dropped in a
blanchet@37322
   699
   case split. *)
blanchet@36402
   700
type backpatches = (label * facts) list * (label list * label list)
blanchet@36402
   701
blanchet@36556
   702
fun used_labels_of_step (Have (_, _, _, by)) =
blanchet@36402
   703
    (case by of
blanchet@36564
   704
       ByMetis (ls, _) => ls
blanchet@36556
   705
     | CaseSplit (proofs, (ls, _)) =>
blanchet@36556
   706
       fold (union (op =) o used_labels_of) proofs ls)
blanchet@36556
   707
  | used_labels_of_step _ = []
blanchet@36556
   708
and used_labels_of proof = fold (union (op =) o used_labels_of_step) proof []
blanchet@36402
   709
blanchet@36402
   710
fun new_labels_of_step (Fix _) = []
blanchet@36486
   711
  | new_labels_of_step (Let _) = []
blanchet@36402
   712
  | new_labels_of_step (Assume (l, _)) = [l]
blanchet@36402
   713
  | new_labels_of_step (Have (_, l, _, _)) = [l]
blanchet@36402
   714
val new_labels_of = maps new_labels_of_step
blanchet@36402
   715
blanchet@36402
   716
val join_proofs =
blanchet@36402
   717
  let
blanchet@36402
   718
    fun aux _ [] = NONE
blanchet@36402
   719
      | aux proof_tail (proofs as (proof1 :: _)) =
blanchet@36402
   720
        if exists null proofs then
blanchet@36402
   721
          NONE
blanchet@36402
   722
        else if forall (curry (op =) (hd proof1) o hd) (tl proofs) then
blanchet@36402
   723
          aux (hd proof1 :: proof_tail) (map tl proofs)
blanchet@36402
   724
        else case hd proof1 of
blanchet@36402
   725
          Have ([], l, t, by) =>
blanchet@36402
   726
          if forall (fn Have ([], l', t', _) :: _ => (l, t) = (l', t')
blanchet@36402
   727
                      | _ => false) (tl proofs) andalso
blanchet@36402
   728
             not (exists (member (op =) (maps new_labels_of proofs))
blanchet@36556
   729
                         (used_labels_of proof_tail)) then
blanchet@36402
   730
            SOME (l, t, map rev proofs, proof_tail)
blanchet@36402
   731
          else
blanchet@36402
   732
            NONE
blanchet@36402
   733
        | _ => NONE
blanchet@36402
   734
  in aux [] o map rev end
blanchet@36402
   735
blanchet@36402
   736
fun case_split_qualifiers proofs =
blanchet@36402
   737
  case length proofs of
blanchet@36402
   738
    0 => []
blanchet@36402
   739
  | 1 => [Then]
blanchet@36402
   740
  | _ => [Ultimately]
blanchet@36402
   741
blanchet@36491
   742
fun redirect_proof thy conjecture_shape hyp_ts concl_t proof =
wenzelm@33310
   743
  let
blanchet@37324
   744
    (* The first pass outputs those steps that are independent of the negated
blanchet@37324
   745
       conjecture. The second pass flips the proof by contradiction to obtain a
blanchet@37324
   746
       direct proof, introducing case splits when an inference depends on
blanchet@37324
   747
       several facts that depend on the negated conjecture. *)
blanchet@37324
   748
    fun find_hyp num = nth hyp_ts (index_in_shape num conjecture_shape)
blanchet@36402
   749
    val concl_ls = map (pair raw_prefix) (List.last conjecture_shape)
blanchet@37324
   750
    val canonicalize_labels =
blanchet@37324
   751
      map (fn l => if member (op =) concl_ls l then hd concl_ls else l)
blanchet@37324
   752
      #> distinct (op =)
blanchet@36402
   753
    fun first_pass ([], contra) = ([], contra)
blanchet@36491
   754
      | first_pass ((step as Fix _) :: proof, contra) =
blanchet@36491
   755
        first_pass (proof, contra) |>> cons step
blanchet@36491
   756
      | first_pass ((step as Let _) :: proof, contra) =
blanchet@36491
   757
        first_pass (proof, contra) |>> cons step
blanchet@36551
   758
      | first_pass ((step as Assume (l as (_, num), t)) :: proof, contra) =
blanchet@36402
   759
        if member (op =) concl_ls l then
blanchet@37324
   760
          first_pass (proof, contra ||> l = hd concl_ls ? cons step)
blanchet@36402
   761
        else
blanchet@36551
   762
          first_pass (proof, contra) |>> cons (Assume (l, find_hyp num))
blanchet@37324
   763
      | first_pass (Have (qs, l, t, ByMetis (ls, ss)) :: proof, contra) =
blanchet@37324
   764
        let
blanchet@37324
   765
          val ls = canonicalize_labels ls
blanchet@37324
   766
          val step = Have (qs, l, t, ByMetis (ls, ss))
blanchet@37324
   767
        in
blanchet@37324
   768
          if exists (member (op =) (fst contra)) ls then
blanchet@37324
   769
            first_pass (proof, contra |>> cons l ||> cons step)
blanchet@37324
   770
          else
blanchet@37324
   771
            first_pass (proof, contra) |>> cons step
blanchet@37324
   772
        end
blanchet@36402
   773
      | first_pass _ = raise Fail "malformed proof"
blanchet@36402
   774
    val (proof_top, (contra_ls, contra_proof)) =
blanchet@36402
   775
      first_pass (proof, (concl_ls, []))
blanchet@36402
   776
    val backpatch_label = the_default ([], []) oo AList.lookup (op =) o fst
blanchet@36402
   777
    fun backpatch_labels patches ls =
blanchet@36402
   778
      fold merge_fact_sets (map (backpatch_label patches) ls) ([], [])
blanchet@36402
   779
    fun second_pass end_qs ([], assums, patches) =
blanchet@37324
   780
        ([Have (end_qs, no_label, concl_t,
blanchet@36564
   781
                ByMetis (backpatch_labels patches (map snd assums)))], patches)
blanchet@36402
   782
      | second_pass end_qs (Assume (l, t) :: proof, assums, patches) =
blanchet@36402
   783
        second_pass end_qs (proof, (t, l) :: assums, patches)
blanchet@36564
   784
      | second_pass end_qs (Have (qs, l, t, ByMetis (ls, ss)) :: proof, assums,
blanchet@36402
   785
                            patches) =
blanchet@36402
   786
        if member (op =) (snd (snd patches)) l andalso
blanchet@37322
   787
           not (member (op =) (fst (snd patches)) l) andalso
blanchet@36402
   788
           not (AList.defined (op =) (fst patches) l) then
blanchet@36402
   789
          second_pass end_qs (proof, assums, patches ||> apsnd (append ls))
blanchet@36402
   790
        else
blanchet@36402
   791
          (case List.partition (member (op =) contra_ls) ls of
blanchet@36402
   792
             ([contra_l], co_ls) =>
blanchet@37322
   793
             if member (op =) qs Show then
blanchet@37322
   794
               second_pass end_qs (proof, assums,
blanchet@37322
   795
                                   patches |>> cons (contra_l, (co_ls, ss)))
blanchet@37322
   796
             else
blanchet@36402
   797
               second_pass end_qs
blanchet@36402
   798
                           (proof, assums,
blanchet@36402
   799
                            patches |>> cons (contra_l, (l :: co_ls, ss)))
blanchet@36402
   800
               |>> cons (if member (op =) (fst (snd patches)) l then
blanchet@36491
   801
                           Assume (l, negate_term thy t)
blanchet@36402
   802
                         else
blanchet@36491
   803
                           Have (qs, l, negate_term thy t,
blanchet@36564
   804
                                 ByMetis (backpatch_label patches l)))
blanchet@36402
   805
           | (contra_ls as _ :: _, co_ls) =>
blanchet@36402
   806
             let
blanchet@36402
   807
               val proofs =
blanchet@36402
   808
                 map_filter
blanchet@36402
   809
                     (fn l =>
blanchet@36402
   810
                         if member (op =) concl_ls l then
blanchet@36402
   811
                           NONE
blanchet@36402
   812
                         else
blanchet@36402
   813
                           let
blanchet@36402
   814
                             val drop_ls = filter (curry (op <>) l) contra_ls
blanchet@36402
   815
                           in
blanchet@36402
   816
                             second_pass []
blanchet@36402
   817
                                 (proof, assums,
blanchet@36402
   818
                                  patches ||> apfst (insert (op =) l)
blanchet@36402
   819
                                          ||> apsnd (union (op =) drop_ls))
blanchet@36402
   820
                             |> fst |> SOME
blanchet@36402
   821
                           end) contra_ls
blanchet@37324
   822
               val (assumes, facts) =
blanchet@37324
   823
                 if member (op =) (fst (snd patches)) l then
blanchet@37324
   824
                   ([Assume (l, negate_term thy t)], (l :: co_ls, ss))
blanchet@37324
   825
                 else
blanchet@37324
   826
                   ([], (co_ls, ss))
blanchet@36402
   827
             in
blanchet@36402
   828
               (case join_proofs proofs of
blanchet@36402
   829
                  SOME (l, t, proofs, proof_tail) =>
blanchet@36402
   830
                  Have (case_split_qualifiers proofs @
blanchet@36402
   831
                        (if null proof_tail then end_qs else []), l, t,
blanchet@36574
   832
                        smart_case_split proofs facts) :: proof_tail
blanchet@36402
   833
                | NONE =>
blanchet@36402
   834
                  [Have (case_split_qualifiers proofs @ end_qs, no_label,
blanchet@36574
   835
                         concl_t, smart_case_split proofs facts)],
blanchet@36402
   836
                patches)
blanchet@37324
   837
               |>> append assumes
blanchet@36402
   838
             end
blanchet@36402
   839
           | _ => raise Fail "malformed proof")
blanchet@36402
   840
       | second_pass _ _ = raise Fail "malformed proof"
blanchet@36486
   841
    val proof_bottom =
blanchet@36486
   842
      second_pass [Show] (contra_proof, [], ([], ([], []))) |> fst
blanchet@36402
   843
  in proof_top @ proof_bottom end
blanchet@36402
   844
blanchet@36402
   845
val kill_duplicate_assumptions_in_proof =
blanchet@36402
   846
  let
blanchet@36402
   847
    fun relabel_facts subst =
blanchet@36402
   848
      apfst (map (fn l => AList.lookup (op =) subst l |> the_default l))
blanchet@36491
   849
    fun do_step (step as Assume (l, t)) (proof, subst, assums) =
blanchet@36402
   850
        (case AList.lookup (op aconv) assums t of
blanchet@36967
   851
           SOME l' => (proof, (l, l') :: subst, assums)
blanchet@36491
   852
         | NONE => (step :: proof, subst, (t, l) :: assums))
blanchet@36402
   853
      | do_step (Have (qs, l, t, by)) (proof, subst, assums) =
blanchet@36402
   854
        (Have (qs, l, t,
blanchet@36402
   855
               case by of
blanchet@36564
   856
                 ByMetis facts => ByMetis (relabel_facts subst facts)
blanchet@36402
   857
               | CaseSplit (proofs, facts) =>
blanchet@36402
   858
                 CaseSplit (map do_proof proofs, relabel_facts subst facts)) ::
blanchet@36402
   859
         proof, subst, assums)
blanchet@36491
   860
      | do_step step (proof, subst, assums) = (step :: proof, subst, assums)
blanchet@36402
   861
    and do_proof proof = fold do_step proof ([], [], []) |> #1 |> rev
blanchet@36402
   862
  in do_proof end
blanchet@36402
   863
blanchet@36402
   864
val then_chain_proof =
blanchet@36402
   865
  let
blanchet@36402
   866
    fun aux _ [] = []
blanchet@36491
   867
      | aux _ ((step as Assume (l, _)) :: proof) = step :: aux l proof
blanchet@36402
   868
      | aux l' (Have (qs, l, t, by) :: proof) =
blanchet@36402
   869
        (case by of
blanchet@36564
   870
           ByMetis (ls, ss) =>
blanchet@36402
   871
           Have (if member (op =) ls l' then
blanchet@36402
   872
                   (Then :: qs, l, t,
blanchet@36564
   873
                    ByMetis (filter_out (curry (op =) l') ls, ss))
blanchet@36402
   874
                 else
blanchet@36564
   875
                   (qs, l, t, ByMetis (ls, ss)))
blanchet@36402
   876
         | CaseSplit (proofs, facts) =>
blanchet@36402
   877
           Have (qs, l, t, CaseSplit (map (aux no_label) proofs, facts))) ::
blanchet@36402
   878
        aux l proof
blanchet@36491
   879
      | aux _ (step :: proof) = step :: aux no_label proof
blanchet@36402
   880
  in aux no_label end
blanchet@36402
   881
blanchet@36402
   882
fun kill_useless_labels_in_proof proof =
blanchet@36402
   883
  let
blanchet@36556
   884
    val used_ls = used_labels_of proof
blanchet@36402
   885
    fun do_label l = if member (op =) used_ls l then l else no_label
blanchet@36556
   886
    fun do_step (Assume (l, t)) = Assume (do_label l, t)
blanchet@36556
   887
      | do_step (Have (qs, l, t, by)) =
blanchet@36402
   888
        Have (qs, do_label l, t,
blanchet@36402
   889
              case by of
blanchet@36402
   890
                CaseSplit (proofs, facts) =>
blanchet@36556
   891
                CaseSplit (map (map do_step) proofs, facts)
blanchet@36402
   892
              | _ => by)
blanchet@36556
   893
      | do_step step = step
blanchet@36556
   894
  in map do_step proof end
blanchet@36402
   895
blanchet@36402
   896
fun prefix_for_depth n = replicate_string (n + 1)
blanchet@36402
   897
blanchet@36402
   898
val relabel_proof =
blanchet@36402
   899
  let
blanchet@36402
   900
    fun aux _ _ _ [] = []
blanchet@36402
   901
      | aux subst depth (next_assum, next_fact) (Assume (l, t) :: proof) =
blanchet@36402
   902
        if l = no_label then
blanchet@36402
   903
          Assume (l, t) :: aux subst depth (next_assum, next_fact) proof
blanchet@36402
   904
        else
blanchet@36402
   905
          let val l' = (prefix_for_depth depth assum_prefix, next_assum) in
blanchet@36402
   906
            Assume (l', t) ::
blanchet@36402
   907
            aux ((l, l') :: subst) depth (next_assum + 1, next_fact) proof
blanchet@36402
   908
          end
blanchet@36402
   909
      | aux subst depth (next_assum, next_fact) (Have (qs, l, t, by) :: proof) =
blanchet@36402
   910
        let
blanchet@36402
   911
          val (l', subst, next_fact) =
blanchet@36402
   912
            if l = no_label then
blanchet@36402
   913
              (l, subst, next_fact)
blanchet@36402
   914
            else
blanchet@36402
   915
              let
blanchet@36402
   916
                val l' = (prefix_for_depth depth fact_prefix, next_fact)
blanchet@36402
   917
              in (l', (l, l') :: subst, next_fact + 1) end
blanchet@36570
   918
          val relabel_facts =
blanchet@36570
   919
            apfst (map (fn l =>
blanchet@36570
   920
                           case AList.lookup (op =) subst l of
blanchet@36570
   921
                             SOME l' => l'
blanchet@36570
   922
                           | NONE => raise Fail ("unknown label " ^
blanchet@36570
   923
                                                 quote (string_for_label l))))
blanchet@36402
   924
          val by =
blanchet@36402
   925
            case by of
blanchet@36564
   926
              ByMetis facts => ByMetis (relabel_facts facts)
blanchet@36402
   927
            | CaseSplit (proofs, facts) =>
blanchet@36402
   928
              CaseSplit (map (aux subst (depth + 1) (1, 1)) proofs,
blanchet@36402
   929
                         relabel_facts facts)
blanchet@36402
   930
        in
blanchet@36402
   931
          Have (qs, l', t, by) ::
blanchet@36402
   932
          aux subst depth (next_assum, next_fact) proof
blanchet@36402
   933
        end
blanchet@36491
   934
      | aux subst depth nextp (step :: proof) =
blanchet@36491
   935
        step :: aux subst depth nextp proof
blanchet@36402
   936
  in aux [] 0 (1, 1) end
blanchet@36402
   937
blanchet@37479
   938
fun string_for_proof ctxt full_types i n =
blanchet@36402
   939
  let
blanchet@37319
   940
    fun fix_print_mode f x =
blanchet@37319
   941
      setmp_CRITICAL show_no_free_types true
blanchet@37319
   942
          (setmp_CRITICAL show_types true
blanchet@37319
   943
               (Print_Mode.setmp (filter (curry (op =) Symbol.xsymbolsN)
blanchet@37319
   944
                                         (print_mode_value ())) f)) x
blanchet@36402
   945
    fun do_indent ind = replicate_string (ind * indent_size) " "
blanchet@36478
   946
    fun do_free (s, T) =
blanchet@36478
   947
      maybe_quote s ^ " :: " ^
blanchet@36478
   948
      maybe_quote (fix_print_mode (Syntax.string_of_typ ctxt) T)
blanchet@36570
   949
    fun do_label l = if l = no_label then "" else string_for_label l ^ ": "
blanchet@36402
   950
    fun do_have qs =
blanchet@36402
   951
      (if member (op =) qs Moreover then "moreover " else "") ^
blanchet@36402
   952
      (if member (op =) qs Ultimately then "ultimately " else "") ^
blanchet@36402
   953
      (if member (op =) qs Then then
blanchet@36402
   954
         if member (op =) qs Show then "thus" else "hence"
blanchet@36402
   955
       else
blanchet@36402
   956
         if member (op =) qs Show then "show" else "have")
blanchet@36478
   957
    val do_term = maybe_quote o fix_print_mode (Syntax.string_of_term ctxt)
blanchet@36570
   958
    fun do_facts (ls, ss) =
blanchet@36570
   959
      let
blanchet@36570
   960
        val ls = ls |> sort_distinct (prod_ord string_ord int_ord)
blanchet@37171
   961
        val ss = ss |> map unprefix_chained |> sort_distinct string_ord
blanchet@37479
   962
      in metis_command full_types 1 1 (ls, ss) end
blanchet@36478
   963
    and do_step ind (Fix xs) =
blanchet@36478
   964
        do_indent ind ^ "fix " ^ space_implode " and " (map do_free xs) ^ "\n"
blanchet@36486
   965
      | do_step ind (Let (t1, t2)) =
blanchet@36486
   966
        do_indent ind ^ "let " ^ do_term t1 ^ " = " ^ do_term t2 ^ "\n"
blanchet@36402
   967
      | do_step ind (Assume (l, t)) =
blanchet@36402
   968
        do_indent ind ^ "assume " ^ do_label l ^ do_term t ^ "\n"
blanchet@36564
   969
      | do_step ind (Have (qs, l, t, ByMetis facts)) =
blanchet@36402
   970
        do_indent ind ^ do_have qs ^ " " ^
blanchet@36479
   971
        do_label l ^ do_term t ^ " " ^ do_facts facts ^ "\n"
blanchet@36402
   972
      | do_step ind (Have (qs, l, t, CaseSplit (proofs, facts))) =
blanchet@36402
   973
        space_implode (do_indent ind ^ "moreover\n")
blanchet@36402
   974
                      (map (do_block ind) proofs) ^
blanchet@36479
   975
        do_indent ind ^ do_have qs ^ " " ^ do_label l ^ do_term t ^ " " ^
blanchet@36478
   976
        do_facts facts ^ "\n"
blanchet@36402
   977
    and do_steps prefix suffix ind steps =
blanchet@36402
   978
      let val s = implode (map (do_step ind) steps) in
blanchet@36402
   979
        replicate_string (ind * indent_size - size prefix) " " ^ prefix ^
blanchet@36402
   980
        String.extract (s, ind * indent_size,
blanchet@36402
   981
                        SOME (size s - ind * indent_size - 1)) ^
blanchet@36402
   982
        suffix ^ "\n"
blanchet@36402
   983
      end
blanchet@36402
   984
    and do_block ind proof = do_steps "{ " " }" (ind + 1) proof
blanchet@36564
   985
    (* One-step proofs are pointless; better use the Metis one-liner
blanchet@36564
   986
       directly. *)
blanchet@36564
   987
    and do_proof [Have (_, _, _, ByMetis _)] = ""
blanchet@36564
   988
      | do_proof proof =
blanchet@36480
   989
        (if i <> 1 then "prefer " ^ string_of_int i ^ "\n" else "") ^
blanchet@36480
   990
        do_indent 0 ^ "proof -\n" ^
blanchet@36480
   991
        do_steps "" "" 1 proof ^
blanchet@36480
   992
        do_indent 0 ^ (if n <> 1 then "next" else "qed") ^ "\n"
blanchet@36488
   993
  in do_proof end
blanchet@36402
   994
blanchet@37479
   995
fun isar_proof_text (pool, debug, isar_shrink_factor, ctxt, conjecture_shape)
blanchet@37479
   996
                    (other_params as (full_types, _, atp_proof, thm_names, goal,
blanchet@37479
   997
                                      i)) =
blanchet@36402
   998
  let
blanchet@36402
   999
    val thy = ProofContext.theory_of ctxt
blanchet@36909
  1000
    val (params, hyp_ts, concl_t) = strip_subgoal goal i
blanchet@36909
  1001
    val frees = fold Term.add_frees (concl_t :: hyp_ts) []
blanchet@36967
  1002
    val tfrees = fold Term.add_tfrees (concl_t :: hyp_ts) []
blanchet@36402
  1003
    val n = Logic.count_prems (prop_of goal)
blanchet@37479
  1004
    val (one_line_proof, lemma_names) = metis_proof_text other_params
blanchet@36283
  1005
    fun isar_proof_for () =
blanchet@36967
  1006
      case proof_from_atp_proof pool ctxt full_types tfrees isar_shrink_factor
blanchet@36924
  1007
                                atp_proof conjecture_shape thm_names params
blanchet@36924
  1008
                                frees
blanchet@36491
  1009
           |> redirect_proof thy conjecture_shape hyp_ts concl_t
blanchet@36402
  1010
           |> kill_duplicate_assumptions_in_proof
blanchet@36402
  1011
           |> then_chain_proof
blanchet@36402
  1012
           |> kill_useless_labels_in_proof
blanchet@36402
  1013
           |> relabel_proof
blanchet@37479
  1014
           |> string_for_proof ctxt full_types i n of
blanchet@36283
  1015
        "" => ""
blanchet@36402
  1016
      | proof => "\nStructured proof:\n" ^ Markup.markup Markup.sendback proof
blanchet@35868
  1017
    val isar_proof =
blanchet@36402
  1018
      if debug then
blanchet@36283
  1019
        isar_proof_for ()
blanchet@36283
  1020
      else
blanchet@36283
  1021
        try isar_proof_for ()
blanchet@36287
  1022
        |> the_default "Warning: The Isar proof construction failed.\n"
blanchet@36283
  1023
  in (one_line_proof ^ isar_proof, lemma_names) end
paulson@21978
  1024
blanchet@36557
  1025
fun proof_text isar_proof isar_params other_params =
blanchet@36557
  1026
  (if isar_proof then isar_proof_text isar_params else metis_proof_text)
blanchet@36557
  1027
      other_params
blanchet@36223
  1028
immler@31038
  1029
end;