src/HOL/Tools/Sledgehammer/sledgehammer_proof_reconstruct.ML
author blanchet
Tue Jul 27 15:28:23 2010 +0200 (2010-07-27)
changeset 38014 81c23d286f0c
parent 38007 f0a4aa17f23f
child 38015 b30c3c2e1030
permissions -rw-r--r--
extract sort constraints from FOFs properly;
we can't rely on having them as separate literals anymore
blanchet@35826
     1
(*  Title:      HOL/Tools/Sledgehammer/sledgehammer_proof_reconstruct.ML
wenzelm@33310
     2
    Author:     Lawrence C Paulson and Claire Quigley, Cambridge University Computer Laboratory
blanchet@36392
     3
    Author:     Jasmin Blanchette, TU Muenchen
paulson@21978
     4
wenzelm@33310
     5
Transfer of proofs from external provers.
wenzelm@33310
     6
*)
wenzelm@33310
     7
blanchet@35826
     8
signature SLEDGEHAMMER_PROOF_RECONSTRUCT =
paulson@24425
     9
sig
blanchet@36281
    10
  type minimize_command = string list -> string
blanchet@36281
    11
blanchet@37479
    12
  val metis_line: bool -> int -> int -> string list -> string
blanchet@36223
    13
  val metis_proof_text:
blanchet@37479
    14
    bool * minimize_command * string * string vector * thm * int
blanchet@36281
    15
    -> string * string list
blanchet@36223
    16
  val isar_proof_text:
blanchet@37996
    17
    string Symtab.table * bool * int * Proof.context * int list
blanchet@37479
    18
    -> bool * minimize_command * string * string vector * thm * int
blanchet@36287
    19
    -> string * string list
blanchet@36223
    20
  val proof_text:
blanchet@37996
    21
    bool -> string Symtab.table * bool * int * Proof.context * int list
blanchet@37479
    22
    -> bool * minimize_command * string * string vector * thm * int
blanchet@36287
    23
    -> string * string list
paulson@24425
    24
end;
paulson@21978
    25
blanchet@35826
    26
structure Sledgehammer_Proof_Reconstruct : SLEDGEHAMMER_PROOF_RECONSTRUCT =
paulson@21978
    27
struct
paulson@21978
    28
blanchet@37578
    29
open Metis_Clauses
blanchet@36478
    30
open Sledgehammer_Util
blanchet@37616
    31
open Sledgehammer_Fact_Filter
blanchet@37624
    32
open Sledgehammer_TPTP_Format
paulson@21978
    33
blanchet@36281
    34
type minimize_command = string list -> string
blanchet@36281
    35
blanchet@38014
    36
(* Simple simplifications to ensure that sort annotations don't leave a trail of
blanchet@38014
    37
   spurious "True"s. *)
blanchet@38014
    38
fun s_not @{const False} = @{const True}
blanchet@38014
    39
  | s_not @{const True} = @{const False}
blanchet@38014
    40
  | s_not (@{const Not} $ t) = t
blanchet@38014
    41
  | s_not t = @{const Not} $ t
blanchet@38014
    42
fun s_conj (@{const True}, t2) = t2
blanchet@38014
    43
  | s_conj (t1, @{const True}) = t1
blanchet@38014
    44
  | s_conj p = HOLogic.mk_conj p
blanchet@38014
    45
fun s_disj (@{const False}, t2) = t2
blanchet@38014
    46
  | s_disj (t1, @{const False}) = t1
blanchet@38014
    47
  | s_disj p = HOLogic.mk_disj p
blanchet@38014
    48
fun s_imp (@{const True}, t2) = t2
blanchet@38014
    49
  | s_imp (t1, @{const False}) = s_not t1
blanchet@38014
    50
  | s_imp p = HOLogic.mk_imp p
blanchet@38014
    51
fun s_iff (@{const True}, t2) = t2
blanchet@38014
    52
  | s_iff (t1, @{const True}) = t1
blanchet@38014
    53
  | s_iff (t1, t2) = HOLogic.eq_const HOLogic.boolT $ t1 $ t2
blanchet@38014
    54
blanchet@38014
    55
fun mk_anot (AConn (ANot, [phi])) = phi
blanchet@38014
    56
  | mk_anot phi = AConn (ANot, [phi])
blanchet@37991
    57
fun mk_aconn c (phi1, phi2) = AConn (c, [phi1, phi2])
blanchet@37991
    58
blanchet@37996
    59
val index_in_shape : int -> int list -> int = find_index o curry (op =)
blanchet@37962
    60
fun is_axiom_clause_number thm_names num =
blanchet@37962
    61
  num > 0 andalso num <= Vector.length thm_names andalso
blanchet@37962
    62
  Vector.sub (thm_names, num - 1) <> ""
blanchet@36570
    63
fun is_conjecture_clause_number conjecture_shape num =
blanchet@36570
    64
  index_in_shape num conjecture_shape >= 0
blanchet@36291
    65
blanchet@37991
    66
fun negate_term (Const (@{const_name All}, T) $ Abs (s, T', t')) =
blanchet@37991
    67
    Const (@{const_name Ex}, T) $ Abs (s, T', negate_term t')
blanchet@37991
    68
  | negate_term (Const (@{const_name Ex}, T) $ Abs (s, T', t')) =
blanchet@37991
    69
    Const (@{const_name All}, T) $ Abs (s, T', negate_term t')
blanchet@37991
    70
  | negate_term (@{const "op -->"} $ t1 $ t2) =
blanchet@37991
    71
    @{const "op &"} $ t1 $ negate_term t2
blanchet@37991
    72
  | negate_term (@{const "op &"} $ t1 $ t2) =
blanchet@37991
    73
    @{const "op |"} $ negate_term t1 $ negate_term t2
blanchet@37991
    74
  | negate_term (@{const "op |"} $ t1 $ t2) =
blanchet@37991
    75
    @{const "op &"} $ negate_term t1 $ negate_term t2
blanchet@37991
    76
  | negate_term (@{const Not} $ t) = t
blanchet@37991
    77
  | negate_term t = @{const Not} $ t
blanchet@37991
    78
blanchet@36491
    79
datatype ('a, 'b, 'c, 'd, 'e) raw_step =
blanchet@36491
    80
  Definition of 'a * 'b * 'c |
blanchet@36491
    81
  Inference of 'a * 'd * 'e list
blanchet@36491
    82
paulson@21978
    83
(**** PARSING OF TSTP FORMAT ****)
paulson@21978
    84
blanchet@37991
    85
datatype int_or_string = Str of string | Int of int
paulson@21978
    86
paulson@21978
    87
(*Strings enclosed in single quotes, e.g. filenames*)
blanchet@37991
    88
val scan_quoted = $$ "'" |-- Scan.repeat (~$$ "'") --| $$ "'" >> implode;
paulson@21978
    89
blanchet@37991
    90
val scan_dollar_name =
blanchet@36548
    91
  Scan.repeat ($$ "$") -- Symbol.scan_id >> (fn (ss, s) => implode ss ^ s)
blanchet@36548
    92
blanchet@36369
    93
(* needed for SPASS's output format *)
blanchet@36548
    94
fun repair_name _ "$true" = "c_True"
blanchet@36548
    95
  | repair_name _ "$false" = "c_False"
blanchet@38007
    96
  | repair_name _ "$$e" = "c_equal" (* seen in Vampire proofs *)
blanchet@36548
    97
  | repair_name _ "equal" = "c_equal" (* probably not needed *)
blanchet@37926
    98
  | repair_name pool s = Symtab.lookup pool s |> the_default s
blanchet@36392
    99
(* Generalized first-order terms, which include file names, numbers, etc. *)
blanchet@36393
   100
(* The "x" argument is not strictly necessary, but without it Poly/ML loops
blanchet@36393
   101
   forever at compile time. *)
blanchet@37991
   102
fun parse_generalized_term x =
blanchet@37991
   103
  (scan_quoted >> (fn s => ATerm (Str s, []))
blanchet@37991
   104
   || scan_dollar_name
blanchet@37991
   105
      -- Scan.optional ($$ "(" |-- parse_generalized_terms --| $$ ")") []
blanchet@37991
   106
      >> (fn (s, gs) => ATerm (Str s, gs))
blanchet@37991
   107
   || scan_integer >> (fn k => ATerm (Int k, []))
blanchet@37991
   108
   || $$ "(" |-- parse_generalized_term --| $$ ")"
blanchet@37991
   109
   || $$ "[" |-- Scan.optional parse_generalized_terms [] --| $$ "]"
blanchet@37991
   110
      >> curry ATerm (Str "list")) x
blanchet@37991
   111
and parse_generalized_terms x =
blanchet@37991
   112
  (parse_generalized_term ::: Scan.repeat ($$ "," |-- parse_generalized_term)) x
blanchet@36393
   113
fun parse_term pool x =
blanchet@37991
   114
  ((scan_dollar_name >> repair_name pool)
blanchet@37991
   115
    -- Scan.optional ($$ "(" |-- parse_terms pool --| $$ ")") [] >> ATerm) x
blanchet@36393
   116
and parse_terms pool x =
blanchet@36393
   117
  (parse_term pool ::: Scan.repeat ($$ "," |-- parse_term pool)) x
paulson@21978
   118
blanchet@36393
   119
fun parse_predicate_term pool =
blanchet@36393
   120
  parse_term pool -- Scan.option (Scan.option ($$ "!") --| $$ "="
blanchet@36393
   121
                                  -- parse_term pool)
blanchet@37991
   122
  >> (fn (u, NONE) => APred u
blanchet@37991
   123
       | (u1, SOME (NONE, u2)) => APred (ATerm ("c_equal", [u1, u2]))
blanchet@37991
   124
       | (u1, SOME (SOME _, u2)) =>
blanchet@37991
   125
         mk_anot (APred (ATerm ("c_equal", [u1, u2]))))
blanchet@37991
   126
blanchet@37991
   127
fun fo_term_head (ATerm (s, _)) = s
blanchet@36291
   128
blanchet@37991
   129
(* TPTP formulas are fully parenthesized, so we don't need to worry about
blanchet@37991
   130
   operator precedence. *)
blanchet@37991
   131
fun parse_formula pool x =
blanchet@37991
   132
  (($$ "(" |-- parse_formula pool --| $$ ")"
blanchet@37991
   133
    || ($$ "!" >> K AForall || $$ "?" >> K AExists)
blanchet@37991
   134
       --| $$ "[" -- parse_terms pool --| $$ "]" --| $$ ":"
blanchet@37991
   135
       -- parse_formula pool
blanchet@37991
   136
       >> (fn ((q, ts), phi) => AQuant (q, map fo_term_head ts, phi))
blanchet@37991
   137
    || $$ "~" |-- parse_formula pool >> mk_anot
blanchet@37991
   138
    || parse_predicate_term pool)
blanchet@37991
   139
   -- Scan.option ((Scan.this_string "=>" >> K AImplies
blanchet@37991
   140
                    || Scan.this_string "<=>" >> K AIff
blanchet@37991
   141
                    || Scan.this_string "<~>" >> K ANotIff
blanchet@37991
   142
                    || Scan.this_string "<=" >> K AIf
blanchet@37991
   143
                    || $$ "|" >> K AOr || $$ "&" >> K AAnd)
blanchet@37991
   144
                   -- parse_formula pool)
blanchet@37991
   145
   >> (fn (phi1, NONE) => phi1
blanchet@37991
   146
        | (phi1, SOME (c, phi2)) => mk_aconn c (phi1, phi2))) x
blanchet@37991
   147
blanchet@37991
   148
fun ints_of_generalized_term (ATerm (label, gs)) =
blanchet@37991
   149
  fold ints_of_generalized_term gs #> (case label of Int k => cons k | _ => I)
blanchet@36392
   150
val parse_tstp_annotations =
blanchet@37991
   151
  Scan.optional ($$ "," |-- parse_generalized_term
blanchet@37991
   152
                   --| Scan.option ($$ "," |-- parse_generalized_terms)
blanchet@37991
   153
                 >> (fn g => ints_of_generalized_term g [])) []
blanchet@36486
   154
blanchet@37991
   155
(* Syntax: (fof|cnf)\(<num>, <formula_role>, <cnf_formula> <annotations>\).
blanchet@36486
   156
   The <num> could be an identifier, but we assume integers. *)
blanchet@37991
   157
 fun parse_tstp_line pool =
blanchet@37991
   158
   ((Scan.this_string "fof" || Scan.this_string "cnf") -- $$ "(")
blanchet@37991
   159
     |-- scan_integer --| $$ "," -- Symbol.scan_id --| $$ ","
blanchet@37991
   160
     -- parse_formula pool -- parse_tstp_annotations --| $$ ")" --| $$ "."
blanchet@37991
   161
    >> (fn (((num, role), phi), deps) =>
blanchet@37991
   162
           case role of
blanchet@37991
   163
             "definition" =>
blanchet@37991
   164
             (case phi of
blanchet@38007
   165
                AConn (AIff, [phi1 as APred _, phi2]) =>
blanchet@38007
   166
                Definition (num, phi1, phi2)
blanchet@38007
   167
              | APred (ATerm ("$$e", _)) =>
blanchet@38007
   168
                Inference (num, phi, deps) (* Vampire's equality proxy axiom *)
blanchet@37991
   169
              | _ => raise Fail "malformed definition")
blanchet@37991
   170
           | _ => Inference (num, phi, deps))
blanchet@36291
   171
blanchet@36291
   172
(**** PARSING OF SPASS OUTPUT ****)
blanchet@36291
   173
blanchet@36392
   174
(* SPASS returns clause references of the form "x.y". We ignore "y", whose role
blanchet@36392
   175
   is not clear anyway. *)
blanchet@37962
   176
val parse_dot_name = scan_integer --| $$ "." --| scan_integer
paulson@21978
   177
blanchet@36392
   178
val parse_spass_annotations =
blanchet@36392
   179
  Scan.optional ($$ ":" |-- Scan.repeat (parse_dot_name
blanchet@36392
   180
                                         --| Scan.option ($$ ","))) []
blanchet@36291
   181
blanchet@36574
   182
(* It is not clear why some literals are followed by sequences of stars and/or
blanchet@36574
   183
   pluses. We ignore them. *)
blanchet@36574
   184
fun parse_decorated_predicate_term pool =
blanchet@36562
   185
  parse_predicate_term pool --| Scan.repeat ($$ "*" || $$ "+" || $$ " ")
blanchet@36291
   186
blanchet@37991
   187
fun mk_horn ([], []) = APred (ATerm ("c_False", []))
blanchet@37991
   188
  | mk_horn ([], pos_lits) = foldr1 (mk_aconn AOr) pos_lits
blanchet@37991
   189
  | mk_horn (neg_lits, []) = mk_anot (foldr1 (mk_aconn AAnd) neg_lits)
blanchet@37991
   190
  | mk_horn (neg_lits, pos_lits) =
blanchet@37991
   191
    mk_aconn AImplies (foldr1 (mk_aconn AAnd) neg_lits,
blanchet@37991
   192
                       foldr1 (mk_aconn AOr) pos_lits)
blanchet@37991
   193
blanchet@36393
   194
fun parse_horn_clause pool =
blanchet@36574
   195
  Scan.repeat (parse_decorated_predicate_term pool) --| $$ "|" --| $$ "|"
blanchet@36574
   196
    -- Scan.repeat (parse_decorated_predicate_term pool) --| $$ "-" --| $$ ">"
blanchet@36574
   197
    -- Scan.repeat (parse_decorated_predicate_term pool)
blanchet@37991
   198
  >> (mk_horn o apfst (op @))
paulson@21978
   199
blanchet@36558
   200
(* Syntax: <num>[0:<inference><annotations>]
blanchet@36558
   201
   <cnf_formulas> || <cnf_formulas> -> <cnf_formulas>. *)
blanchet@36402
   202
fun parse_spass_line pool =
blanchet@37962
   203
  scan_integer --| $$ "[" --| $$ "0" --| $$ ":" --| Symbol.scan_id
blanchet@36558
   204
  -- parse_spass_annotations --| $$ "]" -- parse_horn_clause pool --| $$ "."
blanchet@37991
   205
  >> (fn ((num, deps), u) => Inference (num, u, deps))
blanchet@36291
   206
blanchet@36548
   207
fun parse_line pool = parse_tstp_line pool || parse_spass_line pool
blanchet@36548
   208
fun parse_lines pool = Scan.repeat1 (parse_line pool)
blanchet@36548
   209
fun parse_proof pool =
blanchet@36548
   210
  fst o Scan.finite Symbol.stopper
blanchet@36548
   211
            (Scan.error (!! (fn _ => raise Fail "unrecognized ATP output")
blanchet@36548
   212
                            (parse_lines pool)))
blanchet@36548
   213
  o explode o strip_spaces
paulson@21978
   214
paulson@21978
   215
(**** INTERPRETATION OF TSTP SYNTAX TREES ****)
paulson@21978
   216
blanchet@37991
   217
exception FO_TERM of string fo_term list
blanchet@37994
   218
exception FORMULA of (string, string fo_term) formula list
blanchet@37991
   219
exception SAME of unit
paulson@21978
   220
blanchet@36909
   221
(* Type variables are given the basic sort "HOL.type". Some will later be
blanchet@37991
   222
   constrained by information from type literals, or by type inference. *)
blanchet@37991
   223
fun type_from_fo_term tfrees (u as ATerm (a, us)) =
blanchet@37991
   224
  let val Ts = map (type_from_fo_term tfrees) us in
blanchet@37991
   225
    case strip_prefix_and_undo_ascii type_const_prefix a of
blanchet@37991
   226
      SOME b => Type (invert_const b, Ts)
blanchet@37991
   227
    | NONE =>
blanchet@37991
   228
      if not (null us) then
blanchet@37991
   229
        raise FO_TERM [u]  (* only "tconst"s have type arguments *)
blanchet@37991
   230
      else case strip_prefix_and_undo_ascii tfree_prefix a of
blanchet@37991
   231
        SOME b =>
blanchet@37991
   232
        let val s = "'" ^ b in
blanchet@37991
   233
          TFree (s, AList.lookup (op =) tfrees s |> the_default HOLogic.typeS)
blanchet@37991
   234
        end
blanchet@36486
   235
      | NONE =>
blanchet@37991
   236
        case strip_prefix_and_undo_ascii tvar_prefix a of
blanchet@37991
   237
          SOME b => TVar (("'" ^ b, 0), HOLogic.typeS)
blanchet@36486
   238
        | NONE =>
blanchet@37991
   239
          (* Variable from the ATP, say "X1" *)
blanchet@37991
   240
          Type_Infer.param 0 (a, HOLogic.typeS)
blanchet@37991
   241
  end
paulson@21978
   242
blanchet@38014
   243
(* Type class literal applied to a type. Returns triple of polarity, class,
blanchet@38014
   244
   type. *)
blanchet@38014
   245
fun type_constraint_from_term pos tfrees (u as ATerm (a, us)) =
blanchet@38014
   246
  case (strip_prefix_and_undo_ascii class_prefix a,
blanchet@38014
   247
        map (type_from_fo_term tfrees) us) of
blanchet@38014
   248
    (SOME b, [T]) => (pos, b, T)
blanchet@38014
   249
  | _ => raise FO_TERM [u]
blanchet@38014
   250
blanchet@38014
   251
(** Accumulate type constraints in a clause: negative type literals **)
blanchet@38014
   252
fun add_var (key, z)  = Vartab.map_default (key, []) (cons z)
blanchet@38014
   253
fun add_type_constraint (false, cl, TFree (a ,_)) = add_var ((a, ~1), cl)
blanchet@38014
   254
  | add_type_constraint (false, cl, TVar (ix, _)) = add_var (ix, cl)
blanchet@38014
   255
  | add_type_constraint _ = I
blanchet@38014
   256
blanchet@36486
   257
fun fix_atp_variable_name s =
blanchet@36486
   258
  let
blanchet@36486
   259
    fun subscript_name s n = s ^ nat_subscript n
blanchet@36486
   260
    val s = String.map Char.toLower s
blanchet@36486
   261
  in
blanchet@36486
   262
    case space_explode "_" s of
blanchet@36486
   263
      [_] => (case take_suffix Char.isDigit (String.explode s) of
blanchet@36486
   264
                (cs1 as _ :: _, cs2 as _ :: _) =>
blanchet@36486
   265
                subscript_name (String.implode cs1)
blanchet@36486
   266
                               (the (Int.fromString (String.implode cs2)))
blanchet@36486
   267
              | (_, _) => s)
blanchet@36486
   268
    | [s1, s2] => (case Int.fromString s2 of
blanchet@36486
   269
                     SOME n => subscript_name s1 n
blanchet@36486
   270
                   | NONE => s)
blanchet@36486
   271
    | _ => s
blanchet@36486
   272
  end
blanchet@36486
   273
blanchet@36909
   274
(* First-order translation. No types are known for variables. "HOLogic.typeT"
blanchet@38014
   275
   should allow them to be inferred. *)
blanchet@38014
   276
fun raw_term_from_pred thy full_types tfrees =
blanchet@36909
   277
  let
blanchet@37643
   278
    fun aux opt_T extra_us u =
blanchet@36909
   279
      case u of
blanchet@37991
   280
        ATerm ("hBOOL", [u1]) => aux (SOME @{typ bool}) [] u1
blanchet@37991
   281
      | ATerm ("hAPP", [u1, u2]) => aux opt_T (u2 :: extra_us) u1
blanchet@37991
   282
      | ATerm (a, us) =>
blanchet@36909
   283
        if a = type_wrapper_name then
blanchet@36909
   284
          case us of
blanchet@37643
   285
            [typ_u, term_u] =>
blanchet@37991
   286
            aux (SOME (type_from_fo_term tfrees typ_u)) extra_us term_u
blanchet@37991
   287
          | _ => raise FO_TERM us
blanchet@37991
   288
        else case strip_prefix_and_undo_ascii const_prefix a of
blanchet@36909
   289
          SOME "equal" =>
blanchet@36909
   290
          list_comb (Const (@{const_name "op ="}, HOLogic.typeT),
blanchet@36909
   291
                     map (aux NONE []) us)
blanchet@36909
   292
        | SOME b =>
blanchet@36909
   293
          let
blanchet@36909
   294
            val c = invert_const b
blanchet@36909
   295
            val num_type_args = num_type_args thy c
blanchet@37643
   296
            val (type_us, term_us) =
blanchet@37643
   297
              chop (if full_types then 0 else num_type_args) us
blanchet@37643
   298
            (* Extra args from "hAPP" come after any arguments given directly to
blanchet@37643
   299
               the constant. *)
blanchet@37643
   300
            val term_ts = map (aux NONE []) term_us
blanchet@37643
   301
            val extra_ts = map (aux NONE []) extra_us
blanchet@36909
   302
            val t =
blanchet@36909
   303
              Const (c, if full_types then
blanchet@36909
   304
                          case opt_T of
blanchet@37643
   305
                            SOME T => map fastype_of term_ts ---> T
blanchet@36909
   306
                          | NONE =>
blanchet@36909
   307
                            if num_type_args = 0 then
blanchet@36909
   308
                              Sign.const_instance thy (c, [])
blanchet@36909
   309
                            else
blanchet@36909
   310
                              raise Fail ("no type information for " ^ quote c)
blanchet@36909
   311
                        else
blanchet@37998
   312
                          Sign.const_instance thy (c,
blanchet@37998
   313
                              map (type_from_fo_term tfrees) type_us))
blanchet@37643
   314
          in list_comb (t, term_ts @ extra_ts) end
blanchet@36909
   315
        | NONE => (* a free or schematic variable *)
blanchet@36909
   316
          let
blanchet@37643
   317
            val ts = map (aux NONE []) (us @ extra_us)
blanchet@36909
   318
            val T = map fastype_of ts ---> HOLogic.typeT
blanchet@36909
   319
            val t =
blanchet@37991
   320
              case strip_prefix_and_undo_ascii fixed_var_prefix a of
blanchet@36909
   321
                SOME b => Free (b, T)
blanchet@36909
   322
              | NONE =>
blanchet@37991
   323
                case strip_prefix_and_undo_ascii schematic_var_prefix a of
blanchet@36967
   324
                  SOME b => Var ((b, 0), T)
blanchet@36909
   325
                | NONE =>
blanchet@38014
   326
                  if is_variable a then Var ((fix_atp_variable_name a, 0), T)
blanchet@38014
   327
                  else raise Fail ("Unexpected constant: " ^ quote a)
blanchet@36909
   328
          in list_comb (t, ts) end
blanchet@38014
   329
  in aux (SOME HOLogic.boolT) [] end
paulson@21978
   330
blanchet@38014
   331
fun term_from_pred thy full_types tfrees pos (u as ATerm (s, _)) =
blanchet@38014
   332
  if String.isPrefix class_prefix s then
blanchet@38014
   333
    add_type_constraint (type_constraint_from_term pos tfrees u)
blanchet@38014
   334
    #> pair @{const True}
blanchet@38014
   335
  else
blanchet@38014
   336
    pair (raw_term_from_pred thy full_types tfrees u)
blanchet@36402
   337
blanchet@36555
   338
val combinator_table =
blanchet@36555
   339
  [(@{const_name COMBI}, @{thm COMBI_def_raw}),
blanchet@36555
   340
   (@{const_name COMBK}, @{thm COMBK_def_raw}),
blanchet@36555
   341
   (@{const_name COMBB}, @{thm COMBB_def_raw}),
blanchet@36555
   342
   (@{const_name COMBC}, @{thm COMBC_def_raw}),
blanchet@36555
   343
   (@{const_name COMBS}, @{thm COMBS_def_raw})]
blanchet@36555
   344
blanchet@36555
   345
fun uncombine_term (t1 $ t2) = betapply (pairself uncombine_term (t1, t2))
blanchet@36555
   346
  | uncombine_term (Abs (s, T, t')) = Abs (s, T, uncombine_term t')
blanchet@36555
   347
  | uncombine_term (t as Const (x as (s, _))) =
blanchet@36555
   348
    (case AList.lookup (op =) combinator_table s of
blanchet@36555
   349
       SOME thm => thm |> prop_of |> specialize_type @{theory} x |> Logic.dest_equals |> snd
blanchet@36555
   350
     | NONE => t)
blanchet@36555
   351
  | uncombine_term t = t
blanchet@36555
   352
blanchet@37991
   353
(* Update schematic type variables with detected sort constraints. It's not
blanchet@37991
   354
   totally clear when this code is necessary. *)
blanchet@38014
   355
fun repair_tvar_sorts (t, tvar_tab) =
blanchet@36909
   356
  let
blanchet@37991
   357
    fun do_type (Type (a, Ts)) = Type (a, map do_type Ts)
blanchet@37991
   358
      | do_type (TVar (xi, s)) =
blanchet@37991
   359
        TVar (xi, the_default s (Vartab.lookup tvar_tab xi))
blanchet@37991
   360
      | do_type (TFree z) = TFree z
blanchet@37991
   361
    fun do_term (Const (a, T)) = Const (a, do_type T)
blanchet@37991
   362
      | do_term (Free (a, T)) = Free (a, do_type T)
blanchet@37991
   363
      | do_term (Var (xi, T)) = Var (xi, do_type T)
blanchet@37991
   364
      | do_term (t as Bound _) = t
blanchet@37991
   365
      | do_term (Abs (a, T, t)) = Abs (a, do_type T, do_term t)
blanchet@37991
   366
      | do_term (t1 $ t2) = do_term t1 $ do_term t2
blanchet@37991
   367
  in t |> not (Vartab.is_empty tvar_tab) ? do_term end
blanchet@37991
   368
blanchet@37991
   369
fun quantify_over_free quant_s free_s body_t =
blanchet@37991
   370
  case Term.add_frees body_t [] |> filter (curry (op =) free_s o fst) of
blanchet@37991
   371
    [] => body_t
blanchet@37991
   372
  | frees as (_, free_T) :: _ =>
blanchet@37991
   373
    Abs (free_s, free_T, fold (curry abstract_over) (map Free frees) body_t)
blanchet@37991
   374
blanchet@38014
   375
(* Interpret a list of syntax trees as a clause, extracting sort constraints
blanchet@38014
   376
   as they appear in the formula. *)
blanchet@38014
   377
fun prop_from_formula thy full_types tfrees phi =
blanchet@38014
   378
  let
blanchet@38014
   379
    fun do_formula pos phi =
blanchet@37991
   380
      case phi of
blanchet@38014
   381
        AQuant (_, [], phi) => do_formula pos phi
blanchet@37991
   382
      | AQuant (q, x :: xs, phi') =>
blanchet@38014
   383
        do_formula pos (AQuant (q, xs, phi'))
blanchet@38014
   384
        #>> quantify_over_free (case q of
blanchet@38014
   385
                                  AForall => @{const_name All}
blanchet@38014
   386
                                | AExists => @{const_name Ex}) x
blanchet@38014
   387
      | AConn (ANot, [phi']) => do_formula (not pos) phi' #>> s_not
blanchet@37991
   388
      | AConn (c, [phi1, phi2]) =>
blanchet@38014
   389
        do_formula (pos |> c = AImplies ? not) phi1
blanchet@38014
   390
        ##>> do_formula pos phi2
blanchet@38014
   391
        #>> (case c of
blanchet@38014
   392
               AAnd => s_conj
blanchet@38014
   393
             | AOr => s_disj
blanchet@38014
   394
             | AImplies => s_imp
blanchet@38014
   395
             | AIff => s_iff)
blanchet@38014
   396
      | APred tm => term_from_pred thy full_types tfrees pos tm
blanchet@37991
   397
      | _ => raise FORMULA [phi]
blanchet@38014
   398
  in repair_tvar_sorts (do_formula true phi Vartab.empty) end
blanchet@37991
   399
blanchet@36556
   400
fun check_formula ctxt =
blanchet@38014
   401
  Type_Infer.constrain HOLogic.boolT
blanchet@36486
   402
  #> Syntax.check_term (ProofContext.set_mode ProofContext.mode_schematic ctxt)
paulson@21978
   403
paulson@21978
   404
paulson@21978
   405
(**** Translation of TSTP files to Isar Proofs ****)
paulson@21978
   406
blanchet@36486
   407
fun unvarify_term (Var ((s, 0), T)) = Free (s, T)
blanchet@36486
   408
  | unvarify_term t = raise TERM ("unvarify_term: non-Var", [t])
paulson@21978
   409
blanchet@37991
   410
fun decode_line full_types tfrees (Definition (num, phi1, phi2)) ctxt =
blanchet@36486
   411
    let
blanchet@37991
   412
      val thy = ProofContext.theory_of ctxt
blanchet@37991
   413
      val t1 = prop_from_formula thy full_types tfrees phi1
blanchet@36551
   414
      val vars = snd (strip_comb t1)
blanchet@36486
   415
      val frees = map unvarify_term vars
blanchet@36486
   416
      val unvarify_args = subst_atomic (vars ~~ frees)
blanchet@37991
   417
      val t2 = prop_from_formula thy full_types tfrees phi2
blanchet@36551
   418
      val (t1, t2) =
blanchet@36551
   419
        HOLogic.eq_const HOLogic.typeT $ t1 $ t2
blanchet@36556
   420
        |> unvarify_args |> uncombine_term |> check_formula ctxt
blanchet@36555
   421
        |> HOLogic.dest_eq
blanchet@36486
   422
    in
blanchet@36551
   423
      (Definition (num, t1, t2),
blanchet@36551
   424
       fold Variable.declare_term (maps OldTerm.term_frees [t1, t2]) ctxt)
blanchet@36486
   425
    end
blanchet@37991
   426
  | decode_line full_types tfrees (Inference (num, u, deps)) ctxt =
blanchet@36551
   427
    let
blanchet@37991
   428
      val thy = ProofContext.theory_of ctxt
blanchet@37991
   429
      val t = u |> prop_from_formula thy full_types tfrees
blanchet@37998
   430
                |> uncombine_term |> check_formula ctxt
blanchet@36551
   431
    in
blanchet@36551
   432
      (Inference (num, t, deps),
blanchet@36551
   433
       fold Variable.declare_term (OldTerm.term_frees t) ctxt)
blanchet@36486
   434
    end
blanchet@36967
   435
fun decode_lines ctxt full_types tfrees lines =
blanchet@36967
   436
  fst (fold_map (decode_line full_types tfrees) lines ctxt)
paulson@21978
   437
blanchet@37323
   438
fun aint_actual_inference _ (Definition _) = true
blanchet@37323
   439
  | aint_actual_inference t (Inference (_, t', _)) = not (t aconv t')
blanchet@36486
   440
blanchet@36486
   441
(* No "real" literals means only type information (tfree_tcs, clsrel, or
blanchet@36486
   442
   clsarity). *)
blanchet@36486
   443
val is_only_type_information = curry (op aconv) HOLogic.true_const
blanchet@36486
   444
blanchet@36486
   445
fun replace_one_dep (old, new) dep = if dep = old then new else [dep]
blanchet@36486
   446
fun replace_deps_in_line _ (line as Definition _) = line
blanchet@36486
   447
  | replace_deps_in_line p (Inference (num, t, deps)) =
blanchet@36486
   448
    Inference (num, t, fold (union (op =) o replace_one_dep p) deps [])
paulson@21978
   449
paulson@22491
   450
(*Discard axioms; consolidate adjacent lines that prove the same clause, since they differ
paulson@22491
   451
  only in type information.*)
blanchet@36551
   452
fun add_line _ _ (line as Definition _) lines = line :: lines
blanchet@36551
   453
  | add_line conjecture_shape thm_names (Inference (num, t, [])) lines =
blanchet@36570
   454
    (* No dependencies: axiom, conjecture clause, or internal axioms or
blanchet@36570
   455
       definitions (Vampire). *)
blanchet@36486
   456
    if is_axiom_clause_number thm_names num then
blanchet@36486
   457
      (* Axioms are not proof lines. *)
blanchet@36486
   458
      if is_only_type_information t then
blanchet@36486
   459
        map (replace_deps_in_line (num, [])) lines
blanchet@36486
   460
      (* Is there a repetition? If so, replace later line by earlier one. *)
blanchet@37323
   461
      else case take_prefix (aint_actual_inference t) lines of
blanchet@36486
   462
        (_, []) => lines (*no repetition of proof line*)
blanchet@36486
   463
      | (pre, Inference (num', _, _) :: post) =>
blanchet@36486
   464
        pre @ map (replace_deps_in_line (num', [num])) post
blanchet@36570
   465
    else if is_conjecture_clause_number conjecture_shape num then
blanchet@36486
   466
      Inference (num, t, []) :: lines
blanchet@36551
   467
    else
blanchet@36570
   468
      map (replace_deps_in_line (num, [])) lines
blanchet@36551
   469
  | add_line _ _ (Inference (num, t, deps)) lines =
blanchet@36486
   470
    (* Type information will be deleted later; skip repetition test. *)
blanchet@36486
   471
    if is_only_type_information t then
blanchet@36486
   472
      Inference (num, t, deps) :: lines
blanchet@36486
   473
    (* Is there a repetition? If so, replace later line by earlier one. *)
blanchet@37323
   474
    else case take_prefix (aint_actual_inference t) lines of
blanchet@36486
   475
      (* FIXME: Doesn't this code risk conflating proofs involving different
blanchet@36486
   476
         types?? *)
blanchet@36486
   477
       (_, []) => Inference (num, t, deps) :: lines
blanchet@36486
   478
     | (pre, Inference (num', t', _) :: post) =>
blanchet@36486
   479
       Inference (num, t', deps) ::
blanchet@36486
   480
       pre @ map (replace_deps_in_line (num', [num])) post
paulson@22044
   481
blanchet@36486
   482
(* Recursively delete empty lines (type information) from the proof. *)
blanchet@36486
   483
fun add_nontrivial_line (Inference (num, t, [])) lines =
blanchet@36486
   484
    if is_only_type_information t then delete_dep num lines
blanchet@36486
   485
    else Inference (num, t, []) :: lines
blanchet@36486
   486
  | add_nontrivial_line line lines = line :: lines
blanchet@36395
   487
and delete_dep num lines =
blanchet@36486
   488
  fold_rev add_nontrivial_line (map (replace_deps_in_line (num, [])) lines) []
blanchet@36486
   489
blanchet@37323
   490
(* ATPs sometimes reuse free variable names in the strangest ways. Removing
blanchet@37323
   491
   offending lines often does the trick. *)
blanchet@36560
   492
fun is_bad_free frees (Free x) = not (member (op =) frees x)
blanchet@36560
   493
  | is_bad_free _ _ = false
paulson@22470
   494
blanchet@36570
   495
(* Vampire is keen on producing these. *)
blanchet@36570
   496
fun is_trivial_formula (@{const Not} $ (Const (@{const_name "op ="}, _)
blanchet@36570
   497
                                        $ t1 $ t2)) = (t1 aconv t2)
blanchet@37498
   498
  | is_trivial_formula _ = false
blanchet@36570
   499
blanchet@37498
   500
fun add_desired_line _ _ _ _ (line as Definition (num, _, _)) (j, lines) =
blanchet@37323
   501
    (j, line :: map (replace_deps_in_line (num, [])) lines)
blanchet@37498
   502
  | add_desired_line isar_shrink_factor conjecture_shape thm_names frees
blanchet@36570
   503
                     (Inference (num, t, deps)) (j, lines) =
blanchet@36402
   504
    (j + 1,
blanchet@36570
   505
     if is_axiom_clause_number thm_names num orelse
blanchet@36570
   506
        is_conjecture_clause_number conjecture_shape num orelse
blanchet@36570
   507
        (not (is_only_type_information t) andalso
blanchet@36570
   508
         null (Term.add_tvars t []) andalso
blanchet@36570
   509
         not (exists_subterm (is_bad_free frees) t) andalso
blanchet@36570
   510
         not (is_trivial_formula t) andalso
blanchet@36570
   511
         (null lines orelse (* last line must be kept *)
blanchet@36924
   512
          (length deps >= 2 andalso j mod isar_shrink_factor = 0))) then
blanchet@36570
   513
       Inference (num, t, deps) :: lines  (* keep line *)
blanchet@36402
   514
     else
blanchet@36570
   515
       map (replace_deps_in_line (num, deps)) lines)  (* drop line *)
paulson@21978
   516
blanchet@36402
   517
(** EXTRACTING LEMMAS **)
paulson@21979
   518
blanchet@37991
   519
(* A list consisting of the first number in each line is returned. For TSTP,
blanchet@37991
   520
   interesting lines have the form "fof(108, axiom, ...)", where the number
blanchet@37991
   521
   (108) is extracted. For SPASS, lines have the form "108[0:Inp] ...", where
blanchet@37991
   522
   the first number (108) is extracted. *)
blanchet@37961
   523
fun extract_formula_numbers_in_atp_proof atp_proof =
blanchet@35865
   524
  let
blanchet@37962
   525
    val tokens_of = String.tokens (not o Char.isAlphaNum)
blanchet@37961
   526
    fun extract_num ("fof" :: num :: "axiom" :: _) = Int.fromString num
blanchet@36395
   527
      | extract_num (num :: "0" :: "Inp" :: _) = Int.fromString num
blanchet@36395
   528
      | extract_num _ = NONE
blanchet@36402
   529
  in atp_proof |> split_lines |> map_filter (extract_num o tokens_of) end
blanchet@37399
   530
blanchet@37399
   531
val indent_size = 2
blanchet@37399
   532
val no_label = ("", ~1)
blanchet@37399
   533
blanchet@37399
   534
val raw_prefix = "X"
blanchet@37399
   535
val assum_prefix = "A"
blanchet@37399
   536
val fact_prefix = "F"
blanchet@37399
   537
blanchet@37399
   538
fun string_for_label (s, num) = s ^ string_of_int num
blanchet@37399
   539
blanchet@37399
   540
fun metis_using [] = ""
blanchet@37399
   541
  | metis_using ls =
blanchet@37399
   542
    "using " ^ space_implode " " (map string_for_label ls) ^ " "
blanchet@37399
   543
fun metis_apply _ 1 = "by "
blanchet@37399
   544
  | metis_apply 1 _ = "apply "
blanchet@37399
   545
  | metis_apply i _ = "prefer " ^ string_of_int i ^ " apply "
blanchet@37479
   546
fun metis_name full_types = if full_types then "metisFT" else "metis"
blanchet@37479
   547
fun metis_call full_types [] = metis_name full_types
blanchet@37479
   548
  | metis_call full_types ss =
blanchet@37479
   549
    "(" ^ metis_name full_types ^ " " ^ space_implode " " ss ^ ")"
blanchet@37479
   550
fun metis_command full_types i n (ls, ss) =
blanchet@37479
   551
  metis_using ls ^ metis_apply i n ^ metis_call full_types ss
blanchet@37479
   552
fun metis_line full_types i n ss =
blanchet@36063
   553
  "Try this command: " ^
blanchet@37479
   554
  Markup.markup Markup.sendback (metis_command full_types i n ([], ss)) ^ ".\n"
blanchet@36281
   555
fun minimize_line _ [] = ""
blanchet@36281
   556
  | minimize_line minimize_command facts =
blanchet@36281
   557
    case minimize_command facts of
blanchet@36281
   558
      "" => ""
blanchet@36281
   559
    | command =>
blanchet@36065
   560
      "To minimize the number of lemmas, try this command: " ^
blanchet@36281
   561
      Markup.markup Markup.sendback command ^ ".\n"
immler@31840
   562
blanchet@37171
   563
val unprefix_chained = perhaps (try (unprefix chained_prefix))
blanchet@37171
   564
blanchet@37479
   565
fun metis_proof_text (full_types, minimize_command, atp_proof, thm_names, goal,
blanchet@37479
   566
                      i) =
blanchet@36063
   567
  let
blanchet@37171
   568
    val raw_lemmas =
blanchet@37961
   569
      atp_proof |> extract_formula_numbers_in_atp_proof
blanchet@36402
   570
                |> filter (is_axiom_clause_number thm_names)
blanchet@36402
   571
                |> map (fn i => Vector.sub (thm_names, i - 1))
blanchet@37171
   572
    val (chained_lemmas, other_lemmas) =
blanchet@37171
   573
      raw_lemmas |> List.partition (String.isPrefix chained_prefix)
blanchet@37171
   574
                 |>> map (unprefix chained_prefix)
blanchet@37171
   575
                 |> pairself (sort_distinct string_ord)
blanchet@37171
   576
    val lemmas = other_lemmas @ chained_lemmas
blanchet@36063
   577
    val n = Logic.count_prems (prop_of goal)
blanchet@37171
   578
  in
blanchet@37479
   579
    (metis_line full_types i n other_lemmas ^
blanchet@37479
   580
     minimize_line minimize_command lemmas, lemmas)
blanchet@37171
   581
  end
immler@31037
   582
blanchet@36486
   583
(** Isar proof construction and manipulation **)
blanchet@36486
   584
blanchet@36486
   585
fun merge_fact_sets (ls1, ss1) (ls2, ss2) =
blanchet@36486
   586
  (union (op =) ls1 ls2, union (op =) ss1 ss2)
blanchet@36402
   587
blanchet@36402
   588
type label = string * int
blanchet@36402
   589
type facts = label list * string list
blanchet@36402
   590
blanchet@36402
   591
datatype qualifier = Show | Then | Moreover | Ultimately
blanchet@36291
   592
blanchet@36402
   593
datatype step =
blanchet@36478
   594
  Fix of (string * typ) list |
blanchet@36486
   595
  Let of term * term |
blanchet@36402
   596
  Assume of label * term |
blanchet@36402
   597
  Have of qualifier list * label * term * byline
blanchet@36402
   598
and byline =
blanchet@36564
   599
  ByMetis of facts |
blanchet@36402
   600
  CaseSplit of step list list * facts
blanchet@36402
   601
blanchet@36574
   602
fun smart_case_split [] facts = ByMetis facts
blanchet@36574
   603
  | smart_case_split proofs facts = CaseSplit (proofs, facts)
blanchet@36574
   604
blanchet@36475
   605
fun add_fact_from_dep thm_names num =
blanchet@36475
   606
  if is_axiom_clause_number thm_names num then
blanchet@36480
   607
    apsnd (insert (op =) (Vector.sub (thm_names, num - 1)))
blanchet@36475
   608
  else
blanchet@36480
   609
    apfst (insert (op =) (raw_prefix, num))
blanchet@36402
   610
blanchet@37998
   611
fun forall_of v t = HOLogic.all_const (fastype_of v) $ lambda v t
blanchet@36491
   612
fun forall_vars t = fold_rev forall_of (map Var (Term.add_vars t [])) t
blanchet@36491
   613
blanchet@37498
   614
fun step_for_line _ _ (Definition (_, t1, t2)) = Let (t1, t2)
blanchet@36486
   615
  | step_for_line _ _ (Inference (num, t, [])) = Assume ((raw_prefix, num), t)
blanchet@36486
   616
  | step_for_line thm_names j (Inference (num, t, deps)) =
blanchet@36486
   617
    Have (if j = 1 then [Show] else [], (raw_prefix, num),
blanchet@36491
   618
          forall_vars t,
blanchet@36564
   619
          ByMetis (fold (add_fact_from_dep thm_names) deps ([], [])))
blanchet@36291
   620
blanchet@36967
   621
fun proof_from_atp_proof pool ctxt full_types tfrees isar_shrink_factor
blanchet@36967
   622
                         atp_proof conjecture_shape thm_names params frees =
blanchet@36402
   623
  let
blanchet@36486
   624
    val lines =
blanchet@37991
   625
      atp_proof ^ "$" (* the $ sign acts as a sentinel (FIXME: pick it up) *)
blanchet@36548
   626
      |> parse_proof pool
blanchet@36967
   627
      |> decode_lines ctxt full_types tfrees
blanchet@36551
   628
      |> rpair [] |-> fold_rev (add_line conjecture_shape thm_names)
blanchet@36486
   629
      |> rpair [] |-> fold_rev add_nontrivial_line
blanchet@37498
   630
      |> rpair (0, []) |-> fold_rev (add_desired_line isar_shrink_factor
blanchet@36570
   631
                                               conjecture_shape thm_names frees)
blanchet@36486
   632
      |> snd
blanchet@36402
   633
  in
blanchet@36909
   634
    (if null params then [] else [Fix params]) @
blanchet@36486
   635
    map2 (step_for_line thm_names) (length lines downto 1) lines
blanchet@36402
   636
  end
blanchet@36402
   637
blanchet@36402
   638
(* When redirecting proofs, we keep information about the labels seen so far in
blanchet@36402
   639
   the "backpatches" data structure. The first component indicates which facts
blanchet@36402
   640
   should be associated with forthcoming proof steps. The second component is a
blanchet@37322
   641
   pair ("assum_ls", "drop_ls"), where "assum_ls" are the labels that should
blanchet@37322
   642
   become assumptions and "drop_ls" are the labels that should be dropped in a
blanchet@37322
   643
   case split. *)
blanchet@36402
   644
type backpatches = (label * facts) list * (label list * label list)
blanchet@36402
   645
blanchet@36556
   646
fun used_labels_of_step (Have (_, _, _, by)) =
blanchet@36402
   647
    (case by of
blanchet@36564
   648
       ByMetis (ls, _) => ls
blanchet@36556
   649
     | CaseSplit (proofs, (ls, _)) =>
blanchet@36556
   650
       fold (union (op =) o used_labels_of) proofs ls)
blanchet@36556
   651
  | used_labels_of_step _ = []
blanchet@36556
   652
and used_labels_of proof = fold (union (op =) o used_labels_of_step) proof []
blanchet@36402
   653
blanchet@36402
   654
fun new_labels_of_step (Fix _) = []
blanchet@36486
   655
  | new_labels_of_step (Let _) = []
blanchet@36402
   656
  | new_labels_of_step (Assume (l, _)) = [l]
blanchet@36402
   657
  | new_labels_of_step (Have (_, l, _, _)) = [l]
blanchet@36402
   658
val new_labels_of = maps new_labels_of_step
blanchet@36402
   659
blanchet@36402
   660
val join_proofs =
blanchet@36402
   661
  let
blanchet@36402
   662
    fun aux _ [] = NONE
blanchet@36402
   663
      | aux proof_tail (proofs as (proof1 :: _)) =
blanchet@36402
   664
        if exists null proofs then
blanchet@36402
   665
          NONE
blanchet@36402
   666
        else if forall (curry (op =) (hd proof1) o hd) (tl proofs) then
blanchet@36402
   667
          aux (hd proof1 :: proof_tail) (map tl proofs)
blanchet@36402
   668
        else case hd proof1 of
blanchet@37498
   669
          Have ([], l, t, _) => (* FIXME: should we really ignore the "by"? *)
blanchet@36402
   670
          if forall (fn Have ([], l', t', _) :: _ => (l, t) = (l', t')
blanchet@36402
   671
                      | _ => false) (tl proofs) andalso
blanchet@36402
   672
             not (exists (member (op =) (maps new_labels_of proofs))
blanchet@36556
   673
                         (used_labels_of proof_tail)) then
blanchet@36402
   674
            SOME (l, t, map rev proofs, proof_tail)
blanchet@36402
   675
          else
blanchet@36402
   676
            NONE
blanchet@36402
   677
        | _ => NONE
blanchet@36402
   678
  in aux [] o map rev end
blanchet@36402
   679
blanchet@36402
   680
fun case_split_qualifiers proofs =
blanchet@36402
   681
  case length proofs of
blanchet@36402
   682
    0 => []
blanchet@36402
   683
  | 1 => [Then]
blanchet@36402
   684
  | _ => [Ultimately]
blanchet@36402
   685
blanchet@37991
   686
fun redirect_proof conjecture_shape hyp_ts concl_t proof =
wenzelm@33310
   687
  let
blanchet@37324
   688
    (* The first pass outputs those steps that are independent of the negated
blanchet@37324
   689
       conjecture. The second pass flips the proof by contradiction to obtain a
blanchet@37324
   690
       direct proof, introducing case splits when an inference depends on
blanchet@37324
   691
       several facts that depend on the negated conjecture. *)
blanchet@37324
   692
    fun find_hyp num = nth hyp_ts (index_in_shape num conjecture_shape)
blanchet@37996
   693
    val concl_l = (raw_prefix, List.last conjecture_shape)
blanchet@36402
   694
    fun first_pass ([], contra) = ([], contra)
blanchet@36491
   695
      | first_pass ((step as Fix _) :: proof, contra) =
blanchet@36491
   696
        first_pass (proof, contra) |>> cons step
blanchet@36491
   697
      | first_pass ((step as Let _) :: proof, contra) =
blanchet@36491
   698
        first_pass (proof, contra) |>> cons step
blanchet@37498
   699
      | first_pass ((step as Assume (l as (_, num), _)) :: proof, contra) =
blanchet@37996
   700
        if l = concl_l then
blanchet@37996
   701
          first_pass (proof, contra ||> l = concl_l ? cons step)
blanchet@36402
   702
        else
blanchet@36551
   703
          first_pass (proof, contra) |>> cons (Assume (l, find_hyp num))
blanchet@37324
   704
      | first_pass (Have (qs, l, t, ByMetis (ls, ss)) :: proof, contra) =
blanchet@37996
   705
        let val step = Have (qs, l, t, ByMetis (ls, ss)) in
blanchet@37324
   706
          if exists (member (op =) (fst contra)) ls then
blanchet@37324
   707
            first_pass (proof, contra |>> cons l ||> cons step)
blanchet@37324
   708
          else
blanchet@37324
   709
            first_pass (proof, contra) |>> cons step
blanchet@37324
   710
        end
blanchet@36402
   711
      | first_pass _ = raise Fail "malformed proof"
blanchet@36402
   712
    val (proof_top, (contra_ls, contra_proof)) =
blanchet@37996
   713
      first_pass (proof, ([concl_l], []))
blanchet@36402
   714
    val backpatch_label = the_default ([], []) oo AList.lookup (op =) o fst
blanchet@36402
   715
    fun backpatch_labels patches ls =
blanchet@36402
   716
      fold merge_fact_sets (map (backpatch_label patches) ls) ([], [])
blanchet@36402
   717
    fun second_pass end_qs ([], assums, patches) =
blanchet@37324
   718
        ([Have (end_qs, no_label, concl_t,
blanchet@36564
   719
                ByMetis (backpatch_labels patches (map snd assums)))], patches)
blanchet@36402
   720
      | second_pass end_qs (Assume (l, t) :: proof, assums, patches) =
blanchet@36402
   721
        second_pass end_qs (proof, (t, l) :: assums, patches)
blanchet@36564
   722
      | second_pass end_qs (Have (qs, l, t, ByMetis (ls, ss)) :: proof, assums,
blanchet@36402
   723
                            patches) =
blanchet@36402
   724
        if member (op =) (snd (snd patches)) l andalso
blanchet@37322
   725
           not (member (op =) (fst (snd patches)) l) andalso
blanchet@36402
   726
           not (AList.defined (op =) (fst patches) l) then
blanchet@36402
   727
          second_pass end_qs (proof, assums, patches ||> apsnd (append ls))
blanchet@36402
   728
        else
blanchet@36402
   729
          (case List.partition (member (op =) contra_ls) ls of
blanchet@36402
   730
             ([contra_l], co_ls) =>
blanchet@37322
   731
             if member (op =) qs Show then
blanchet@37322
   732
               second_pass end_qs (proof, assums,
blanchet@37322
   733
                                   patches |>> cons (contra_l, (co_ls, ss)))
blanchet@37322
   734
             else
blanchet@36402
   735
               second_pass end_qs
blanchet@36402
   736
                           (proof, assums,
blanchet@36402
   737
                            patches |>> cons (contra_l, (l :: co_ls, ss)))
blanchet@36402
   738
               |>> cons (if member (op =) (fst (snd patches)) l then
blanchet@37991
   739
                           Assume (l, negate_term t)
blanchet@36402
   740
                         else
blanchet@37991
   741
                           Have (qs, l, negate_term t,
blanchet@36564
   742
                                 ByMetis (backpatch_label patches l)))
blanchet@36402
   743
           | (contra_ls as _ :: _, co_ls) =>
blanchet@36402
   744
             let
blanchet@36402
   745
               val proofs =
blanchet@36402
   746
                 map_filter
blanchet@36402
   747
                     (fn l =>
blanchet@37996
   748
                         if l = concl_l then
blanchet@36402
   749
                           NONE
blanchet@36402
   750
                         else
blanchet@36402
   751
                           let
blanchet@36402
   752
                             val drop_ls = filter (curry (op <>) l) contra_ls
blanchet@36402
   753
                           in
blanchet@36402
   754
                             second_pass []
blanchet@36402
   755
                                 (proof, assums,
blanchet@36402
   756
                                  patches ||> apfst (insert (op =) l)
blanchet@36402
   757
                                          ||> apsnd (union (op =) drop_ls))
blanchet@36402
   758
                             |> fst |> SOME
blanchet@36402
   759
                           end) contra_ls
blanchet@37324
   760
               val (assumes, facts) =
blanchet@37324
   761
                 if member (op =) (fst (snd patches)) l then
blanchet@37991
   762
                   ([Assume (l, negate_term t)], (l :: co_ls, ss))
blanchet@37324
   763
                 else
blanchet@37324
   764
                   ([], (co_ls, ss))
blanchet@36402
   765
             in
blanchet@36402
   766
               (case join_proofs proofs of
blanchet@36402
   767
                  SOME (l, t, proofs, proof_tail) =>
blanchet@36402
   768
                  Have (case_split_qualifiers proofs @
blanchet@36402
   769
                        (if null proof_tail then end_qs else []), l, t,
blanchet@36574
   770
                        smart_case_split proofs facts) :: proof_tail
blanchet@36402
   771
                | NONE =>
blanchet@36402
   772
                  [Have (case_split_qualifiers proofs @ end_qs, no_label,
blanchet@36574
   773
                         concl_t, smart_case_split proofs facts)],
blanchet@36402
   774
                patches)
blanchet@37324
   775
               |>> append assumes
blanchet@36402
   776
             end
blanchet@36402
   777
           | _ => raise Fail "malformed proof")
blanchet@36402
   778
       | second_pass _ _ = raise Fail "malformed proof"
blanchet@36486
   779
    val proof_bottom =
blanchet@36486
   780
      second_pass [Show] (contra_proof, [], ([], ([], []))) |> fst
blanchet@36402
   781
  in proof_top @ proof_bottom end
blanchet@36402
   782
blanchet@36402
   783
val kill_duplicate_assumptions_in_proof =
blanchet@36402
   784
  let
blanchet@36402
   785
    fun relabel_facts subst =
blanchet@36402
   786
      apfst (map (fn l => AList.lookup (op =) subst l |> the_default l))
blanchet@36491
   787
    fun do_step (step as Assume (l, t)) (proof, subst, assums) =
blanchet@36402
   788
        (case AList.lookup (op aconv) assums t of
blanchet@36967
   789
           SOME l' => (proof, (l, l') :: subst, assums)
blanchet@36491
   790
         | NONE => (step :: proof, subst, (t, l) :: assums))
blanchet@36402
   791
      | do_step (Have (qs, l, t, by)) (proof, subst, assums) =
blanchet@36402
   792
        (Have (qs, l, t,
blanchet@36402
   793
               case by of
blanchet@36564
   794
                 ByMetis facts => ByMetis (relabel_facts subst facts)
blanchet@36402
   795
               | CaseSplit (proofs, facts) =>
blanchet@36402
   796
                 CaseSplit (map do_proof proofs, relabel_facts subst facts)) ::
blanchet@36402
   797
         proof, subst, assums)
blanchet@36491
   798
      | do_step step (proof, subst, assums) = (step :: proof, subst, assums)
blanchet@36402
   799
    and do_proof proof = fold do_step proof ([], [], []) |> #1 |> rev
blanchet@36402
   800
  in do_proof end
blanchet@36402
   801
blanchet@36402
   802
val then_chain_proof =
blanchet@36402
   803
  let
blanchet@36402
   804
    fun aux _ [] = []
blanchet@36491
   805
      | aux _ ((step as Assume (l, _)) :: proof) = step :: aux l proof
blanchet@36402
   806
      | aux l' (Have (qs, l, t, by) :: proof) =
blanchet@36402
   807
        (case by of
blanchet@36564
   808
           ByMetis (ls, ss) =>
blanchet@36402
   809
           Have (if member (op =) ls l' then
blanchet@36402
   810
                   (Then :: qs, l, t,
blanchet@36564
   811
                    ByMetis (filter_out (curry (op =) l') ls, ss))
blanchet@36402
   812
                 else
blanchet@36564
   813
                   (qs, l, t, ByMetis (ls, ss)))
blanchet@36402
   814
         | CaseSplit (proofs, facts) =>
blanchet@36402
   815
           Have (qs, l, t, CaseSplit (map (aux no_label) proofs, facts))) ::
blanchet@36402
   816
        aux l proof
blanchet@36491
   817
      | aux _ (step :: proof) = step :: aux no_label proof
blanchet@36402
   818
  in aux no_label end
blanchet@36402
   819
blanchet@36402
   820
fun kill_useless_labels_in_proof proof =
blanchet@36402
   821
  let
blanchet@36556
   822
    val used_ls = used_labels_of proof
blanchet@36402
   823
    fun do_label l = if member (op =) used_ls l then l else no_label
blanchet@36556
   824
    fun do_step (Assume (l, t)) = Assume (do_label l, t)
blanchet@36556
   825
      | do_step (Have (qs, l, t, by)) =
blanchet@36402
   826
        Have (qs, do_label l, t,
blanchet@36402
   827
              case by of
blanchet@36402
   828
                CaseSplit (proofs, facts) =>
blanchet@36556
   829
                CaseSplit (map (map do_step) proofs, facts)
blanchet@36402
   830
              | _ => by)
blanchet@36556
   831
      | do_step step = step
blanchet@36556
   832
  in map do_step proof end
blanchet@36402
   833
blanchet@36402
   834
fun prefix_for_depth n = replicate_string (n + 1)
blanchet@36402
   835
blanchet@36402
   836
val relabel_proof =
blanchet@36402
   837
  let
blanchet@36402
   838
    fun aux _ _ _ [] = []
blanchet@36402
   839
      | aux subst depth (next_assum, next_fact) (Assume (l, t) :: proof) =
blanchet@36402
   840
        if l = no_label then
blanchet@36402
   841
          Assume (l, t) :: aux subst depth (next_assum, next_fact) proof
blanchet@36402
   842
        else
blanchet@36402
   843
          let val l' = (prefix_for_depth depth assum_prefix, next_assum) in
blanchet@36402
   844
            Assume (l', t) ::
blanchet@36402
   845
            aux ((l, l') :: subst) depth (next_assum + 1, next_fact) proof
blanchet@36402
   846
          end
blanchet@36402
   847
      | aux subst depth (next_assum, next_fact) (Have (qs, l, t, by) :: proof) =
blanchet@36402
   848
        let
blanchet@36402
   849
          val (l', subst, next_fact) =
blanchet@36402
   850
            if l = no_label then
blanchet@36402
   851
              (l, subst, next_fact)
blanchet@36402
   852
            else
blanchet@36402
   853
              let
blanchet@36402
   854
                val l' = (prefix_for_depth depth fact_prefix, next_fact)
blanchet@36402
   855
              in (l', (l, l') :: subst, next_fact + 1) end
blanchet@36570
   856
          val relabel_facts =
blanchet@36570
   857
            apfst (map (fn l =>
blanchet@36570
   858
                           case AList.lookup (op =) subst l of
blanchet@36570
   859
                             SOME l' => l'
blanchet@36570
   860
                           | NONE => raise Fail ("unknown label " ^
blanchet@36570
   861
                                                 quote (string_for_label l))))
blanchet@36402
   862
          val by =
blanchet@36402
   863
            case by of
blanchet@36564
   864
              ByMetis facts => ByMetis (relabel_facts facts)
blanchet@36402
   865
            | CaseSplit (proofs, facts) =>
blanchet@36402
   866
              CaseSplit (map (aux subst (depth + 1) (1, 1)) proofs,
blanchet@36402
   867
                         relabel_facts facts)
blanchet@36402
   868
        in
blanchet@36402
   869
          Have (qs, l', t, by) ::
blanchet@36402
   870
          aux subst depth (next_assum, next_fact) proof
blanchet@36402
   871
        end
blanchet@36491
   872
      | aux subst depth nextp (step :: proof) =
blanchet@36491
   873
        step :: aux subst depth nextp proof
blanchet@36402
   874
  in aux [] 0 (1, 1) end
blanchet@36402
   875
blanchet@37479
   876
fun string_for_proof ctxt full_types i n =
blanchet@36402
   877
  let
blanchet@37319
   878
    fun fix_print_mode f x =
blanchet@37319
   879
      setmp_CRITICAL show_no_free_types true
blanchet@37319
   880
          (setmp_CRITICAL show_types true
blanchet@37319
   881
               (Print_Mode.setmp (filter (curry (op =) Symbol.xsymbolsN)
blanchet@37319
   882
                                         (print_mode_value ())) f)) x
blanchet@36402
   883
    fun do_indent ind = replicate_string (ind * indent_size) " "
blanchet@36478
   884
    fun do_free (s, T) =
blanchet@36478
   885
      maybe_quote s ^ " :: " ^
blanchet@36478
   886
      maybe_quote (fix_print_mode (Syntax.string_of_typ ctxt) T)
blanchet@36570
   887
    fun do_label l = if l = no_label then "" else string_for_label l ^ ": "
blanchet@36402
   888
    fun do_have qs =
blanchet@36402
   889
      (if member (op =) qs Moreover then "moreover " else "") ^
blanchet@36402
   890
      (if member (op =) qs Ultimately then "ultimately " else "") ^
blanchet@36402
   891
      (if member (op =) qs Then then
blanchet@36402
   892
         if member (op =) qs Show then "thus" else "hence"
blanchet@36402
   893
       else
blanchet@36402
   894
         if member (op =) qs Show then "show" else "have")
blanchet@36478
   895
    val do_term = maybe_quote o fix_print_mode (Syntax.string_of_term ctxt)
blanchet@36570
   896
    fun do_facts (ls, ss) =
blanchet@36570
   897
      let
blanchet@36570
   898
        val ls = ls |> sort_distinct (prod_ord string_ord int_ord)
blanchet@37171
   899
        val ss = ss |> map unprefix_chained |> sort_distinct string_ord
blanchet@37479
   900
      in metis_command full_types 1 1 (ls, ss) end
blanchet@36478
   901
    and do_step ind (Fix xs) =
blanchet@36478
   902
        do_indent ind ^ "fix " ^ space_implode " and " (map do_free xs) ^ "\n"
blanchet@36486
   903
      | do_step ind (Let (t1, t2)) =
blanchet@36486
   904
        do_indent ind ^ "let " ^ do_term t1 ^ " = " ^ do_term t2 ^ "\n"
blanchet@36402
   905
      | do_step ind (Assume (l, t)) =
blanchet@36402
   906
        do_indent ind ^ "assume " ^ do_label l ^ do_term t ^ "\n"
blanchet@36564
   907
      | do_step ind (Have (qs, l, t, ByMetis facts)) =
blanchet@36402
   908
        do_indent ind ^ do_have qs ^ " " ^
blanchet@36479
   909
        do_label l ^ do_term t ^ " " ^ do_facts facts ^ "\n"
blanchet@36402
   910
      | do_step ind (Have (qs, l, t, CaseSplit (proofs, facts))) =
blanchet@36402
   911
        space_implode (do_indent ind ^ "moreover\n")
blanchet@36402
   912
                      (map (do_block ind) proofs) ^
blanchet@36479
   913
        do_indent ind ^ do_have qs ^ " " ^ do_label l ^ do_term t ^ " " ^
blanchet@36478
   914
        do_facts facts ^ "\n"
blanchet@36402
   915
    and do_steps prefix suffix ind steps =
blanchet@36402
   916
      let val s = implode (map (do_step ind) steps) in
blanchet@36402
   917
        replicate_string (ind * indent_size - size prefix) " " ^ prefix ^
blanchet@36402
   918
        String.extract (s, ind * indent_size,
blanchet@36402
   919
                        SOME (size s - ind * indent_size - 1)) ^
blanchet@36402
   920
        suffix ^ "\n"
blanchet@36402
   921
      end
blanchet@36402
   922
    and do_block ind proof = do_steps "{ " " }" (ind + 1) proof
blanchet@36564
   923
    (* One-step proofs are pointless; better use the Metis one-liner
blanchet@36564
   924
       directly. *)
blanchet@36564
   925
    and do_proof [Have (_, _, _, ByMetis _)] = ""
blanchet@36564
   926
      | do_proof proof =
blanchet@36480
   927
        (if i <> 1 then "prefer " ^ string_of_int i ^ "\n" else "") ^
blanchet@36480
   928
        do_indent 0 ^ "proof -\n" ^
blanchet@36480
   929
        do_steps "" "" 1 proof ^
blanchet@36480
   930
        do_indent 0 ^ (if n <> 1 then "next" else "qed") ^ "\n"
blanchet@36488
   931
  in do_proof end
blanchet@36402
   932
blanchet@37479
   933
fun isar_proof_text (pool, debug, isar_shrink_factor, ctxt, conjecture_shape)
blanchet@37479
   934
                    (other_params as (full_types, _, atp_proof, thm_names, goal,
blanchet@37479
   935
                                      i)) =
blanchet@36402
   936
  let
blanchet@36909
   937
    val (params, hyp_ts, concl_t) = strip_subgoal goal i
blanchet@36909
   938
    val frees = fold Term.add_frees (concl_t :: hyp_ts) []
blanchet@36967
   939
    val tfrees = fold Term.add_tfrees (concl_t :: hyp_ts) []
blanchet@36402
   940
    val n = Logic.count_prems (prop_of goal)
blanchet@37479
   941
    val (one_line_proof, lemma_names) = metis_proof_text other_params
blanchet@36283
   942
    fun isar_proof_for () =
blanchet@36967
   943
      case proof_from_atp_proof pool ctxt full_types tfrees isar_shrink_factor
blanchet@36924
   944
                                atp_proof conjecture_shape thm_names params
blanchet@36924
   945
                                frees
blanchet@37991
   946
           |> redirect_proof conjecture_shape hyp_ts concl_t
blanchet@36402
   947
           |> kill_duplicate_assumptions_in_proof
blanchet@36402
   948
           |> then_chain_proof
blanchet@36402
   949
           |> kill_useless_labels_in_proof
blanchet@36402
   950
           |> relabel_proof
blanchet@37479
   951
           |> string_for_proof ctxt full_types i n of
blanchet@36283
   952
        "" => ""
blanchet@36402
   953
      | proof => "\nStructured proof:\n" ^ Markup.markup Markup.sendback proof
blanchet@35868
   954
    val isar_proof =
blanchet@36402
   955
      if debug then
blanchet@36283
   956
        isar_proof_for ()
blanchet@36283
   957
      else
blanchet@36283
   958
        try isar_proof_for ()
blanchet@36287
   959
        |> the_default "Warning: The Isar proof construction failed.\n"
blanchet@36283
   960
  in (one_line_proof ^ isar_proof, lemma_names) end
paulson@21978
   961
blanchet@36557
   962
fun proof_text isar_proof isar_params other_params =
blanchet@36557
   963
  (if isar_proof then isar_proof_text isar_params else metis_proof_text)
blanchet@36557
   964
      other_params
blanchet@36223
   965
immler@31038
   966
end;