blanchet@43926
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(* Title: HOL/Tools/ATP/atp_reconstruct.ML
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blanchet@38261
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Author: Lawrence C. Paulson, Cambridge University Computer Laboratory
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blanchet@38261
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Author: Claire Quigley, Cambridge University Computer Laboratory
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blanchet@36392
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Author: Jasmin Blanchette, TU Muenchen
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paulson@21978
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blanchet@43926
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Proof reconstruction from ATP proofs.
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wenzelm@33318
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*)
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wenzelm@33318
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blanchet@43926
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signature ATP_RECONSTRUCT =
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paulson@24425
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sig
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nik@44537
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type ('a, 'b) ho_term = ('a, 'b) ATP_Problem.ho_term
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blanchet@43968
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type ('a, 'b, 'c) formula = ('a, 'b, 'c) ATP_Problem.formula
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type 'a proof = 'a ATP_Proof.proof
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blanchet@43926
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type locality = ATP_Translate.locality
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datatype reconstructor =
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blanchet@43874
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Metis |
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blanchet@44069
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Metis_Full_Types |
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blanchet@44069
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Metis_No_Types |
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SMT of string
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blanchet@43891
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datatype play =
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Played of reconstructor * Time.time |
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Trust_Playable of reconstructor * Time.time option|
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Failed_to_Play of reconstructor
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blanchet@43874
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blanchet@36281
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type minimize_command = string list -> string
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type one_line_params =
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blanchet@43891
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play * string * (string * locality) list * minimize_command * int * int
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blanchet@39053
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type isar_params =
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blanchet@44175
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bool * bool * int * string Symtab.table * int list list * int
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blanchet@43943
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* (string * locality) list vector * int Symtab.table * string proof * thm
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blanchet@43322
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val used_facts_in_atp_proof :
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blanchet@44175
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Proof.context -> int -> (string * locality) list vector -> string proof
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blanchet@44175
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-> (string * locality) list
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blanchet@43745
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val used_facts_in_unsound_atp_proof :
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blanchet@44175
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Proof.context -> int list list -> int -> (string * locality) list vector
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blanchet@44175
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-> 'a proof -> string list option
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blanchet@43874
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val uses_typed_helpers : int list -> 'a proof -> bool
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val one_line_proof_text : one_line_params -> string
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val make_tvar : string -> typ
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val make_tfree : Proof.context -> string -> typ
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blanchet@43935
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val term_from_atp :
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nik@44537
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Proof.context -> bool -> int Symtab.table -> typ option -> (string, string) ho_term
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-> term
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val prop_from_atp :
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Proof.context -> bool -> int Symtab.table
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nik@44537
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-> (string, string, (string, string) ho_term) formula -> term
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blanchet@43809
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val isar_proof_text :
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Proof.context -> bool -> isar_params -> one_line_params -> string
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blanchet@43809
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val proof_text :
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blanchet@43874
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Proof.context -> bool -> isar_params -> one_line_params -> string
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paulson@24425
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end;
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paulson@21978
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blanchet@43926
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structure ATP_Reconstruct : ATP_RECONSTRUCT =
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paulson@21978
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struct
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paulson@21978
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blanchet@43926
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open ATP_Util
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open ATP_Problem
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open ATP_Proof
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open ATP_Translate
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blanchet@35826
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datatype reconstructor =
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blanchet@43874
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Metis |
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blanchet@44069
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Metis_Full_Types |
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blanchet@44069
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Metis_No_Types |
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blanchet@43874
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SMT of string
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blanchet@43874
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blanchet@43891
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datatype play =
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blanchet@43891
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Played of reconstructor * Time.time |
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Trust_Playable of reconstructor * Time.time option |
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blanchet@44007
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Failed_to_Play of reconstructor
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blanchet@43874
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type minimize_command = string list -> string
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blanchet@43874
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type one_line_params =
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blanchet@43891
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play * string * (string * locality) list * minimize_command * int * int
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blanchet@39053
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type isar_params =
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blanchet@44175
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bool * bool * int * string Symtab.table * int list list * int
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blanchet@43878
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* (string * locality) list vector * int Symtab.table * string proof * thm
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blanchet@36281
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blanchet@43750
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val is_typed_helper_name =
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blanchet@43750
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String.isPrefix helper_prefix andf String.isSuffix typed_helper_suffix
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blanchet@43750
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blanchet@39740
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fun find_first_in_list_vector vec key =
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Vector.foldl (fn (ps, NONE) => AList.lookup (op =) ps key
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| (_, value) => value) NONE vec
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blanchet@39740
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val unprefix_fact_number = space_implode "_" o tl o space_explode "_"
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val vampire_step_prefix = "f" (* grrr... *)
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blanchet@41451
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blanchet@43750
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val extract_step_number =
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blanchet@43750
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Int.fromString o perhaps (try (unprefix vampire_step_prefix))
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blanchet@43750
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fun resolve_one_named_fact fact_names s =
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case try (unprefix fact_prefix) s of
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SOME s' =>
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let val s' = s' |> unprefix_fact_number |> unascii_of in
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s' |> find_first_in_list_vector fact_names |> Option.map (pair s')
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end
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| NONE => NONE
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fun resolve_fact _ fact_names (_, SOME ss) =
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map_filter (resolve_one_named_fact fact_names) ss
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| resolve_fact facts_offset fact_names (num, NONE) =
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(case extract_step_number num of
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blanchet@43750
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SOME j =>
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let val j = j - facts_offset in
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blanchet@43750
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if j > 0 andalso j <= Vector.length fact_names then
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Vector.sub (fact_names, j - 1)
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else
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[]
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end
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| NONE => [])
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blanchet@44175
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fun is_fact conjecture_shape = not o null o resolve_fact 0 conjecture_shape
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blanchet@39693
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blanchet@44352
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fun resolve_one_named_conjecture s =
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blanchet@44352
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case try (unprefix conjecture_prefix) s of
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SOME s' => Int.fromString s'
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| NONE => NONE
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fun resolve_conjecture _ (_, SOME ss) =
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map_filter resolve_one_named_conjecture ss
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| resolve_conjecture conjecture_shape (num, NONE) =
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case extract_step_number num of
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SOME i => (case find_index (exists (curry (op =) i)) conjecture_shape of
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~1 => []
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| j => [j])
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blanchet@43616
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| NONE => []
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blanchet@43320
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blanchet@43320
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fun is_conjecture conjecture_shape =
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blanchet@43320
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not o null o resolve_conjecture conjecture_shape
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blanchet@43320
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blanchet@44352
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fun is_typed_helper _ (_, SOME ss) = exists is_typed_helper_name ss
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blanchet@43750
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| is_typed_helper typed_helpers (num, NONE) =
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blanchet@43750
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(case extract_step_number num of
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blanchet@43750
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SOME i => member (op =) typed_helpers i
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| NONE => false)
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blanchet@43750
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blanchet@43809
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val leo2_ext = "extcnf_equal_neg"
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blanchet@43809
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val isa_ext = Thm.get_name_hint @{thm ext}
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blanchet@43809
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val isa_short_ext = Long_Name.base_name isa_ext
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blanchet@43809
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blanchet@43809
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fun ext_name ctxt =
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blanchet@43809
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if Thm.eq_thm_prop (@{thm ext},
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blanchet@43809
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singleton (Attrib.eval_thms ctxt) (Facts.named isa_short_ext, [])) then
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blanchet@43809
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isa_short_ext
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blanchet@43809
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else
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blanchet@43809
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isa_ext
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blanchet@43809
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blanchet@44175
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fun add_fact _ facts_offset fact_names (Inference (name, _, [])) =
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blanchet@44175
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union (op =) (resolve_fact facts_offset fact_names name)
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blanchet@44175
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| add_fact ctxt _ _ (Inference (_, _, deps)) =
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blanchet@43809
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if AList.defined (op =) deps leo2_ext then
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blanchet@44282
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insert (op =) (ext_name ctxt, Extensionality)
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blanchet@43809
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else
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blanchet@43809
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I
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blanchet@44175
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| add_fact _ _ _ _ = I
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blanchet@39693
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blanchet@44175
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fun used_facts_in_atp_proof ctxt facts_offset fact_names atp_proof =
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blanchet@44154
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if null atp_proof then Vector.foldl (uncurry (union (op =))) [] fact_names
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blanchet@44175
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else fold (add_fact ctxt facts_offset fact_names) atp_proof []
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blanchet@43320
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blanchet@44149
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fun is_conjecture_used_in_proof conjecture_shape =
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blanchet@43320
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exists (fn Inference (name, _, []) => is_conjecture conjecture_shape name
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blanchet@43320
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| _ => false)
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blanchet@43320
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blanchet@44175
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fun used_facts_in_unsound_atp_proof _ _ _ _ [] = NONE
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blanchet@44175
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| used_facts_in_unsound_atp_proof ctxt conjecture_shape facts_offset
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blanchet@43745
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fact_names atp_proof =
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blanchet@44149
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let
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blanchet@44149
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val used_facts =
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blanchet@44175
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used_facts_in_atp_proof ctxt facts_offset fact_names atp_proof
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blanchet@44149
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in
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blanchet@44149
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if forall (is_locality_global o snd) used_facts andalso
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blanchet@44149
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not (is_conjecture_used_in_proof conjecture_shape atp_proof) then
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blanchet@44149
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SOME (map fst used_facts)
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blanchet@44149
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else
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blanchet@44149
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NONE
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blanchet@44149
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end
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blanchet@43320
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blanchet@43874
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fun uses_typed_helpers typed_helpers =
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blanchet@43874
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exists (fn Inference (name, _, []) => is_typed_helper typed_helpers name
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blanchet@43874
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| _ => false)
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blanchet@43874
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blanchet@43874
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blanchet@43320
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(** Soft-core proof reconstruction: Metis one-liner **)
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blanchet@43320
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blanchet@44069
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(* unfortunate leaking abstraction *)
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blanchet@44074
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fun name_of_reconstructor Metis = "metis"
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blanchet@44074
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| name_of_reconstructor Metis_Full_Types = "metis (full_types)"
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blanchet@44074
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| name_of_reconstructor Metis_No_Types = "metis (no_types)"
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blanchet@44074
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| name_of_reconstructor (SMT _) = "smt"
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blanchet@43874
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blanchet@43874
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fun reconstructor_settings (SMT settings) = settings
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blanchet@43874
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| reconstructor_settings _ = ""
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blanchet@43874
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blanchet@43320
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fun string_for_label (s, num) = s ^ string_of_int num
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blanchet@43320
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blanchet@43874
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fun show_time NONE = ""
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blanchet@43875
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| show_time (SOME ext_time) = " (" ^ string_from_ext_time ext_time ^ ")"
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blanchet@43874
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blanchet@43320
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fun set_settings "" = ""
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blanchet@43320
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| set_settings settings = "using [[" ^ settings ^ "]] "
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blanchet@43320
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fun apply_on_subgoal settings _ 1 = set_settings settings ^ "by "
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blanchet@43320
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| apply_on_subgoal settings 1 _ = set_settings settings ^ "apply "
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blanchet@43320
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| apply_on_subgoal settings i n =
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blanchet@43320
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"prefer " ^ string_of_int i ^ " " ^ apply_on_subgoal settings 1 n
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blanchet@43320
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fun command_call name [] = name
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blanchet@43320
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| command_call name args = "(" ^ name ^ " " ^ space_implode " " args ^ ")"
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blanchet@43874
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fun try_command_line banner time command =
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blanchet@43874
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banner ^ ": " ^ Markup.markup Markup.sendback command ^ show_time time ^ "."
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blanchet@43320
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fun using_labels [] = ""
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blanchet@43320
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| using_labels ls =
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blanchet@43320
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"using " ^ space_implode " " (map string_for_label ls) ^ " "
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blanchet@43874
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fun reconstructor_command reconstructor i n (ls, ss) =
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blanchet@43874
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using_labels ls ^
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blanchet@43874
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apply_on_subgoal (reconstructor_settings reconstructor) i n ^
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blanchet@44074
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command_call (name_of_reconstructor reconstructor) ss
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blanchet@43320
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fun minimize_line _ [] = ""
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blanchet@43320
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| minimize_line minimize_command ss =
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blanchet@43320
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case minimize_command ss of
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blanchet@43320
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"" => ""
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blanchet@43847
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| command => "\nTo minimize: " ^ Markup.markup Markup.sendback command ^ "."
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blanchet@39693
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225 |
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blanchet@40966
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val split_used_facts =
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blanchet@40966
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List.partition (curry (op =) Chained o snd)
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blanchet@39693
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#> pairself (sort_distinct (string_ord o pairself fst))
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blanchet@39693
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blanchet@43874
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fun one_line_proof_text (preplay, banner, used_facts, minimize_command,
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blanchet@43878
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subgoal, subgoal_count) =
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blanchet@39693
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let
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blanchet@43874
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val (chained, extra) = split_used_facts used_facts
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blanchet@44007
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val (failed, reconstructor, ext_time) =
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blanchet@43874
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case preplay of
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blanchet@43891
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Played (reconstructor, time) =>
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blanchet@44007
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(false, reconstructor, (SOME (false, time)))
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blanchet@43874
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| Trust_Playable (reconstructor, time) =>
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blanchet@44007
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(false, reconstructor,
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blanchet@43874
|
240 |
case time of
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blanchet@43874
|
241 |
NONE => NONE
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blanchet@43874
|
242 |
| SOME time =>
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blanchet@43874
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243 |
if time = Time.zeroTime then NONE else SOME (true, time))
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blanchet@44007
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244 |
| Failed_to_Play reconstructor => (true, reconstructor, NONE)
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blanchet@43874
|
245 |
val try_line =
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blanchet@44007
|
246 |
([], map fst extra)
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blanchet@44007
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247 |
|> reconstructor_command reconstructor subgoal subgoal_count
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blanchet@44007
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|> (if failed then enclose "One-line proof reconstruction failed: " "."
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blanchet@44007
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249 |
else try_command_line banner ext_time)
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blanchet@43874
|
250 |
in try_line ^ minimize_line minimize_command (map fst (extra @ chained)) end
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blanchet@39693
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251 |
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blanchet@39693
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252 |
(** Hard-core proof reconstruction: structured Isar proofs **)
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blanchet@39693
|
253 |
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blanchet@39671
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254 |
fun forall_of v t = HOLogic.all_const (fastype_of v) $ lambda v t
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blanchet@39671
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fun exists_of v t = HOLogic.exists_const (fastype_of v) $ lambda v t
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blanchet@39671
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blanchet@43976
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fun make_tvar s = TVar (("'" ^ s, 0), HOLogic.typeS)
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blanchet@43976
|
258 |
fun make_tfree ctxt w =
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blanchet@43976
|
259 |
let val ww = "'" ^ w in
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blanchet@43976
|
260 |
TFree (ww, the_default HOLogic.typeS (Variable.def_sort ctxt (ww, ~1)))
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blanchet@43976
|
261 |
end
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blanchet@43976
|
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blanchet@39693
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val indent_size = 2
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blanchet@39693
|
264 |
val no_label = ("", ~1)
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blanchet@39693
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265 |
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blanchet@39693
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266 |
val raw_prefix = "X"
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blanchet@39693
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267 |
val assum_prefix = "A"
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blanchet@43051
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val have_prefix = "F"
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blanchet@39616
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blanchet@39693
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fun raw_label_for_name conjecture_shape name =
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blanchet@39693
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case resolve_conjecture conjecture_shape name of
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blanchet@39693
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272 |
[j] => (conjecture_prefix, j)
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blanchet@39695
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| _ => case Int.fromString (fst name) of
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blanchet@39693
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SOME j => (raw_prefix, j)
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blanchet@39695
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| NONE => (raw_prefix ^ fst name, 0)
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blanchet@39693
|
276 |
|
paulson@21978
|
277 |
(**** INTERPRETATION OF TSTP SYNTAX TREES ****)
|
paulson@21978
|
278 |
|
nik@44537
|
279 |
exception HO_TERM of (string, string) ho_term list
|
nik@44537
|
280 |
exception FORMULA of (string, string, (string, string) ho_term) formula list
|
blanchet@38225
|
281 |
exception SAME of unit
|
paulson@21978
|
282 |
|
blanchet@36901
|
283 |
(* Type variables are given the basic sort "HOL.type". Some will later be
|
blanchet@38225
|
284 |
constrained by information from type literals, or by type inference. *)
|
blanchet@43976
|
285 |
fun typ_from_atp ctxt (u as ATerm (a, us)) =
|
blanchet@43976
|
286 |
let val Ts = map (typ_from_atp ctxt) us in
|
blanchet@38987
|
287 |
case strip_prefix_and_unascii type_const_prefix a of
|
blanchet@38225
|
288 |
SOME b => Type (invert_const b, Ts)
|
blanchet@38225
|
289 |
| NONE =>
|
blanchet@38225
|
290 |
if not (null us) then
|
nik@44537
|
291 |
raise HO_TERM [u] (* only "tconst"s have type arguments *)
|
blanchet@38987
|
292 |
else case strip_prefix_and_unascii tfree_prefix a of
|
blanchet@43976
|
293 |
SOME b => make_tfree ctxt b
|
blanchet@36482
|
294 |
| NONE =>
|
blanchet@44173
|
295 |
(* Could be an Isabelle variable or a variable from the ATP, say "X1"
|
blanchet@44173
|
296 |
or "_5018". Sometimes variables from the ATP are indistinguishable
|
blanchet@44173
|
297 |
from Isabelle variables, which forces us to use a type parameter in
|
blanchet@44173
|
298 |
all cases. *)
|
blanchet@44173
|
299 |
(a |> perhaps (strip_prefix_and_unascii tvar_prefix), HOLogic.typeS)
|
blanchet@44173
|
300 |
|> Type_Infer.param 0
|
blanchet@38225
|
301 |
end
|
paulson@21978
|
302 |
|
blanchet@38248
|
303 |
(* Type class literal applied to a type. Returns triple of polarity, class,
|
blanchet@38248
|
304 |
type. *)
|
blanchet@43976
|
305 |
fun type_constraint_from_term ctxt (u as ATerm (a, us)) =
|
blanchet@43976
|
306 |
case (strip_prefix_and_unascii class_prefix a, map (typ_from_atp ctxt) us) of
|
blanchet@43477
|
307 |
(SOME b, [T]) => (b, T)
|
nik@44537
|
308 |
| _ => raise HO_TERM [u]
|
blanchet@38248
|
309 |
|
blanchet@38331
|
310 |
(** Accumulate type constraints in a formula: negative type literals **)
|
blanchet@38248
|
311 |
fun add_var (key, z) = Vartab.map_default (key, []) (cons z)
|
blanchet@43477
|
312 |
fun add_type_constraint false (cl, TFree (a ,_)) = add_var ((a, ~1), cl)
|
blanchet@43477
|
313 |
| add_type_constraint false (cl, TVar (ix, _)) = add_var (ix, cl)
|
blanchet@43477
|
314 |
| add_type_constraint _ _ = I
|
blanchet@38248
|
315 |
|
blanchet@43935
|
316 |
fun repair_variable_name f s =
|
blanchet@36482
|
317 |
let
|
blanchet@36482
|
318 |
fun subscript_name s n = s ^ nat_subscript n
|
blanchet@38713
|
319 |
val s = String.map f s
|
blanchet@36482
|
320 |
in
|
blanchet@36482
|
321 |
case space_explode "_" s of
|
blanchet@36482
|
322 |
[_] => (case take_suffix Char.isDigit (String.explode s) of
|
blanchet@36482
|
323 |
(cs1 as _ :: _, cs2 as _ :: _) =>
|
blanchet@36482
|
324 |
subscript_name (String.implode cs1)
|
blanchet@36482
|
325 |
(the (Int.fromString (String.implode cs2)))
|
blanchet@36482
|
326 |
| (_, _) => s)
|
blanchet@36482
|
327 |
| [s1, s2] => (case Int.fromString s2 of
|
blanchet@36482
|
328 |
SOME n => subscript_name s1 n
|
blanchet@36482
|
329 |
| NONE => s)
|
blanchet@36482
|
330 |
| _ => s
|
blanchet@36482
|
331 |
end
|
blanchet@44023
|
332 |
|
blanchet@44023
|
333 |
fun slack_fastype_of t = fastype_of t handle TERM _ => HOLogic.typeT
|
blanchet@44023
|
334 |
|
blanchet@36901
|
335 |
(* First-order translation. No types are known for variables. "HOLogic.typeT"
|
blanchet@38248
|
336 |
should allow them to be inferred. *)
|
blanchet@43976
|
337 |
fun term_from_atp ctxt textual sym_tab =
|
blanchet@36901
|
338 |
let
|
blanchet@43976
|
339 |
val thy = Proof_Context.theory_of ctxt
|
blanchet@44053
|
340 |
(* For Metis, we use 1 rather than 0 because variable references in clauses
|
blanchet@44053
|
341 |
may otherwise conflict with variable constraints in the goal. At least,
|
blanchet@44053
|
342 |
type inference often fails otherwise. See also "axiom_inference" in
|
blanchet@44053
|
343 |
"Metis_Reconstruct". *)
|
blanchet@43935
|
344 |
val var_index = if textual then 0 else 1
|
blanchet@43972
|
345 |
fun do_term extra_ts opt_T u =
|
blanchet@36901
|
346 |
case u of
|
blanchet@43410
|
347 |
ATerm (a, us) =>
|
blanchet@43803
|
348 |
if String.isPrefix simple_type_prefix a then
|
blanchet@43803
|
349 |
@{const True} (* ignore TPTP type information *)
|
blanchet@43841
|
350 |
else if a = tptp_equal then
|
blanchet@43934
|
351 |
let val ts = map (do_term [] NONE) us in
|
blanchet@43935
|
352 |
if textual andalso length ts = 2 andalso
|
blanchet@43935
|
353 |
hd ts aconv List.last ts then
|
blanchet@39352
|
354 |
(* Vampire is keen on producing these. *)
|
blanchet@39352
|
355 |
@{const True}
|
blanchet@39352
|
356 |
else
|
blanchet@39352
|
357 |
list_comb (Const (@{const_name HOL.eq}, HOLogic.typeT), ts)
|
blanchet@39352
|
358 |
end
|
blanchet@43841
|
359 |
else case strip_prefix_and_unascii const_prefix a of
|
blanchet@43841
|
360 |
SOME s =>
|
blanchet@43626
|
361 |
let
|
blanchet@43626
|
362 |
val ((s', s), mangled_us) = s |> unmangled_const |>> `invert_const
|
blanchet@43626
|
363 |
in
|
blanchet@43620
|
364 |
if s' = type_tag_name then
|
blanchet@43460
|
365 |
case mangled_us @ us of
|
blanchet@43460
|
366 |
[typ_u, term_u] =>
|
blanchet@43976
|
367 |
do_term extra_ts (SOME (typ_from_atp ctxt typ_u)) term_u
|
nik@44537
|
368 |
| _ => raise HO_TERM us
|
blanchet@43807
|
369 |
else if s' = predicator_name then
|
blanchet@43934
|
370 |
do_term [] (SOME @{typ bool}) (hd us)
|
blanchet@43807
|
371 |
else if s' = app_op_name then
|
blanchet@43972
|
372 |
let val extra_t = do_term [] NONE (List.last us) in
|
blanchet@43972
|
373 |
do_term (extra_t :: extra_ts)
|
blanchet@43972
|
374 |
(case opt_T of
|
blanchet@44023
|
375 |
SOME T => SOME (slack_fastype_of extra_t --> T)
|
blanchet@43972
|
376 |
| NONE => NONE)
|
blanchet@43972
|
377 |
(nth us (length us - 2))
|
blanchet@43972
|
378 |
end
|
blanchet@43807
|
379 |
else if s' = type_pred_name then
|
blanchet@43422
|
380 |
@{const True} (* ignore type predicates *)
|
blanchet@43420
|
381 |
else
|
blanchet@43420
|
382 |
let
|
blanchet@44032
|
383 |
val new_skolem = String.isPrefix new_skolem_const_prefix s
|
blanchet@43620
|
384 |
val num_ty_args =
|
blanchet@43620
|
385 |
length us - the_default 0 (Symtab.lookup sym_tab s)
|
blanchet@43420
|
386 |
val (type_us, term_us) =
|
blanchet@43420
|
387 |
chop num_ty_args us |>> append mangled_us
|
blanchet@43934
|
388 |
val term_ts = map (do_term [] NONE) term_us
|
blanchet@43420
|
389 |
val T =
|
blanchet@44024
|
390 |
(if not (null type_us) andalso
|
blanchet@44024
|
391 |
num_type_args thy s' = length type_us then
|
blanchet@44032
|
392 |
let val Ts = type_us |> map (typ_from_atp ctxt) in
|
blanchet@44032
|
393 |
if new_skolem then
|
blanchet@44032
|
394 |
SOME (Type_Infer.paramify_vars (tl Ts ---> hd Ts))
|
blanchet@44041
|
395 |
else if textual then
|
blanchet@44041
|
396 |
try (Sign.const_instance thy) (s', Ts)
|
blanchet@44032
|
397 |
else
|
blanchet@44041
|
398 |
NONE
|
blanchet@44032
|
399 |
end
|
blanchet@44024
|
400 |
else
|
blanchet@44024
|
401 |
NONE)
|
blanchet@44024
|
402 |
|> (fn SOME T => T
|
blanchet@44024
|
403 |
| NONE => map slack_fastype_of term_ts --->
|
blanchet@44024
|
404 |
(case opt_T of
|
blanchet@44024
|
405 |
SOME T => T
|
blanchet@44024
|
406 |
| NONE => HOLogic.typeT))
|
blanchet@44032
|
407 |
val t =
|
blanchet@44032
|
408 |
if new_skolem then
|
blanchet@44032
|
409 |
Var ((new_skolem_var_name_from_const s, var_index), T)
|
blanchet@44032
|
410 |
else
|
blanchet@44032
|
411 |
Const (unproxify_const s', T)
|
blanchet@44032
|
412 |
in list_comb (t, term_ts @ extra_ts) end
|
blanchet@43420
|
413 |
end
|
blanchet@36901
|
414 |
| NONE => (* a free or schematic variable *)
|
blanchet@36901
|
415 |
let
|
blanchet@43972
|
416 |
val ts = map (do_term [] NONE) us @ extra_ts
|
blanchet@44023
|
417 |
val T = map slack_fastype_of ts ---> HOLogic.typeT
|
blanchet@36901
|
418 |
val t =
|
blanchet@38987
|
419 |
case strip_prefix_and_unascii fixed_var_prefix a of
|
blanchet@36901
|
420 |
SOME b => Free (b, T)
|
blanchet@36901
|
421 |
| NONE =>
|
blanchet@38987
|
422 |
case strip_prefix_and_unascii schematic_var_prefix a of
|
blanchet@43935
|
423 |
SOME b => Var ((b, var_index), T)
|
blanchet@36901
|
424 |
| NONE =>
|
blanchet@43936
|
425 |
Var ((a |> textual ? repair_variable_name Char.toLower,
|
blanchet@43936
|
426 |
var_index), T)
|
blanchet@36901
|
427 |
in list_comb (t, ts) end
|
blanchet@43934
|
428 |
in do_term [] end
|
paulson@21978
|
429 |
|
blanchet@43976
|
430 |
fun term_from_atom ctxt textual sym_tab pos (u as ATerm (s, _)) =
|
blanchet@38248
|
431 |
if String.isPrefix class_prefix s then
|
blanchet@43976
|
432 |
add_type_constraint pos (type_constraint_from_term ctxt u)
|
blanchet@38248
|
433 |
#> pair @{const True}
|
blanchet@38248
|
434 |
else
|
blanchet@43976
|
435 |
pair (term_from_atp ctxt textual sym_tab (SOME @{typ bool}) u)
|
blanchet@36402
|
436 |
|
blanchet@36553
|
437 |
val combinator_table =
|
blanchet@40134
|
438 |
[(@{const_name Meson.COMBI}, @{thm Meson.COMBI_def_raw}),
|
blanchet@40134
|
439 |
(@{const_name Meson.COMBK}, @{thm Meson.COMBK_def_raw}),
|
blanchet@40134
|
440 |
(@{const_name Meson.COMBB}, @{thm Meson.COMBB_def_raw}),
|
blanchet@40134
|
441 |
(@{const_name Meson.COMBC}, @{thm Meson.COMBC_def_raw}),
|
blanchet@40134
|
442 |
(@{const_name Meson.COMBS}, @{thm Meson.COMBS_def_raw})]
|
blanchet@36553
|
443 |
|
blanchet@43626
|
444 |
fun uncombine_term thy =
|
blanchet@43626
|
445 |
let
|
blanchet@43626
|
446 |
fun aux (t1 $ t2) = betapply (pairself aux (t1, t2))
|
blanchet@43626
|
447 |
| aux (Abs (s, T, t')) = Abs (s, T, aux t')
|
blanchet@43626
|
448 |
| aux (t as Const (x as (s, _))) =
|
blanchet@43626
|
449 |
(case AList.lookup (op =) combinator_table s of
|
blanchet@43626
|
450 |
SOME thm => thm |> prop_of |> specialize_type thy x
|
blanchet@43626
|
451 |
|> Logic.dest_equals |> snd
|
blanchet@43626
|
452 |
| NONE => t)
|
blanchet@43626
|
453 |
| aux t = t
|
blanchet@43626
|
454 |
in aux end
|
blanchet@36553
|
455 |
|
blanchet@38225
|
456 |
(* Update schematic type variables with detected sort constraints. It's not
|
blanchet@43434
|
457 |
totally clear whether this code is necessary. *)
|
blanchet@38248
|
458 |
fun repair_tvar_sorts (t, tvar_tab) =
|
blanchet@36901
|
459 |
let
|
blanchet@38225
|
460 |
fun do_type (Type (a, Ts)) = Type (a, map do_type Ts)
|
blanchet@38225
|
461 |
| do_type (TVar (xi, s)) =
|
blanchet@38225
|
462 |
TVar (xi, the_default s (Vartab.lookup tvar_tab xi))
|
blanchet@38225
|
463 |
| do_type (TFree z) = TFree z
|
blanchet@38225
|
464 |
fun do_term (Const (a, T)) = Const (a, do_type T)
|
blanchet@38225
|
465 |
| do_term (Free (a, T)) = Free (a, do_type T)
|
blanchet@38225
|
466 |
| do_term (Var (xi, T)) = Var (xi, do_type T)
|
blanchet@38225
|
467 |
| do_term (t as Bound _) = t
|
blanchet@38225
|
468 |
| do_term (Abs (a, T, t)) = Abs (a, do_type T, do_term t)
|
blanchet@38225
|
469 |
| do_term (t1 $ t2) = do_term t1 $ do_term t2
|
blanchet@38225
|
470 |
in t |> not (Vartab.is_empty tvar_tab) ? do_term end
|
blanchet@38225
|
471 |
|
blanchet@39671
|
472 |
fun quantify_over_var quant_of var_s t =
|
blanchet@39671
|
473 |
let
|
blanchet@39671
|
474 |
val vars = [] |> Term.add_vars t |> filter (fn ((s, _), _) => s = var_s)
|
blanchet@39671
|
475 |
|> map Var
|
blanchet@39671
|
476 |
in fold_rev quant_of vars t end
|
blanchet@38225
|
477 |
|
blanchet@38331
|
478 |
(* Interpret an ATP formula as a HOL term, extracting sort constraints as they
|
blanchet@38331
|
479 |
appear in the formula. *)
|
blanchet@44025
|
480 |
fun prop_from_atp ctxt textual sym_tab phi =
|
blanchet@38248
|
481 |
let
|
blanchet@38248
|
482 |
fun do_formula pos phi =
|
blanchet@38225
|
483 |
case phi of
|
blanchet@38248
|
484 |
AQuant (_, [], phi) => do_formula pos phi
|
blanchet@43397
|
485 |
| AQuant (q, (s, _) :: xs, phi') =>
|
blanchet@38248
|
486 |
do_formula pos (AQuant (q, xs, phi'))
|
blanchet@43397
|
487 |
(* FIXME: TFF *)
|
blanchet@39671
|
488 |
#>> quantify_over_var (case q of
|
blanchet@39671
|
489 |
AForall => forall_of
|
blanchet@39671
|
490 |
| AExists => exists_of)
|
blanchet@43936
|
491 |
(s |> textual ? repair_variable_name Char.toLower)
|
blanchet@38248
|
492 |
| AConn (ANot, [phi']) => do_formula (not pos) phi' #>> s_not
|
blanchet@38225
|
493 |
| AConn (c, [phi1, phi2]) =>
|
blanchet@38248
|
494 |
do_formula (pos |> c = AImplies ? not) phi1
|
blanchet@38248
|
495 |
##>> do_formula pos phi2
|
blanchet@38248
|
496 |
#>> (case c of
|
blanchet@38248
|
497 |
AAnd => s_conj
|
blanchet@38248
|
498 |
| AOr => s_disj
|
blanchet@38248
|
499 |
| AImplies => s_imp
|
blanchet@38284
|
500 |
| AIff => s_iff
|
blanchet@44004
|
501 |
| ANot => raise Fail "impossible connective")
|
blanchet@43976
|
502 |
| AAtom tm => term_from_atom ctxt textual sym_tab pos tm
|
blanchet@38225
|
503 |
| _ => raise FORMULA [phi]
|
blanchet@38248
|
504 |
in repair_tvar_sorts (do_formula true phi Vartab.empty) end
|
blanchet@38225
|
505 |
|
blanchet@43972
|
506 |
fun infer_formula_types ctxt =
|
wenzelm@39541
|
507 |
Type.constraint HOLogic.boolT
|
blanchet@43626
|
508 |
#> Syntax.check_term
|
blanchet@43626
|
509 |
(Proof_Context.set_mode Proof_Context.mode_schematic ctxt)
|
paulson@21978
|
510 |
|
blanchet@44025
|
511 |
fun uncombined_etc_prop_from_atp ctxt textual sym_tab =
|
blanchet@43977
|
512 |
let val thy = Proof_Context.theory_of ctxt in
|
blanchet@44025
|
513 |
prop_from_atp ctxt textual sym_tab
|
blanchet@44017
|
514 |
#> textual ? uncombine_term thy #> infer_formula_types ctxt
|
blanchet@43977
|
515 |
end
|
blanchet@43977
|
516 |
|
blanchet@43934
|
517 |
(**** Translation of TSTP files to Isar proofs ****)
|
paulson@21978
|
518 |
|
blanchet@36482
|
519 |
fun unvarify_term (Var ((s, 0), T)) = Free (s, T)
|
blanchet@36482
|
520 |
| unvarify_term t = raise TERM ("unvarify_term: non-Var", [t])
|
paulson@21978
|
521 |
|
blanchet@43976
|
522 |
fun decode_line sym_tab (Definition (name, phi1, phi2)) ctxt =
|
blanchet@36482
|
523 |
let
|
wenzelm@43232
|
524 |
val thy = Proof_Context.theory_of ctxt
|
blanchet@44025
|
525 |
val t1 = prop_from_atp ctxt true sym_tab phi1
|
blanchet@36549
|
526 |
val vars = snd (strip_comb t1)
|
blanchet@36482
|
527 |
val frees = map unvarify_term vars
|
blanchet@36482
|
528 |
val unvarify_args = subst_atomic (vars ~~ frees)
|
blanchet@44025
|
529 |
val t2 = prop_from_atp ctxt true sym_tab phi2
|
blanchet@36549
|
530 |
val (t1, t2) =
|
blanchet@36549
|
531 |
HOLogic.eq_const HOLogic.typeT $ t1 $ t2
|
blanchet@43972
|
532 |
|> unvarify_args |> uncombine_term thy |> infer_formula_types ctxt
|
blanchet@36553
|
533 |
|> HOLogic.dest_eq
|
blanchet@36482
|
534 |
in
|
blanchet@39614
|
535 |
(Definition (name, t1, t2),
|
blanchet@36549
|
536 |
fold Variable.declare_term (maps OldTerm.term_frees [t1, t2]) ctxt)
|
blanchet@36482
|
537 |
end
|
blanchet@43976
|
538 |
| decode_line sym_tab (Inference (name, u, deps)) ctxt =
|
blanchet@44025
|
539 |
let val t = u |> uncombined_etc_prop_from_atp ctxt true sym_tab in
|
blanchet@39614
|
540 |
(Inference (name, t, deps),
|
blanchet@36549
|
541 |
fold Variable.declare_term (OldTerm.term_frees t) ctxt)
|
blanchet@36482
|
542 |
end
|
blanchet@43976
|
543 |
fun decode_lines ctxt sym_tab lines =
|
blanchet@43976
|
544 |
fst (fold_map (decode_line sym_tab) lines ctxt)
|
paulson@21978
|
545 |
|
blanchet@38281
|
546 |
fun is_same_inference _ (Definition _) = false
|
blanchet@38281
|
547 |
| is_same_inference t (Inference (_, t', _)) = t aconv t'
|
blanchet@36482
|
548 |
|
blanchet@36482
|
549 |
(* No "real" literals means only type information (tfree_tcs, clsrel, or
|
blanchet@36482
|
550 |
clsarity). *)
|
blanchet@36482
|
551 |
val is_only_type_information = curry (op aconv) HOLogic.true_const
|
blanchet@36482
|
552 |
|
blanchet@39619
|
553 |
fun replace_one_dependency (old, new) dep =
|
blanchet@43809
|
554 |
if is_same_atp_step dep old then new else [dep]
|
blanchet@39619
|
555 |
fun replace_dependencies_in_line _ (line as Definition _) = line
|
blanchet@39619
|
556 |
| replace_dependencies_in_line p (Inference (name, t, deps)) =
|
blanchet@39619
|
557 |
Inference (name, t, fold (union (op =) o replace_one_dependency p) deps [])
|
paulson@21978
|
558 |
|
blanchet@40445
|
559 |
(* Discard facts; consolidate adjacent lines that prove the same formula, since
|
blanchet@38331
|
560 |
they differ only in type information.*)
|
blanchet@44175
|
561 |
fun add_line _ _ (line as Definition _) lines = line :: lines
|
blanchet@44175
|
562 |
| add_line conjecture_shape fact_names (Inference (name, t, [])) lines =
|
blanchet@40445
|
563 |
(* No dependencies: fact, conjecture, or (for Vampire) internal facts or
|
blanchet@38331
|
564 |
definitions. *)
|
blanchet@44175
|
565 |
if is_fact fact_names name then
|
blanchet@40445
|
566 |
(* Facts are not proof lines. *)
|
blanchet@36482
|
567 |
if is_only_type_information t then
|
blanchet@39619
|
568 |
map (replace_dependencies_in_line (name, [])) lines
|
blanchet@36482
|
569 |
(* Is there a repetition? If so, replace later line by earlier one. *)
|
blanchet@38281
|
570 |
else case take_prefix (not o is_same_inference t) lines of
|
blanchet@39619
|
571 |
(_, []) => lines (* no repetition of proof line *)
|
blanchet@39614
|
572 |
| (pre, Inference (name', _, _) :: post) =>
|
blanchet@39619
|
573 |
pre @ map (replace_dependencies_in_line (name', [name])) post
|
blanchet@40250
|
574 |
| _ => raise Fail "unexpected inference"
|
blanchet@39616
|
575 |
else if is_conjecture conjecture_shape name then
|
blanchet@43477
|
576 |
Inference (name, s_not t, []) :: lines
|
blanchet@36482
|
577 |
else
|
blanchet@39619
|
578 |
map (replace_dependencies_in_line (name, [])) lines
|
blanchet@44175
|
579 |
| add_line _ _ (Inference (name, t, deps)) lines =
|
blanchet@36482
|
580 |
(* Type information will be deleted later; skip repetition test. *)
|
blanchet@36482
|
581 |
if is_only_type_information t then
|
blanchet@39614
|
582 |
Inference (name, t, deps) :: lines
|
blanchet@36482
|
583 |
(* Is there a repetition? If so, replace later line by earlier one. *)
|
blanchet@38281
|
584 |
else case take_prefix (not o is_same_inference t) lines of
|
blanchet@36482
|
585 |
(* FIXME: Doesn't this code risk conflating proofs involving different
|
blanchet@38281
|
586 |
types? *)
|
blanchet@39614
|
587 |
(_, []) => Inference (name, t, deps) :: lines
|
blanchet@39614
|
588 |
| (pre, Inference (name', t', _) :: post) =>
|
blanchet@39614
|
589 |
Inference (name, t', deps) ::
|
blanchet@39619
|
590 |
pre @ map (replace_dependencies_in_line (name', [name])) post
|
blanchet@40250
|
591 |
| _ => raise Fail "unexpected inference"
|
paulson@22044
|
592 |
|
blanchet@36482
|
593 |
(* Recursively delete empty lines (type information) from the proof. *)
|
blanchet@39614
|
594 |
fun add_nontrivial_line (Inference (name, t, [])) lines =
|
blanchet@39619
|
595 |
if is_only_type_information t then delete_dependency name lines
|
blanchet@39614
|
596 |
else Inference (name, t, []) :: lines
|
blanchet@36482
|
597 |
| add_nontrivial_line line lines = line :: lines
|
blanchet@39619
|
598 |
and delete_dependency name lines =
|
blanchet@39619
|
599 |
fold_rev add_nontrivial_line
|
blanchet@39619
|
600 |
(map (replace_dependencies_in_line (name, [])) lines) []
|
paulson@22470
|
601 |
|
blanchet@37320
|
602 |
(* ATPs sometimes reuse free variable names in the strangest ways. Removing
|
blanchet@37320
|
603 |
offending lines often does the trick. *)
|
blanchet@36558
|
604 |
fun is_bad_free frees (Free x) = not (member (op =) frees x)
|
blanchet@36558
|
605 |
| is_bad_free _ _ = false
|
paulson@22731
|
606 |
|
blanchet@44175
|
607 |
fun add_desired_line _ _ _ _ (line as Definition (name, _, _)) (j, lines) =
|
blanchet@39619
|
608 |
(j, line :: map (replace_dependencies_in_line (name, [])) lines)
|
blanchet@44175
|
609 |
| add_desired_line isar_shrink_factor conjecture_shape fact_names frees
|
blanchet@44175
|
610 |
(Inference (name, t, deps)) (j, lines) =
|
blanchet@36402
|
611 |
(j + 1,
|
blanchet@44175
|
612 |
if is_fact fact_names name orelse is_conjecture conjecture_shape name orelse
|
blanchet@39619
|
613 |
(* the last line must be kept *)
|
blanchet@39619
|
614 |
j = 0 orelse
|
blanchet@36568
|
615 |
(not (is_only_type_information t) andalso
|
blanchet@36568
|
616 |
null (Term.add_tvars t []) andalso
|
blanchet@36568
|
617 |
not (exists_subterm (is_bad_free frees) t) andalso
|
blanchet@39619
|
618 |
length deps >= 2 andalso j mod isar_shrink_factor = 0 andalso
|
blanchet@39619
|
619 |
(* kill next to last line, which usually results in a trivial step *)
|
blanchet@39619
|
620 |
j <> 1) then
|
blanchet@39614
|
621 |
Inference (name, t, deps) :: lines (* keep line *)
|
blanchet@36402
|
622 |
else
|
blanchet@39619
|
623 |
map (replace_dependencies_in_line (name, deps)) lines) (* drop line *)
|
paulson@21978
|
624 |
|
blanchet@36482
|
625 |
(** Isar proof construction and manipulation **)
|
blanchet@36482
|
626 |
|
blanchet@36482
|
627 |
fun merge_fact_sets (ls1, ss1) (ls2, ss2) =
|
blanchet@36482
|
628 |
(union (op =) ls1 ls2, union (op =) ss1 ss2)
|
blanchet@36402
|
629 |
|
blanchet@36402
|
630 |
type label = string * int
|
blanchet@36402
|
631 |
type facts = label list * string list
|
blanchet@36402
|
632 |
|
blanchet@39692
|
633 |
datatype isar_qualifier = Show | Then | Moreover | Ultimately
|
blanchet@36402
|
634 |
|
blanchet@39692
|
635 |
datatype isar_step =
|
blanchet@36474
|
636 |
Fix of (string * typ) list |
|
blanchet@36482
|
637 |
Let of term * term |
|
blanchet@36402
|
638 |
Assume of label * term |
|
blanchet@39692
|
639 |
Have of isar_qualifier list * label * term * byline
|
blanchet@36402
|
640 |
and byline =
|
blanchet@36562
|
641 |
ByMetis of facts |
|
blanchet@39692
|
642 |
CaseSplit of isar_step list list * facts
|
blanchet@36402
|
643 |
|
blanchet@36572
|
644 |
fun smart_case_split [] facts = ByMetis facts
|
blanchet@36572
|
645 |
| smart_case_split proofs facts = CaseSplit (proofs, facts)
|
blanchet@36572
|
646 |
|
blanchet@44175
|
647 |
fun add_fact_from_dependency conjecture_shape facts_offset fact_names name =
|
blanchet@44175
|
648 |
if is_fact fact_names name then
|
blanchet@44175
|
649 |
apsnd (union (op =) (map fst (resolve_fact facts_offset fact_names name)))
|
blanchet@36471
|
650 |
else
|
blanchet@39616
|
651 |
apfst (insert (op =) (raw_label_for_name conjecture_shape name))
|
blanchet@36402
|
652 |
|
blanchet@44175
|
653 |
fun step_for_line _ _ _ _ (Definition (_, t1, t2)) = Let (t1, t2)
|
blanchet@44175
|
654 |
| step_for_line conjecture_shape _ _ _ (Inference (name, t, [])) =
|
blanchet@39616
|
655 |
Assume (raw_label_for_name conjecture_shape name, t)
|
blanchet@44175
|
656 |
| step_for_line conjecture_shape facts_offset fact_names j
|
blanchet@44175
|
657 |
(Inference (name, t, deps)) =
|
blanchet@39616
|
658 |
Have (if j = 1 then [Show] else [],
|
blanchet@39671
|
659 |
raw_label_for_name conjecture_shape name,
|
blanchet@39671
|
660 |
fold_rev forall_of (map Var (Term.add_vars t [])) t,
|
blanchet@44175
|
661 |
ByMetis (fold (add_fact_from_dependency conjecture_shape facts_offset
|
blanchet@44175
|
662 |
fact_names)
|
blanchet@39619
|
663 |
deps ([], [])))
|
blanchet@36291
|
664 |
|
blanchet@39694
|
665 |
fun repair_name "$true" = "c_True"
|
blanchet@39694
|
666 |
| repair_name "$false" = "c_False"
|
blanchet@43841
|
667 |
| repair_name "$$e" = tptp_equal (* seen in Vampire proofs *)
|
blanchet@39694
|
668 |
| repair_name s =
|
blanchet@43841
|
669 |
if is_tptp_equal s orelse
|
blanchet@43841
|
670 |
(* seen in Vampire proofs *)
|
blanchet@43841
|
671 |
(String.isPrefix "sQ" s andalso String.isSuffix "_eqProxy" s) then
|
blanchet@43841
|
672 |
tptp_equal
|
blanchet@39694
|
673 |
else
|
blanchet@39694
|
674 |
s
|
blanchet@39694
|
675 |
|
blanchet@44175
|
676 |
fun isar_proof_from_atp_proof pool ctxt isar_shrink_factor conjecture_shape
|
blanchet@44175
|
677 |
facts_offset fact_names sym_tab params frees atp_proof =
|
wenzelm@33318
|
678 |
let
|
blanchet@36482
|
679 |
val lines =
|
blanchet@43320
|
680 |
atp_proof
|
blanchet@43809
|
681 |
|> clean_up_atp_proof_dependencies
|
blanchet@39694
|
682 |
|> nasty_atp_proof pool
|
blanchet@39694
|
683 |
|> map_term_names_in_atp_proof repair_name
|
blanchet@43976
|
684 |
|> decode_lines ctxt sym_tab
|
blanchet@44175
|
685 |
|> rpair [] |-> fold_rev (add_line conjecture_shape fact_names)
|
blanchet@36482
|
686 |
|> rpair [] |-> fold_rev add_nontrivial_line
|
blanchet@43518
|
687 |
|> rpair (0, [])
|
blanchet@44175
|
688 |
|-> fold_rev (add_desired_line isar_shrink_factor conjecture_shape
|
blanchet@44175
|
689 |
fact_names frees)
|
blanchet@36482
|
690 |
|> snd
|
blanchet@36402
|
691 |
in
|
blanchet@36901
|
692 |
(if null params then [] else [Fix params]) @
|
blanchet@44175
|
693 |
map2 (step_for_line conjecture_shape facts_offset fact_names)
|
blanchet@43412
|
694 |
(length lines downto 1) lines
|
blanchet@36402
|
695 |
end
|
blanchet@36402
|
696 |
|
blanchet@36402
|
697 |
(* When redirecting proofs, we keep information about the labels seen so far in
|
blanchet@36402
|
698 |
the "backpatches" data structure. The first component indicates which facts
|
blanchet@36402
|
699 |
should be associated with forthcoming proof steps. The second component is a
|
blanchet@37319
|
700 |
pair ("assum_ls", "drop_ls"), where "assum_ls" are the labels that should
|
blanchet@37319
|
701 |
become assumptions and "drop_ls" are the labels that should be dropped in a
|
blanchet@37319
|
702 |
case split. *)
|
blanchet@36402
|
703 |
type backpatches = (label * facts) list * (label list * label list)
|
blanchet@36402
|
704 |
|
blanchet@36554
|
705 |
fun used_labels_of_step (Have (_, _, _, by)) =
|
blanchet@36402
|
706 |
(case by of
|
blanchet@36562
|
707 |
ByMetis (ls, _) => ls
|
blanchet@36554
|
708 |
| CaseSplit (proofs, (ls, _)) =>
|
blanchet@36554
|
709 |
fold (union (op =) o used_labels_of) proofs ls)
|
blanchet@36554
|
710 |
| used_labels_of_step _ = []
|
blanchet@36554
|
711 |
and used_labels_of proof = fold (union (op =) o used_labels_of_step) proof []
|
blanchet@36402
|
712 |
|
blanchet@36402
|
713 |
fun new_labels_of_step (Fix _) = []
|
blanchet@36482
|
714 |
| new_labels_of_step (Let _) = []
|
blanchet@36402
|
715 |
| new_labels_of_step (Assume (l, _)) = [l]
|
blanchet@36402
|
716 |
| new_labels_of_step (Have (_, l, _, _)) = [l]
|
blanchet@36402
|
717 |
val new_labels_of = maps new_labels_of_step
|
blanchet@36402
|
718 |
|
blanchet@36402
|
719 |
val join_proofs =
|
blanchet@36402
|
720 |
let
|
blanchet@36402
|
721 |
fun aux _ [] = NONE
|
blanchet@36402
|
722 |
| aux proof_tail (proofs as (proof1 :: _)) =
|
blanchet@36402
|
723 |
if exists null proofs then
|
blanchet@36402
|
724 |
NONE
|
blanchet@36402
|
725 |
else if forall (curry (op =) (hd proof1) o hd) (tl proofs) then
|
blanchet@36402
|
726 |
aux (hd proof1 :: proof_tail) (map tl proofs)
|
blanchet@36402
|
727 |
else case hd proof1 of
|
blanchet@37498
|
728 |
Have ([], l, t, _) => (* FIXME: should we really ignore the "by"? *)
|
blanchet@36402
|
729 |
if forall (fn Have ([], l', t', _) :: _ => (l, t) = (l', t')
|
blanchet@36402
|
730 |
| _ => false) (tl proofs) andalso
|
blanchet@36402
|
731 |
not (exists (member (op =) (maps new_labels_of proofs))
|
blanchet@36554
|
732 |
(used_labels_of proof_tail)) then
|
blanchet@36402
|
733 |
SOME (l, t, map rev proofs, proof_tail)
|
blanchet@36402
|
734 |
else
|
blanchet@36402
|
735 |
NONE
|
blanchet@36402
|
736 |
| _ => NONE
|
blanchet@36402
|
737 |
in aux [] o map rev end
|
blanchet@36402
|
738 |
|
blanchet@36402
|
739 |
fun case_split_qualifiers proofs =
|
blanchet@36402
|
740 |
case length proofs of
|
blanchet@36402
|
741 |
0 => []
|
blanchet@36402
|
742 |
| 1 => [Then]
|
blanchet@36402
|
743 |
| _ => [Ultimately]
|
blanchet@36402
|
744 |
|
blanchet@39618
|
745 |
fun redirect_proof hyp_ts concl_t proof =
|
blanchet@36402
|
746 |
let
|
blanchet@37321
|
747 |
(* The first pass outputs those steps that are independent of the negated
|
blanchet@37321
|
748 |
conjecture. The second pass flips the proof by contradiction to obtain a
|
blanchet@37321
|
749 |
direct proof, introducing case splits when an inference depends on
|
blanchet@37321
|
750 |
several facts that depend on the negated conjecture. *)
|
blanchet@39618
|
751 |
val concl_l = (conjecture_prefix, length hyp_ts)
|
blanchet@38286
|
752 |
fun first_pass ([], contra) = ([], contra)
|
blanchet@38286
|
753 |
| first_pass ((step as Fix _) :: proof, contra) =
|
blanchet@38286
|
754 |
first_pass (proof, contra) |>> cons step
|
blanchet@38286
|
755 |
| first_pass ((step as Let _) :: proof, contra) =
|
blanchet@38286
|
756 |
first_pass (proof, contra) |>> cons step
|
blanchet@39616
|
757 |
| first_pass ((step as Assume (l as (_, j), _)) :: proof, contra) =
|
blanchet@39618
|
758 |
if l = concl_l then first_pass (proof, contra ||> cons step)
|
blanchet@39618
|
759 |
else first_pass (proof, contra) |>> cons (Assume (l, nth hyp_ts j))
|
blanchet@38286
|
760 |
| first_pass (Have (qs, l, t, ByMetis (ls, ss)) :: proof, contra) =
|
blanchet@39618
|
761 |
let val step = Have (qs, l, t, ByMetis (ls, ss)) in
|
blanchet@38286
|
762 |
if exists (member (op =) (fst contra)) ls then
|
blanchet@38286
|
763 |
first_pass (proof, contra |>> cons l ||> cons step)
|
blanchet@38286
|
764 |
else
|
blanchet@38286
|
765 |
first_pass (proof, contra) |>> cons step
|
blanchet@38286
|
766 |
end
|
blanchet@38286
|
767 |
| first_pass _ = raise Fail "malformed proof"
|
blanchet@36402
|
768 |
val (proof_top, (contra_ls, contra_proof)) =
|
blanchet@39618
|
769 |
first_pass (proof, ([concl_l], []))
|
blanchet@36402
|
770 |
val backpatch_label = the_default ([], []) oo AList.lookup (op =) o fst
|
blanchet@36402
|
771 |
fun backpatch_labels patches ls =
|
blanchet@36402
|
772 |
fold merge_fact_sets (map (backpatch_label patches) ls) ([], [])
|
blanchet@36402
|
773 |
fun second_pass end_qs ([], assums, patches) =
|
blanchet@37321
|
774 |
([Have (end_qs, no_label, concl_t,
|
blanchet@36562
|
775 |
ByMetis (backpatch_labels patches (map snd assums)))], patches)
|
blanchet@36402
|
776 |
| second_pass end_qs (Assume (l, t) :: proof, assums, patches) =
|
blanchet@36402
|
777 |
second_pass end_qs (proof, (t, l) :: assums, patches)
|
blanchet@36562
|
778 |
| second_pass end_qs (Have (qs, l, t, ByMetis (ls, ss)) :: proof, assums,
|
blanchet@36402
|
779 |
patches) =
|
blanchet@39619
|
780 |
(if member (op =) (snd (snd patches)) l andalso
|
blanchet@39619
|
781 |
not (member (op =) (fst (snd patches)) l) andalso
|
blanchet@39619
|
782 |
not (AList.defined (op =) (fst patches) l) then
|
blanchet@39619
|
783 |
second_pass end_qs (proof, assums, patches ||> apsnd (append ls))
|
blanchet@39619
|
784 |
else case List.partition (member (op =) contra_ls) ls of
|
blanchet@39619
|
785 |
([contra_l], co_ls) =>
|
blanchet@39619
|
786 |
if member (op =) qs Show then
|
blanchet@39619
|
787 |
second_pass end_qs (proof, assums,
|
blanchet@39619
|
788 |
patches |>> cons (contra_l, (co_ls, ss)))
|
blanchet@39619
|
789 |
else
|
blanchet@39619
|
790 |
second_pass end_qs
|
blanchet@39619
|
791 |
(proof, assums,
|
blanchet@39619
|
792 |
patches |>> cons (contra_l, (l :: co_ls, ss)))
|
blanchet@39619
|
793 |
|>> cons (if member (op =) (fst (snd patches)) l then
|
blanchet@43477
|
794 |
Assume (l, s_not t)
|
blanchet@39619
|
795 |
else
|
blanchet@43477
|
796 |
Have (qs, l, s_not t,
|
blanchet@39619
|
797 |
ByMetis (backpatch_label patches l)))
|
blanchet@39619
|
798 |
| (contra_ls as _ :: _, co_ls) =>
|
blanchet@39619
|
799 |
let
|
blanchet@39619
|
800 |
val proofs =
|
blanchet@39619
|
801 |
map_filter
|
blanchet@39619
|
802 |
(fn l =>
|
blanchet@39619
|
803 |
if l = concl_l then
|
blanchet@39619
|
804 |
NONE
|
blanchet@39619
|
805 |
else
|
blanchet@39619
|
806 |
let
|
blanchet@39619
|
807 |
val drop_ls = filter (curry (op <>) l) contra_ls
|
blanchet@39619
|
808 |
in
|
blanchet@39619
|
809 |
second_pass []
|
blanchet@39619
|
810 |
(proof, assums,
|
blanchet@39619
|
811 |
patches ||> apfst (insert (op =) l)
|
blanchet@39619
|
812 |
||> apsnd (union (op =) drop_ls))
|
blanchet@39619
|
813 |
|> fst |> SOME
|
blanchet@39619
|
814 |
end) contra_ls
|
blanchet@39619
|
815 |
val (assumes, facts) =
|
blanchet@39619
|
816 |
if member (op =) (fst (snd patches)) l then
|
blanchet@43477
|
817 |
([Assume (l, s_not t)], (l :: co_ls, ss))
|
blanchet@39619
|
818 |
else
|
blanchet@39619
|
819 |
([], (co_ls, ss))
|
blanchet@39619
|
820 |
in
|
blanchet@39619
|
821 |
(case join_proofs proofs of
|
blanchet@39619
|
822 |
SOME (l, t, proofs, proof_tail) =>
|
blanchet@39619
|
823 |
Have (case_split_qualifiers proofs @
|
blanchet@39619
|
824 |
(if null proof_tail then end_qs else []), l, t,
|
blanchet@39619
|
825 |
smart_case_split proofs facts) :: proof_tail
|
blanchet@39619
|
826 |
| NONE =>
|
blanchet@39619
|
827 |
[Have (case_split_qualifiers proofs @ end_qs, no_label,
|
blanchet@39619
|
828 |
concl_t, smart_case_split proofs facts)],
|
blanchet@39619
|
829 |
patches)
|
blanchet@39619
|
830 |
|>> append assumes
|
blanchet@39619
|
831 |
end
|
blanchet@39619
|
832 |
| _ => raise Fail "malformed proof")
|
blanchet@36402
|
833 |
| second_pass _ _ = raise Fail "malformed proof"
|
blanchet@36482
|
834 |
val proof_bottom =
|
blanchet@36482
|
835 |
second_pass [Show] (contra_proof, [], ([], ([], []))) |> fst
|
blanchet@36402
|
836 |
in proof_top @ proof_bottom end
|
blanchet@36402
|
837 |
|
blanchet@38715
|
838 |
(* FIXME: Still needed? Probably not. *)
|
blanchet@36402
|
839 |
val kill_duplicate_assumptions_in_proof =
|
blanchet@36402
|
840 |
let
|
blanchet@36402
|
841 |
fun relabel_facts subst =
|
blanchet@36402
|
842 |
apfst (map (fn l => AList.lookup (op =) subst l |> the_default l))
|
blanchet@36487
|
843 |
fun do_step (step as Assume (l, t)) (proof, subst, assums) =
|
blanchet@36402
|
844 |
(case AList.lookup (op aconv) assums t of
|
blanchet@36960
|
845 |
SOME l' => (proof, (l, l') :: subst, assums)
|
blanchet@36487
|
846 |
| NONE => (step :: proof, subst, (t, l) :: assums))
|
blanchet@36402
|
847 |
| do_step (Have (qs, l, t, by)) (proof, subst, assums) =
|
blanchet@36402
|
848 |
(Have (qs, l, t,
|
blanchet@36402
|
849 |
case by of
|
blanchet@36562
|
850 |
ByMetis facts => ByMetis (relabel_facts subst facts)
|
blanchet@36402
|
851 |
| CaseSplit (proofs, facts) =>
|
blanchet@36402
|
852 |
CaseSplit (map do_proof proofs, relabel_facts subst facts)) ::
|
blanchet@36402
|
853 |
proof, subst, assums)
|
blanchet@36487
|
854 |
| do_step step (proof, subst, assums) = (step :: proof, subst, assums)
|
blanchet@36402
|
855 |
and do_proof proof = fold do_step proof ([], [], []) |> #1 |> rev
|
blanchet@36402
|
856 |
in do_proof end
|
blanchet@36402
|
857 |
|
blanchet@36402
|
858 |
val then_chain_proof =
|
blanchet@36402
|
859 |
let
|
blanchet@36402
|
860 |
fun aux _ [] = []
|
blanchet@36487
|
861 |
| aux _ ((step as Assume (l, _)) :: proof) = step :: aux l proof
|
blanchet@36402
|
862 |
| aux l' (Have (qs, l, t, by) :: proof) =
|
blanchet@36402
|
863 |
(case by of
|
blanchet@36562
|
864 |
ByMetis (ls, ss) =>
|
blanchet@36402
|
865 |
Have (if member (op =) ls l' then
|
blanchet@36402
|
866 |
(Then :: qs, l, t,
|
blanchet@36562
|
867 |
ByMetis (filter_out (curry (op =) l') ls, ss))
|
blanchet@36402
|
868 |
else
|
blanchet@36562
|
869 |
(qs, l, t, ByMetis (ls, ss)))
|
blanchet@36402
|
870 |
| CaseSplit (proofs, facts) =>
|
blanchet@36402
|
871 |
Have (qs, l, t, CaseSplit (map (aux no_label) proofs, facts))) ::
|
blanchet@36402
|
872 |
aux l proof
|
blanchet@36487
|
873 |
| aux _ (step :: proof) = step :: aux no_label proof
|
blanchet@36402
|
874 |
in aux no_label end
|
blanchet@36402
|
875 |
|
blanchet@36402
|
876 |
fun kill_useless_labels_in_proof proof =
|
blanchet@36402
|
877 |
let
|
blanchet@36554
|
878 |
val used_ls = used_labels_of proof
|
blanchet@36402
|
879 |
fun do_label l = if member (op =) used_ls l then l else no_label
|
blanchet@36554
|
880 |
fun do_step (Assume (l, t)) = Assume (do_label l, t)
|
blanchet@36554
|
881 |
| do_step (Have (qs, l, t, by)) =
|
blanchet@36402
|
882 |
Have (qs, do_label l, t,
|
blanchet@36402
|
883 |
case by of
|
blanchet@36402
|
884 |
CaseSplit (proofs, facts) =>
|
blanchet@36554
|
885 |
CaseSplit (map (map do_step) proofs, facts)
|
blanchet@36402
|
886 |
| _ => by)
|
blanchet@36554
|
887 |
| do_step step = step
|
blanchet@36554
|
888 |
in map do_step proof end
|
blanchet@36402
|
889 |
|
blanchet@36402
|
890 |
fun prefix_for_depth n = replicate_string (n + 1)
|
blanchet@36402
|
891 |
|
blanchet@36402
|
892 |
val relabel_proof =
|
blanchet@36402
|
893 |
let
|
blanchet@36402
|
894 |
fun aux _ _ _ [] = []
|
blanchet@36402
|
895 |
| aux subst depth (next_assum, next_fact) (Assume (l, t) :: proof) =
|
blanchet@36402
|
896 |
if l = no_label then
|
blanchet@36402
|
897 |
Assume (l, t) :: aux subst depth (next_assum, next_fact) proof
|
blanchet@36402
|
898 |
else
|
blanchet@36402
|
899 |
let val l' = (prefix_for_depth depth assum_prefix, next_assum) in
|
blanchet@36402
|
900 |
Assume (l', t) ::
|
blanchet@36402
|
901 |
aux ((l, l') :: subst) depth (next_assum + 1, next_fact) proof
|
blanchet@36402
|
902 |
end
|
blanchet@36402
|
903 |
| aux subst depth (next_assum, next_fact) (Have (qs, l, t, by) :: proof) =
|
blanchet@36402
|
904 |
let
|
blanchet@36402
|
905 |
val (l', subst, next_fact) =
|
blanchet@36402
|
906 |
if l = no_label then
|
blanchet@36402
|
907 |
(l, subst, next_fact)
|
blanchet@36402
|
908 |
else
|
blanchet@36402
|
909 |
let
|
blanchet@43051
|
910 |
val l' = (prefix_for_depth depth have_prefix, next_fact)
|
blanchet@36402
|
911 |
in (l', (l, l') :: subst, next_fact + 1) end
|
blanchet@36568
|
912 |
val relabel_facts =
|
blanchet@39616
|
913 |
apfst (maps (the_list o AList.lookup (op =) subst))
|
blanchet@36402
|
914 |
val by =
|
blanchet@36402
|
915 |
case by of
|
blanchet@36562
|
916 |
ByMetis facts => ByMetis (relabel_facts facts)
|
blanchet@36402
|
917 |
| CaseSplit (proofs, facts) =>
|
blanchet@36402
|
918 |
CaseSplit (map (aux subst (depth + 1) (1, 1)) proofs,
|
blanchet@36402
|
919 |
relabel_facts facts)
|
blanchet@36402
|
920 |
in
|
blanchet@36402
|
921 |
Have (qs, l', t, by) ::
|
blanchet@36402
|
922 |
aux subst depth (next_assum, next_fact) proof
|
blanchet@36402
|
923 |
end
|
blanchet@36487
|
924 |
| aux subst depth nextp (step :: proof) =
|
blanchet@36487
|
925 |
step :: aux subst depth nextp proof
|
blanchet@36402
|
926 |
in aux [] 0 (1, 1) end
|
blanchet@36402
|
927 |
|
blanchet@43750
|
928 |
fun string_for_proof ctxt0 full_types i n =
|
blanchet@36402
|
929 |
let
|
blanchet@43626
|
930 |
val ctxt =
|
blanchet@43626
|
931 |
ctxt0 |> Config.put show_free_types false
|
blanchet@43626
|
932 |
|> Config.put show_types true
|
blanchet@43626
|
933 |
|> Config.put show_sorts true
|
blanchet@37316
|
934 |
fun fix_print_mode f x =
|
wenzelm@39393
|
935 |
Print_Mode.setmp (filter (curry (op =) Symbol.xsymbolsN)
|
wenzelm@39393
|
936 |
(print_mode_value ())) f x
|
blanchet@36402
|
937 |
fun do_indent ind = replicate_string (ind * indent_size) " "
|
blanchet@36474
|
938 |
fun do_free (s, T) =
|
blanchet@36474
|
939 |
maybe_quote s ^ " :: " ^
|
blanchet@36474
|
940 |
maybe_quote (fix_print_mode (Syntax.string_of_typ ctxt) T)
|
blanchet@36568
|
941 |
fun do_label l = if l = no_label then "" else string_for_label l ^ ": "
|
blanchet@36402
|
942 |
fun do_have qs =
|
blanchet@36402
|
943 |
(if member (op =) qs Moreover then "moreover " else "") ^
|
blanchet@36402
|
944 |
(if member (op =) qs Ultimately then "ultimately " else "") ^
|
blanchet@36402
|
945 |
(if member (op =) qs Then then
|
blanchet@36402
|
946 |
if member (op =) qs Show then "thus" else "hence"
|
blanchet@36402
|
947 |
else
|
blanchet@36402
|
948 |
if member (op =) qs Show then "show" else "have")
|
blanchet@36474
|
949 |
val do_term = maybe_quote o fix_print_mode (Syntax.string_of_term ctxt)
|
blanchet@44069
|
950 |
val reconstructor = if full_types then Metis_Full_Types else Metis
|
blanchet@36568
|
951 |
fun do_facts (ls, ss) =
|
blanchet@43874
|
952 |
reconstructor_command reconstructor 1 1
|
blanchet@43874
|
953 |
(ls |> sort_distinct (prod_ord string_ord int_ord),
|
blanchet@43874
|
954 |
ss |> sort_distinct string_ord)
|
blanchet@36474
|
955 |
and do_step ind (Fix xs) =
|
blanchet@36474
|
956 |
do_indent ind ^ "fix " ^ space_implode " and " (map do_free xs) ^ "\n"
|
blanchet@36482
|
957 |
| do_step ind (Let (t1, t2)) =
|
blanchet@36482
|
958 |
do_indent ind ^ "let " ^ do_term t1 ^ " = " ^ do_term t2 ^ "\n"
|
blanchet@36402
|
959 |
| do_step ind (Assume (l, t)) =
|
blanchet@36402
|
960 |
do_indent ind ^ "assume " ^ do_label l ^ do_term t ^ "\n"
|
blanchet@36562
|
961 |
| do_step ind (Have (qs, l, t, ByMetis facts)) =
|
blanchet@36402
|
962 |
do_indent ind ^ do_have qs ^ " " ^
|
blanchet@36475
|
963 |
do_label l ^ do_term t ^ " " ^ do_facts facts ^ "\n"
|
blanchet@36402
|
964 |
| do_step ind (Have (qs, l, t, CaseSplit (proofs, facts))) =
|
blanchet@36402
|
965 |
space_implode (do_indent ind ^ "moreover\n")
|
blanchet@36402
|
966 |
(map (do_block ind) proofs) ^
|
blanchet@36475
|
967 |
do_indent ind ^ do_have qs ^ " " ^ do_label l ^ do_term t ^ " " ^
|
blanchet@36474
|
968 |
do_facts facts ^ "\n"
|
blanchet@36402
|
969 |
and do_steps prefix suffix ind steps =
|
blanchet@36402
|
970 |
let val s = implode (map (do_step ind) steps) in
|
blanchet@36402
|
971 |
replicate_string (ind * indent_size - size prefix) " " ^ prefix ^
|
blanchet@36402
|
972 |
String.extract (s, ind * indent_size,
|
blanchet@36402
|
973 |
SOME (size s - ind * indent_size - 1)) ^
|
blanchet@36402
|
974 |
suffix ^ "\n"
|
blanchet@36402
|
975 |
end
|
blanchet@36402
|
976 |
and do_block ind proof = do_steps "{ " " }" (ind + 1) proof
|
blanchet@36562
|
977 |
(* One-step proofs are pointless; better use the Metis one-liner
|
blanchet@36562
|
978 |
directly. *)
|
blanchet@36562
|
979 |
and do_proof [Have (_, _, _, ByMetis _)] = ""
|
blanchet@36562
|
980 |
| do_proof proof =
|
blanchet@36476
|
981 |
(if i <> 1 then "prefer " ^ string_of_int i ^ "\n" else "") ^
|
blanchet@39692
|
982 |
do_indent 0 ^ "proof -\n" ^ do_steps "" "" 1 proof ^ do_indent 0 ^
|
blanchet@39692
|
983 |
(if n <> 1 then "next" else "qed")
|
blanchet@36484
|
984 |
in do_proof end
|
blanchet@36402
|
985 |
|
blanchet@43903
|
986 |
fun isar_proof_text ctxt isar_proof_requested
|
blanchet@44175
|
987 |
(debug, full_types, isar_shrink_factor, pool, conjecture_shape,
|
blanchet@44175
|
988 |
facts_offset, fact_names, sym_tab, atp_proof, goal)
|
blanchet@43878
|
989 |
(one_line_params as (_, _, _, _, subgoal, subgoal_count)) =
|
blanchet@36402
|
990 |
let
|
blanchet@43903
|
991 |
val isar_shrink_factor =
|
blanchet@43903
|
992 |
(if isar_proof_requested then 1 else 2) * isar_shrink_factor
|
blanchet@43878
|
993 |
val (params, hyp_ts, concl_t) = strip_subgoal ctxt goal subgoal
|
blanchet@36901
|
994 |
val frees = fold Term.add_frees (concl_t :: hyp_ts) []
|
blanchet@43874
|
995 |
val one_line_proof = one_line_proof_text one_line_params
|
blanchet@36283
|
996 |
fun isar_proof_for () =
|
blanchet@43874
|
997 |
case atp_proof
|
blanchet@44175
|
998 |
|> isar_proof_from_atp_proof pool ctxt isar_shrink_factor
|
blanchet@43976
|
999 |
conjecture_shape facts_offset fact_names sym_tab params frees
|
blanchet@39618
|
1000 |
|> redirect_proof hyp_ts concl_t
|
blanchet@36402
|
1001 |
|> kill_duplicate_assumptions_in_proof
|
blanchet@36402
|
1002 |
|> then_chain_proof
|
blanchet@36402
|
1003 |
|> kill_useless_labels_in_proof
|
blanchet@36402
|
1004 |
|> relabel_proof
|
blanchet@43878
|
1005 |
|> string_for_proof ctxt full_types subgoal subgoal_count of
|
blanchet@43903
|
1006 |
"" =>
|
blanchet@43903
|
1007 |
if isar_proof_requested then
|
blanchet@43903
|
1008 |
"\nNo structured proof available (proof too short)."
|
blanchet@43903
|
1009 |
else
|
blanchet@43903
|
1010 |
""
|
blanchet@43903
|
1011 |
| proof =>
|
blanchet@43903
|
1012 |
"\n\n" ^ (if isar_proof_requested then "Structured proof"
|
blanchet@43903
|
1013 |
else "Perhaps this will work") ^
|
blanchet@43903
|
1014 |
":\n" ^ Markup.markup Markup.sendback proof
|
blanchet@35868
|
1015 |
val isar_proof =
|
blanchet@36402
|
1016 |
if debug then
|
blanchet@36283
|
1017 |
isar_proof_for ()
|
blanchet@36283
|
1018 |
else
|
blanchet@43903
|
1019 |
case try isar_proof_for () of
|
blanchet@43903
|
1020 |
SOME s => s
|
blanchet@43903
|
1021 |
| NONE => if isar_proof_requested then
|
blanchet@43903
|
1022 |
"\nWarning: The Isar proof construction failed."
|
blanchet@43903
|
1023 |
else
|
blanchet@43903
|
1024 |
""
|
blanchet@43874
|
1025 |
in one_line_proof ^ isar_proof end
|
immler@31038
|
1026 |
|
blanchet@43874
|
1027 |
fun proof_text ctxt isar_proof isar_params
|
blanchet@43874
|
1028 |
(one_line_params as (preplay, _, _, _, _, _)) =
|
blanchet@44007
|
1029 |
(if case preplay of Failed_to_Play _ => true | _ => isar_proof then
|
blanchet@43903
|
1030 |
isar_proof_text ctxt isar_proof isar_params
|
blanchet@43874
|
1031 |
else
|
blanchet@43874
|
1032 |
one_line_proof_text) one_line_params
|
blanchet@36223
|
1033 |
|
immler@31038
|
1034 |
end;
|