src/HOL/Tools/Sledgehammer/sledgehammer_proof_reconstruct.ML
author wenzelm
Thu May 27 17:41:27 2010 +0200 (2010-05-27)
changeset 37145 01aa36932739
parent 36968 62e29faa3718
child 37146 f652333bbf8e
permissions -rw-r--r--
renamed structure TypeInfer to Type_Infer, keeping the old name as legacy alias for some time;
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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_type_args: theory -> string -> int
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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 * 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 * 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_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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(* 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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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*)
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fun num_type_args thy s =
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  length (Sign.const_typargs thy (s, Sign.the_const_type thy s))
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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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          let
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            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@36909
   327
                          Sign.const_instance thy (c,
blanchet@36967
   328
                                    map (type_from_node tfrees)
blanchet@36967
   329
                                        (drop num_term_args us)))
blanchet@36909
   330
          in list_comb (t, ts) end
blanchet@36909
   331
        | NONE => (* a free or schematic variable *)
blanchet@36909
   332
          let
blanchet@36909
   333
            val ts = map (aux NONE []) (us @ args)
blanchet@36909
   334
            val T = map fastype_of ts ---> HOLogic.typeT
blanchet@36909
   335
            val t =
blanchet@36909
   336
              case strip_prefix fixed_var_prefix a of
blanchet@36909
   337
                SOME b => Free (b, T)
blanchet@36909
   338
              | NONE =>
blanchet@36909
   339
                case strip_prefix schematic_var_prefix a of
blanchet@36967
   340
                  SOME b => Var ((b, 0), T)
blanchet@36909
   341
                | NONE =>
blanchet@36909
   342
                  (* Variable from the ATP, say "X1" *)
blanchet@36967
   343
                  Var ((fix_atp_variable_name a, 0), T)
blanchet@36909
   344
          in list_comb (t, ts) end
blanchet@36909
   345
  in aux end
paulson@21978
   346
blanchet@36392
   347
(* Type class literal applied to a type. Returns triple of polarity, class,
blanchet@36392
   348
   type. *)
blanchet@36967
   349
fun type_constraint_from_node pos tfrees (StrNode ("c_Not", [u])) =
blanchet@36967
   350
    type_constraint_from_node (not pos) tfrees u
blanchet@36967
   351
  | type_constraint_from_node pos tfrees u = case u of
blanchet@36909
   352
        IntLeaf _ => raise NODE [u]
blanchet@36486
   353
      | StrNode (a, us) =>
blanchet@36967
   354
            (case (strip_prefix class_prefix a,
blanchet@36967
   355
                   map (type_from_node tfrees) us) of
blanchet@36486
   356
                 (SOME b, [T]) => (pos, b, T)
blanchet@36909
   357
               | _ => raise NODE [u])
paulson@21978
   358
paulson@21978
   359
(** Accumulate type constraints in a clause: negative type literals **)
paulson@21978
   360
blanchet@36485
   361
fun add_var (key, z)  = Vartab.map_default (key, []) (cons z)
paulson@21978
   362
blanchet@36909
   363
fun add_type_constraint (false, cl, TFree (a ,_)) = add_var ((a, ~1), cl)
blanchet@36909
   364
  | add_type_constraint (false, cl, TVar (ix, _)) = add_var (ix, cl)
blanchet@36909
   365
  | add_type_constraint _ = I
paulson@21978
   366
blanchet@36491
   367
fun is_positive_literal (@{const Not} $ _) = false
blanchet@36402
   368
  | is_positive_literal t = true
blanchet@36402
   369
blanchet@36485
   370
fun negate_term thy (Const (@{const_name All}, T) $ Abs (s, T', t')) =
blanchet@36402
   371
    Const (@{const_name Ex}, T) $ Abs (s, T', negate_term thy t')
blanchet@36402
   372
  | negate_term thy (Const (@{const_name Ex}, T) $ Abs (s, T', t')) =
blanchet@36402
   373
    Const (@{const_name All}, T) $ Abs (s, T', negate_term thy t')
blanchet@36402
   374
  | negate_term thy (@{const "op -->"} $ t1 $ t2) =
blanchet@36402
   375
    @{const "op &"} $ t1 $ negate_term thy t2
blanchet@36402
   376
  | negate_term thy (@{const "op &"} $ t1 $ t2) =
blanchet@36402
   377
    @{const "op |"} $ negate_term thy t1 $ negate_term thy t2
blanchet@36402
   378
  | negate_term thy (@{const "op |"} $ t1 $ t2) =
blanchet@36402
   379
    @{const "op &"} $ negate_term thy t1 $ negate_term thy t2
blanchet@36486
   380
  | negate_term _ (@{const Not} $ t) = t
blanchet@36486
   381
  | negate_term _ t = @{const Not} $ t
blanchet@36402
   382
blanchet@36402
   383
fun clause_for_literals _ [] = HOLogic.false_const
blanchet@36402
   384
  | clause_for_literals _ [lit] = lit
blanchet@36402
   385
  | clause_for_literals thy lits =
blanchet@36402
   386
    case List.partition is_positive_literal lits of
blanchet@36402
   387
      (pos_lits as _ :: _, neg_lits as _ :: _) =>
blanchet@36402
   388
      @{const "op -->"}
blanchet@36402
   389
          $ foldr1 HOLogic.mk_conj (map (negate_term thy) neg_lits)
blanchet@36402
   390
          $ foldr1 HOLogic.mk_disj pos_lits
blanchet@36402
   391
    | _ => foldr1 HOLogic.mk_disj lits
blanchet@36402
   392
blanchet@36402
   393
(* Final treatment of the list of "real" literals from a clause.
blanchet@36402
   394
   No "real" literals means only type information. *)
blanchet@36402
   395
fun finish_clause _ [] = HOLogic.true_const
blanchet@36402
   396
  | finish_clause thy lits =
blanchet@36402
   397
    lits |> filter_out (curry (op =) HOLogic.false_const) |> rev
blanchet@36402
   398
         |> clause_for_literals thy
paulson@22491
   399
paulson@21978
   400
(*Accumulate sort constraints in vt, with "real" literals in lits.*)
blanchet@36967
   401
fun lits_of_nodes thy full_types tfrees =
blanchet@36967
   402
  let
blanchet@36967
   403
    fun aux (vt, lits) [] = (vt, finish_clause thy lits)
blanchet@36967
   404
      | aux (vt, lits) (u :: us) =
blanchet@36967
   405
        aux (add_type_constraint
blanchet@36967
   406
                 (type_constraint_from_node true tfrees u) vt, lits) us
blanchet@36967
   407
        handle NODE _ =>
blanchet@36967
   408
               aux (vt, term_from_node thy full_types tfrees (SOME @{typ bool})
blanchet@36967
   409
                                       [] u :: lits) us
blanchet@36967
   410
  in aux end
paulson@21978
   411
blanchet@36967
   412
(* Update TVars with detected sort constraints. It's not totally clear when
blanchet@36967
   413
   this code is necessary. *)
blanchet@36967
   414
fun repair_tvar_sorts vt =
blanchet@36556
   415
  let
blanchet@36556
   416
    fun do_type (Type (a, Ts)) = Type (a, map do_type Ts)
blanchet@36556
   417
      | do_type (TVar (xi, s)) = TVar (xi, the_default s (Vartab.lookup vt xi))
blanchet@36967
   418
      | do_type (TFree z) = TFree z
blanchet@36556
   419
    fun do_term (Const (a, T)) = Const (a, do_type T)
blanchet@36556
   420
      | do_term (Free (a, T)) = Free (a, do_type T)
blanchet@36556
   421
      | do_term (Var (xi, T)) = Var (xi, do_type T)
blanchet@36556
   422
      | do_term (t as Bound _) = t
blanchet@36556
   423
      | do_term (Abs (a, T, t)) = Abs (a, do_type T, do_term t)
blanchet@36556
   424
      | do_term (t1 $ t2) = do_term t1 $ do_term t2
blanchet@36556
   425
  in not (Vartab.is_empty vt) ? do_term end
blanchet@36551
   426
blanchet@36551
   427
fun unskolemize_term t =
blanchet@36909
   428
  Term.add_consts t []
blanchet@36909
   429
  |> filter (is_skolem_const_name o fst) |> map Const
blanchet@36909
   430
  |> rpair t |-> fold forall_of
paulson@21978
   431
blanchet@36555
   432
val combinator_table =
blanchet@36555
   433
  [(@{const_name COMBI}, @{thm COMBI_def_raw}),
blanchet@36555
   434
   (@{const_name COMBK}, @{thm COMBK_def_raw}),
blanchet@36555
   435
   (@{const_name COMBB}, @{thm COMBB_def_raw}),
blanchet@36555
   436
   (@{const_name COMBC}, @{thm COMBC_def_raw}),
blanchet@36555
   437
   (@{const_name COMBS}, @{thm COMBS_def_raw})]
blanchet@36555
   438
blanchet@36555
   439
fun uncombine_term (t1 $ t2) = betapply (pairself uncombine_term (t1, t2))
blanchet@36555
   440
  | uncombine_term (Abs (s, T, t')) = Abs (s, T, uncombine_term t')
blanchet@36555
   441
  | uncombine_term (t as Const (x as (s, _))) =
blanchet@36555
   442
    (case AList.lookup (op =) combinator_table s of
blanchet@36555
   443
       SOME thm => thm |> prop_of |> specialize_type @{theory} x |> Logic.dest_equals |> snd
blanchet@36555
   444
     | NONE => t)
blanchet@36555
   445
  | uncombine_term t = t
blanchet@36555
   446
blanchet@36486
   447
(* Interpret a list of syntax trees as a clause, given by "real" literals and
blanchet@36486
   448
   sort constraints. "vt" holds the initial sort constraints, from the
blanchet@36486
   449
   conjecture clauses. *)
blanchet@36967
   450
fun clause_of_nodes ctxt full_types tfrees us =
blanchet@36909
   451
  let
blanchet@36909
   452
    val thy = ProofContext.theory_of ctxt
blanchet@36967
   453
    val (vt, t) = lits_of_nodes thy full_types tfrees (Vartab.empty, []) us
blanchet@36967
   454
  in repair_tvar_sorts vt t end
blanchet@36556
   455
fun check_formula ctxt =
wenzelm@37145
   456
  Type_Infer.constrain @{typ bool}
blanchet@36486
   457
  #> Syntax.check_term (ProofContext.set_mode ProofContext.mode_schematic ctxt)
paulson@21978
   458
paulson@21978
   459
paulson@21978
   460
(**** Translation of TSTP files to Isar Proofs ****)
paulson@21978
   461
blanchet@36486
   462
fun unvarify_term (Var ((s, 0), T)) = Free (s, T)
blanchet@36486
   463
  | unvarify_term t = raise TERM ("unvarify_term: non-Var", [t])
paulson@21978
   464
blanchet@36967
   465
fun decode_line full_types tfrees (Definition (num, u, us)) ctxt =
blanchet@36486
   466
    let
blanchet@36967
   467
      val t1 = clause_of_nodes ctxt full_types tfrees [u]
blanchet@36551
   468
      val vars = snd (strip_comb t1)
blanchet@36486
   469
      val frees = map unvarify_term vars
blanchet@36486
   470
      val unvarify_args = subst_atomic (vars ~~ frees)
blanchet@36967
   471
      val t2 = clause_of_nodes ctxt full_types tfrees us
blanchet@36551
   472
      val (t1, t2) =
blanchet@36551
   473
        HOLogic.eq_const HOLogic.typeT $ t1 $ t2
blanchet@36556
   474
        |> unvarify_args |> uncombine_term |> check_formula ctxt
blanchet@36555
   475
        |> HOLogic.dest_eq
blanchet@36486
   476
    in
blanchet@36551
   477
      (Definition (num, t1, t2),
blanchet@36551
   478
       fold Variable.declare_term (maps OldTerm.term_frees [t1, t2]) ctxt)
blanchet@36486
   479
    end
blanchet@36967
   480
  | decode_line full_types tfrees (Inference (num, us, deps)) ctxt =
blanchet@36551
   481
    let
blanchet@36967
   482
      val t = us |> clause_of_nodes ctxt full_types tfrees
blanchet@36556
   483
                 |> unskolemize_term |> uncombine_term |> check_formula ctxt
blanchet@36551
   484
    in
blanchet@36551
   485
      (Inference (num, t, deps),
blanchet@36551
   486
       fold Variable.declare_term (OldTerm.term_frees t) ctxt)
blanchet@36486
   487
    end
blanchet@36967
   488
fun decode_lines ctxt full_types tfrees lines =
blanchet@36967
   489
  fst (fold_map (decode_line full_types tfrees) lines ctxt)
paulson@21978
   490
blanchet@36486
   491
fun aint_inference _ (Definition _) = true
blanchet@36486
   492
  | aint_inference t (Inference (_, t', _)) = not (t aconv t')
blanchet@36486
   493
blanchet@36486
   494
(* No "real" literals means only type information (tfree_tcs, clsrel, or
blanchet@36486
   495
   clsarity). *)
blanchet@36486
   496
val is_only_type_information = curry (op aconv) HOLogic.true_const
blanchet@36486
   497
blanchet@36486
   498
fun replace_one_dep (old, new) dep = if dep = old then new else [dep]
blanchet@36486
   499
fun replace_deps_in_line _ (line as Definition _) = line
blanchet@36486
   500
  | replace_deps_in_line p (Inference (num, t, deps)) =
blanchet@36486
   501
    Inference (num, t, fold (union (op =) o replace_one_dep p) deps [])
paulson@21978
   502
paulson@22491
   503
(*Discard axioms; consolidate adjacent lines that prove the same clause, since they differ
paulson@22491
   504
  only in type information.*)
blanchet@36551
   505
fun add_line _ _ (line as Definition _) lines = line :: lines
blanchet@36551
   506
  | add_line conjecture_shape thm_names (Inference (num, t, [])) lines =
blanchet@36570
   507
    (* No dependencies: axiom, conjecture clause, or internal axioms or
blanchet@36570
   508
       definitions (Vampire). *)
blanchet@36486
   509
    if is_axiom_clause_number thm_names num then
blanchet@36486
   510
      (* Axioms are not proof lines. *)
blanchet@36486
   511
      if is_only_type_information t then
blanchet@36486
   512
        map (replace_deps_in_line (num, [])) lines
blanchet@36486
   513
      (* Is there a repetition? If so, replace later line by earlier one. *)
blanchet@36486
   514
      else case take_prefix (aint_inference t) lines of
blanchet@36486
   515
        (_, []) => lines (*no repetition of proof line*)
blanchet@36486
   516
      | (pre, Inference (num', _, _) :: post) =>
blanchet@36486
   517
        pre @ map (replace_deps_in_line (num', [num])) post
blanchet@36570
   518
    else if is_conjecture_clause_number conjecture_shape num then
blanchet@36486
   519
      Inference (num, t, []) :: lines
blanchet@36551
   520
    else
blanchet@36570
   521
      map (replace_deps_in_line (num, [])) lines
blanchet@36551
   522
  | add_line _ _ (Inference (num, t, deps)) lines =
blanchet@36486
   523
    (* Type information will be deleted later; skip repetition test. *)
blanchet@36486
   524
    if is_only_type_information t then
blanchet@36486
   525
      Inference (num, t, deps) :: lines
blanchet@36486
   526
    (* Is there a repetition? If so, replace later line by earlier one. *)
blanchet@36486
   527
    else case take_prefix (aint_inference t) lines of
blanchet@36486
   528
      (* FIXME: Doesn't this code risk conflating proofs involving different
blanchet@36486
   529
         types?? *)
blanchet@36486
   530
       (_, []) => Inference (num, t, deps) :: lines
blanchet@36486
   531
     | (pre, Inference (num', t', _) :: post) =>
blanchet@36486
   532
       Inference (num, t', deps) ::
blanchet@36486
   533
       pre @ map (replace_deps_in_line (num', [num])) post
paulson@22044
   534
blanchet@36486
   535
(* Recursively delete empty lines (type information) from the proof. *)
blanchet@36486
   536
fun add_nontrivial_line (Inference (num, t, [])) lines =
blanchet@36486
   537
    if is_only_type_information t then delete_dep num lines
blanchet@36486
   538
    else Inference (num, t, []) :: lines
blanchet@36486
   539
  | add_nontrivial_line line lines = line :: lines
blanchet@36395
   540
and delete_dep num lines =
blanchet@36486
   541
  fold_rev add_nontrivial_line (map (replace_deps_in_line (num, [])) lines) []
blanchet@36486
   542
blanchet@36560
   543
(* ATPs sometimes reuse free variable names in the strangest ways. Surprisingly,
blanchet@36560
   544
   removing the offending lines often does the trick. *)
blanchet@36560
   545
fun is_bad_free frees (Free x) = not (member (op =) frees x)
blanchet@36560
   546
  | is_bad_free _ _ = false
paulson@22470
   547
blanchet@36570
   548
(* Vampire is keen on producing these. *)
blanchet@36570
   549
fun is_trivial_formula (@{const Not} $ (Const (@{const_name "op ="}, _)
blanchet@36570
   550
                                        $ t1 $ t2)) = (t1 aconv t2)
blanchet@36570
   551
  | is_trivial_formula t = false
blanchet@36570
   552
blanchet@36570
   553
fun add_desired_line _ _ _ _ _ (line as Definition _) (j, lines) =
blanchet@36560
   554
    (j, line :: lines)
blanchet@36924
   555
  | add_desired_line ctxt isar_shrink_factor conjecture_shape thm_names frees
blanchet@36570
   556
                     (Inference (num, t, deps)) (j, lines) =
blanchet@36402
   557
    (j + 1,
blanchet@36570
   558
     if is_axiom_clause_number thm_names num orelse
blanchet@36570
   559
        is_conjecture_clause_number conjecture_shape num orelse
blanchet@36570
   560
        (not (is_only_type_information t) andalso
blanchet@36570
   561
         null (Term.add_tvars t []) andalso
blanchet@36570
   562
         not (exists_subterm (is_bad_free frees) t) andalso
blanchet@36570
   563
         not (is_trivial_formula t) andalso
blanchet@36570
   564
         (null lines orelse (* last line must be kept *)
blanchet@36924
   565
          (length deps >= 2 andalso j mod isar_shrink_factor = 0))) then
blanchet@36570
   566
       Inference (num, t, deps) :: lines  (* keep line *)
blanchet@36402
   567
     else
blanchet@36570
   568
       map (replace_deps_in_line (num, deps)) lines)  (* drop line *)
paulson@21978
   569
blanchet@36402
   570
(** EXTRACTING LEMMAS **)
paulson@21979
   571
blanchet@36223
   572
(* A list consisting of the first number in each line is returned.
blanchet@36395
   573
   TSTP: Interesting lines have the form "cnf(108, axiom, ...)", where the
blanchet@36223
   574
   number (108) is extracted.
blanchet@36395
   575
   SPASS: Lines have the form "108[0:Inp] ...", where the first number (108) is
blanchet@36223
   576
   extracted. *)
blanchet@36402
   577
fun extract_clause_numbers_in_atp_proof atp_proof =
blanchet@35865
   578
  let
blanchet@36395
   579
    val tokens_of = String.tokens (not o is_ident_char)
blanchet@36402
   580
    fun extract_num ("cnf" :: num :: "axiom" :: _) = Int.fromString num
blanchet@36395
   581
      | extract_num (num :: "0" :: "Inp" :: _) = Int.fromString num
blanchet@36395
   582
      | extract_num _ = NONE
blanchet@36402
   583
  in atp_proof |> split_lines |> map_filter (extract_num o tokens_of) end
wenzelm@33310
   584
  
blanchet@36968
   585
(* Used to label theorems chained into the goal. *)
blanchet@36395
   586
val chained_hint = "sledgehammer_chained"
blanchet@35865
   587
blanchet@36063
   588
fun apply_command _ 1 = "by "
blanchet@36063
   589
  | apply_command 1 _ = "apply "
blanchet@36063
   590
  | apply_command i _ = "prefer " ^ string_of_int i ^ " apply "
blanchet@36570
   591
fun metis_command i n [] = apply_command i n ^ "metis"
blanchet@36570
   592
  | metis_command i n ss =
blanchet@36570
   593
    apply_command i n ^ "(metis " ^ space_implode " " ss ^ ")"
blanchet@36063
   594
fun metis_line i n xs =
blanchet@36063
   595
  "Try this command: " ^
blanchet@36063
   596
  Markup.markup Markup.sendback (metis_command i n xs) ^ ".\n" 
blanchet@36281
   597
fun minimize_line _ [] = ""
blanchet@36281
   598
  | minimize_line minimize_command facts =
blanchet@36281
   599
    case minimize_command facts of
blanchet@36281
   600
      "" => ""
blanchet@36281
   601
    | command =>
blanchet@36065
   602
      "To minimize the number of lemmas, try this command: " ^
blanchet@36281
   603
      Markup.markup Markup.sendback command ^ ".\n"
immler@31840
   604
krauss@36606
   605
fun metis_proof_text (minimize_command, atp_proof, thm_names, goal, i) =
blanchet@36063
   606
  let
blanchet@36231
   607
    val lemmas =
blanchet@36402
   608
      atp_proof |> extract_clause_numbers_in_atp_proof
blanchet@36402
   609
                |> filter (is_axiom_clause_number thm_names)
blanchet@36402
   610
                |> map (fn i => Vector.sub (thm_names, i - 1))
blanchet@36402
   611
                |> filter_out (fn s => s = "??.unknown" orelse s = chained_hint)
blanchet@36402
   612
                |> sort_distinct string_ord
blanchet@36063
   613
    val n = Logic.count_prems (prop_of goal)
blanchet@36395
   614
  in (metis_line i n lemmas ^ minimize_line minimize_command lemmas, lemmas) end
immler@31037
   615
blanchet@36486
   616
(** Isar proof construction and manipulation **)
blanchet@36486
   617
blanchet@36486
   618
fun merge_fact_sets (ls1, ss1) (ls2, ss2) =
blanchet@36486
   619
  (union (op =) ls1 ls2, union (op =) ss1 ss2)
blanchet@36402
   620
blanchet@36402
   621
type label = string * int
blanchet@36402
   622
type facts = label list * string list
blanchet@36402
   623
blanchet@36402
   624
datatype qualifier = Show | Then | Moreover | Ultimately
blanchet@36291
   625
blanchet@36402
   626
datatype step =
blanchet@36478
   627
  Fix of (string * typ) list |
blanchet@36486
   628
  Let of term * term |
blanchet@36402
   629
  Assume of label * term |
blanchet@36402
   630
  Have of qualifier list * label * term * byline
blanchet@36402
   631
and byline =
blanchet@36564
   632
  ByMetis of facts |
blanchet@36402
   633
  CaseSplit of step list list * facts
blanchet@36402
   634
blanchet@36574
   635
fun smart_case_split [] facts = ByMetis facts
blanchet@36574
   636
  | smart_case_split proofs facts = CaseSplit (proofs, facts)
blanchet@36574
   637
blanchet@36402
   638
val raw_prefix = "X"
blanchet@36402
   639
val assum_prefix = "A"
blanchet@36402
   640
val fact_prefix = "F"
blanchet@36402
   641
blanchet@36570
   642
fun string_for_label (s, num) = s ^ string_of_int num
blanchet@36570
   643
blanchet@36475
   644
fun add_fact_from_dep thm_names num =
blanchet@36475
   645
  if is_axiom_clause_number thm_names num then
blanchet@36480
   646
    apsnd (insert (op =) (Vector.sub (thm_names, num - 1)))
blanchet@36475
   647
  else
blanchet@36480
   648
    apfst (insert (op =) (raw_prefix, num))
blanchet@36402
   649
blanchet@36491
   650
fun forall_vars t = fold_rev forall_of (map Var (Term.add_vars t [])) t
blanchet@36491
   651
blanchet@36486
   652
fun step_for_line _ _ (Definition (num, t1, t2)) = Let (t1, t2)
blanchet@36486
   653
  | step_for_line _ _ (Inference (num, t, [])) = Assume ((raw_prefix, num), t)
blanchet@36486
   654
  | step_for_line thm_names j (Inference (num, t, deps)) =
blanchet@36486
   655
    Have (if j = 1 then [Show] else [], (raw_prefix, num),
blanchet@36491
   656
          forall_vars t,
blanchet@36564
   657
          ByMetis (fold (add_fact_from_dep thm_names) deps ([], [])))
blanchet@36291
   658
blanchet@36967
   659
fun proof_from_atp_proof pool ctxt full_types tfrees isar_shrink_factor
blanchet@36967
   660
                         atp_proof conjecture_shape thm_names params frees =
blanchet@36402
   661
  let
blanchet@36486
   662
    val lines =
blanchet@36574
   663
      atp_proof ^ "$" (* the $ sign acts as a sentinel *)
blanchet@36548
   664
      |> parse_proof pool
blanchet@36967
   665
      |> decode_lines ctxt full_types tfrees
blanchet@36551
   666
      |> rpair [] |-> fold_rev (add_line conjecture_shape thm_names)
blanchet@36486
   667
      |> rpair [] |-> fold_rev add_nontrivial_line
blanchet@36924
   668
      |> rpair (0, []) |-> fold_rev (add_desired_line ctxt isar_shrink_factor
blanchet@36570
   669
                                               conjecture_shape thm_names frees)
blanchet@36486
   670
      |> snd
blanchet@36402
   671
  in
blanchet@36909
   672
    (if null params then [] else [Fix params]) @
blanchet@36486
   673
    map2 (step_for_line thm_names) (length lines downto 1) lines
blanchet@36402
   674
  end
blanchet@36402
   675
blanchet@36402
   676
val indent_size = 2
blanchet@36402
   677
val no_label = ("", ~1)
blanchet@36402
   678
blanchet@36402
   679
fun no_show qs = not (member (op =) qs Show)
blanchet@36402
   680
blanchet@36402
   681
(* When redirecting proofs, we keep information about the labels seen so far in
blanchet@36402
   682
   the "backpatches" data structure. The first component indicates which facts
blanchet@36402
   683
   should be associated with forthcoming proof steps. The second component is a
blanchet@36402
   684
   pair ("keep_ls", "drop_ls"), where "keep_ls" are the labels to keep and
blanchet@36402
   685
   "drop_ls" are those that should be dropped in a case split. *)
blanchet@36402
   686
type backpatches = (label * facts) list * (label list * label list)
blanchet@36402
   687
blanchet@36556
   688
fun used_labels_of_step (Have (_, _, _, by)) =
blanchet@36402
   689
    (case by of
blanchet@36564
   690
       ByMetis (ls, _) => ls
blanchet@36556
   691
     | CaseSplit (proofs, (ls, _)) =>
blanchet@36556
   692
       fold (union (op =) o used_labels_of) proofs ls)
blanchet@36556
   693
  | used_labels_of_step _ = []
blanchet@36556
   694
and used_labels_of proof = fold (union (op =) o used_labels_of_step) proof []
blanchet@36402
   695
blanchet@36402
   696
fun new_labels_of_step (Fix _) = []
blanchet@36486
   697
  | new_labels_of_step (Let _) = []
blanchet@36402
   698
  | new_labels_of_step (Assume (l, _)) = [l]
blanchet@36402
   699
  | new_labels_of_step (Have (_, l, _, _)) = [l]
blanchet@36402
   700
val new_labels_of = maps new_labels_of_step
blanchet@36402
   701
blanchet@36402
   702
val join_proofs =
blanchet@36402
   703
  let
blanchet@36402
   704
    fun aux _ [] = NONE
blanchet@36402
   705
      | aux proof_tail (proofs as (proof1 :: _)) =
blanchet@36402
   706
        if exists null proofs then
blanchet@36402
   707
          NONE
blanchet@36402
   708
        else if forall (curry (op =) (hd proof1) o hd) (tl proofs) then
blanchet@36402
   709
          aux (hd proof1 :: proof_tail) (map tl proofs)
blanchet@36402
   710
        else case hd proof1 of
blanchet@36402
   711
          Have ([], l, t, by) =>
blanchet@36402
   712
          if forall (fn Have ([], l', t', _) :: _ => (l, t) = (l', t')
blanchet@36402
   713
                      | _ => false) (tl proofs) andalso
blanchet@36402
   714
             not (exists (member (op =) (maps new_labels_of proofs))
blanchet@36556
   715
                         (used_labels_of proof_tail)) then
blanchet@36402
   716
            SOME (l, t, map rev proofs, proof_tail)
blanchet@36402
   717
          else
blanchet@36402
   718
            NONE
blanchet@36402
   719
        | _ => NONE
blanchet@36402
   720
  in aux [] o map rev end
blanchet@36402
   721
blanchet@36402
   722
fun case_split_qualifiers proofs =
blanchet@36402
   723
  case length proofs of
blanchet@36402
   724
    0 => []
blanchet@36402
   725
  | 1 => [Then]
blanchet@36402
   726
  | _ => [Ultimately]
blanchet@36402
   727
blanchet@36491
   728
fun redirect_proof thy conjecture_shape hyp_ts concl_t proof =
wenzelm@33310
   729
  let
blanchet@36402
   730
    val concl_ls = map (pair raw_prefix) (List.last conjecture_shape)
blanchet@36551
   731
    fun find_hyp num = nth hyp_ts (index_in_shape num conjecture_shape)
blanchet@36402
   732
    fun first_pass ([], contra) = ([], contra)
blanchet@36491
   733
      | first_pass ((step as Fix _) :: proof, contra) =
blanchet@36491
   734
        first_pass (proof, contra) |>> cons step
blanchet@36491
   735
      | first_pass ((step as Let _) :: proof, contra) =
blanchet@36491
   736
        first_pass (proof, contra) |>> cons step
blanchet@36551
   737
      | first_pass ((step as Assume (l as (_, num), t)) :: proof, contra) =
blanchet@36402
   738
        if member (op =) concl_ls l then
blanchet@36491
   739
          first_pass (proof, contra ||> cons step)
blanchet@36402
   740
        else
blanchet@36551
   741
          first_pass (proof, contra) |>> cons (Assume (l, find_hyp num))
blanchet@36564
   742
      | first_pass ((step as Have (qs, l, t, ByMetis (ls, ss))) :: proof,
blanchet@36491
   743
                    contra) =
blanchet@36402
   744
        if exists (member (op =) (fst contra)) ls then
blanchet@36491
   745
          first_pass (proof, contra |>> cons l ||> cons step)
blanchet@36402
   746
        else
blanchet@36491
   747
          first_pass (proof, contra) |>> cons step
blanchet@36402
   748
      | first_pass _ = raise Fail "malformed proof"
blanchet@36402
   749
    val (proof_top, (contra_ls, contra_proof)) =
blanchet@36402
   750
      first_pass (proof, (concl_ls, []))
blanchet@36402
   751
    val backpatch_label = the_default ([], []) oo AList.lookup (op =) o fst
blanchet@36402
   752
    fun backpatch_labels patches ls =
blanchet@36402
   753
      fold merge_fact_sets (map (backpatch_label patches) ls) ([], [])
blanchet@36402
   754
    fun second_pass end_qs ([], assums, patches) =
blanchet@36402
   755
        ([Have (end_qs, no_label,
blanchet@36402
   756
                if length assums < length concl_ls then
blanchet@36491
   757
                  clause_for_literals thy (map (negate_term thy o fst) assums)
blanchet@36402
   758
                else
blanchet@36402
   759
                  concl_t,
blanchet@36564
   760
                ByMetis (backpatch_labels patches (map snd assums)))], patches)
blanchet@36402
   761
      | second_pass end_qs (Assume (l, t) :: proof, assums, patches) =
blanchet@36402
   762
        second_pass end_qs (proof, (t, l) :: assums, patches)
blanchet@36564
   763
      | second_pass end_qs (Have (qs, l, t, ByMetis (ls, ss)) :: proof, assums,
blanchet@36402
   764
                            patches) =
blanchet@36402
   765
        if member (op =) (snd (snd patches)) l andalso
blanchet@36402
   766
           not (AList.defined (op =) (fst patches) l) then
blanchet@36402
   767
          second_pass end_qs (proof, assums, patches ||> apsnd (append ls))
blanchet@36402
   768
        else
blanchet@36402
   769
          (case List.partition (member (op =) contra_ls) ls of
blanchet@36402
   770
             ([contra_l], co_ls) =>
blanchet@36402
   771
             if no_show qs then
blanchet@36402
   772
               second_pass end_qs
blanchet@36402
   773
                           (proof, assums,
blanchet@36402
   774
                            patches |>> cons (contra_l, (l :: co_ls, ss)))
blanchet@36402
   775
               |>> cons (if member (op =) (fst (snd patches)) l then
blanchet@36491
   776
                           Assume (l, negate_term thy t)
blanchet@36402
   777
                         else
blanchet@36491
   778
                           Have (qs, l, negate_term thy t,
blanchet@36564
   779
                                 ByMetis (backpatch_label patches l)))
blanchet@36402
   780
             else
blanchet@36402
   781
               second_pass end_qs (proof, assums,
blanchet@36402
   782
                                   patches |>> cons (contra_l, (co_ls, ss)))
blanchet@36402
   783
           | (contra_ls as _ :: _, co_ls) =>
blanchet@36402
   784
             let
blanchet@36402
   785
               val proofs =
blanchet@36402
   786
                 map_filter
blanchet@36402
   787
                     (fn l =>
blanchet@36402
   788
                         if member (op =) concl_ls l then
blanchet@36402
   789
                           NONE
blanchet@36402
   790
                         else
blanchet@36402
   791
                           let
blanchet@36402
   792
                             val drop_ls = filter (curry (op <>) l) contra_ls
blanchet@36402
   793
                           in
blanchet@36402
   794
                             second_pass []
blanchet@36402
   795
                                 (proof, assums,
blanchet@36402
   796
                                  patches ||> apfst (insert (op =) l)
blanchet@36402
   797
                                          ||> apsnd (union (op =) drop_ls))
blanchet@36402
   798
                             |> fst |> SOME
blanchet@36402
   799
                           end) contra_ls
blanchet@36402
   800
               val facts = (co_ls, [])
blanchet@36402
   801
             in
blanchet@36402
   802
               (case join_proofs proofs of
blanchet@36402
   803
                  SOME (l, t, proofs, proof_tail) =>
blanchet@36402
   804
                  Have (case_split_qualifiers proofs @
blanchet@36402
   805
                        (if null proof_tail then end_qs else []), l, t,
blanchet@36574
   806
                        smart_case_split proofs facts) :: proof_tail
blanchet@36402
   807
                | NONE =>
blanchet@36402
   808
                  [Have (case_split_qualifiers proofs @ end_qs, no_label,
blanchet@36574
   809
                         concl_t, smart_case_split proofs facts)],
blanchet@36402
   810
                patches)
blanchet@36402
   811
             end
blanchet@36402
   812
           | _ => raise Fail "malformed proof")
blanchet@36402
   813
       | second_pass _ _ = raise Fail "malformed proof"
blanchet@36486
   814
    val proof_bottom =
blanchet@36486
   815
      second_pass [Show] (contra_proof, [], ([], ([], []))) |> fst
blanchet@36402
   816
  in proof_top @ proof_bottom end
blanchet@36402
   817
blanchet@36402
   818
val kill_duplicate_assumptions_in_proof =
blanchet@36402
   819
  let
blanchet@36402
   820
    fun relabel_facts subst =
blanchet@36402
   821
      apfst (map (fn l => AList.lookup (op =) subst l |> the_default l))
blanchet@36491
   822
    fun do_step (step as Assume (l, t)) (proof, subst, assums) =
blanchet@36402
   823
        (case AList.lookup (op aconv) assums t of
blanchet@36967
   824
           SOME l' => (proof, (l, l') :: subst, assums)
blanchet@36491
   825
         | NONE => (step :: proof, subst, (t, l) :: assums))
blanchet@36402
   826
      | do_step (Have (qs, l, t, by)) (proof, subst, assums) =
blanchet@36402
   827
        (Have (qs, l, t,
blanchet@36402
   828
               case by of
blanchet@36564
   829
                 ByMetis facts => ByMetis (relabel_facts subst facts)
blanchet@36402
   830
               | CaseSplit (proofs, facts) =>
blanchet@36402
   831
                 CaseSplit (map do_proof proofs, relabel_facts subst facts)) ::
blanchet@36402
   832
         proof, subst, assums)
blanchet@36491
   833
      | do_step step (proof, subst, assums) = (step :: proof, subst, assums)
blanchet@36402
   834
    and do_proof proof = fold do_step proof ([], [], []) |> #1 |> rev
blanchet@36402
   835
  in do_proof end
blanchet@36402
   836
blanchet@36402
   837
val then_chain_proof =
blanchet@36402
   838
  let
blanchet@36402
   839
    fun aux _ [] = []
blanchet@36491
   840
      | aux _ ((step as Assume (l, _)) :: proof) = step :: aux l proof
blanchet@36402
   841
      | aux l' (Have (qs, l, t, by) :: proof) =
blanchet@36402
   842
        (case by of
blanchet@36564
   843
           ByMetis (ls, ss) =>
blanchet@36402
   844
           Have (if member (op =) ls l' then
blanchet@36402
   845
                   (Then :: qs, l, t,
blanchet@36564
   846
                    ByMetis (filter_out (curry (op =) l') ls, ss))
blanchet@36402
   847
                 else
blanchet@36564
   848
                   (qs, l, t, ByMetis (ls, ss)))
blanchet@36402
   849
         | CaseSplit (proofs, facts) =>
blanchet@36402
   850
           Have (qs, l, t, CaseSplit (map (aux no_label) proofs, facts))) ::
blanchet@36402
   851
        aux l proof
blanchet@36491
   852
      | aux _ (step :: proof) = step :: aux no_label proof
blanchet@36402
   853
  in aux no_label end
blanchet@36402
   854
blanchet@36402
   855
fun kill_useless_labels_in_proof proof =
blanchet@36402
   856
  let
blanchet@36556
   857
    val used_ls = used_labels_of proof
blanchet@36402
   858
    fun do_label l = if member (op =) used_ls l then l else no_label
blanchet@36556
   859
    fun do_step (Assume (l, t)) = Assume (do_label l, t)
blanchet@36556
   860
      | do_step (Have (qs, l, t, by)) =
blanchet@36402
   861
        Have (qs, do_label l, t,
blanchet@36402
   862
              case by of
blanchet@36402
   863
                CaseSplit (proofs, facts) =>
blanchet@36556
   864
                CaseSplit (map (map do_step) proofs, facts)
blanchet@36402
   865
              | _ => by)
blanchet@36556
   866
      | do_step step = step
blanchet@36556
   867
  in map do_step proof end
blanchet@36402
   868
blanchet@36402
   869
fun prefix_for_depth n = replicate_string (n + 1)
blanchet@36402
   870
blanchet@36402
   871
val relabel_proof =
blanchet@36402
   872
  let
blanchet@36402
   873
    fun aux _ _ _ [] = []
blanchet@36402
   874
      | aux subst depth (next_assum, next_fact) (Assume (l, t) :: proof) =
blanchet@36402
   875
        if l = no_label then
blanchet@36402
   876
          Assume (l, t) :: aux subst depth (next_assum, next_fact) proof
blanchet@36402
   877
        else
blanchet@36402
   878
          let val l' = (prefix_for_depth depth assum_prefix, next_assum) in
blanchet@36402
   879
            Assume (l', t) ::
blanchet@36402
   880
            aux ((l, l') :: subst) depth (next_assum + 1, next_fact) proof
blanchet@36402
   881
          end
blanchet@36402
   882
      | aux subst depth (next_assum, next_fact) (Have (qs, l, t, by) :: proof) =
blanchet@36402
   883
        let
blanchet@36402
   884
          val (l', subst, next_fact) =
blanchet@36402
   885
            if l = no_label then
blanchet@36402
   886
              (l, subst, next_fact)
blanchet@36402
   887
            else
blanchet@36402
   888
              let
blanchet@36402
   889
                val l' = (prefix_for_depth depth fact_prefix, next_fact)
blanchet@36402
   890
              in (l', (l, l') :: subst, next_fact + 1) end
blanchet@36570
   891
          val relabel_facts =
blanchet@36570
   892
            apfst (map (fn l =>
blanchet@36570
   893
                           case AList.lookup (op =) subst l of
blanchet@36570
   894
                             SOME l' => l'
blanchet@36570
   895
                           | NONE => raise Fail ("unknown label " ^
blanchet@36570
   896
                                                 quote (string_for_label l))))
blanchet@36402
   897
          val by =
blanchet@36402
   898
            case by of
blanchet@36564
   899
              ByMetis facts => ByMetis (relabel_facts facts)
blanchet@36402
   900
            | CaseSplit (proofs, facts) =>
blanchet@36402
   901
              CaseSplit (map (aux subst (depth + 1) (1, 1)) proofs,
blanchet@36402
   902
                         relabel_facts facts)
blanchet@36402
   903
        in
blanchet@36402
   904
          Have (qs, l', t, by) ::
blanchet@36402
   905
          aux subst depth (next_assum, next_fact) proof
blanchet@36402
   906
        end
blanchet@36491
   907
      | aux subst depth nextp (step :: proof) =
blanchet@36491
   908
        step :: aux subst depth nextp proof
blanchet@36402
   909
  in aux [] 0 (1, 1) end
blanchet@36402
   910
blanchet@36488
   911
fun string_for_proof ctxt i n =
blanchet@36402
   912
  let
blanchet@36478
   913
    fun fix_print_mode f =
blanchet@36478
   914
      PrintMode.setmp (filter (curry (op =) Symbol.xsymbolsN)
blanchet@36478
   915
                      (print_mode_value ())) f
blanchet@36402
   916
    fun do_indent ind = replicate_string (ind * indent_size) " "
blanchet@36478
   917
    fun do_free (s, T) =
blanchet@36478
   918
      maybe_quote s ^ " :: " ^
blanchet@36478
   919
      maybe_quote (fix_print_mode (Syntax.string_of_typ ctxt) T)
blanchet@36570
   920
    fun do_label l = if l = no_label then "" else string_for_label l ^ ": "
blanchet@36402
   921
    fun do_have qs =
blanchet@36402
   922
      (if member (op =) qs Moreover then "moreover " else "") ^
blanchet@36402
   923
      (if member (op =) qs Ultimately then "ultimately " else "") ^
blanchet@36402
   924
      (if member (op =) qs Then then
blanchet@36402
   925
         if member (op =) qs Show then "thus" else "hence"
blanchet@36402
   926
       else
blanchet@36402
   927
         if member (op =) qs Show then "show" else "have")
blanchet@36478
   928
    val do_term = maybe_quote o fix_print_mode (Syntax.string_of_term ctxt)
blanchet@36570
   929
    fun do_facts (ls, ss) =
blanchet@36570
   930
      let
blanchet@36570
   931
        val ls = ls |> sort_distinct (prod_ord string_ord int_ord)
blanchet@36570
   932
        val ss = ss |> sort_distinct string_ord
blanchet@36570
   933
      in metis_command 1 1 (map string_for_label ls @ ss) end
blanchet@36478
   934
    and do_step ind (Fix xs) =
blanchet@36478
   935
        do_indent ind ^ "fix " ^ space_implode " and " (map do_free xs) ^ "\n"
blanchet@36486
   936
      | do_step ind (Let (t1, t2)) =
blanchet@36486
   937
        do_indent ind ^ "let " ^ do_term t1 ^ " = " ^ do_term t2 ^ "\n"
blanchet@36402
   938
      | do_step ind (Assume (l, t)) =
blanchet@36402
   939
        do_indent ind ^ "assume " ^ do_label l ^ do_term t ^ "\n"
blanchet@36564
   940
      | do_step ind (Have (qs, l, t, ByMetis facts)) =
blanchet@36402
   941
        do_indent ind ^ do_have qs ^ " " ^
blanchet@36479
   942
        do_label l ^ do_term t ^ " " ^ do_facts facts ^ "\n"
blanchet@36402
   943
      | do_step ind (Have (qs, l, t, CaseSplit (proofs, facts))) =
blanchet@36402
   944
        space_implode (do_indent ind ^ "moreover\n")
blanchet@36402
   945
                      (map (do_block ind) proofs) ^
blanchet@36479
   946
        do_indent ind ^ do_have qs ^ " " ^ do_label l ^ do_term t ^ " " ^
blanchet@36478
   947
        do_facts facts ^ "\n"
blanchet@36402
   948
    and do_steps prefix suffix ind steps =
blanchet@36402
   949
      let val s = implode (map (do_step ind) steps) in
blanchet@36402
   950
        replicate_string (ind * indent_size - size prefix) " " ^ prefix ^
blanchet@36402
   951
        String.extract (s, ind * indent_size,
blanchet@36402
   952
                        SOME (size s - ind * indent_size - 1)) ^
blanchet@36402
   953
        suffix ^ "\n"
blanchet@36402
   954
      end
blanchet@36402
   955
    and do_block ind proof = do_steps "{ " " }" (ind + 1) proof
blanchet@36564
   956
    (* One-step proofs are pointless; better use the Metis one-liner
blanchet@36564
   957
       directly. *)
blanchet@36564
   958
    and do_proof [Have (_, _, _, ByMetis _)] = ""
blanchet@36564
   959
      | do_proof proof =
blanchet@36480
   960
        (if i <> 1 then "prefer " ^ string_of_int i ^ "\n" else "") ^
blanchet@36480
   961
        do_indent 0 ^ "proof -\n" ^
blanchet@36480
   962
        do_steps "" "" 1 proof ^
blanchet@36480
   963
        do_indent 0 ^ (if n <> 1 then "next" else "qed") ^ "\n"
blanchet@36488
   964
  in do_proof end
blanchet@36402
   965
blanchet@36924
   966
fun isar_proof_text (pool, debug, full_types, isar_shrink_factor, ctxt,
blanchet@36909
   967
                     conjecture_shape)
krauss@36606
   968
                    (minimize_command, atp_proof, thm_names, goal, i) =
blanchet@36402
   969
  let
blanchet@36402
   970
    val thy = ProofContext.theory_of ctxt
blanchet@36909
   971
    val (params, hyp_ts, concl_t) = strip_subgoal goal i
blanchet@36909
   972
    val frees = fold Term.add_frees (concl_t :: hyp_ts) []
blanchet@36967
   973
    val tfrees = fold Term.add_tfrees (concl_t :: hyp_ts) []
blanchet@36402
   974
    val n = Logic.count_prems (prop_of goal)
blanchet@36223
   975
    val (one_line_proof, lemma_names) =
blanchet@36402
   976
      metis_proof_text (minimize_command, atp_proof, thm_names, goal, i)
blanchet@36283
   977
    fun isar_proof_for () =
blanchet@36967
   978
      case proof_from_atp_proof pool ctxt full_types tfrees isar_shrink_factor
blanchet@36924
   979
                                atp_proof conjecture_shape thm_names params
blanchet@36924
   980
                                frees
blanchet@36491
   981
           |> redirect_proof thy conjecture_shape hyp_ts concl_t
blanchet@36402
   982
           |> kill_duplicate_assumptions_in_proof
blanchet@36402
   983
           |> then_chain_proof
blanchet@36402
   984
           |> kill_useless_labels_in_proof
blanchet@36402
   985
           |> relabel_proof
blanchet@36488
   986
           |> string_for_proof ctxt i n of
blanchet@36283
   987
        "" => ""
blanchet@36402
   988
      | proof => "\nStructured proof:\n" ^ Markup.markup Markup.sendback proof
blanchet@35868
   989
    val isar_proof =
blanchet@36402
   990
      if debug then
blanchet@36283
   991
        isar_proof_for ()
blanchet@36283
   992
      else
blanchet@36283
   993
        try isar_proof_for ()
blanchet@36287
   994
        |> the_default "Warning: The Isar proof construction failed.\n"
blanchet@36283
   995
  in (one_line_proof ^ isar_proof, lemma_names) end
paulson@21978
   996
blanchet@36557
   997
fun proof_text isar_proof isar_params other_params =
blanchet@36557
   998
  (if isar_proof then isar_proof_text isar_params else metis_proof_text)
blanchet@36557
   999
      other_params
blanchet@36223
  1000
immler@31038
  1001
end;