src/HOL/Tools/Sledgehammer/sledgehammer_proof_reconstruct.ML
author blanchet
Tue Jul 27 19:17:15 2010 +0200 (2010-07-27)
changeset 38027 505657ddb047
parent 38019 e207a64e1e0b
child 38028 22dcaec5fa77
permissions -rw-r--r--
standardize "Author" tags
blanchet@35826
     1
(*  Title:      HOL/Tools/Sledgehammer/sledgehammer_proof_reconstruct.ML
blanchet@38027
     2
    Author:     Lawrence C. Paulson, Cambridge University Computer Laboratory
blanchet@38027
     3
    Author:     Claire Quigley, Cambridge University Computer Laboratory
blanchet@36392
     4
    Author:     Jasmin Blanchette, TU Muenchen
paulson@21978
     5
wenzelm@33310
     6
Transfer of proofs from external provers.
wenzelm@33310
     7
*)
wenzelm@33310
     8
blanchet@35826
     9
signature SLEDGEHAMMER_PROOF_RECONSTRUCT =
paulson@24425
    10
sig
blanchet@36281
    11
  type minimize_command = string list -> string
blanchet@36281
    12
blanchet@37479
    13
  val metis_line: bool -> int -> int -> string list -> string
blanchet@36223
    14
  val metis_proof_text:
blanchet@37479
    15
    bool * minimize_command * string * string vector * thm * int
blanchet@36281
    16
    -> string * string list
blanchet@36223
    17
  val isar_proof_text:
blanchet@37996
    18
    string Symtab.table * bool * int * Proof.context * int list
blanchet@37479
    19
    -> bool * minimize_command * string * string vector * thm * int
blanchet@36287
    20
    -> string * string list
blanchet@36223
    21
  val proof_text:
blanchet@37996
    22
    bool -> string Symtab.table * bool * int * Proof.context * int list
blanchet@37479
    23
    -> bool * minimize_command * string * string vector * thm * int
blanchet@36287
    24
    -> string * string list
paulson@24425
    25
end;
paulson@21978
    26
blanchet@35826
    27
structure Sledgehammer_Proof_Reconstruct : SLEDGEHAMMER_PROOF_RECONSTRUCT =
paulson@21978
    28
struct
paulson@21978
    29
blanchet@37578
    30
open Metis_Clauses
blanchet@36478
    31
open Sledgehammer_Util
blanchet@37616
    32
open Sledgehammer_Fact_Filter
blanchet@38019
    33
open ATP_Problem
paulson@21978
    34
blanchet@36281
    35
type minimize_command = string list -> string
blanchet@36281
    36
blanchet@38014
    37
(* Simple simplifications to ensure that sort annotations don't leave a trail of
blanchet@38014
    38
   spurious "True"s. *)
blanchet@38014
    39
fun s_not @{const False} = @{const True}
blanchet@38014
    40
  | s_not @{const True} = @{const False}
blanchet@38014
    41
  | s_not (@{const Not} $ t) = t
blanchet@38014
    42
  | s_not t = @{const Not} $ t
blanchet@38014
    43
fun s_conj (@{const True}, t2) = t2
blanchet@38014
    44
  | s_conj (t1, @{const True}) = t1
blanchet@38014
    45
  | s_conj p = HOLogic.mk_conj p
blanchet@38014
    46
fun s_disj (@{const False}, t2) = t2
blanchet@38014
    47
  | s_disj (t1, @{const False}) = t1
blanchet@38014
    48
  | s_disj p = HOLogic.mk_disj p
blanchet@38014
    49
fun s_imp (@{const True}, t2) = t2
blanchet@38014
    50
  | s_imp (t1, @{const False}) = s_not t1
blanchet@38014
    51
  | s_imp p = HOLogic.mk_imp p
blanchet@38014
    52
fun s_iff (@{const True}, t2) = t2
blanchet@38014
    53
  | s_iff (t1, @{const True}) = t1
blanchet@38014
    54
  | s_iff (t1, t2) = HOLogic.eq_const HOLogic.boolT $ t1 $ t2
blanchet@38014
    55
blanchet@38014
    56
fun mk_anot (AConn (ANot, [phi])) = phi
blanchet@38014
    57
  | mk_anot phi = AConn (ANot, [phi])
blanchet@37991
    58
fun mk_aconn c (phi1, phi2) = AConn (c, [phi1, phi2])
blanchet@37991
    59
blanchet@37996
    60
val index_in_shape : int -> int list -> int = find_index o curry (op =)
blanchet@37962
    61
fun is_axiom_clause_number thm_names num =
blanchet@37962
    62
  num > 0 andalso num <= Vector.length thm_names andalso
blanchet@37962
    63
  Vector.sub (thm_names, num - 1) <> ""
blanchet@36570
    64
fun is_conjecture_clause_number conjecture_shape num =
blanchet@36570
    65
  index_in_shape num conjecture_shape >= 0
blanchet@36291
    66
blanchet@37991
    67
fun negate_term (Const (@{const_name All}, T) $ Abs (s, T', t')) =
blanchet@37991
    68
    Const (@{const_name Ex}, T) $ Abs (s, T', negate_term t')
blanchet@37991
    69
  | negate_term (Const (@{const_name Ex}, T) $ Abs (s, T', t')) =
blanchet@37991
    70
    Const (@{const_name All}, T) $ Abs (s, T', negate_term t')
blanchet@37991
    71
  | negate_term (@{const "op -->"} $ t1 $ t2) =
blanchet@37991
    72
    @{const "op &"} $ t1 $ negate_term t2
blanchet@37991
    73
  | negate_term (@{const "op &"} $ t1 $ t2) =
blanchet@37991
    74
    @{const "op |"} $ negate_term t1 $ negate_term t2
blanchet@37991
    75
  | negate_term (@{const "op |"} $ t1 $ t2) =
blanchet@37991
    76
    @{const "op &"} $ negate_term t1 $ negate_term t2
blanchet@37991
    77
  | negate_term (@{const Not} $ t) = t
blanchet@37991
    78
  | negate_term t = @{const Not} $ t
blanchet@37991
    79
blanchet@36491
    80
datatype ('a, 'b, 'c, 'd, 'e) raw_step =
blanchet@36491
    81
  Definition of 'a * 'b * 'c |
blanchet@36491
    82
  Inference of 'a * 'd * 'e list
blanchet@36491
    83
paulson@21978
    84
(**** PARSING OF TSTP FORMAT ****)
paulson@21978
    85
blanchet@37991
    86
datatype int_or_string = Str of string | Int of int
paulson@21978
    87
paulson@21978
    88
(*Strings enclosed in single quotes, e.g. filenames*)
blanchet@37991
    89
val scan_quoted = $$ "'" |-- Scan.repeat (~$$ "'") --| $$ "'" >> implode;
paulson@21978
    90
blanchet@37991
    91
val scan_dollar_name =
blanchet@36548
    92
  Scan.repeat ($$ "$") -- Symbol.scan_id >> (fn (ss, s) => implode ss ^ s)
blanchet@36548
    93
blanchet@36369
    94
(* needed for SPASS's output format *)
blanchet@36548
    95
fun repair_name _ "$true" = "c_True"
blanchet@36548
    96
  | repair_name _ "$false" = "c_False"
blanchet@38007
    97
  | repair_name _ "$$e" = "c_equal" (* seen in Vampire proofs *)
blanchet@36548
    98
  | repair_name _ "equal" = "c_equal" (* probably not needed *)
blanchet@37926
    99
  | repair_name pool s = Symtab.lookup pool s |> the_default s
blanchet@36392
   100
(* Generalized first-order terms, which include file names, numbers, etc. *)
blanchet@36393
   101
(* The "x" argument is not strictly necessary, but without it Poly/ML loops
blanchet@36393
   102
   forever at compile time. *)
blanchet@37991
   103
fun parse_generalized_term x =
blanchet@37991
   104
  (scan_quoted >> (fn s => ATerm (Str s, []))
blanchet@37991
   105
   || scan_dollar_name
blanchet@37991
   106
      -- Scan.optional ($$ "(" |-- parse_generalized_terms --| $$ ")") []
blanchet@37991
   107
      >> (fn (s, gs) => ATerm (Str s, gs))
blanchet@37991
   108
   || scan_integer >> (fn k => ATerm (Int k, []))
blanchet@37991
   109
   || $$ "(" |-- parse_generalized_term --| $$ ")"
blanchet@37991
   110
   || $$ "[" |-- Scan.optional parse_generalized_terms [] --| $$ "]"
blanchet@37991
   111
      >> curry ATerm (Str "list")) x
blanchet@37991
   112
and parse_generalized_terms x =
blanchet@37991
   113
  (parse_generalized_term ::: Scan.repeat ($$ "," |-- parse_generalized_term)) x
blanchet@36393
   114
fun parse_term pool x =
blanchet@37991
   115
  ((scan_dollar_name >> repair_name pool)
blanchet@37991
   116
    -- Scan.optional ($$ "(" |-- parse_terms pool --| $$ ")") [] >> ATerm) x
blanchet@36393
   117
and parse_terms pool x =
blanchet@36393
   118
  (parse_term pool ::: Scan.repeat ($$ "," |-- parse_term pool)) x
paulson@21978
   119
blanchet@36393
   120
fun parse_predicate_term pool =
blanchet@36393
   121
  parse_term pool -- Scan.option (Scan.option ($$ "!") --| $$ "="
blanchet@36393
   122
                                  -- parse_term pool)
blanchet@37991
   123
  >> (fn (u, NONE) => APred u
blanchet@37991
   124
       | (u1, SOME (NONE, u2)) => APred (ATerm ("c_equal", [u1, u2]))
blanchet@37991
   125
       | (u1, SOME (SOME _, u2)) =>
blanchet@37991
   126
         mk_anot (APred (ATerm ("c_equal", [u1, u2]))))
blanchet@37991
   127
blanchet@37991
   128
fun fo_term_head (ATerm (s, _)) = s
blanchet@36291
   129
blanchet@37991
   130
(* TPTP formulas are fully parenthesized, so we don't need to worry about
blanchet@37991
   131
   operator precedence. *)
blanchet@37991
   132
fun parse_formula pool x =
blanchet@37991
   133
  (($$ "(" |-- parse_formula pool --| $$ ")"
blanchet@37991
   134
    || ($$ "!" >> K AForall || $$ "?" >> K AExists)
blanchet@37991
   135
       --| $$ "[" -- parse_terms pool --| $$ "]" --| $$ ":"
blanchet@37991
   136
       -- parse_formula pool
blanchet@37991
   137
       >> (fn ((q, ts), phi) => AQuant (q, map fo_term_head ts, phi))
blanchet@37991
   138
    || $$ "~" |-- parse_formula pool >> mk_anot
blanchet@37991
   139
    || parse_predicate_term pool)
blanchet@37991
   140
   -- Scan.option ((Scan.this_string "=>" >> K AImplies
blanchet@37991
   141
                    || Scan.this_string "<=>" >> K AIff
blanchet@37991
   142
                    || Scan.this_string "<~>" >> K ANotIff
blanchet@37991
   143
                    || Scan.this_string "<=" >> K AIf
blanchet@37991
   144
                    || $$ "|" >> K AOr || $$ "&" >> K AAnd)
blanchet@37991
   145
                   -- parse_formula pool)
blanchet@37991
   146
   >> (fn (phi1, NONE) => phi1
blanchet@37991
   147
        | (phi1, SOME (c, phi2)) => mk_aconn c (phi1, phi2))) x
blanchet@37991
   148
blanchet@37991
   149
fun ints_of_generalized_term (ATerm (label, gs)) =
blanchet@37991
   150
  fold ints_of_generalized_term gs #> (case label of Int k => cons k | _ => I)
blanchet@36392
   151
val parse_tstp_annotations =
blanchet@37991
   152
  Scan.optional ($$ "," |-- parse_generalized_term
blanchet@37991
   153
                   --| Scan.option ($$ "," |-- parse_generalized_terms)
blanchet@37991
   154
                 >> (fn g => ints_of_generalized_term g [])) []
blanchet@36486
   155
blanchet@37991
   156
(* Syntax: (fof|cnf)\(<num>, <formula_role>, <cnf_formula> <annotations>\).
blanchet@36486
   157
   The <num> could be an identifier, but we assume integers. *)
blanchet@37991
   158
 fun parse_tstp_line pool =
blanchet@37991
   159
   ((Scan.this_string "fof" || Scan.this_string "cnf") -- $$ "(")
blanchet@37991
   160
     |-- scan_integer --| $$ "," -- Symbol.scan_id --| $$ ","
blanchet@37991
   161
     -- parse_formula pool -- parse_tstp_annotations --| $$ ")" --| $$ "."
blanchet@37991
   162
    >> (fn (((num, role), phi), deps) =>
blanchet@37991
   163
           case role of
blanchet@37991
   164
             "definition" =>
blanchet@37991
   165
             (case phi of
blanchet@38007
   166
                AConn (AIff, [phi1 as APred _, phi2]) =>
blanchet@38007
   167
                Definition (num, phi1, phi2)
blanchet@38007
   168
              | APred (ATerm ("$$e", _)) =>
blanchet@38007
   169
                Inference (num, phi, deps) (* Vampire's equality proxy axiom *)
blanchet@37991
   170
              | _ => raise Fail "malformed definition")
blanchet@37991
   171
           | _ => Inference (num, phi, deps))
blanchet@36291
   172
blanchet@36291
   173
(**** PARSING OF SPASS OUTPUT ****)
blanchet@36291
   174
blanchet@36392
   175
(* SPASS returns clause references of the form "x.y". We ignore "y", whose role
blanchet@36392
   176
   is not clear anyway. *)
blanchet@37962
   177
val parse_dot_name = scan_integer --| $$ "." --| scan_integer
paulson@21978
   178
blanchet@36392
   179
val parse_spass_annotations =
blanchet@36392
   180
  Scan.optional ($$ ":" |-- Scan.repeat (parse_dot_name
blanchet@36392
   181
                                         --| Scan.option ($$ ","))) []
blanchet@36291
   182
blanchet@36574
   183
(* It is not clear why some literals are followed by sequences of stars and/or
blanchet@36574
   184
   pluses. We ignore them. *)
blanchet@36574
   185
fun parse_decorated_predicate_term pool =
blanchet@36562
   186
  parse_predicate_term pool --| Scan.repeat ($$ "*" || $$ "+" || $$ " ")
blanchet@36291
   187
blanchet@37991
   188
fun mk_horn ([], []) = APred (ATerm ("c_False", []))
blanchet@37991
   189
  | mk_horn ([], pos_lits) = foldr1 (mk_aconn AOr) pos_lits
blanchet@37991
   190
  | mk_horn (neg_lits, []) = mk_anot (foldr1 (mk_aconn AAnd) neg_lits)
blanchet@37991
   191
  | mk_horn (neg_lits, pos_lits) =
blanchet@37991
   192
    mk_aconn AImplies (foldr1 (mk_aconn AAnd) neg_lits,
blanchet@37991
   193
                       foldr1 (mk_aconn AOr) pos_lits)
blanchet@37991
   194
blanchet@36393
   195
fun parse_horn_clause pool =
blanchet@36574
   196
  Scan.repeat (parse_decorated_predicate_term pool) --| $$ "|" --| $$ "|"
blanchet@36574
   197
    -- Scan.repeat (parse_decorated_predicate_term pool) --| $$ "-" --| $$ ">"
blanchet@36574
   198
    -- Scan.repeat (parse_decorated_predicate_term pool)
blanchet@37991
   199
  >> (mk_horn o apfst (op @))
paulson@21978
   200
blanchet@36558
   201
(* Syntax: <num>[0:<inference><annotations>]
blanchet@36558
   202
   <cnf_formulas> || <cnf_formulas> -> <cnf_formulas>. *)
blanchet@36402
   203
fun parse_spass_line pool =
blanchet@37962
   204
  scan_integer --| $$ "[" --| $$ "0" --| $$ ":" --| Symbol.scan_id
blanchet@36558
   205
  -- parse_spass_annotations --| $$ "]" -- parse_horn_clause pool --| $$ "."
blanchet@37991
   206
  >> (fn ((num, deps), u) => Inference (num, u, deps))
blanchet@36291
   207
blanchet@36548
   208
fun parse_line pool = parse_tstp_line pool || parse_spass_line pool
blanchet@36548
   209
fun parse_lines pool = Scan.repeat1 (parse_line pool)
blanchet@36548
   210
fun parse_proof pool =
blanchet@36548
   211
  fst o Scan.finite Symbol.stopper
blanchet@36548
   212
            (Scan.error (!! (fn _ => raise Fail "unrecognized ATP output")
blanchet@36548
   213
                            (parse_lines pool)))
blanchet@36548
   214
  o explode o strip_spaces
paulson@21978
   215
paulson@21978
   216
(**** INTERPRETATION OF TSTP SYNTAX TREES ****)
paulson@21978
   217
blanchet@37991
   218
exception FO_TERM of string fo_term list
blanchet@37994
   219
exception FORMULA of (string, string fo_term) formula list
blanchet@37991
   220
exception SAME of unit
paulson@21978
   221
blanchet@36909
   222
(* Type variables are given the basic sort "HOL.type". Some will later be
blanchet@37991
   223
   constrained by information from type literals, or by type inference. *)
blanchet@37991
   224
fun type_from_fo_term tfrees (u as ATerm (a, us)) =
blanchet@37991
   225
  let val Ts = map (type_from_fo_term tfrees) us in
blanchet@37991
   226
    case strip_prefix_and_undo_ascii type_const_prefix a of
blanchet@37991
   227
      SOME b => Type (invert_const b, Ts)
blanchet@37991
   228
    | NONE =>
blanchet@37991
   229
      if not (null us) then
blanchet@37991
   230
        raise FO_TERM [u]  (* only "tconst"s have type arguments *)
blanchet@37991
   231
      else case strip_prefix_and_undo_ascii tfree_prefix a of
blanchet@37991
   232
        SOME b =>
blanchet@37991
   233
        let val s = "'" ^ b in
blanchet@37991
   234
          TFree (s, AList.lookup (op =) tfrees s |> the_default HOLogic.typeS)
blanchet@37991
   235
        end
blanchet@36486
   236
      | NONE =>
blanchet@37991
   237
        case strip_prefix_and_undo_ascii tvar_prefix a of
blanchet@37991
   238
          SOME b => TVar (("'" ^ b, 0), HOLogic.typeS)
blanchet@36486
   239
        | NONE =>
blanchet@37991
   240
          (* Variable from the ATP, say "X1" *)
blanchet@37991
   241
          Type_Infer.param 0 (a, HOLogic.typeS)
blanchet@37991
   242
  end
paulson@21978
   243
blanchet@38014
   244
(* Type class literal applied to a type. Returns triple of polarity, class,
blanchet@38014
   245
   type. *)
blanchet@38014
   246
fun type_constraint_from_term pos tfrees (u as ATerm (a, us)) =
blanchet@38014
   247
  case (strip_prefix_and_undo_ascii class_prefix a,
blanchet@38014
   248
        map (type_from_fo_term tfrees) us) of
blanchet@38014
   249
    (SOME b, [T]) => (pos, b, T)
blanchet@38014
   250
  | _ => raise FO_TERM [u]
blanchet@38014
   251
blanchet@38014
   252
(** Accumulate type constraints in a clause: negative type literals **)
blanchet@38014
   253
fun add_var (key, z)  = Vartab.map_default (key, []) (cons z)
blanchet@38014
   254
fun add_type_constraint (false, cl, TFree (a ,_)) = add_var ((a, ~1), cl)
blanchet@38014
   255
  | add_type_constraint (false, cl, TVar (ix, _)) = add_var (ix, cl)
blanchet@38014
   256
  | add_type_constraint _ = I
blanchet@38014
   257
blanchet@36486
   258
fun fix_atp_variable_name s =
blanchet@36486
   259
  let
blanchet@36486
   260
    fun subscript_name s n = s ^ nat_subscript n
blanchet@36486
   261
    val s = String.map Char.toLower s
blanchet@36486
   262
  in
blanchet@36486
   263
    case space_explode "_" s of
blanchet@36486
   264
      [_] => (case take_suffix Char.isDigit (String.explode s) of
blanchet@36486
   265
                (cs1 as _ :: _, cs2 as _ :: _) =>
blanchet@36486
   266
                subscript_name (String.implode cs1)
blanchet@36486
   267
                               (the (Int.fromString (String.implode cs2)))
blanchet@36486
   268
              | (_, _) => s)
blanchet@36486
   269
    | [s1, s2] => (case Int.fromString s2 of
blanchet@36486
   270
                     SOME n => subscript_name s1 n
blanchet@36486
   271
                   | NONE => s)
blanchet@36486
   272
    | _ => s
blanchet@36486
   273
  end
blanchet@36486
   274
blanchet@36909
   275
(* First-order translation. No types are known for variables. "HOLogic.typeT"
blanchet@38014
   276
   should allow them to be inferred. *)
blanchet@38014
   277
fun raw_term_from_pred thy full_types tfrees =
blanchet@36909
   278
  let
blanchet@37643
   279
    fun aux opt_T extra_us u =
blanchet@36909
   280
      case u of
blanchet@37991
   281
        ATerm ("hBOOL", [u1]) => aux (SOME @{typ bool}) [] u1
blanchet@37991
   282
      | ATerm ("hAPP", [u1, u2]) => aux opt_T (u2 :: extra_us) u1
blanchet@37991
   283
      | ATerm (a, us) =>
blanchet@36909
   284
        if a = type_wrapper_name then
blanchet@36909
   285
          case us of
blanchet@37643
   286
            [typ_u, term_u] =>
blanchet@37991
   287
            aux (SOME (type_from_fo_term tfrees typ_u)) extra_us term_u
blanchet@37991
   288
          | _ => raise FO_TERM us
blanchet@37991
   289
        else case strip_prefix_and_undo_ascii const_prefix a of
blanchet@36909
   290
          SOME "equal" =>
blanchet@36909
   291
          list_comb (Const (@{const_name "op ="}, HOLogic.typeT),
blanchet@36909
   292
                     map (aux NONE []) us)
blanchet@36909
   293
        | SOME b =>
blanchet@36909
   294
          let
blanchet@36909
   295
            val c = invert_const b
blanchet@36909
   296
            val num_type_args = num_type_args thy c
blanchet@37643
   297
            val (type_us, term_us) =
blanchet@37643
   298
              chop (if full_types then 0 else num_type_args) us
blanchet@37643
   299
            (* Extra args from "hAPP" come after any arguments given directly to
blanchet@37643
   300
               the constant. *)
blanchet@37643
   301
            val term_ts = map (aux NONE []) term_us
blanchet@37643
   302
            val extra_ts = map (aux NONE []) extra_us
blanchet@36909
   303
            val t =
blanchet@36909
   304
              Const (c, if full_types then
blanchet@36909
   305
                          case opt_T of
blanchet@37643
   306
                            SOME T => map fastype_of term_ts ---> T
blanchet@36909
   307
                          | NONE =>
blanchet@36909
   308
                            if num_type_args = 0 then
blanchet@36909
   309
                              Sign.const_instance thy (c, [])
blanchet@36909
   310
                            else
blanchet@36909
   311
                              raise Fail ("no type information for " ^ quote c)
blanchet@36909
   312
                        else
blanchet@37998
   313
                          Sign.const_instance thy (c,
blanchet@37998
   314
                              map (type_from_fo_term tfrees) type_us))
blanchet@37643
   315
          in list_comb (t, term_ts @ extra_ts) end
blanchet@36909
   316
        | NONE => (* a free or schematic variable *)
blanchet@36909
   317
          let
blanchet@37643
   318
            val ts = map (aux NONE []) (us @ extra_us)
blanchet@36909
   319
            val T = map fastype_of ts ---> HOLogic.typeT
blanchet@36909
   320
            val t =
blanchet@37991
   321
              case strip_prefix_and_undo_ascii fixed_var_prefix a of
blanchet@36909
   322
                SOME b => Free (b, T)
blanchet@36909
   323
              | NONE =>
blanchet@37991
   324
                case strip_prefix_and_undo_ascii schematic_var_prefix a of
blanchet@36967
   325
                  SOME b => Var ((b, 0), T)
blanchet@36909
   326
                | NONE =>
blanchet@38017
   327
                  if is_tptp_variable a then
blanchet@38017
   328
                    Var ((fix_atp_variable_name a, 0), T)
blanchet@38017
   329
                  else
blanchet@38017
   330
                    raise Fail ("Unexpected constant: " ^ quote a)
blanchet@36909
   331
          in list_comb (t, ts) end
blanchet@38014
   332
  in aux (SOME HOLogic.boolT) [] end
paulson@21978
   333
blanchet@38014
   334
fun term_from_pred thy full_types tfrees pos (u as ATerm (s, _)) =
blanchet@38014
   335
  if String.isPrefix class_prefix s then
blanchet@38014
   336
    add_type_constraint (type_constraint_from_term pos tfrees u)
blanchet@38014
   337
    #> pair @{const True}
blanchet@38014
   338
  else
blanchet@38014
   339
    pair (raw_term_from_pred thy full_types tfrees u)
blanchet@36402
   340
blanchet@36555
   341
val combinator_table =
blanchet@36555
   342
  [(@{const_name COMBI}, @{thm COMBI_def_raw}),
blanchet@36555
   343
   (@{const_name COMBK}, @{thm COMBK_def_raw}),
blanchet@36555
   344
   (@{const_name COMBB}, @{thm COMBB_def_raw}),
blanchet@36555
   345
   (@{const_name COMBC}, @{thm COMBC_def_raw}),
blanchet@36555
   346
   (@{const_name COMBS}, @{thm COMBS_def_raw})]
blanchet@36555
   347
blanchet@36555
   348
fun uncombine_term (t1 $ t2) = betapply (pairself uncombine_term (t1, t2))
blanchet@36555
   349
  | uncombine_term (Abs (s, T, t')) = Abs (s, T, uncombine_term t')
blanchet@36555
   350
  | uncombine_term (t as Const (x as (s, _))) =
blanchet@36555
   351
    (case AList.lookup (op =) combinator_table s of
blanchet@36555
   352
       SOME thm => thm |> prop_of |> specialize_type @{theory} x |> Logic.dest_equals |> snd
blanchet@36555
   353
     | NONE => t)
blanchet@36555
   354
  | uncombine_term t = t
blanchet@36555
   355
blanchet@37991
   356
(* Update schematic type variables with detected sort constraints. It's not
blanchet@37991
   357
   totally clear when this code is necessary. *)
blanchet@38014
   358
fun repair_tvar_sorts (t, tvar_tab) =
blanchet@36909
   359
  let
blanchet@37991
   360
    fun do_type (Type (a, Ts)) = Type (a, map do_type Ts)
blanchet@37991
   361
      | do_type (TVar (xi, s)) =
blanchet@37991
   362
        TVar (xi, the_default s (Vartab.lookup tvar_tab xi))
blanchet@37991
   363
      | do_type (TFree z) = TFree z
blanchet@37991
   364
    fun do_term (Const (a, T)) = Const (a, do_type T)
blanchet@37991
   365
      | do_term (Free (a, T)) = Free (a, do_type T)
blanchet@37991
   366
      | do_term (Var (xi, T)) = Var (xi, do_type T)
blanchet@37991
   367
      | do_term (t as Bound _) = t
blanchet@37991
   368
      | do_term (Abs (a, T, t)) = Abs (a, do_type T, do_term t)
blanchet@37991
   369
      | do_term (t1 $ t2) = do_term t1 $ do_term t2
blanchet@37991
   370
  in t |> not (Vartab.is_empty tvar_tab) ? do_term end
blanchet@37991
   371
blanchet@37991
   372
fun quantify_over_free quant_s free_s body_t =
blanchet@37991
   373
  case Term.add_frees body_t [] |> filter (curry (op =) free_s o fst) of
blanchet@37991
   374
    [] => body_t
blanchet@37991
   375
  | frees as (_, free_T) :: _ =>
blanchet@37991
   376
    Abs (free_s, free_T, fold (curry abstract_over) (map Free frees) body_t)
blanchet@37991
   377
blanchet@38014
   378
(* Interpret a list of syntax trees as a clause, extracting sort constraints
blanchet@38014
   379
   as they appear in the formula. *)
blanchet@38014
   380
fun prop_from_formula thy full_types tfrees phi =
blanchet@38014
   381
  let
blanchet@38014
   382
    fun do_formula pos phi =
blanchet@37991
   383
      case phi of
blanchet@38014
   384
        AQuant (_, [], phi) => do_formula pos phi
blanchet@37991
   385
      | AQuant (q, x :: xs, phi') =>
blanchet@38014
   386
        do_formula pos (AQuant (q, xs, phi'))
blanchet@38014
   387
        #>> quantify_over_free (case q of
blanchet@38014
   388
                                  AForall => @{const_name All}
blanchet@38014
   389
                                | AExists => @{const_name Ex}) x
blanchet@38014
   390
      | AConn (ANot, [phi']) => do_formula (not pos) phi' #>> s_not
blanchet@37991
   391
      | AConn (c, [phi1, phi2]) =>
blanchet@38014
   392
        do_formula (pos |> c = AImplies ? not) phi1
blanchet@38014
   393
        ##>> do_formula pos phi2
blanchet@38014
   394
        #>> (case c of
blanchet@38014
   395
               AAnd => s_conj
blanchet@38014
   396
             | AOr => s_disj
blanchet@38014
   397
             | AImplies => s_imp
blanchet@38014
   398
             | AIff => s_iff)
blanchet@38014
   399
      | APred tm => term_from_pred thy full_types tfrees pos tm
blanchet@37991
   400
      | _ => raise FORMULA [phi]
blanchet@38014
   401
  in repair_tvar_sorts (do_formula true phi Vartab.empty) end
blanchet@37991
   402
blanchet@36556
   403
fun check_formula ctxt =
blanchet@38014
   404
  Type_Infer.constrain HOLogic.boolT
blanchet@36486
   405
  #> Syntax.check_term (ProofContext.set_mode ProofContext.mode_schematic ctxt)
paulson@21978
   406
paulson@21978
   407
paulson@21978
   408
(**** Translation of TSTP files to Isar Proofs ****)
paulson@21978
   409
blanchet@36486
   410
fun unvarify_term (Var ((s, 0), T)) = Free (s, T)
blanchet@36486
   411
  | unvarify_term t = raise TERM ("unvarify_term: non-Var", [t])
paulson@21978
   412
blanchet@37991
   413
fun decode_line full_types tfrees (Definition (num, phi1, phi2)) ctxt =
blanchet@36486
   414
    let
blanchet@37991
   415
      val thy = ProofContext.theory_of ctxt
blanchet@37991
   416
      val t1 = prop_from_formula thy full_types tfrees phi1
blanchet@36551
   417
      val vars = snd (strip_comb t1)
blanchet@36486
   418
      val frees = map unvarify_term vars
blanchet@36486
   419
      val unvarify_args = subst_atomic (vars ~~ frees)
blanchet@37991
   420
      val t2 = prop_from_formula thy full_types tfrees phi2
blanchet@36551
   421
      val (t1, t2) =
blanchet@36551
   422
        HOLogic.eq_const HOLogic.typeT $ t1 $ t2
blanchet@36556
   423
        |> unvarify_args |> uncombine_term |> check_formula ctxt
blanchet@36555
   424
        |> HOLogic.dest_eq
blanchet@36486
   425
    in
blanchet@36551
   426
      (Definition (num, t1, t2),
blanchet@36551
   427
       fold Variable.declare_term (maps OldTerm.term_frees [t1, t2]) ctxt)
blanchet@36486
   428
    end
blanchet@37991
   429
  | decode_line full_types tfrees (Inference (num, u, deps)) ctxt =
blanchet@36551
   430
    let
blanchet@37991
   431
      val thy = ProofContext.theory_of ctxt
blanchet@37991
   432
      val t = u |> prop_from_formula thy full_types tfrees
blanchet@37998
   433
                |> uncombine_term |> check_formula ctxt
blanchet@36551
   434
    in
blanchet@36551
   435
      (Inference (num, t, deps),
blanchet@36551
   436
       fold Variable.declare_term (OldTerm.term_frees t) ctxt)
blanchet@36486
   437
    end
blanchet@36967
   438
fun decode_lines ctxt full_types tfrees lines =
blanchet@36967
   439
  fst (fold_map (decode_line full_types tfrees) lines ctxt)
paulson@21978
   440
blanchet@37323
   441
fun aint_actual_inference _ (Definition _) = true
blanchet@37323
   442
  | aint_actual_inference t (Inference (_, t', _)) = not (t aconv t')
blanchet@36486
   443
blanchet@36486
   444
(* No "real" literals means only type information (tfree_tcs, clsrel, or
blanchet@36486
   445
   clsarity). *)
blanchet@36486
   446
val is_only_type_information = curry (op aconv) HOLogic.true_const
blanchet@36486
   447
blanchet@36486
   448
fun replace_one_dep (old, new) dep = if dep = old then new else [dep]
blanchet@36486
   449
fun replace_deps_in_line _ (line as Definition _) = line
blanchet@36486
   450
  | replace_deps_in_line p (Inference (num, t, deps)) =
blanchet@36486
   451
    Inference (num, t, fold (union (op =) o replace_one_dep p) deps [])
paulson@21978
   452
paulson@22491
   453
(*Discard axioms; consolidate adjacent lines that prove the same clause, since they differ
paulson@22491
   454
  only in type information.*)
blanchet@36551
   455
fun add_line _ _ (line as Definition _) lines = line :: lines
blanchet@36551
   456
  | add_line conjecture_shape thm_names (Inference (num, t, [])) lines =
blanchet@36570
   457
    (* No dependencies: axiom, conjecture clause, or internal axioms or
blanchet@36570
   458
       definitions (Vampire). *)
blanchet@36486
   459
    if is_axiom_clause_number thm_names num then
blanchet@36486
   460
      (* Axioms are not proof lines. *)
blanchet@36486
   461
      if is_only_type_information t then
blanchet@36486
   462
        map (replace_deps_in_line (num, [])) lines
blanchet@36486
   463
      (* Is there a repetition? If so, replace later line by earlier one. *)
blanchet@37323
   464
      else case take_prefix (aint_actual_inference t) lines of
blanchet@36486
   465
        (_, []) => lines (*no repetition of proof line*)
blanchet@36486
   466
      | (pre, Inference (num', _, _) :: post) =>
blanchet@36486
   467
        pre @ map (replace_deps_in_line (num', [num])) post
blanchet@36570
   468
    else if is_conjecture_clause_number conjecture_shape num then
blanchet@36486
   469
      Inference (num, t, []) :: lines
blanchet@36551
   470
    else
blanchet@36570
   471
      map (replace_deps_in_line (num, [])) lines
blanchet@36551
   472
  | add_line _ _ (Inference (num, t, deps)) lines =
blanchet@36486
   473
    (* Type information will be deleted later; skip repetition test. *)
blanchet@36486
   474
    if is_only_type_information t then
blanchet@36486
   475
      Inference (num, t, deps) :: lines
blanchet@36486
   476
    (* Is there a repetition? If so, replace later line by earlier one. *)
blanchet@37323
   477
    else case take_prefix (aint_actual_inference t) lines of
blanchet@36486
   478
      (* FIXME: Doesn't this code risk conflating proofs involving different
blanchet@36486
   479
         types?? *)
blanchet@36486
   480
       (_, []) => Inference (num, t, deps) :: lines
blanchet@36486
   481
     | (pre, Inference (num', t', _) :: post) =>
blanchet@36486
   482
       Inference (num, t', deps) ::
blanchet@36486
   483
       pre @ map (replace_deps_in_line (num', [num])) post
paulson@22044
   484
blanchet@36486
   485
(* Recursively delete empty lines (type information) from the proof. *)
blanchet@36486
   486
fun add_nontrivial_line (Inference (num, t, [])) lines =
blanchet@36486
   487
    if is_only_type_information t then delete_dep num lines
blanchet@36486
   488
    else Inference (num, t, []) :: lines
blanchet@36486
   489
  | add_nontrivial_line line lines = line :: lines
blanchet@36395
   490
and delete_dep num lines =
blanchet@36486
   491
  fold_rev add_nontrivial_line (map (replace_deps_in_line (num, [])) lines) []
blanchet@36486
   492
blanchet@37323
   493
(* ATPs sometimes reuse free variable names in the strangest ways. Removing
blanchet@37323
   494
   offending lines often does the trick. *)
blanchet@36560
   495
fun is_bad_free frees (Free x) = not (member (op =) frees x)
blanchet@36560
   496
  | is_bad_free _ _ = false
paulson@22470
   497
blanchet@36570
   498
(* Vampire is keen on producing these. *)
blanchet@36570
   499
fun is_trivial_formula (@{const Not} $ (Const (@{const_name "op ="}, _)
blanchet@36570
   500
                                        $ t1 $ t2)) = (t1 aconv t2)
blanchet@37498
   501
  | is_trivial_formula _ = false
blanchet@36570
   502
blanchet@37498
   503
fun add_desired_line _ _ _ _ (line as Definition (num, _, _)) (j, lines) =
blanchet@37323
   504
    (j, line :: map (replace_deps_in_line (num, [])) lines)
blanchet@37498
   505
  | add_desired_line isar_shrink_factor conjecture_shape thm_names frees
blanchet@36570
   506
                     (Inference (num, t, deps)) (j, lines) =
blanchet@36402
   507
    (j + 1,
blanchet@36570
   508
     if is_axiom_clause_number thm_names num orelse
blanchet@36570
   509
        is_conjecture_clause_number conjecture_shape num orelse
blanchet@36570
   510
        (not (is_only_type_information t) andalso
blanchet@36570
   511
         null (Term.add_tvars t []) andalso
blanchet@36570
   512
         not (exists_subterm (is_bad_free frees) t) andalso
blanchet@36570
   513
         not (is_trivial_formula t) andalso
blanchet@36570
   514
         (null lines orelse (* last line must be kept *)
blanchet@36924
   515
          (length deps >= 2 andalso j mod isar_shrink_factor = 0))) then
blanchet@36570
   516
       Inference (num, t, deps) :: lines  (* keep line *)
blanchet@36402
   517
     else
blanchet@36570
   518
       map (replace_deps_in_line (num, deps)) lines)  (* drop line *)
paulson@21978
   519
blanchet@36402
   520
(** EXTRACTING LEMMAS **)
paulson@21979
   521
blanchet@37991
   522
(* A list consisting of the first number in each line is returned. For TSTP,
blanchet@37991
   523
   interesting lines have the form "fof(108, axiom, ...)", where the number
blanchet@37991
   524
   (108) is extracted. For SPASS, lines have the form "108[0:Inp] ...", where
blanchet@37991
   525
   the first number (108) is extracted. *)
blanchet@37961
   526
fun extract_formula_numbers_in_atp_proof atp_proof =
blanchet@35865
   527
  let
blanchet@37962
   528
    val tokens_of = String.tokens (not o Char.isAlphaNum)
blanchet@37961
   529
    fun extract_num ("fof" :: num :: "axiom" :: _) = Int.fromString num
blanchet@36395
   530
      | extract_num (num :: "0" :: "Inp" :: _) = Int.fromString num
blanchet@36395
   531
      | extract_num _ = NONE
blanchet@36402
   532
  in atp_proof |> split_lines |> map_filter (extract_num o tokens_of) end
blanchet@37399
   533
blanchet@37399
   534
val indent_size = 2
blanchet@37399
   535
val no_label = ("", ~1)
blanchet@37399
   536
blanchet@37399
   537
val raw_prefix = "X"
blanchet@37399
   538
val assum_prefix = "A"
blanchet@37399
   539
val fact_prefix = "F"
blanchet@37399
   540
blanchet@37399
   541
fun string_for_label (s, num) = s ^ string_of_int num
blanchet@37399
   542
blanchet@37399
   543
fun metis_using [] = ""
blanchet@37399
   544
  | metis_using ls =
blanchet@37399
   545
    "using " ^ space_implode " " (map string_for_label ls) ^ " "
blanchet@37399
   546
fun metis_apply _ 1 = "by "
blanchet@37399
   547
  | metis_apply 1 _ = "apply "
blanchet@37399
   548
  | metis_apply i _ = "prefer " ^ string_of_int i ^ " apply "
blanchet@37479
   549
fun metis_name full_types = if full_types then "metisFT" else "metis"
blanchet@37479
   550
fun metis_call full_types [] = metis_name full_types
blanchet@37479
   551
  | metis_call full_types ss =
blanchet@37479
   552
    "(" ^ metis_name full_types ^ " " ^ space_implode " " ss ^ ")"
blanchet@37479
   553
fun metis_command full_types i n (ls, ss) =
blanchet@37479
   554
  metis_using ls ^ metis_apply i n ^ metis_call full_types ss
blanchet@37479
   555
fun metis_line full_types i n ss =
blanchet@36063
   556
  "Try this command: " ^
blanchet@37479
   557
  Markup.markup Markup.sendback (metis_command full_types i n ([], ss)) ^ ".\n"
blanchet@36281
   558
fun minimize_line _ [] = ""
blanchet@36281
   559
  | minimize_line minimize_command facts =
blanchet@36281
   560
    case minimize_command facts of
blanchet@36281
   561
      "" => ""
blanchet@36281
   562
    | command =>
blanchet@36065
   563
      "To minimize the number of lemmas, try this command: " ^
blanchet@36281
   564
      Markup.markup Markup.sendback command ^ ".\n"
immler@31840
   565
blanchet@37171
   566
val unprefix_chained = perhaps (try (unprefix chained_prefix))
blanchet@37171
   567
blanchet@38015
   568
fun used_facts thm_names =
blanchet@38015
   569
  extract_formula_numbers_in_atp_proof
blanchet@38015
   570
  #> filter (is_axiom_clause_number thm_names)
blanchet@38015
   571
  #> map (fn i => Vector.sub (thm_names, i - 1))
blanchet@38015
   572
  #> List.partition (String.isPrefix chained_prefix)
blanchet@38015
   573
  #>> map (unprefix chained_prefix)
blanchet@38015
   574
  #> pairself (sort_distinct string_ord)
blanchet@38015
   575
blanchet@37479
   576
fun metis_proof_text (full_types, minimize_command, atp_proof, thm_names, goal,
blanchet@37479
   577
                      i) =
blanchet@36063
   578
  let
blanchet@38015
   579
    val (chained_lemmas, other_lemmas) = used_facts thm_names atp_proof
blanchet@37171
   580
    val lemmas = other_lemmas @ chained_lemmas
blanchet@36063
   581
    val n = Logic.count_prems (prop_of goal)
blanchet@37171
   582
  in
blanchet@37479
   583
    (metis_line full_types i n other_lemmas ^
blanchet@37479
   584
     minimize_line minimize_command lemmas, lemmas)
blanchet@37171
   585
  end
immler@31037
   586
blanchet@36486
   587
(** Isar proof construction and manipulation **)
blanchet@36486
   588
blanchet@36486
   589
fun merge_fact_sets (ls1, ss1) (ls2, ss2) =
blanchet@36486
   590
  (union (op =) ls1 ls2, union (op =) ss1 ss2)
blanchet@36402
   591
blanchet@36402
   592
type label = string * int
blanchet@36402
   593
type facts = label list * string list
blanchet@36402
   594
blanchet@36402
   595
datatype qualifier = Show | Then | Moreover | Ultimately
blanchet@36291
   596
blanchet@36402
   597
datatype step =
blanchet@36478
   598
  Fix of (string * typ) list |
blanchet@36486
   599
  Let of term * term |
blanchet@36402
   600
  Assume of label * term |
blanchet@36402
   601
  Have of qualifier list * label * term * byline
blanchet@36402
   602
and byline =
blanchet@36564
   603
  ByMetis of facts |
blanchet@36402
   604
  CaseSplit of step list list * facts
blanchet@36402
   605
blanchet@36574
   606
fun smart_case_split [] facts = ByMetis facts
blanchet@36574
   607
  | smart_case_split proofs facts = CaseSplit (proofs, facts)
blanchet@36574
   608
blanchet@36475
   609
fun add_fact_from_dep thm_names num =
blanchet@36475
   610
  if is_axiom_clause_number thm_names num then
blanchet@36480
   611
    apsnd (insert (op =) (Vector.sub (thm_names, num - 1)))
blanchet@36475
   612
  else
blanchet@36480
   613
    apfst (insert (op =) (raw_prefix, num))
blanchet@36402
   614
blanchet@37998
   615
fun forall_of v t = HOLogic.all_const (fastype_of v) $ lambda v t
blanchet@36491
   616
fun forall_vars t = fold_rev forall_of (map Var (Term.add_vars t [])) t
blanchet@36491
   617
blanchet@37498
   618
fun step_for_line _ _ (Definition (_, t1, t2)) = Let (t1, t2)
blanchet@36486
   619
  | step_for_line _ _ (Inference (num, t, [])) = Assume ((raw_prefix, num), t)
blanchet@36486
   620
  | step_for_line thm_names j (Inference (num, t, deps)) =
blanchet@36486
   621
    Have (if j = 1 then [Show] else [], (raw_prefix, num),
blanchet@36491
   622
          forall_vars t,
blanchet@36564
   623
          ByMetis (fold (add_fact_from_dep thm_names) deps ([], [])))
blanchet@36291
   624
blanchet@36967
   625
fun proof_from_atp_proof pool ctxt full_types tfrees isar_shrink_factor
blanchet@36967
   626
                         atp_proof conjecture_shape thm_names params frees =
blanchet@36402
   627
  let
blanchet@36486
   628
    val lines =
blanchet@37991
   629
      atp_proof ^ "$" (* the $ sign acts as a sentinel (FIXME: pick it up) *)
blanchet@36548
   630
      |> parse_proof pool
blanchet@36967
   631
      |> decode_lines ctxt full_types tfrees
blanchet@36551
   632
      |> rpair [] |-> fold_rev (add_line conjecture_shape thm_names)
blanchet@36486
   633
      |> rpair [] |-> fold_rev add_nontrivial_line
blanchet@37498
   634
      |> rpair (0, []) |-> fold_rev (add_desired_line isar_shrink_factor
blanchet@36570
   635
                                               conjecture_shape thm_names frees)
blanchet@36486
   636
      |> snd
blanchet@36402
   637
  in
blanchet@36909
   638
    (if null params then [] else [Fix params]) @
blanchet@36486
   639
    map2 (step_for_line thm_names) (length lines downto 1) lines
blanchet@36402
   640
  end
blanchet@36402
   641
blanchet@36402
   642
(* When redirecting proofs, we keep information about the labels seen so far in
blanchet@36402
   643
   the "backpatches" data structure. The first component indicates which facts
blanchet@36402
   644
   should be associated with forthcoming proof steps. The second component is a
blanchet@37322
   645
   pair ("assum_ls", "drop_ls"), where "assum_ls" are the labels that should
blanchet@37322
   646
   become assumptions and "drop_ls" are the labels that should be dropped in a
blanchet@37322
   647
   case split. *)
blanchet@36402
   648
type backpatches = (label * facts) list * (label list * label list)
blanchet@36402
   649
blanchet@36556
   650
fun used_labels_of_step (Have (_, _, _, by)) =
blanchet@36402
   651
    (case by of
blanchet@36564
   652
       ByMetis (ls, _) => ls
blanchet@36556
   653
     | CaseSplit (proofs, (ls, _)) =>
blanchet@36556
   654
       fold (union (op =) o used_labels_of) proofs ls)
blanchet@36556
   655
  | used_labels_of_step _ = []
blanchet@36556
   656
and used_labels_of proof = fold (union (op =) o used_labels_of_step) proof []
blanchet@36402
   657
blanchet@36402
   658
fun new_labels_of_step (Fix _) = []
blanchet@36486
   659
  | new_labels_of_step (Let _) = []
blanchet@36402
   660
  | new_labels_of_step (Assume (l, _)) = [l]
blanchet@36402
   661
  | new_labels_of_step (Have (_, l, _, _)) = [l]
blanchet@36402
   662
val new_labels_of = maps new_labels_of_step
blanchet@36402
   663
blanchet@36402
   664
val join_proofs =
blanchet@36402
   665
  let
blanchet@36402
   666
    fun aux _ [] = NONE
blanchet@36402
   667
      | aux proof_tail (proofs as (proof1 :: _)) =
blanchet@36402
   668
        if exists null proofs then
blanchet@36402
   669
          NONE
blanchet@36402
   670
        else if forall (curry (op =) (hd proof1) o hd) (tl proofs) then
blanchet@36402
   671
          aux (hd proof1 :: proof_tail) (map tl proofs)
blanchet@36402
   672
        else case hd proof1 of
blanchet@37498
   673
          Have ([], l, t, _) => (* FIXME: should we really ignore the "by"? *)
blanchet@36402
   674
          if forall (fn Have ([], l', t', _) :: _ => (l, t) = (l', t')
blanchet@36402
   675
                      | _ => false) (tl proofs) andalso
blanchet@36402
   676
             not (exists (member (op =) (maps new_labels_of proofs))
blanchet@36556
   677
                         (used_labels_of proof_tail)) then
blanchet@36402
   678
            SOME (l, t, map rev proofs, proof_tail)
blanchet@36402
   679
          else
blanchet@36402
   680
            NONE
blanchet@36402
   681
        | _ => NONE
blanchet@36402
   682
  in aux [] o map rev end
blanchet@36402
   683
blanchet@36402
   684
fun case_split_qualifiers proofs =
blanchet@36402
   685
  case length proofs of
blanchet@36402
   686
    0 => []
blanchet@36402
   687
  | 1 => [Then]
blanchet@36402
   688
  | _ => [Ultimately]
blanchet@36402
   689
blanchet@37991
   690
fun redirect_proof conjecture_shape hyp_ts concl_t proof =
wenzelm@33310
   691
  let
blanchet@37324
   692
    (* The first pass outputs those steps that are independent of the negated
blanchet@37324
   693
       conjecture. The second pass flips the proof by contradiction to obtain a
blanchet@37324
   694
       direct proof, introducing case splits when an inference depends on
blanchet@37324
   695
       several facts that depend on the negated conjecture. *)
blanchet@37324
   696
    fun find_hyp num = nth hyp_ts (index_in_shape num conjecture_shape)
blanchet@37996
   697
    val concl_l = (raw_prefix, List.last conjecture_shape)
blanchet@36402
   698
    fun first_pass ([], contra) = ([], contra)
blanchet@36491
   699
      | first_pass ((step as Fix _) :: proof, contra) =
blanchet@36491
   700
        first_pass (proof, contra) |>> cons step
blanchet@36491
   701
      | first_pass ((step as Let _) :: proof, contra) =
blanchet@36491
   702
        first_pass (proof, contra) |>> cons step
blanchet@37498
   703
      | first_pass ((step as Assume (l as (_, num), _)) :: proof, contra) =
blanchet@37996
   704
        if l = concl_l then
blanchet@37996
   705
          first_pass (proof, contra ||> l = concl_l ? cons step)
blanchet@36402
   706
        else
blanchet@36551
   707
          first_pass (proof, contra) |>> cons (Assume (l, find_hyp num))
blanchet@37324
   708
      | first_pass (Have (qs, l, t, ByMetis (ls, ss)) :: proof, contra) =
blanchet@37996
   709
        let val step = Have (qs, l, t, ByMetis (ls, ss)) in
blanchet@37324
   710
          if exists (member (op =) (fst contra)) ls then
blanchet@37324
   711
            first_pass (proof, contra |>> cons l ||> cons step)
blanchet@37324
   712
          else
blanchet@37324
   713
            first_pass (proof, contra) |>> cons step
blanchet@37324
   714
        end
blanchet@36402
   715
      | first_pass _ = raise Fail "malformed proof"
blanchet@36402
   716
    val (proof_top, (contra_ls, contra_proof)) =
blanchet@37996
   717
      first_pass (proof, ([concl_l], []))
blanchet@36402
   718
    val backpatch_label = the_default ([], []) oo AList.lookup (op =) o fst
blanchet@36402
   719
    fun backpatch_labels patches ls =
blanchet@36402
   720
      fold merge_fact_sets (map (backpatch_label patches) ls) ([], [])
blanchet@36402
   721
    fun second_pass end_qs ([], assums, patches) =
blanchet@37324
   722
        ([Have (end_qs, no_label, concl_t,
blanchet@36564
   723
                ByMetis (backpatch_labels patches (map snd assums)))], patches)
blanchet@36402
   724
      | second_pass end_qs (Assume (l, t) :: proof, assums, patches) =
blanchet@36402
   725
        second_pass end_qs (proof, (t, l) :: assums, patches)
blanchet@36564
   726
      | second_pass end_qs (Have (qs, l, t, ByMetis (ls, ss)) :: proof, assums,
blanchet@36402
   727
                            patches) =
blanchet@36402
   728
        if member (op =) (snd (snd patches)) l andalso
blanchet@37322
   729
           not (member (op =) (fst (snd patches)) l) andalso
blanchet@36402
   730
           not (AList.defined (op =) (fst patches) l) then
blanchet@36402
   731
          second_pass end_qs (proof, assums, patches ||> apsnd (append ls))
blanchet@36402
   732
        else
blanchet@36402
   733
          (case List.partition (member (op =) contra_ls) ls of
blanchet@36402
   734
             ([contra_l], co_ls) =>
blanchet@37322
   735
             if member (op =) qs Show then
blanchet@37322
   736
               second_pass end_qs (proof, assums,
blanchet@37322
   737
                                   patches |>> cons (contra_l, (co_ls, ss)))
blanchet@37322
   738
             else
blanchet@36402
   739
               second_pass end_qs
blanchet@36402
   740
                           (proof, assums,
blanchet@36402
   741
                            patches |>> cons (contra_l, (l :: co_ls, ss)))
blanchet@36402
   742
               |>> cons (if member (op =) (fst (snd patches)) l then
blanchet@37991
   743
                           Assume (l, negate_term t)
blanchet@36402
   744
                         else
blanchet@37991
   745
                           Have (qs, l, negate_term t,
blanchet@36564
   746
                                 ByMetis (backpatch_label patches l)))
blanchet@36402
   747
           | (contra_ls as _ :: _, co_ls) =>
blanchet@36402
   748
             let
blanchet@36402
   749
               val proofs =
blanchet@36402
   750
                 map_filter
blanchet@36402
   751
                     (fn l =>
blanchet@37996
   752
                         if l = concl_l then
blanchet@36402
   753
                           NONE
blanchet@36402
   754
                         else
blanchet@36402
   755
                           let
blanchet@36402
   756
                             val drop_ls = filter (curry (op <>) l) contra_ls
blanchet@36402
   757
                           in
blanchet@36402
   758
                             second_pass []
blanchet@36402
   759
                                 (proof, assums,
blanchet@36402
   760
                                  patches ||> apfst (insert (op =) l)
blanchet@36402
   761
                                          ||> apsnd (union (op =) drop_ls))
blanchet@36402
   762
                             |> fst |> SOME
blanchet@36402
   763
                           end) contra_ls
blanchet@37324
   764
               val (assumes, facts) =
blanchet@37324
   765
                 if member (op =) (fst (snd patches)) l then
blanchet@37991
   766
                   ([Assume (l, negate_term t)], (l :: co_ls, ss))
blanchet@37324
   767
                 else
blanchet@37324
   768
                   ([], (co_ls, ss))
blanchet@36402
   769
             in
blanchet@36402
   770
               (case join_proofs proofs of
blanchet@36402
   771
                  SOME (l, t, proofs, proof_tail) =>
blanchet@36402
   772
                  Have (case_split_qualifiers proofs @
blanchet@36402
   773
                        (if null proof_tail then end_qs else []), l, t,
blanchet@36574
   774
                        smart_case_split proofs facts) :: proof_tail
blanchet@36402
   775
                | NONE =>
blanchet@36402
   776
                  [Have (case_split_qualifiers proofs @ end_qs, no_label,
blanchet@36574
   777
                         concl_t, smart_case_split proofs facts)],
blanchet@36402
   778
                patches)
blanchet@37324
   779
               |>> append assumes
blanchet@36402
   780
             end
blanchet@36402
   781
           | _ => raise Fail "malformed proof")
blanchet@36402
   782
       | second_pass _ _ = raise Fail "malformed proof"
blanchet@36486
   783
    val proof_bottom =
blanchet@36486
   784
      second_pass [Show] (contra_proof, [], ([], ([], []))) |> fst
blanchet@36402
   785
  in proof_top @ proof_bottom end
blanchet@36402
   786
blanchet@36402
   787
val kill_duplicate_assumptions_in_proof =
blanchet@36402
   788
  let
blanchet@36402
   789
    fun relabel_facts subst =
blanchet@36402
   790
      apfst (map (fn l => AList.lookup (op =) subst l |> the_default l))
blanchet@36491
   791
    fun do_step (step as Assume (l, t)) (proof, subst, assums) =
blanchet@36402
   792
        (case AList.lookup (op aconv) assums t of
blanchet@36967
   793
           SOME l' => (proof, (l, l') :: subst, assums)
blanchet@36491
   794
         | NONE => (step :: proof, subst, (t, l) :: assums))
blanchet@36402
   795
      | do_step (Have (qs, l, t, by)) (proof, subst, assums) =
blanchet@36402
   796
        (Have (qs, l, t,
blanchet@36402
   797
               case by of
blanchet@36564
   798
                 ByMetis facts => ByMetis (relabel_facts subst facts)
blanchet@36402
   799
               | CaseSplit (proofs, facts) =>
blanchet@36402
   800
                 CaseSplit (map do_proof proofs, relabel_facts subst facts)) ::
blanchet@36402
   801
         proof, subst, assums)
blanchet@36491
   802
      | do_step step (proof, subst, assums) = (step :: proof, subst, assums)
blanchet@36402
   803
    and do_proof proof = fold do_step proof ([], [], []) |> #1 |> rev
blanchet@36402
   804
  in do_proof end
blanchet@36402
   805
blanchet@36402
   806
val then_chain_proof =
blanchet@36402
   807
  let
blanchet@36402
   808
    fun aux _ [] = []
blanchet@36491
   809
      | aux _ ((step as Assume (l, _)) :: proof) = step :: aux l proof
blanchet@36402
   810
      | aux l' (Have (qs, l, t, by) :: proof) =
blanchet@36402
   811
        (case by of
blanchet@36564
   812
           ByMetis (ls, ss) =>
blanchet@36402
   813
           Have (if member (op =) ls l' then
blanchet@36402
   814
                   (Then :: qs, l, t,
blanchet@36564
   815
                    ByMetis (filter_out (curry (op =) l') ls, ss))
blanchet@36402
   816
                 else
blanchet@36564
   817
                   (qs, l, t, ByMetis (ls, ss)))
blanchet@36402
   818
         | CaseSplit (proofs, facts) =>
blanchet@36402
   819
           Have (qs, l, t, CaseSplit (map (aux no_label) proofs, facts))) ::
blanchet@36402
   820
        aux l proof
blanchet@36491
   821
      | aux _ (step :: proof) = step :: aux no_label proof
blanchet@36402
   822
  in aux no_label end
blanchet@36402
   823
blanchet@36402
   824
fun kill_useless_labels_in_proof proof =
blanchet@36402
   825
  let
blanchet@36556
   826
    val used_ls = used_labels_of proof
blanchet@36402
   827
    fun do_label l = if member (op =) used_ls l then l else no_label
blanchet@36556
   828
    fun do_step (Assume (l, t)) = Assume (do_label l, t)
blanchet@36556
   829
      | do_step (Have (qs, l, t, by)) =
blanchet@36402
   830
        Have (qs, do_label l, t,
blanchet@36402
   831
              case by of
blanchet@36402
   832
                CaseSplit (proofs, facts) =>
blanchet@36556
   833
                CaseSplit (map (map do_step) proofs, facts)
blanchet@36402
   834
              | _ => by)
blanchet@36556
   835
      | do_step step = step
blanchet@36556
   836
  in map do_step proof end
blanchet@36402
   837
blanchet@36402
   838
fun prefix_for_depth n = replicate_string (n + 1)
blanchet@36402
   839
blanchet@36402
   840
val relabel_proof =
blanchet@36402
   841
  let
blanchet@36402
   842
    fun aux _ _ _ [] = []
blanchet@36402
   843
      | aux subst depth (next_assum, next_fact) (Assume (l, t) :: proof) =
blanchet@36402
   844
        if l = no_label then
blanchet@36402
   845
          Assume (l, t) :: aux subst depth (next_assum, next_fact) proof
blanchet@36402
   846
        else
blanchet@36402
   847
          let val l' = (prefix_for_depth depth assum_prefix, next_assum) in
blanchet@36402
   848
            Assume (l', t) ::
blanchet@36402
   849
            aux ((l, l') :: subst) depth (next_assum + 1, next_fact) proof
blanchet@36402
   850
          end
blanchet@36402
   851
      | aux subst depth (next_assum, next_fact) (Have (qs, l, t, by) :: proof) =
blanchet@36402
   852
        let
blanchet@36402
   853
          val (l', subst, next_fact) =
blanchet@36402
   854
            if l = no_label then
blanchet@36402
   855
              (l, subst, next_fact)
blanchet@36402
   856
            else
blanchet@36402
   857
              let
blanchet@36402
   858
                val l' = (prefix_for_depth depth fact_prefix, next_fact)
blanchet@36402
   859
              in (l', (l, l') :: subst, next_fact + 1) end
blanchet@36570
   860
          val relabel_facts =
blanchet@36570
   861
            apfst (map (fn l =>
blanchet@36570
   862
                           case AList.lookup (op =) subst l of
blanchet@36570
   863
                             SOME l' => l'
blanchet@36570
   864
                           | NONE => raise Fail ("unknown label " ^
blanchet@36570
   865
                                                 quote (string_for_label l))))
blanchet@36402
   866
          val by =
blanchet@36402
   867
            case by of
blanchet@36564
   868
              ByMetis facts => ByMetis (relabel_facts facts)
blanchet@36402
   869
            | CaseSplit (proofs, facts) =>
blanchet@36402
   870
              CaseSplit (map (aux subst (depth + 1) (1, 1)) proofs,
blanchet@36402
   871
                         relabel_facts facts)
blanchet@36402
   872
        in
blanchet@36402
   873
          Have (qs, l', t, by) ::
blanchet@36402
   874
          aux subst depth (next_assum, next_fact) proof
blanchet@36402
   875
        end
blanchet@36491
   876
      | aux subst depth nextp (step :: proof) =
blanchet@36491
   877
        step :: aux subst depth nextp proof
blanchet@36402
   878
  in aux [] 0 (1, 1) end
blanchet@36402
   879
blanchet@37479
   880
fun string_for_proof ctxt full_types i n =
blanchet@36402
   881
  let
blanchet@37319
   882
    fun fix_print_mode f x =
blanchet@37319
   883
      setmp_CRITICAL show_no_free_types true
blanchet@37319
   884
          (setmp_CRITICAL show_types true
blanchet@37319
   885
               (Print_Mode.setmp (filter (curry (op =) Symbol.xsymbolsN)
blanchet@37319
   886
                                         (print_mode_value ())) f)) x
blanchet@36402
   887
    fun do_indent ind = replicate_string (ind * indent_size) " "
blanchet@36478
   888
    fun do_free (s, T) =
blanchet@36478
   889
      maybe_quote s ^ " :: " ^
blanchet@36478
   890
      maybe_quote (fix_print_mode (Syntax.string_of_typ ctxt) T)
blanchet@36570
   891
    fun do_label l = if l = no_label then "" else string_for_label l ^ ": "
blanchet@36402
   892
    fun do_have qs =
blanchet@36402
   893
      (if member (op =) qs Moreover then "moreover " else "") ^
blanchet@36402
   894
      (if member (op =) qs Ultimately then "ultimately " else "") ^
blanchet@36402
   895
      (if member (op =) qs Then then
blanchet@36402
   896
         if member (op =) qs Show then "thus" else "hence"
blanchet@36402
   897
       else
blanchet@36402
   898
         if member (op =) qs Show then "show" else "have")
blanchet@36478
   899
    val do_term = maybe_quote o fix_print_mode (Syntax.string_of_term ctxt)
blanchet@36570
   900
    fun do_facts (ls, ss) =
blanchet@36570
   901
      let
blanchet@36570
   902
        val ls = ls |> sort_distinct (prod_ord string_ord int_ord)
blanchet@37171
   903
        val ss = ss |> map unprefix_chained |> sort_distinct string_ord
blanchet@37479
   904
      in metis_command full_types 1 1 (ls, ss) end
blanchet@36478
   905
    and do_step ind (Fix xs) =
blanchet@36478
   906
        do_indent ind ^ "fix " ^ space_implode " and " (map do_free xs) ^ "\n"
blanchet@36486
   907
      | do_step ind (Let (t1, t2)) =
blanchet@36486
   908
        do_indent ind ^ "let " ^ do_term t1 ^ " = " ^ do_term t2 ^ "\n"
blanchet@36402
   909
      | do_step ind (Assume (l, t)) =
blanchet@36402
   910
        do_indent ind ^ "assume " ^ do_label l ^ do_term t ^ "\n"
blanchet@36564
   911
      | do_step ind (Have (qs, l, t, ByMetis facts)) =
blanchet@36402
   912
        do_indent ind ^ do_have qs ^ " " ^
blanchet@36479
   913
        do_label l ^ do_term t ^ " " ^ do_facts facts ^ "\n"
blanchet@36402
   914
      | do_step ind (Have (qs, l, t, CaseSplit (proofs, facts))) =
blanchet@36402
   915
        space_implode (do_indent ind ^ "moreover\n")
blanchet@36402
   916
                      (map (do_block ind) proofs) ^
blanchet@36479
   917
        do_indent ind ^ do_have qs ^ " " ^ do_label l ^ do_term t ^ " " ^
blanchet@36478
   918
        do_facts facts ^ "\n"
blanchet@36402
   919
    and do_steps prefix suffix ind steps =
blanchet@36402
   920
      let val s = implode (map (do_step ind) steps) in
blanchet@36402
   921
        replicate_string (ind * indent_size - size prefix) " " ^ prefix ^
blanchet@36402
   922
        String.extract (s, ind * indent_size,
blanchet@36402
   923
                        SOME (size s - ind * indent_size - 1)) ^
blanchet@36402
   924
        suffix ^ "\n"
blanchet@36402
   925
      end
blanchet@36402
   926
    and do_block ind proof = do_steps "{ " " }" (ind + 1) proof
blanchet@36564
   927
    (* One-step proofs are pointless; better use the Metis one-liner
blanchet@36564
   928
       directly. *)
blanchet@36564
   929
    and do_proof [Have (_, _, _, ByMetis _)] = ""
blanchet@36564
   930
      | do_proof proof =
blanchet@36480
   931
        (if i <> 1 then "prefer " ^ string_of_int i ^ "\n" else "") ^
blanchet@36480
   932
        do_indent 0 ^ "proof -\n" ^
blanchet@36480
   933
        do_steps "" "" 1 proof ^
blanchet@36480
   934
        do_indent 0 ^ (if n <> 1 then "next" else "qed") ^ "\n"
blanchet@36488
   935
  in do_proof end
blanchet@36402
   936
blanchet@37479
   937
fun isar_proof_text (pool, debug, isar_shrink_factor, ctxt, conjecture_shape)
blanchet@37479
   938
                    (other_params as (full_types, _, atp_proof, thm_names, goal,
blanchet@37479
   939
                                      i)) =
blanchet@36402
   940
  let
blanchet@36909
   941
    val (params, hyp_ts, concl_t) = strip_subgoal goal i
blanchet@36909
   942
    val frees = fold Term.add_frees (concl_t :: hyp_ts) []
blanchet@36967
   943
    val tfrees = fold Term.add_tfrees (concl_t :: hyp_ts) []
blanchet@36402
   944
    val n = Logic.count_prems (prop_of goal)
blanchet@37479
   945
    val (one_line_proof, lemma_names) = metis_proof_text other_params
blanchet@36283
   946
    fun isar_proof_for () =
blanchet@36967
   947
      case proof_from_atp_proof pool ctxt full_types tfrees isar_shrink_factor
blanchet@36924
   948
                                atp_proof conjecture_shape thm_names params
blanchet@36924
   949
                                frees
blanchet@37991
   950
           |> redirect_proof conjecture_shape hyp_ts concl_t
blanchet@36402
   951
           |> kill_duplicate_assumptions_in_proof
blanchet@36402
   952
           |> then_chain_proof
blanchet@36402
   953
           |> kill_useless_labels_in_proof
blanchet@36402
   954
           |> relabel_proof
blanchet@37479
   955
           |> string_for_proof ctxt full_types i n of
blanchet@36283
   956
        "" => ""
blanchet@36402
   957
      | proof => "\nStructured proof:\n" ^ Markup.markup Markup.sendback proof
blanchet@35868
   958
    val isar_proof =
blanchet@36402
   959
      if debug then
blanchet@36283
   960
        isar_proof_for ()
blanchet@36283
   961
      else
blanchet@36283
   962
        try isar_proof_for ()
blanchet@36287
   963
        |> the_default "Warning: The Isar proof construction failed.\n"
blanchet@36283
   964
  in (one_line_proof ^ isar_proof, lemma_names) end
paulson@21978
   965
blanchet@36557
   966
fun proof_text isar_proof isar_params other_params =
blanchet@36557
   967
  (if isar_proof then isar_proof_text isar_params else metis_proof_text)
blanchet@36557
   968
      other_params
blanchet@36223
   969
immler@31038
   970
end;