src/HOL/Tools/Sledgehammer/sledgehammer_proof_reconstruct.ML
author blanchet
Wed Apr 28 21:59:29 2010 +0200 (2010-04-28)
changeset 36551 cc42df660808
parent 36548 a8a6d7172c8c
child 36555 8ff45c2076da
permissions -rw-r--r--
improve unskolemization
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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 chained_hint: string
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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_typargs: theory -> string -> int
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  val make_tvar: string -> typ
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  val strip_prefix: string -> string -> string option
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  val metis_line: int -> int -> string list -> string
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  val metis_proof_text:
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    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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    -> 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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    -> 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_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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(* Hack: Could return false positives (e.g., a user happens to declare a
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   constant called "SomeTheory.sko_means_shoe_in_$wedish". *)
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val is_skolem_const_name =
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  Long_Name.base_name
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  #> String.isPrefix skolem_prefix andf String.isSubstring skolem_infix
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fun is_axiom_clause_number thm_names num = num <= Vector.length thm_names
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val index_in_shape = find_index o exists o curry (op =)
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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 _ "$$e" = "c_equal" (* seen in Vampire proofs *)
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  | repair_name _ "equal" = "c_equal" (* probably not needed *)
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  | repair_name pool s = ugly_name pool s
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(* Generalized first-order terms, which include file names, numbers, etc. *)
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(* The "x" argument is not strictly necessary, but without it Poly/ML loops
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   forever at compile time. *)
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fun parse_term pool x =
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     (parse_quoted >> str_leaf
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   || parse_integer >> IntLeaf
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   || (parse_dollar_name >> repair_name pool)
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      -- Scan.optional ($$ "(" |-- 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. We
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   ignore them. *)
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fun parse_starred_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_starred_predicate_term pool) --| $$ "-" --| $$ ">"
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  -- Scan.repeat (parse_starred_predicate_term pool)
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  >> (fn ([], []) => [str_leaf "c_False"]
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       | (clauses1, clauses2) => map negate_node clauses1 @ clauses2)
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(* Syntax: <num>[0:<inference><annotations>] ||
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           <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" --| $$ ":" --| Symbol.scan_id
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  -- parse_spass_annotations --| $$ "]" --| $$ "|" --| $$ "|"
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  -- 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
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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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fun make_tvar s = TVar (("'" ^ s, 0), HOLogic.typeS);
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fun make_tparam s = TypeInfer.param 0 (s, HOLogic.typeS)
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fun make_var (b,T) = Var((b,0),T);
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(*Type variables are given the basic sort, HOL.type. Some will later be constrained
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  by information from type literals, or by type inference.*)
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fun type_of_node (u as IntLeaf _) = raise NODE u
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  | type_of_node (u as StrNode (a, us)) =
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    let val Ts = map type_of_node 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 tconsts have type arguments*)
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        else case strip_prefix tfree_prefix a of
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          SOME b => TFree ("'" ^ b, HOLogic.typeS)
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        | NONE =>
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          case strip_prefix tvar_prefix a of
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            SOME b => make_tvar b
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          | NONE => make_tparam a  (* Variable from the ATP, say "X1" *)
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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*)
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fun num_typargs thy s = length (Sign.const_typargs thy (s, Sign.the_const_type thy s));
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(*Generates a constant, given its type arguments*)
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fun const_of thy (a,Ts) = Const(a, Sign.const_instance thy (a,Ts));
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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 should allow
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  them to be inferred.*)
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fun term_of_node args thy u =
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  case u of
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    IntLeaf _ => raise NODE u
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  | StrNode ("hBOOL", [u]) => term_of_node [] thy u  (* ignore hBOOL *)
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  | StrNode ("hAPP", [u1, u2]) => term_of_node (u2 :: args) thy u1
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  | StrNode (a, us) =>
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    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 (term_of_node [] thy) us)
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    | SOME b =>
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      let
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        val c = invert_const b
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        val nterms = length us - num_typargs thy c
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        val ts = map (term_of_node [] thy) (take nterms us @ args)
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        (*Extra args from hAPP come AFTER any arguments given directly to the
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          constant.*)
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        val Ts = map type_of_node (drop nterms us)
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      in list_comb(const_of thy (c, Ts), ts) end
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    | NONE => (*a variable, not a constant*)
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      let
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        val opr =
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          (* a Free variable is typically a Skolem function *)
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          case strip_prefix fixed_var_prefix a of
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            SOME b => Free (b, HOLogic.typeT)
blanchet@36486
   312
          | NONE =>
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   313
            case strip_prefix schematic_var_prefix a of
blanchet@36486
   314
              SOME b => make_var (b, HOLogic.typeT)
blanchet@36486
   315
            | NONE =>
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   316
              (* Variable from the ATP, say "X1" *)
blanchet@36486
   317
              make_var (fix_atp_variable_name a, HOLogic.typeT)
blanchet@36486
   318
      in list_comb (opr, map (term_of_node [] thy) (us @ args)) end
paulson@21978
   319
blanchet@36392
   320
(* Type class literal applied to a type. Returns triple of polarity, class,
blanchet@36392
   321
   type. *)
blanchet@36486
   322
fun constraint_of_node pos (StrNode ("c_Not", [u])) =
blanchet@36486
   323
    constraint_of_node (not pos) u
blanchet@36486
   324
  | constraint_of_node pos u = case u of
blanchet@36486
   325
        IntLeaf _ => raise NODE u
blanchet@36486
   326
      | StrNode (a, us) =>
blanchet@36486
   327
            (case (strip_prefix class_prefix a, map type_of_node us) of
blanchet@36486
   328
                 (SOME b, [T]) => (pos, b, T)
blanchet@36486
   329
               | _ => raise NODE u)
paulson@21978
   330
paulson@21978
   331
(** Accumulate type constraints in a clause: negative type literals **)
paulson@21978
   332
blanchet@36485
   333
fun add_var (key, z)  = Vartab.map_default (key, []) (cons z)
paulson@21978
   334
blanchet@36485
   335
fun add_constraint ((false, cl, TFree(a,_)), vt) = add_var ((a,~1),cl) vt
blanchet@36485
   336
  | add_constraint ((false, cl, TVar(ix,_)), vt) = add_var (ix,cl) vt
paulson@21978
   337
  | add_constraint (_, vt) = vt;
paulson@21978
   338
blanchet@36491
   339
fun is_positive_literal (@{const Not} $ _) = false
blanchet@36402
   340
  | is_positive_literal t = true
blanchet@36402
   341
blanchet@36485
   342
fun negate_term thy (Const (@{const_name All}, T) $ Abs (s, T', t')) =
blanchet@36402
   343
    Const (@{const_name Ex}, T) $ Abs (s, T', negate_term thy t')
blanchet@36402
   344
  | negate_term thy (Const (@{const_name Ex}, T) $ Abs (s, T', t')) =
blanchet@36402
   345
    Const (@{const_name All}, T) $ Abs (s, T', negate_term thy t')
blanchet@36402
   346
  | negate_term thy (@{const "op -->"} $ t1 $ t2) =
blanchet@36402
   347
    @{const "op &"} $ t1 $ negate_term thy t2
blanchet@36402
   348
  | negate_term thy (@{const "op &"} $ t1 $ t2) =
blanchet@36402
   349
    @{const "op |"} $ negate_term thy t1 $ negate_term thy t2
blanchet@36402
   350
  | negate_term thy (@{const "op |"} $ t1 $ t2) =
blanchet@36402
   351
    @{const "op &"} $ negate_term thy t1 $ negate_term thy t2
blanchet@36486
   352
  | negate_term _ (@{const Not} $ t) = t
blanchet@36486
   353
  | negate_term _ t = @{const Not} $ t
blanchet@36402
   354
blanchet@36402
   355
fun clause_for_literals _ [] = HOLogic.false_const
blanchet@36402
   356
  | clause_for_literals _ [lit] = lit
blanchet@36402
   357
  | clause_for_literals thy lits =
blanchet@36402
   358
    case List.partition is_positive_literal lits of
blanchet@36402
   359
      (pos_lits as _ :: _, neg_lits as _ :: _) =>
blanchet@36402
   360
      @{const "op -->"}
blanchet@36402
   361
          $ foldr1 HOLogic.mk_conj (map (negate_term thy) neg_lits)
blanchet@36402
   362
          $ foldr1 HOLogic.mk_disj pos_lits
blanchet@36402
   363
    | _ => foldr1 HOLogic.mk_disj lits
blanchet@36402
   364
blanchet@36402
   365
(* Final treatment of the list of "real" literals from a clause.
blanchet@36402
   366
   No "real" literals means only type information. *)
blanchet@36402
   367
fun finish_clause _ [] = HOLogic.true_const
blanchet@36402
   368
  | finish_clause thy lits =
blanchet@36402
   369
    lits |> filter_out (curry (op =) HOLogic.false_const) |> rev
blanchet@36402
   370
         |> clause_for_literals thy
paulson@22491
   371
paulson@21978
   372
(*Accumulate sort constraints in vt, with "real" literals in lits.*)
blanchet@36486
   373
fun lits_of_nodes thy (vt, lits) [] = (vt, finish_clause thy lits)
blanchet@36486
   374
  | lits_of_nodes thy (vt, lits) (u :: us) =
blanchet@36486
   375
    lits_of_nodes thy (add_constraint (constraint_of_node true u, vt), lits) us
blanchet@36486
   376
    handle NODE _ => lits_of_nodes thy (vt, term_of_node [] thy u :: lits) us
paulson@21978
   377
paulson@21978
   378
(*Update TVars/TFrees with detected sort constraints.*)
blanchet@36393
   379
fun repair_sorts vt =
paulson@21978
   380
  let fun tysubst (Type (a, Ts)) = Type (a, map tysubst Ts)
wenzelm@33035
   381
        | tysubst (TVar (xi, s)) = TVar (xi, the_default s (Vartab.lookup vt xi))
wenzelm@33035
   382
        | tysubst (TFree (x, s)) = TFree (x, the_default s (Vartab.lookup vt (x, ~1)))
paulson@21978
   383
      fun tmsubst (Const (a, T)) = Const (a, tysubst T)
paulson@21978
   384
        | tmsubst (Free (a, T)) = Free (a, tysubst T)
paulson@21978
   385
        | tmsubst (Var (xi, T)) = Var (xi, tysubst T)
paulson@21978
   386
        | tmsubst (t as Bound _) = t
paulson@21978
   387
        | tmsubst (Abs (a, T, t)) = Abs (a, tysubst T, tmsubst t)
blanchet@36486
   388
        | tmsubst (t1 $ t2) = tmsubst t1 $ tmsubst t2
blanchet@36551
   389
  in not (Vartab.is_empty vt) ? tmsubst end
blanchet@36551
   390
blanchet@36551
   391
fun unskolemize_term t =
blanchet@36551
   392
  fold forall_of (Term.add_consts t []
blanchet@36551
   393
                 |> filter (is_skolem_const_name o fst) |> map Const) t
paulson@21978
   394
blanchet@36486
   395
(* Interpret a list of syntax trees as a clause, given by "real" literals and
blanchet@36486
   396
   sort constraints. "vt" holds the initial sort constraints, from the
blanchet@36486
   397
   conjecture clauses. *)
blanchet@36486
   398
fun clause_of_nodes ctxt vt us =
blanchet@36551
   399
  let val (vt, t) = lits_of_nodes (ProofContext.theory_of ctxt) (vt, []) us in
blanchet@36551
   400
    t |> repair_sorts vt
blanchet@36291
   401
  end
blanchet@36486
   402
fun check_clause ctxt =
blanchet@36486
   403
  TypeInfer.constrain HOLogic.boolT
blanchet@36486
   404
  #> Syntax.check_term (ProofContext.set_mode ProofContext.mode_schematic ctxt)
paulson@21978
   405
blanchet@36486
   406
(** Global sort constraints on TFrees (from tfree_tcs) are positive unit
blanchet@36486
   407
    clauses. **)
paulson@21978
   408
blanchet@36486
   409
fun add_tfree_constraint (true, cl, TFree (a, _)) = add_var ((a, ~1), cl)
blanchet@36486
   410
  | add_tfree_constraint _ = I
paulson@21978
   411
fun tfree_constraints_of_clauses vt [] = vt
blanchet@36486
   412
  | tfree_constraints_of_clauses vt ([lit] :: uss) =
blanchet@36486
   413
    (tfree_constraints_of_clauses (add_tfree_constraint
blanchet@36486
   414
                                          (constraint_of_node true lit) vt) uss
blanchet@36486
   415
     handle NODE _ => (* Not a positive type constraint? Ignore the literal. *)
blanchet@36486
   416
     tfree_constraints_of_clauses vt uss)
blanchet@36486
   417
  | tfree_constraints_of_clauses vt (_ :: uss) =
blanchet@36486
   418
    tfree_constraints_of_clauses vt uss
paulson@21978
   419
paulson@21978
   420
paulson@21978
   421
(**** Translation of TSTP files to Isar Proofs ****)
paulson@21978
   422
blanchet@36486
   423
fun unvarify_term (Var ((s, 0), T)) = Free (s, T)
blanchet@36486
   424
  | unvarify_term t = raise TERM ("unvarify_term: non-Var", [t])
paulson@21978
   425
blanchet@36486
   426
fun clauses_in_lines (Definition (_, u, us)) = u :: us
blanchet@36486
   427
  | clauses_in_lines (Inference (_, us, _)) = us
paulson@21978
   428
blanchet@36486
   429
fun decode_line vt (Definition (num, u, us)) ctxt =
blanchet@36486
   430
    let
blanchet@36551
   431
      val t1 = clause_of_nodes ctxt vt [u]
blanchet@36551
   432
      val vars = snd (strip_comb t1)
blanchet@36486
   433
      val frees = map unvarify_term vars
blanchet@36486
   434
      val unvarify_args = subst_atomic (vars ~~ frees)
blanchet@36551
   435
      val t2 = clause_of_nodes ctxt vt us
blanchet@36551
   436
      val (t1, t2) =
blanchet@36551
   437
        HOLogic.eq_const HOLogic.typeT $ t1 $ t2
blanchet@36486
   438
        |> unvarify_args |> check_clause ctxt |> HOLogic.dest_eq
blanchet@36486
   439
    in
blanchet@36551
   440
      (Definition (num, t1, t2),
blanchet@36551
   441
       fold Variable.declare_term (maps OldTerm.term_frees [t1, t2]) ctxt)
blanchet@36486
   442
    end
blanchet@36486
   443
  | decode_line vt (Inference (num, us, deps)) ctxt =
blanchet@36551
   444
    let
blanchet@36551
   445
      val t = us |> clause_of_nodes ctxt vt |> unskolemize_term
blanchet@36551
   446
                 |> check_clause ctxt
blanchet@36551
   447
    in
blanchet@36551
   448
      (Inference (num, t, deps),
blanchet@36551
   449
       fold Variable.declare_term (OldTerm.term_frees t) ctxt)
blanchet@36486
   450
    end
blanchet@36486
   451
fun decode_lines ctxt lines =
blanchet@36486
   452
  let
blanchet@36486
   453
    val vt = tfree_constraints_of_clauses Vartab.empty
blanchet@36486
   454
                                          (map clauses_in_lines lines)
blanchet@36486
   455
  in #1 (fold_map (decode_line vt) lines ctxt) end
paulson@21978
   456
blanchet@36486
   457
fun aint_inference _ (Definition _) = true
blanchet@36486
   458
  | aint_inference t (Inference (_, t', _)) = not (t aconv t')
blanchet@36486
   459
blanchet@36486
   460
(* No "real" literals means only type information (tfree_tcs, clsrel, or
blanchet@36486
   461
   clsarity). *)
blanchet@36486
   462
val is_only_type_information = curry (op aconv) HOLogic.true_const
blanchet@36486
   463
blanchet@36486
   464
fun replace_one_dep (old, new) dep = if dep = old then new else [dep]
blanchet@36486
   465
fun replace_deps_in_line _ (line as Definition _) = line
blanchet@36486
   466
  | replace_deps_in_line p (Inference (num, t, deps)) =
blanchet@36486
   467
    Inference (num, t, fold (union (op =) o replace_one_dep p) deps [])
paulson@21978
   468
paulson@22491
   469
(*Discard axioms; consolidate adjacent lines that prove the same clause, since they differ
paulson@22491
   470
  only in type information.*)
blanchet@36551
   471
fun add_line _ _ (line as Definition _) lines = line :: lines
blanchet@36551
   472
  | add_line conjecture_shape thm_names (Inference (num, t, [])) lines =
blanchet@36551
   473
    (* No dependencies: axiom, conjecture clause, or internal axioms
blanchet@36551
   474
       (Vampire). *)
blanchet@36486
   475
    if is_axiom_clause_number thm_names num then
blanchet@36486
   476
      (* Axioms are not proof lines. *)
blanchet@36486
   477
      if is_only_type_information t then
blanchet@36486
   478
        map (replace_deps_in_line (num, [])) lines
blanchet@36486
   479
      (* Is there a repetition? If so, replace later line by earlier one. *)
blanchet@36486
   480
      else case take_prefix (aint_inference t) lines of
blanchet@36486
   481
        (_, []) => lines (*no repetition of proof line*)
blanchet@36486
   482
      | (pre, Inference (num', _, _) :: post) =>
blanchet@36486
   483
        pre @ map (replace_deps_in_line (num', [num])) post
blanchet@36551
   484
    else if index_in_shape num conjecture_shape >= 0 then
blanchet@36486
   485
      Inference (num, t, []) :: lines
blanchet@36551
   486
    else
blanchet@36551
   487
      lines
blanchet@36551
   488
  | add_line _ _ (Inference (num, t, deps)) lines =
blanchet@36486
   489
    (* Type information will be deleted later; skip repetition test. *)
blanchet@36486
   490
    if is_only_type_information t then
blanchet@36486
   491
      Inference (num, t, deps) :: lines
blanchet@36486
   492
    (* Is there a repetition? If so, replace later line by earlier one. *)
blanchet@36486
   493
    else case take_prefix (aint_inference t) lines of
blanchet@36486
   494
      (* FIXME: Doesn't this code risk conflating proofs involving different
blanchet@36486
   495
         types?? *)
blanchet@36486
   496
       (_, []) => Inference (num, t, deps) :: lines
blanchet@36486
   497
     | (pre, Inference (num', t', _) :: post) =>
blanchet@36486
   498
       Inference (num, t', deps) ::
blanchet@36486
   499
       pre @ map (replace_deps_in_line (num', [num])) post
paulson@22044
   500
blanchet@36486
   501
(* Recursively delete empty lines (type information) from the proof. *)
blanchet@36486
   502
fun add_nontrivial_line (Inference (num, t, [])) lines =
blanchet@36486
   503
    if is_only_type_information t then delete_dep num lines
blanchet@36486
   504
    else Inference (num, t, []) :: lines
blanchet@36486
   505
  | add_nontrivial_line line lines = line :: lines
blanchet@36395
   506
and delete_dep num lines =
blanchet@36486
   507
  fold_rev add_nontrivial_line (map (replace_deps_in_line (num, [])) lines) []
blanchet@36486
   508
blanchet@36551
   509
(* FIXME: this seems not to have worked and is obsolete anyway *)
blanchet@36486
   510
fun is_bad_free (Free (a, _)) = String.isPrefix skolem_prefix a
blanchet@36486
   511
  | is_bad_free _ = false
paulson@22470
   512
blanchet@36486
   513
fun add_desired_line _ _ (line as Definition _) (j, lines) = (j, line :: lines)
blanchet@36486
   514
  | add_desired_line ctxt _ (Inference (num, t, [])) (j, lines) =
blanchet@36486
   515
    (j, Inference (num, t, []) :: lines)  (* conjecture clauses must be kept *)
blanchet@36486
   516
  | add_desired_line ctxt shrink_factor (Inference (num, t, deps)) (j, lines) =
blanchet@36402
   517
    (j + 1,
blanchet@36486
   518
     if is_only_type_information t orelse
blanchet@36486
   519
        not (null (Term.add_tvars t [])) orelse
blanchet@36486
   520
        exists_subterm is_bad_free t orelse
blanchet@36474
   521
        (length deps < 2 orelse j mod shrink_factor <> 0) then
blanchet@36486
   522
       map (replace_deps_in_line (num, deps)) lines  (* delete line *)
blanchet@36402
   523
     else
blanchet@36486
   524
       Inference (num, t, deps) :: lines)
paulson@21978
   525
blanchet@36402
   526
(** EXTRACTING LEMMAS **)
paulson@21979
   527
blanchet@36223
   528
(* A list consisting of the first number in each line is returned.
blanchet@36395
   529
   TSTP: Interesting lines have the form "cnf(108, axiom, ...)", where the
blanchet@36223
   530
   number (108) is extracted.
blanchet@36395
   531
   SPASS: Lines have the form "108[0:Inp] ...", where the first number (108) is
blanchet@36223
   532
   extracted. *)
blanchet@36402
   533
fun extract_clause_numbers_in_atp_proof atp_proof =
blanchet@35865
   534
  let
blanchet@36395
   535
    val tokens_of = String.tokens (not o is_ident_char)
blanchet@36402
   536
    fun extract_num ("cnf" :: num :: "axiom" :: _) = Int.fromString num
blanchet@36402
   537
      | extract_num ("cnf" :: num :: "negated_conjecture" :: _) =
blanchet@36402
   538
        Int.fromString num
blanchet@36395
   539
      | extract_num (num :: "0" :: "Inp" :: _) = Int.fromString num
blanchet@36395
   540
      | extract_num _ = NONE
blanchet@36402
   541
  in atp_proof |> split_lines |> map_filter (extract_num o tokens_of) end
wenzelm@33310
   542
  
blanchet@36395
   543
(* Used to label theorems chained into the Sledgehammer call (or rather
blanchet@36395
   544
   goal?) *)
blanchet@36395
   545
val chained_hint = "sledgehammer_chained"
blanchet@35865
   546
blanchet@36063
   547
fun apply_command _ 1 = "by "
blanchet@36063
   548
  | apply_command 1 _ = "apply "
blanchet@36063
   549
  | apply_command i _ = "prefer " ^ string_of_int i ^ " apply "
blanchet@36063
   550
fun metis_command i n [] =
blanchet@36063
   551
    apply_command i n ^ "metis"
blanchet@36063
   552
  | metis_command i n xs =
blanchet@36063
   553
    apply_command i n ^ "(metis " ^ space_implode " " xs ^ ")"
blanchet@36063
   554
fun metis_line i n xs =
blanchet@36063
   555
  "Try this command: " ^
blanchet@36063
   556
  Markup.markup Markup.sendback (metis_command i n xs) ^ ".\n" 
blanchet@36281
   557
fun minimize_line _ [] = ""
blanchet@36281
   558
  | minimize_line minimize_command facts =
blanchet@36281
   559
    case minimize_command facts of
blanchet@36281
   560
      "" => ""
blanchet@36281
   561
    | command =>
blanchet@36065
   562
      "To minimize the number of lemmas, try this command: " ^
blanchet@36281
   563
      Markup.markup Markup.sendback command ^ ".\n"
immler@31840
   564
blanchet@36402
   565
fun metis_proof_text (minimize_command, atp_proof, thm_names, goal, i) =
blanchet@36063
   566
  let
blanchet@36231
   567
    val lemmas =
blanchet@36402
   568
      atp_proof |> extract_clause_numbers_in_atp_proof
blanchet@36402
   569
                |> filter (is_axiom_clause_number thm_names)
blanchet@36402
   570
                |> map (fn i => Vector.sub (thm_names, i - 1))
blanchet@36402
   571
                |> filter_out (fn s => s = "??.unknown" orelse s = chained_hint)
blanchet@36402
   572
                |> sort_distinct string_ord
blanchet@36063
   573
    val n = Logic.count_prems (prop_of goal)
blanchet@36395
   574
  in (metis_line i n lemmas ^ minimize_line minimize_command lemmas, lemmas) end
immler@31037
   575
blanchet@36486
   576
(** Isar proof construction and manipulation **)
blanchet@36486
   577
blanchet@36486
   578
fun merge_fact_sets (ls1, ss1) (ls2, ss2) =
blanchet@36486
   579
  (union (op =) ls1 ls2, union (op =) ss1 ss2)
blanchet@36402
   580
blanchet@36402
   581
type label = string * int
blanchet@36402
   582
type facts = label list * string list
blanchet@36402
   583
blanchet@36402
   584
datatype qualifier = Show | Then | Moreover | Ultimately
blanchet@36291
   585
blanchet@36402
   586
datatype step =
blanchet@36478
   587
  Fix of (string * typ) list |
blanchet@36486
   588
  Let of term * term |
blanchet@36402
   589
  Assume of label * term |
blanchet@36402
   590
  Have of qualifier list * label * term * byline
blanchet@36402
   591
and byline =
blanchet@36402
   592
  Facts of facts |
blanchet@36402
   593
  CaseSplit of step list list * facts
blanchet@36402
   594
blanchet@36402
   595
val raw_prefix = "X"
blanchet@36402
   596
val assum_prefix = "A"
blanchet@36402
   597
val fact_prefix = "F"
blanchet@36402
   598
blanchet@36475
   599
fun add_fact_from_dep thm_names num =
blanchet@36475
   600
  if is_axiom_clause_number thm_names num then
blanchet@36480
   601
    apsnd (insert (op =) (Vector.sub (thm_names, num - 1)))
blanchet@36475
   602
  else
blanchet@36480
   603
    apfst (insert (op =) (raw_prefix, num))
blanchet@36402
   604
blanchet@36491
   605
fun forall_vars t = fold_rev forall_of (map Var (Term.add_vars t [])) t
blanchet@36491
   606
blanchet@36486
   607
fun step_for_line _ _ (Definition (num, t1, t2)) = Let (t1, t2)
blanchet@36486
   608
  | step_for_line _ _ (Inference (num, t, [])) = Assume ((raw_prefix, num), t)
blanchet@36486
   609
  | step_for_line thm_names j (Inference (num, t, deps)) =
blanchet@36486
   610
    Have (if j = 1 then [Show] else [], (raw_prefix, num),
blanchet@36491
   611
          forall_vars t,
blanchet@36475
   612
          Facts (fold (add_fact_from_dep thm_names) deps ([], [])))
blanchet@36291
   613
blanchet@36551
   614
fun proof_from_atp_proof pool ctxt shrink_factor atp_proof conjecture_shape
blanchet@36551
   615
                         thm_names frees =
blanchet@36402
   616
  let
blanchet@36486
   617
    val lines =
blanchet@36548
   618
      atp_proof ^ "$" (* the $ sign is a dummy token *)
blanchet@36548
   619
      |> parse_proof pool
blanchet@36486
   620
      |> decode_lines ctxt
blanchet@36551
   621
      |> rpair [] |-> fold_rev (add_line conjecture_shape thm_names)
blanchet@36486
   622
      |> rpair [] |-> fold_rev add_nontrivial_line
blanchet@36486
   623
      |> rpair (0, []) |-> fold_rev (add_desired_line ctxt shrink_factor)
blanchet@36486
   624
      |> snd
blanchet@36402
   625
  in
blanchet@36402
   626
    (if null frees then [] else [Fix frees]) @
blanchet@36486
   627
    map2 (step_for_line thm_names) (length lines downto 1) lines
blanchet@36402
   628
  end
blanchet@36402
   629
blanchet@36402
   630
val indent_size = 2
blanchet@36402
   631
val no_label = ("", ~1)
blanchet@36402
   632
blanchet@36402
   633
fun no_show qs = not (member (op =) qs Show)
blanchet@36402
   634
blanchet@36402
   635
(* When redirecting proofs, we keep information about the labels seen so far in
blanchet@36402
   636
   the "backpatches" data structure. The first component indicates which facts
blanchet@36402
   637
   should be associated with forthcoming proof steps. The second component is a
blanchet@36402
   638
   pair ("keep_ls", "drop_ls"), where "keep_ls" are the labels to keep and
blanchet@36402
   639
   "drop_ls" are those that should be dropped in a case split. *)
blanchet@36402
   640
type backpatches = (label * facts) list * (label list * label list)
blanchet@36402
   641
blanchet@36402
   642
fun using_of_step (Have (_, _, _, by)) =
blanchet@36402
   643
    (case by of
blanchet@36402
   644
       Facts (ls, _) => ls
blanchet@36402
   645
     | CaseSplit (proofs, (ls, _)) => fold (union (op =) o using_of) proofs ls)
blanchet@36402
   646
  | using_of_step _ = []
blanchet@36402
   647
and using_of proof = fold (union (op =) o using_of_step) proof []
blanchet@36402
   648
blanchet@36402
   649
fun new_labels_of_step (Fix _) = []
blanchet@36486
   650
  | new_labels_of_step (Let _) = []
blanchet@36402
   651
  | new_labels_of_step (Assume (l, _)) = [l]
blanchet@36402
   652
  | new_labels_of_step (Have (_, l, _, _)) = [l]
blanchet@36402
   653
val new_labels_of = maps new_labels_of_step
blanchet@36402
   654
blanchet@36402
   655
val join_proofs =
blanchet@36402
   656
  let
blanchet@36402
   657
    fun aux _ [] = NONE
blanchet@36402
   658
      | aux proof_tail (proofs as (proof1 :: _)) =
blanchet@36402
   659
        if exists null proofs then
blanchet@36402
   660
          NONE
blanchet@36402
   661
        else if forall (curry (op =) (hd proof1) o hd) (tl proofs) then
blanchet@36402
   662
          aux (hd proof1 :: proof_tail) (map tl proofs)
blanchet@36402
   663
        else case hd proof1 of
blanchet@36402
   664
          Have ([], l, t, by) =>
blanchet@36402
   665
          if forall (fn Have ([], l', t', _) :: _ => (l, t) = (l', t')
blanchet@36402
   666
                      | _ => false) (tl proofs) andalso
blanchet@36402
   667
             not (exists (member (op =) (maps new_labels_of proofs))
blanchet@36402
   668
                         (using_of proof_tail)) then
blanchet@36402
   669
            SOME (l, t, map rev proofs, proof_tail)
blanchet@36402
   670
          else
blanchet@36402
   671
            NONE
blanchet@36402
   672
        | _ => NONE
blanchet@36402
   673
  in aux [] o map rev end
blanchet@36402
   674
blanchet@36402
   675
fun case_split_qualifiers proofs =
blanchet@36402
   676
  case length proofs of
blanchet@36402
   677
    0 => []
blanchet@36402
   678
  | 1 => [Then]
blanchet@36402
   679
  | _ => [Ultimately]
blanchet@36402
   680
blanchet@36491
   681
fun redirect_proof thy conjecture_shape hyp_ts concl_t proof =
wenzelm@33310
   682
  let
blanchet@36402
   683
    val concl_ls = map (pair raw_prefix) (List.last conjecture_shape)
blanchet@36551
   684
    fun find_hyp num = nth hyp_ts (index_in_shape num conjecture_shape)
blanchet@36402
   685
    fun first_pass ([], contra) = ([], contra)
blanchet@36491
   686
      | first_pass ((step as Fix _) :: proof, contra) =
blanchet@36491
   687
        first_pass (proof, contra) |>> cons step
blanchet@36491
   688
      | first_pass ((step as Let _) :: proof, contra) =
blanchet@36491
   689
        first_pass (proof, contra) |>> cons step
blanchet@36551
   690
      | first_pass ((step as Assume (l as (_, num), t)) :: proof, contra) =
blanchet@36402
   691
        if member (op =) concl_ls l then
blanchet@36491
   692
          first_pass (proof, contra ||> cons step)
blanchet@36402
   693
        else
blanchet@36551
   694
          first_pass (proof, contra) |>> cons (Assume (l, find_hyp num))
blanchet@36491
   695
      | first_pass ((step as Have (qs, l, t, Facts (ls, ss))) :: proof,
blanchet@36491
   696
                    contra) =
blanchet@36402
   697
        if exists (member (op =) (fst contra)) ls then
blanchet@36491
   698
          first_pass (proof, contra |>> cons l ||> cons step)
blanchet@36402
   699
        else
blanchet@36491
   700
          first_pass (proof, contra) |>> cons step
blanchet@36402
   701
      | first_pass _ = raise Fail "malformed proof"
blanchet@36402
   702
    val (proof_top, (contra_ls, contra_proof)) =
blanchet@36402
   703
      first_pass (proof, (concl_ls, []))
blanchet@36402
   704
    val backpatch_label = the_default ([], []) oo AList.lookup (op =) o fst
blanchet@36402
   705
    fun backpatch_labels patches ls =
blanchet@36402
   706
      fold merge_fact_sets (map (backpatch_label patches) ls) ([], [])
blanchet@36402
   707
    fun second_pass end_qs ([], assums, patches) =
blanchet@36402
   708
        ([Have (end_qs, no_label,
blanchet@36402
   709
                if length assums < length concl_ls then
blanchet@36491
   710
                  clause_for_literals thy (map (negate_term thy o fst) assums)
blanchet@36402
   711
                else
blanchet@36402
   712
                  concl_t,
blanchet@36402
   713
                Facts (backpatch_labels patches (map snd assums)))], patches)
blanchet@36402
   714
      | second_pass end_qs (Assume (l, t) :: proof, assums, patches) =
blanchet@36402
   715
        second_pass end_qs (proof, (t, l) :: assums, patches)
blanchet@36402
   716
      | second_pass end_qs (Have (qs, l, t, Facts (ls, ss)) :: proof, assums,
blanchet@36402
   717
                            patches) =
blanchet@36402
   718
        if member (op =) (snd (snd patches)) l andalso
blanchet@36402
   719
           not (AList.defined (op =) (fst patches) l) then
blanchet@36402
   720
          second_pass end_qs (proof, assums, patches ||> apsnd (append ls))
blanchet@36402
   721
        else
blanchet@36402
   722
          (case List.partition (member (op =) contra_ls) ls of
blanchet@36402
   723
             ([contra_l], co_ls) =>
blanchet@36402
   724
             if no_show qs then
blanchet@36402
   725
               second_pass end_qs
blanchet@36402
   726
                           (proof, assums,
blanchet@36402
   727
                            patches |>> cons (contra_l, (l :: co_ls, ss)))
blanchet@36402
   728
               |>> cons (if member (op =) (fst (snd patches)) l then
blanchet@36491
   729
                           Assume (l, negate_term thy t)
blanchet@36402
   730
                         else
blanchet@36491
   731
                           Have (qs, l, negate_term thy t,
blanchet@36402
   732
                                 Facts (backpatch_label patches l)))
blanchet@36402
   733
             else
blanchet@36402
   734
               second_pass end_qs (proof, assums,
blanchet@36402
   735
                                   patches |>> cons (contra_l, (co_ls, ss)))
blanchet@36402
   736
           | (contra_ls as _ :: _, co_ls) =>
blanchet@36402
   737
             let
blanchet@36402
   738
               val proofs =
blanchet@36402
   739
                 map_filter
blanchet@36402
   740
                     (fn l =>
blanchet@36402
   741
                         if member (op =) concl_ls l then
blanchet@36402
   742
                           NONE
blanchet@36402
   743
                         else
blanchet@36402
   744
                           let
blanchet@36402
   745
                             val drop_ls = filter (curry (op <>) l) contra_ls
blanchet@36402
   746
                           in
blanchet@36402
   747
                             second_pass []
blanchet@36402
   748
                                 (proof, assums,
blanchet@36402
   749
                                  patches ||> apfst (insert (op =) l)
blanchet@36402
   750
                                          ||> apsnd (union (op =) drop_ls))
blanchet@36402
   751
                             |> fst |> SOME
blanchet@36402
   752
                           end) contra_ls
blanchet@36402
   753
               val facts = (co_ls, [])
blanchet@36402
   754
             in
blanchet@36402
   755
               (case join_proofs proofs of
blanchet@36402
   756
                  SOME (l, t, proofs, proof_tail) =>
blanchet@36402
   757
                  Have (case_split_qualifiers proofs @
blanchet@36402
   758
                        (if null proof_tail then end_qs else []), l, t,
blanchet@36402
   759
                        CaseSplit (proofs, facts)) :: proof_tail
blanchet@36402
   760
                | NONE =>
blanchet@36402
   761
                  [Have (case_split_qualifiers proofs @ end_qs, no_label,
blanchet@36402
   762
                         concl_t, CaseSplit (proofs, facts))],
blanchet@36402
   763
                patches)
blanchet@36402
   764
             end
blanchet@36402
   765
           | _ => raise Fail "malformed proof")
blanchet@36402
   766
       | second_pass _ _ = raise Fail "malformed proof"
blanchet@36486
   767
    val proof_bottom =
blanchet@36486
   768
      second_pass [Show] (contra_proof, [], ([], ([], []))) |> fst
blanchet@36402
   769
  in proof_top @ proof_bottom end
blanchet@36402
   770
blanchet@36402
   771
val kill_duplicate_assumptions_in_proof =
blanchet@36402
   772
  let
blanchet@36402
   773
    fun relabel_facts subst =
blanchet@36402
   774
      apfst (map (fn l => AList.lookup (op =) subst l |> the_default l))
blanchet@36491
   775
    fun do_step (step as Assume (l, t)) (proof, subst, assums) =
blanchet@36402
   776
        (case AList.lookup (op aconv) assums t of
blanchet@36402
   777
           SOME l' => (proof, (l', l) :: subst, assums)
blanchet@36491
   778
         | NONE => (step :: proof, subst, (t, l) :: assums))
blanchet@36402
   779
      | do_step (Have (qs, l, t, by)) (proof, subst, assums) =
blanchet@36402
   780
        (Have (qs, l, t,
blanchet@36402
   781
               case by of
blanchet@36402
   782
                 Facts facts => Facts (relabel_facts subst facts)
blanchet@36402
   783
               | CaseSplit (proofs, facts) =>
blanchet@36402
   784
                 CaseSplit (map do_proof proofs, relabel_facts subst facts)) ::
blanchet@36402
   785
         proof, subst, assums)
blanchet@36491
   786
      | do_step step (proof, subst, assums) = (step :: proof, subst, assums)
blanchet@36402
   787
    and do_proof proof = fold do_step proof ([], [], []) |> #1 |> rev
blanchet@36402
   788
  in do_proof end
blanchet@36402
   789
blanchet@36402
   790
val then_chain_proof =
blanchet@36402
   791
  let
blanchet@36402
   792
    fun aux _ [] = []
blanchet@36491
   793
      | aux _ ((step as Assume (l, _)) :: proof) = step :: aux l proof
blanchet@36402
   794
      | aux l' (Have (qs, l, t, by) :: proof) =
blanchet@36402
   795
        (case by of
blanchet@36402
   796
           Facts (ls, ss) =>
blanchet@36402
   797
           Have (if member (op =) ls l' then
blanchet@36402
   798
                   (Then :: qs, l, t,
blanchet@36402
   799
                    Facts (filter_out (curry (op =) l') ls, ss))
blanchet@36402
   800
                 else
blanchet@36402
   801
                   (qs, l, t, Facts (ls, ss)))
blanchet@36402
   802
         | CaseSplit (proofs, facts) =>
blanchet@36402
   803
           Have (qs, l, t, CaseSplit (map (aux no_label) proofs, facts))) ::
blanchet@36402
   804
        aux l proof
blanchet@36491
   805
      | aux _ (step :: proof) = step :: aux no_label proof
blanchet@36402
   806
  in aux no_label end
blanchet@36402
   807
blanchet@36402
   808
fun kill_useless_labels_in_proof proof =
blanchet@36402
   809
  let
blanchet@36402
   810
    val used_ls = using_of proof
blanchet@36402
   811
    fun do_label l = if member (op =) used_ls l then l else no_label
blanchet@36486
   812
    fun kill (Assume (l, t)) = Assume (do_label l, t)
blanchet@36402
   813
      | kill (Have (qs, l, t, by)) =
blanchet@36402
   814
        Have (qs, do_label l, t,
blanchet@36402
   815
              case by of
blanchet@36402
   816
                CaseSplit (proofs, facts) =>
blanchet@36402
   817
                CaseSplit (map (map kill) proofs, facts)
blanchet@36402
   818
              | _ => by)
blanchet@36491
   819
      | kill step = step
blanchet@36402
   820
  in map kill proof end
blanchet@36402
   821
blanchet@36402
   822
fun prefix_for_depth n = replicate_string (n + 1)
blanchet@36402
   823
blanchet@36402
   824
val relabel_proof =
blanchet@36402
   825
  let
blanchet@36402
   826
    fun aux _ _ _ [] = []
blanchet@36402
   827
      | aux subst depth (next_assum, next_fact) (Assume (l, t) :: proof) =
blanchet@36402
   828
        if l = no_label then
blanchet@36402
   829
          Assume (l, t) :: aux subst depth (next_assum, next_fact) proof
blanchet@36402
   830
        else
blanchet@36402
   831
          let val l' = (prefix_for_depth depth assum_prefix, next_assum) in
blanchet@36402
   832
            Assume (l', t) ::
blanchet@36402
   833
            aux ((l, l') :: subst) depth (next_assum + 1, next_fact) proof
blanchet@36402
   834
          end
blanchet@36402
   835
      | aux subst depth (next_assum, next_fact) (Have (qs, l, t, by) :: proof) =
blanchet@36402
   836
        let
blanchet@36402
   837
          val (l', subst, next_fact) =
blanchet@36402
   838
            if l = no_label then
blanchet@36402
   839
              (l, subst, next_fact)
blanchet@36402
   840
            else
blanchet@36402
   841
              let
blanchet@36402
   842
                val l' = (prefix_for_depth depth fact_prefix, next_fact)
blanchet@36402
   843
              in (l', (l, l') :: subst, next_fact + 1) end
blanchet@36486
   844
          val relabel_facts = apfst (map_filter (AList.lookup (op =) subst))
blanchet@36402
   845
          val by =
blanchet@36402
   846
            case by of
blanchet@36402
   847
              Facts facts => Facts (relabel_facts facts)
blanchet@36402
   848
            | CaseSplit (proofs, facts) =>
blanchet@36402
   849
              CaseSplit (map (aux subst (depth + 1) (1, 1)) proofs,
blanchet@36402
   850
                         relabel_facts facts)
blanchet@36402
   851
        in
blanchet@36402
   852
          Have (qs, l', t, by) ::
blanchet@36402
   853
          aux subst depth (next_assum, next_fact) proof
blanchet@36402
   854
        end
blanchet@36491
   855
      | aux subst depth nextp (step :: proof) =
blanchet@36491
   856
        step :: aux subst depth nextp proof
blanchet@36402
   857
  in aux [] 0 (1, 1) end
blanchet@36402
   858
blanchet@36488
   859
fun string_for_proof ctxt i n =
blanchet@36402
   860
  let
blanchet@36478
   861
    fun fix_print_mode f =
blanchet@36478
   862
      PrintMode.setmp (filter (curry (op =) Symbol.xsymbolsN)
blanchet@36478
   863
                      (print_mode_value ())) f
blanchet@36402
   864
    fun do_indent ind = replicate_string (ind * indent_size) " "
blanchet@36478
   865
    fun do_free (s, T) =
blanchet@36478
   866
      maybe_quote s ^ " :: " ^
blanchet@36478
   867
      maybe_quote (fix_print_mode (Syntax.string_of_typ ctxt) T)
blanchet@36551
   868
    fun do_raw_label (s, num) = s ^ string_of_int num
blanchet@36402
   869
    fun do_label l = if l = no_label then "" else do_raw_label l ^ ": "
blanchet@36402
   870
    fun do_have qs =
blanchet@36402
   871
      (if member (op =) qs Moreover then "moreover " else "") ^
blanchet@36402
   872
      (if member (op =) qs Ultimately then "ultimately " else "") ^
blanchet@36402
   873
      (if member (op =) qs Then then
blanchet@36402
   874
         if member (op =) qs Show then "thus" else "hence"
blanchet@36402
   875
       else
blanchet@36402
   876
         if member (op =) qs Show then "show" else "have")
blanchet@36478
   877
    val do_term = maybe_quote o fix_print_mode (Syntax.string_of_term ctxt)
blanchet@36402
   878
    fun do_using [] = ""
blanchet@36402
   879
      | do_using ls = "using " ^ (space_implode " " (map do_raw_label ls)) ^ " "
blanchet@36486
   880
    fun do_by_facts [] = "by metis"
blanchet@36486
   881
      | do_by_facts ss = "by (metis " ^ space_implode " " ss ^ ")"
blanchet@36486
   882
    fun do_facts (ls, ss) = do_using ls ^ do_by_facts ss
blanchet@36478
   883
    and do_step ind (Fix xs) =
blanchet@36478
   884
        do_indent ind ^ "fix " ^ space_implode " and " (map do_free xs) ^ "\n"
blanchet@36486
   885
      | do_step ind (Let (t1, t2)) =
blanchet@36486
   886
        do_indent ind ^ "let " ^ do_term t1 ^ " = " ^ do_term t2 ^ "\n"
blanchet@36402
   887
      | do_step ind (Assume (l, t)) =
blanchet@36402
   888
        do_indent ind ^ "assume " ^ do_label l ^ do_term t ^ "\n"
blanchet@36402
   889
      | do_step ind (Have (qs, l, t, Facts facts)) =
blanchet@36402
   890
        do_indent ind ^ do_have qs ^ " " ^
blanchet@36479
   891
        do_label l ^ do_term t ^ " " ^ do_facts facts ^ "\n"
blanchet@36402
   892
      | do_step ind (Have (qs, l, t, CaseSplit (proofs, facts))) =
blanchet@36402
   893
        space_implode (do_indent ind ^ "moreover\n")
blanchet@36402
   894
                      (map (do_block ind) proofs) ^
blanchet@36479
   895
        do_indent ind ^ do_have qs ^ " " ^ do_label l ^ do_term t ^ " " ^
blanchet@36478
   896
        do_facts facts ^ "\n"
blanchet@36402
   897
    and do_steps prefix suffix ind steps =
blanchet@36402
   898
      let val s = implode (map (do_step ind) steps) in
blanchet@36402
   899
        replicate_string (ind * indent_size - size prefix) " " ^ prefix ^
blanchet@36402
   900
        String.extract (s, ind * indent_size,
blanchet@36402
   901
                        SOME (size s - ind * indent_size - 1)) ^
blanchet@36402
   902
        suffix ^ "\n"
blanchet@36402
   903
      end
blanchet@36402
   904
    and do_block ind proof = do_steps "{ " " }" (ind + 1) proof
blanchet@36480
   905
    (* One-step proofs are pointless; better use the Metis one-liner. *)
blanchet@36480
   906
    and do_proof [_] = ""
blanchet@36480
   907
      | do_proof proof =
blanchet@36480
   908
        (if i <> 1 then "prefer " ^ string_of_int i ^ "\n" else "") ^
blanchet@36480
   909
        do_indent 0 ^ "proof -\n" ^
blanchet@36480
   910
        do_steps "" "" 1 proof ^
blanchet@36480
   911
        do_indent 0 ^ (if n <> 1 then "next" else "qed") ^ "\n"
blanchet@36488
   912
  in do_proof end
blanchet@36402
   913
blanchet@36488
   914
fun isar_proof_text (pool, debug, shrink_factor, ctxt, conjecture_shape)
blanchet@36402
   915
                    (minimize_command, atp_proof, thm_names, goal, i) =
blanchet@36402
   916
  let
blanchet@36402
   917
    val thy = ProofContext.theory_of ctxt
blanchet@36402
   918
    val (frees, hyp_ts, concl_t) = strip_subgoal goal i
blanchet@36402
   919
    val n = Logic.count_prems (prop_of goal)
blanchet@36223
   920
    val (one_line_proof, lemma_names) =
blanchet@36402
   921
      metis_proof_text (minimize_command, atp_proof, thm_names, goal, i)
blanchet@36283
   922
    fun isar_proof_for () =
blanchet@36551
   923
      case proof_from_atp_proof pool ctxt shrink_factor atp_proof
blanchet@36551
   924
                                conjecture_shape thm_names frees
blanchet@36491
   925
           |> redirect_proof thy conjecture_shape hyp_ts concl_t
blanchet@36402
   926
           |> kill_duplicate_assumptions_in_proof
blanchet@36402
   927
           |> then_chain_proof
blanchet@36402
   928
           |> kill_useless_labels_in_proof
blanchet@36402
   929
           |> relabel_proof
blanchet@36488
   930
           |> string_for_proof ctxt i n of
blanchet@36283
   931
        "" => ""
blanchet@36402
   932
      | proof => "\nStructured proof:\n" ^ Markup.markup Markup.sendback proof
blanchet@35868
   933
    val isar_proof =
blanchet@36402
   934
      if debug then
blanchet@36283
   935
        isar_proof_for ()
blanchet@36283
   936
      else
blanchet@36283
   937
        try isar_proof_for ()
blanchet@36287
   938
        |> the_default "Warning: The Isar proof construction failed.\n"
blanchet@36283
   939
  in (one_line_proof ^ isar_proof, lemma_names) end
paulson@21978
   940
blanchet@36422
   941
fun proof_text isar_proof isar_params =
blanchet@36422
   942
  if isar_proof then isar_proof_text isar_params else metis_proof_text
blanchet@36223
   943
immler@31038
   944
end;