blanchet@35826: (*  Title:      HOL/Tools/Sledgehammer/sledgehammer_proof_reconstruct.ML
wenzelm@33310:     Author:     Lawrence C Paulson and Claire Quigley, Cambridge University Computer Laboratory
blanchet@36392:     Author:     Jasmin Blanchette, TU Muenchen
paulson@21978: 
wenzelm@33310: Transfer of proofs from external provers.
wenzelm@33310: *)
wenzelm@33310: 
blanchet@35826: signature SLEDGEHAMMER_PROOF_RECONSTRUCT =
paulson@24425: sig
blanchet@36281:   type minimize_command = string list -> string
blanchet@36393:   type name_pool = Sledgehammer_FOL_Clause.name_pool
blanchet@36281: 
paulson@25492:   val chained_hint: string
paulson@24425:   val invert_const: string -> string
paulson@24425:   val invert_type_const: string -> string
blanchet@36909:   val num_type_args: theory -> string -> int
paulson@24425:   val strip_prefix: string -> string -> string option
blanchet@36063:   val metis_line: int -> int -> string list -> string
blanchet@36223:   val metis_proof_text:
blanchet@36287:     minimize_command * string * string vector * thm * int
blanchet@36281:     -> string * string list
blanchet@36223:   val isar_proof_text:
blanchet@36909:     name_pool option * bool * bool * int * Proof.context * int list list
blanchet@36287:     -> minimize_command * string * string vector * thm * int
blanchet@36287:     -> string * string list
blanchet@36223:   val proof_text:
blanchet@36909:     bool -> name_pool option * bool * bool * int * Proof.context * int list list
blanchet@36287:     -> minimize_command * string * string vector * thm * int
blanchet@36287:     -> string * string list
paulson@24425: end;
paulson@21978: 
blanchet@35826: structure Sledgehammer_Proof_Reconstruct : SLEDGEHAMMER_PROOF_RECONSTRUCT =
paulson@21978: struct
paulson@21978: 
blanchet@36478: open Sledgehammer_Util
blanchet@35865: open Sledgehammer_FOL_Clause
blanchet@36909: open Sledgehammer_HOL_Clause
blanchet@35865: open Sledgehammer_Fact_Preprocessor
paulson@21978: 
blanchet@36281: type minimize_command = string list -> string
blanchet@36281: 
blanchet@36291: fun is_ident_char c = Char.isAlphaNum c orelse c = #"_"
blanchet@36392: fun is_head_digit s = Char.isDigit (String.sub (s, 0))
blanchet@36291: 
blanchet@36551: (* Hack: Could return false positives (e.g., a user happens to declare a
blanchet@36551:    constant called "SomeTheory.sko_means_shoe_in_$wedish". *)
blanchet@36551: val is_skolem_const_name =
blanchet@36551:   Long_Name.base_name
blanchet@36551:   #> String.isPrefix skolem_prefix andf String.isSubstring skolem_infix
blanchet@36551: 
krauss@36607: val index_in_shape : int -> int list list -> int =
krauss@36607:   find_index o exists o curry (op =)
blanchet@36402: fun is_axiom_clause_number thm_names num = num <= Vector.length thm_names
blanchet@36570: fun is_conjecture_clause_number conjecture_shape num =
blanchet@36570:   index_in_shape num conjecture_shape >= 0
blanchet@36291: 
blanchet@36393: fun ugly_name NONE s = s
blanchet@36393:   | ugly_name (SOME the_pool) s =
blanchet@36393:     case Symtab.lookup (snd the_pool) s of
blanchet@36393:       SOME s' => s'
blanchet@36393:     | NONE => s
blanchet@36393: 
blanchet@36491: fun smart_lambda v t =
blanchet@36551:   Abs (case v of
blanchet@36551:          Const (s, _) =>
blanchet@36551:          List.last (space_explode skolem_infix (Long_Name.base_name s))
blanchet@36551:        | Var ((s, _), _) => s
blanchet@36551:        | Free (s, _) => s
blanchet@36551:        | _ => "", fastype_of v, abstract_over (v, t))
blanchet@36491: fun forall_of v t = HOLogic.all_const (fastype_of v) $ smart_lambda v t
blanchet@36491: 
blanchet@36491: datatype ('a, 'b, 'c, 'd, 'e) raw_step =
blanchet@36491:   Definition of 'a * 'b * 'c |
blanchet@36491:   Inference of 'a * 'd * 'e list
blanchet@36491: 
paulson@21978: (**** PARSING OF TSTP FORMAT ****)
paulson@21978: 
blanchet@36548: fun strip_spaces_in_list [] = ""
blanchet@36548:   | strip_spaces_in_list [c1] = if Char.isSpace c1 then "" else str c1
blanchet@36548:   | strip_spaces_in_list [c1, c2] =
blanchet@36548:     strip_spaces_in_list [c1] ^ strip_spaces_in_list [c2]
blanchet@36548:   | strip_spaces_in_list (c1 :: c2 :: c3 :: cs) =
blanchet@36548:     if Char.isSpace c1 then
blanchet@36548:       strip_spaces_in_list (c2 :: c3 :: cs)
blanchet@36548:     else if Char.isSpace c2 then
blanchet@36548:       if Char.isSpace c3 then
blanchet@36548:         strip_spaces_in_list (c1 :: c3 :: cs)
blanchet@36548:       else
blanchet@36548:         str c1 ^ (if forall is_ident_char [c1, c3] then " " else "") ^
blanchet@36548:         strip_spaces_in_list (c3 :: cs)
blanchet@36548:     else
blanchet@36548:       str c1 ^ strip_spaces_in_list (c2 :: c3 :: cs)
blanchet@36548: val strip_spaces = strip_spaces_in_list o String.explode
blanchet@36548: 
blanchet@36291: (* Syntax trees, either term list or formulae *)
blanchet@36486: datatype node = IntLeaf of int | StrNode of string * node list
paulson@21978: 
blanchet@36548: fun str_leaf s = StrNode (s, [])
paulson@21978: 
blanchet@36486: fun scons (x, y) = StrNode ("cons", [x, y])
blanchet@36548: val slist_of = List.foldl scons (str_leaf "nil")
paulson@21978: 
paulson@21978: (*Strings enclosed in single quotes, e.g. filenames*)
blanchet@36392: val parse_quoted = $$ "'" |-- Scan.repeat (~$$ "'") --| $$ "'" >> implode;
paulson@21978: 
paulson@21978: (*Integer constants, typically proof line numbers*)
blanchet@36392: val parse_integer = Scan.many1 is_head_digit >> (the o Int.fromString o implode)
paulson@21978: 
blanchet@36548: val parse_dollar_name =
blanchet@36548:   Scan.repeat ($$ "$") -- Symbol.scan_id >> (fn (ss, s) => implode ss ^ s)
blanchet@36548: 
blanchet@36369: (* needed for SPASS's output format *)
blanchet@36548: fun repair_name _ "$true" = "c_True"
blanchet@36548:   | repair_name _ "$false" = "c_False"
blanchet@36559:   | repair_name _ "$$e" = "c_equal" (* seen in Vampire 11 proofs *)
blanchet@36548:   | repair_name _ "equal" = "c_equal" (* probably not needed *)
blanchet@36393:   | repair_name pool s = ugly_name pool s
blanchet@36392: (* Generalized first-order terms, which include file names, numbers, etc. *)
blanchet@36393: (* The "x" argument is not strictly necessary, but without it Poly/ML loops
blanchet@36393:    forever at compile time. *)
blanchet@36393: fun parse_term pool x =
blanchet@36548:      (parse_quoted >> str_leaf
blanchet@36486:    || parse_integer >> IntLeaf
blanchet@36548:    || (parse_dollar_name >> repair_name pool)
blanchet@36486:       -- Scan.optional ($$ "(" |-- parse_terms pool --| $$ ")") [] >> StrNode
blanchet@36393:    || $$ "(" |-- parse_term pool --| $$ ")"
blanchet@36393:    || $$ "[" |-- Scan.optional (parse_terms pool) [] --| $$ "]" >> slist_of) x
blanchet@36393: and parse_terms pool x =
blanchet@36393:   (parse_term pool ::: Scan.repeat ($$ "," |-- parse_term pool)) x
paulson@21978: 
blanchet@36486: fun negate_node u = StrNode ("c_Not", [u])
blanchet@36486: fun equate_nodes u1 u2 = StrNode ("c_equal", [u1, u2])
paulson@21978: 
blanchet@36392: (* Apply equal or not-equal to a term. *)
blanchet@36486: fun repair_predicate_term (u, NONE) = u
blanchet@36486:   | repair_predicate_term (u1, SOME (NONE, u2)) = equate_nodes u1 u2
blanchet@36486:   | repair_predicate_term (u1, SOME (SOME _, u2)) =
blanchet@36486:     negate_node (equate_nodes u1 u2)
blanchet@36393: fun parse_predicate_term pool =
blanchet@36393:   parse_term pool -- Scan.option (Scan.option ($$ "!") --| $$ "="
blanchet@36393:                                   -- parse_term pool)
blanchet@36393:   >> repair_predicate_term
blanchet@36393: fun parse_literal pool x =
blanchet@36486:   ($$ "~" |-- parse_literal pool >> negate_node || parse_predicate_term pool) x
blanchet@36393: fun parse_literals pool =
blanchet@36393:   parse_literal pool ::: Scan.repeat ($$ "|" |-- parse_literal pool)
blanchet@36548: fun parse_parenthesized_literals pool =
blanchet@36548:   $$ "(" |-- parse_literals pool --| $$ ")" || parse_literals pool
blanchet@36393: fun parse_clause pool =
blanchet@36548:   parse_parenthesized_literals pool
blanchet@36548:     ::: Scan.repeat ($$ "|" |-- parse_parenthesized_literals pool)
blanchet@36548:   >> List.concat
blanchet@36291: 
blanchet@36486: fun ints_of_node (IntLeaf n) = cons n
blanchet@36486:   | ints_of_node (StrNode (_, us)) = fold ints_of_node us
blanchet@36392: val parse_tstp_annotations =
blanchet@36393:   Scan.optional ($$ "," |-- parse_term NONE
blanchet@36393:                    --| Scan.option ($$ "," |-- parse_terms NONE)
blanchet@36486:                  >> (fn source => ints_of_node source [])) []
blanchet@36486: 
blanchet@36486: fun parse_definition pool =
blanchet@36486:   $$ "(" |-- parse_literal NONE --| Scan.this_string "<=>"
blanchet@36486:   -- parse_clause pool --| $$ ")"
blanchet@36291: 
blanchet@36486: (* Syntax: cnf(<num>, <formula_role>, <cnf_formula> <annotations>).
blanchet@36486:    The <num> could be an identifier, but we assume integers. *)
blanchet@36486: fun finish_tstp_definition_line (num, (u, us)) = Definition (num, u, us)
blanchet@36486: fun finish_tstp_inference_line ((num, us), deps) = Inference (num, us, deps)
blanchet@36393: fun parse_tstp_line pool =
blanchet@36486:      ((Scan.this_string "fof" -- $$ "(") |-- parse_integer --| $$ ","
blanchet@36486:        --| Scan.this_string "definition" --| $$ "," -- parse_definition pool
blanchet@36486:        --| parse_tstp_annotations --| $$ ")" --| $$ "."
blanchet@36486:       >> finish_tstp_definition_line)
blanchet@36486:   || ((Scan.this_string "cnf" -- $$ "(") |-- parse_integer --| $$ ","
blanchet@36486:        --| Symbol.scan_id --| $$ "," -- parse_clause pool
blanchet@36486:        -- parse_tstp_annotations --| $$ ")" --| $$ "."
blanchet@36486:       >> finish_tstp_inference_line)
blanchet@36291: 
blanchet@36291: (**** PARSING OF SPASS OUTPUT ****)
blanchet@36291: 
blanchet@36392: (* SPASS returns clause references of the form "x.y". We ignore "y", whose role
blanchet@36392:    is not clear anyway. *)
blanchet@36392: val parse_dot_name = parse_integer --| $$ "." --| parse_integer
paulson@21978: 
blanchet@36392: val parse_spass_annotations =
blanchet@36392:   Scan.optional ($$ ":" |-- Scan.repeat (parse_dot_name
blanchet@36392:                                          --| Scan.option ($$ ","))) []
blanchet@36291: 
blanchet@36574: (* It is not clear why some literals are followed by sequences of stars and/or
blanchet@36574:    pluses. We ignore them. *)
blanchet@36574: fun parse_decorated_predicate_term pool =
blanchet@36562:   parse_predicate_term pool --| Scan.repeat ($$ "*" || $$ "+" || $$ " ")
blanchet@36291: 
blanchet@36393: fun parse_horn_clause pool =
blanchet@36574:   Scan.repeat (parse_decorated_predicate_term pool) --| $$ "|" --| $$ "|"
blanchet@36574:     -- Scan.repeat (parse_decorated_predicate_term pool) --| $$ "-" --| $$ ">"
blanchet@36574:     -- Scan.repeat (parse_decorated_predicate_term pool)
blanchet@36558:   >> (fn (([], []), []) => [str_leaf "c_False"]
blanchet@36558:        | ((clauses1, clauses2), clauses3) =>
blanchet@36558:          map negate_node (clauses1 @ clauses2) @ clauses3)
paulson@21978: 
blanchet@36558: (* Syntax: <num>[0:<inference><annotations>]
blanchet@36558:    <cnf_formulas> || <cnf_formulas> -> <cnf_formulas>. *)
blanchet@36486: fun finish_spass_line ((num, deps), us) = Inference (num, us, deps)
blanchet@36402: fun parse_spass_line pool =
blanchet@36392:   parse_integer --| $$ "[" --| $$ "0" --| $$ ":" --| Symbol.scan_id
blanchet@36558:   -- parse_spass_annotations --| $$ "]" -- parse_horn_clause pool --| $$ "."
blanchet@36486:   >> finish_spass_line
blanchet@36291: 
blanchet@36548: fun parse_line pool = parse_tstp_line pool || parse_spass_line pool
blanchet@36548: fun parse_lines pool = Scan.repeat1 (parse_line pool)
blanchet@36548: fun parse_proof pool =
blanchet@36548:   fst o Scan.finite Symbol.stopper
blanchet@36548:             (Scan.error (!! (fn _ => raise Fail "unrecognized ATP output")
blanchet@36548:                             (parse_lines pool)))
blanchet@36548:   o explode o strip_spaces
paulson@21978: 
paulson@21978: (**** INTERPRETATION OF TSTP SYNTAX TREES ****)
paulson@21978: 
blanchet@36909: exception NODE of node list
paulson@21978: 
paulson@21978: (*If string s has the prefix s1, return the result of deleting it.*)
wenzelm@23139: fun strip_prefix s1 s =
immler@31038:   if String.isPrefix s1 s
blanchet@35865:   then SOME (undo_ascii_of (String.extract (s, size s1, NONE)))
paulson@21978:   else NONE;
paulson@21978: 
paulson@21978: (*Invert the table of translations between Isabelle and ATPs*)
paulson@21978: val type_const_trans_table_inv =
blanchet@35865:       Symtab.make (map swap (Symtab.dest type_const_trans_table));
paulson@21978: 
paulson@21978: fun invert_type_const c =
paulson@21978:     case Symtab.lookup type_const_trans_table_inv c of
paulson@21978:         SOME c' => c'
paulson@21978:       | NONE => c;
paulson@21978: 
blanchet@36909: (* Type variables are given the basic sort "HOL.type". Some will later be
blanchet@36909:   constrained by information from type literals, or by type inference. *)
blanchet@36967: fun type_from_node _ (u as IntLeaf _) = raise NODE [u]
blanchet@36967:   | type_from_node tfrees (u as StrNode (a, us)) =
blanchet@36967:     let val Ts = map (type_from_node tfrees) us in
blanchet@36486:       case strip_prefix tconst_prefix a of
blanchet@36486:         SOME b => Type (invert_type_const b, Ts)
blanchet@36486:       | NONE =>
blanchet@36486:         if not (null us) then
blanchet@36909:           raise NODE [u]  (* only "tconst"s have type arguments *)
blanchet@36486:         else case strip_prefix tfree_prefix a of
blanchet@36967:           SOME b =>
blanchet@36967:           let val s = "'" ^ b in
blanchet@36967:             TFree (s, AList.lookup (op =) tfrees s |> the_default HOLogic.typeS)
blanchet@36967:           end
blanchet@36486:         | NONE =>
blanchet@36486:           case strip_prefix tvar_prefix a of
blanchet@36967:             SOME b => TVar (("'" ^ b, 0), HOLogic.typeS)
blanchet@36967:           | NONE =>
blanchet@36967:             (* Variable from the ATP, say "X1" *)
wenzelm@37145:             Type_Infer.param 0 (a, HOLogic.typeS)
blanchet@36486:     end
paulson@21978: 
paulson@21978: (*Invert the table of translations between Isabelle and ATPs*)
paulson@21978: val const_trans_table_inv =
blanchet@36402:   Symtab.update ("fequal", @{const_name "op ="})
blanchet@36402:                 (Symtab.make (map swap (Symtab.dest const_trans_table)))
paulson@21978: 
blanchet@36402: fun invert_const c = c |> Symtab.lookup const_trans_table_inv |> the_default c
paulson@21978: 
paulson@21978: (*The number of type arguments of a constant, zero if it's monomorphic*)
blanchet@36909: fun num_type_args thy s =
blanchet@36909:   length (Sign.const_typargs thy (s, Sign.the_const_type thy s))
paulson@21978: 
blanchet@36486: fun fix_atp_variable_name s =
blanchet@36486:   let
blanchet@36486:     fun subscript_name s n = s ^ nat_subscript n
blanchet@36486:     val s = String.map Char.toLower s
blanchet@36486:   in
blanchet@36486:     case space_explode "_" s of
blanchet@36486:       [_] => (case take_suffix Char.isDigit (String.explode s) of
blanchet@36486:                 (cs1 as _ :: _, cs2 as _ :: _) =>
blanchet@36486:                 subscript_name (String.implode cs1)
blanchet@36486:                                (the (Int.fromString (String.implode cs2)))
blanchet@36486:               | (_, _) => s)
blanchet@36486:     | [s1, s2] => (case Int.fromString s2 of
blanchet@36486:                      SOME n => subscript_name s1 n
blanchet@36486:                    | NONE => s)
blanchet@36486:     | _ => s
blanchet@36486:   end
blanchet@36486: 
blanchet@36909: (* First-order translation. No types are known for variables. "HOLogic.typeT"
blanchet@36909:    should allow them to be inferred.*)
blanchet@36967: fun term_from_node thy full_types tfrees =
blanchet@36909:   let
blanchet@36909:     fun aux opt_T args u =
blanchet@36909:       case u of
blanchet@36909:         IntLeaf _ => raise NODE [u]
blanchet@36909:       | StrNode ("hBOOL", [u1]) => aux (SOME @{typ bool}) [] u1
blanchet@36909:       | StrNode ("hAPP", [u1, u2]) => aux opt_T (u2 :: args) u1
blanchet@36909:       | StrNode ("c_Not", [u1]) => @{const Not} $ aux (SOME @{typ bool}) [] u1
blanchet@36909:       | StrNode (a, us) =>
blanchet@36909:         if a = type_wrapper_name then
blanchet@36909:           case us of
blanchet@36967:             [term_u, typ_u] =>
blanchet@36967:             aux (SOME (type_from_node tfrees typ_u)) args term_u
blanchet@36909:           | _ => raise NODE us
blanchet@36909:         else case strip_prefix const_prefix a of
blanchet@36909:           SOME "equal" =>
blanchet@36909:           list_comb (Const (@{const_name "op ="}, HOLogic.typeT),
blanchet@36909:                      map (aux NONE []) us)
blanchet@36909:         | SOME b =>
blanchet@36909:           let
blanchet@36909:             val c = invert_const b
blanchet@36909:             val num_type_args = num_type_args thy c
blanchet@36909:             val actual_num_type_args = if full_types then 0 else num_type_args
blanchet@36909:             val num_term_args = length us - actual_num_type_args
blanchet@36909:             val ts = map (aux NONE []) (take num_term_args us @ args)
blanchet@36909:             val t =
blanchet@36909:               Const (c, if full_types then
blanchet@36909:                           case opt_T of
blanchet@36909:                             SOME T => map fastype_of ts ---> T
blanchet@36909:                           | NONE =>
blanchet@36909:                             if num_type_args = 0 then
blanchet@36909:                               Sign.const_instance thy (c, [])
blanchet@36909:                             else
blanchet@36909:                               raise Fail ("no type information for " ^ quote c)
blanchet@36909:                         else
blanchet@36909:                           (* Extra args from "hAPP" come after any arguments
blanchet@36909:                              given directly to the constant. *)
blanchet@36909:                           Sign.const_instance thy (c,
blanchet@36967:                                     map (type_from_node tfrees)
blanchet@36967:                                         (drop num_term_args us)))
blanchet@36909:           in list_comb (t, ts) end
blanchet@36909:         | NONE => (* a free or schematic variable *)
blanchet@36909:           let
blanchet@36909:             val ts = map (aux NONE []) (us @ args)
blanchet@36909:             val T = map fastype_of ts ---> HOLogic.typeT
blanchet@36909:             val t =
blanchet@36909:               case strip_prefix fixed_var_prefix a of
blanchet@36909:                 SOME b => Free (b, T)
blanchet@36909:               | NONE =>
blanchet@36909:                 case strip_prefix schematic_var_prefix a of
blanchet@36967:                   SOME b => Var ((b, 0), T)
blanchet@36909:                 | NONE =>
blanchet@36909:                   (* Variable from the ATP, say "X1" *)
blanchet@36967:                   Var ((fix_atp_variable_name a, 0), T)
blanchet@36909:           in list_comb (t, ts) end
blanchet@36909:   in aux end
paulson@21978: 
blanchet@36392: (* Type class literal applied to a type. Returns triple of polarity, class,
blanchet@36392:    type. *)
blanchet@36967: fun type_constraint_from_node pos tfrees (StrNode ("c_Not", [u])) =
blanchet@36967:     type_constraint_from_node (not pos) tfrees u
blanchet@36967:   | type_constraint_from_node pos tfrees u = case u of
blanchet@36909:         IntLeaf _ => raise NODE [u]
blanchet@36486:       | StrNode (a, us) =>
blanchet@36967:             (case (strip_prefix class_prefix a,
blanchet@36967:                    map (type_from_node tfrees) us) of
blanchet@36486:                  (SOME b, [T]) => (pos, b, T)
blanchet@36909:                | _ => raise NODE [u])
paulson@21978: 
paulson@21978: (** Accumulate type constraints in a clause: negative type literals **)
paulson@21978: 
blanchet@36485: fun add_var (key, z)  = Vartab.map_default (key, []) (cons z)
paulson@21978: 
blanchet@36909: fun add_type_constraint (false, cl, TFree (a ,_)) = add_var ((a, ~1), cl)
blanchet@36909:   | add_type_constraint (false, cl, TVar (ix, _)) = add_var (ix, cl)
blanchet@36909:   | add_type_constraint _ = I
paulson@21978: 
blanchet@36491: fun is_positive_literal (@{const Not} $ _) = false
blanchet@36402:   | is_positive_literal t = true
blanchet@36402: 
blanchet@36485: fun negate_term thy (Const (@{const_name All}, T) $ Abs (s, T', t')) =
blanchet@36402:     Const (@{const_name Ex}, T) $ Abs (s, T', negate_term thy t')
blanchet@36402:   | negate_term thy (Const (@{const_name Ex}, T) $ Abs (s, T', t')) =
blanchet@36402:     Const (@{const_name All}, T) $ Abs (s, T', negate_term thy t')
blanchet@36402:   | negate_term thy (@{const "op -->"} $ t1 $ t2) =
blanchet@36402:     @{const "op &"} $ t1 $ negate_term thy t2
blanchet@36402:   | negate_term thy (@{const "op &"} $ t1 $ t2) =
blanchet@36402:     @{const "op |"} $ negate_term thy t1 $ negate_term thy t2
blanchet@36402:   | negate_term thy (@{const "op |"} $ t1 $ t2) =
blanchet@36402:     @{const "op &"} $ negate_term thy t1 $ negate_term thy t2
blanchet@36486:   | negate_term _ (@{const Not} $ t) = t
blanchet@36486:   | negate_term _ t = @{const Not} $ t
blanchet@36402: 
blanchet@36402: fun clause_for_literals _ [] = HOLogic.false_const
blanchet@36402:   | clause_for_literals _ [lit] = lit
blanchet@36402:   | clause_for_literals thy lits =
blanchet@36402:     case List.partition is_positive_literal lits of
blanchet@36402:       (pos_lits as _ :: _, neg_lits as _ :: _) =>
blanchet@36402:       @{const "op -->"}
blanchet@36402:           $ foldr1 HOLogic.mk_conj (map (negate_term thy) neg_lits)
blanchet@36402:           $ foldr1 HOLogic.mk_disj pos_lits
blanchet@36402:     | _ => foldr1 HOLogic.mk_disj lits
blanchet@36402: 
blanchet@36402: (* Final treatment of the list of "real" literals from a clause.
blanchet@36402:    No "real" literals means only type information. *)
blanchet@36402: fun finish_clause _ [] = HOLogic.true_const
blanchet@36402:   | finish_clause thy lits =
blanchet@36402:     lits |> filter_out (curry (op =) HOLogic.false_const) |> rev
blanchet@36402:          |> clause_for_literals thy
paulson@22491: 
paulson@21978: (*Accumulate sort constraints in vt, with "real" literals in lits.*)
blanchet@36967: fun lits_of_nodes thy full_types tfrees =
blanchet@36967:   let
blanchet@36967:     fun aux (vt, lits) [] = (vt, finish_clause thy lits)
blanchet@36967:       | aux (vt, lits) (u :: us) =
blanchet@36967:         aux (add_type_constraint
blanchet@36967:                  (type_constraint_from_node true tfrees u) vt, lits) us
blanchet@36967:         handle NODE _ =>
blanchet@36967:                aux (vt, term_from_node thy full_types tfrees (SOME @{typ bool})
blanchet@36967:                                        [] u :: lits) us
blanchet@36967:   in aux end
paulson@21978: 
blanchet@36967: (* Update TVars with detected sort constraints. It's not totally clear when
blanchet@36967:    this code is necessary. *)
blanchet@36967: fun repair_tvar_sorts vt =
blanchet@36556:   let
blanchet@36556:     fun do_type (Type (a, Ts)) = Type (a, map do_type Ts)
blanchet@36556:       | do_type (TVar (xi, s)) = TVar (xi, the_default s (Vartab.lookup vt xi))
blanchet@36967:       | do_type (TFree z) = TFree z
blanchet@36556:     fun do_term (Const (a, T)) = Const (a, do_type T)
blanchet@36556:       | do_term (Free (a, T)) = Free (a, do_type T)
blanchet@36556:       | do_term (Var (xi, T)) = Var (xi, do_type T)
blanchet@36556:       | do_term (t as Bound _) = t
blanchet@36556:       | do_term (Abs (a, T, t)) = Abs (a, do_type T, do_term t)
blanchet@36556:       | do_term (t1 $ t2) = do_term t1 $ do_term t2
blanchet@36556:   in not (Vartab.is_empty vt) ? do_term end
blanchet@36551: 
blanchet@36551: fun unskolemize_term t =
blanchet@36909:   Term.add_consts t []
blanchet@36909:   |> filter (is_skolem_const_name o fst) |> map Const
blanchet@36909:   |> rpair t |-> fold forall_of
paulson@21978: 
blanchet@36555: val combinator_table =
blanchet@36555:   [(@{const_name COMBI}, @{thm COMBI_def_raw}),
blanchet@36555:    (@{const_name COMBK}, @{thm COMBK_def_raw}),
blanchet@36555:    (@{const_name COMBB}, @{thm COMBB_def_raw}),
blanchet@36555:    (@{const_name COMBC}, @{thm COMBC_def_raw}),
blanchet@36555:    (@{const_name COMBS}, @{thm COMBS_def_raw})]
blanchet@36555: 
blanchet@36555: fun uncombine_term (t1 $ t2) = betapply (pairself uncombine_term (t1, t2))
blanchet@36555:   | uncombine_term (Abs (s, T, t')) = Abs (s, T, uncombine_term t')
blanchet@36555:   | uncombine_term (t as Const (x as (s, _))) =
blanchet@36555:     (case AList.lookup (op =) combinator_table s of
blanchet@36555:        SOME thm => thm |> prop_of |> specialize_type @{theory} x |> Logic.dest_equals |> snd
blanchet@36555:      | NONE => t)
blanchet@36555:   | uncombine_term t = t
blanchet@36555: 
blanchet@36486: (* Interpret a list of syntax trees as a clause, given by "real" literals and
blanchet@36486:    sort constraints. "vt" holds the initial sort constraints, from the
blanchet@36486:    conjecture clauses. *)
blanchet@36967: fun clause_of_nodes ctxt full_types tfrees us =
blanchet@36909:   let
blanchet@36909:     val thy = ProofContext.theory_of ctxt
blanchet@36967:     val (vt, t) = lits_of_nodes thy full_types tfrees (Vartab.empty, []) us
blanchet@36967:   in repair_tvar_sorts vt t end
blanchet@36556: fun check_formula ctxt =
wenzelm@37145:   Type_Infer.constrain @{typ bool}
blanchet@36486:   #> Syntax.check_term (ProofContext.set_mode ProofContext.mode_schematic ctxt)
paulson@21978: 
paulson@21978: 
paulson@21978: (**** Translation of TSTP files to Isar Proofs ****)
paulson@21978: 
blanchet@36486: fun unvarify_term (Var ((s, 0), T)) = Free (s, T)
blanchet@36486:   | unvarify_term t = raise TERM ("unvarify_term: non-Var", [t])
paulson@21978: 
blanchet@36967: fun decode_line full_types tfrees (Definition (num, u, us)) ctxt =
blanchet@36486:     let
blanchet@36967:       val t1 = clause_of_nodes ctxt full_types tfrees [u]
blanchet@36551:       val vars = snd (strip_comb t1)
blanchet@36486:       val frees = map unvarify_term vars
blanchet@36486:       val unvarify_args = subst_atomic (vars ~~ frees)
blanchet@36967:       val t2 = clause_of_nodes ctxt full_types tfrees us
blanchet@36551:       val (t1, t2) =
blanchet@36551:         HOLogic.eq_const HOLogic.typeT $ t1 $ t2
blanchet@36556:         |> unvarify_args |> uncombine_term |> check_formula ctxt
blanchet@36555:         |> HOLogic.dest_eq
blanchet@36486:     in
blanchet@36551:       (Definition (num, t1, t2),
blanchet@36551:        fold Variable.declare_term (maps OldTerm.term_frees [t1, t2]) ctxt)
blanchet@36486:     end
blanchet@36967:   | decode_line full_types tfrees (Inference (num, us, deps)) ctxt =
blanchet@36551:     let
blanchet@36967:       val t = us |> clause_of_nodes ctxt full_types tfrees
blanchet@36556:                  |> unskolemize_term |> uncombine_term |> check_formula ctxt
blanchet@36551:     in
blanchet@36551:       (Inference (num, t, deps),
blanchet@36551:        fold Variable.declare_term (OldTerm.term_frees t) ctxt)
blanchet@36486:     end
blanchet@36967: fun decode_lines ctxt full_types tfrees lines =
blanchet@36967:   fst (fold_map (decode_line full_types tfrees) lines ctxt)
paulson@21978: 
blanchet@36486: fun aint_inference _ (Definition _) = true
blanchet@36486:   | aint_inference t (Inference (_, t', _)) = not (t aconv t')
blanchet@36486: 
blanchet@36486: (* No "real" literals means only type information (tfree_tcs, clsrel, or
blanchet@36486:    clsarity). *)
blanchet@36486: val is_only_type_information = curry (op aconv) HOLogic.true_const
blanchet@36486: 
blanchet@36486: fun replace_one_dep (old, new) dep = if dep = old then new else [dep]
blanchet@36486: fun replace_deps_in_line _ (line as Definition _) = line
blanchet@36486:   | replace_deps_in_line p (Inference (num, t, deps)) =
blanchet@36486:     Inference (num, t, fold (union (op =) o replace_one_dep p) deps [])
paulson@21978: 
paulson@22491: (*Discard axioms; consolidate adjacent lines that prove the same clause, since they differ
paulson@22491:   only in type information.*)
blanchet@36551: fun add_line _ _ (line as Definition _) lines = line :: lines
blanchet@36551:   | add_line conjecture_shape thm_names (Inference (num, t, [])) lines =
blanchet@36570:     (* No dependencies: axiom, conjecture clause, or internal axioms or
blanchet@36570:        definitions (Vampire). *)
blanchet@36486:     if is_axiom_clause_number thm_names num then
blanchet@36486:       (* Axioms are not proof lines. *)
blanchet@36486:       if is_only_type_information t then
blanchet@36486:         map (replace_deps_in_line (num, [])) lines
blanchet@36486:       (* Is there a repetition? If so, replace later line by earlier one. *)
blanchet@36486:       else case take_prefix (aint_inference t) lines of
blanchet@36486:         (_, []) => lines (*no repetition of proof line*)
blanchet@36486:       | (pre, Inference (num', _, _) :: post) =>
blanchet@36486:         pre @ map (replace_deps_in_line (num', [num])) post
blanchet@36570:     else if is_conjecture_clause_number conjecture_shape num then
blanchet@36486:       Inference (num, t, []) :: lines
blanchet@36551:     else
blanchet@36570:       map (replace_deps_in_line (num, [])) lines
blanchet@36551:   | add_line _ _ (Inference (num, t, deps)) lines =
blanchet@36486:     (* Type information will be deleted later; skip repetition test. *)
blanchet@36486:     if is_only_type_information t then
blanchet@36486:       Inference (num, t, deps) :: lines
blanchet@36486:     (* Is there a repetition? If so, replace later line by earlier one. *)
blanchet@36486:     else case take_prefix (aint_inference t) lines of
blanchet@36486:       (* FIXME: Doesn't this code risk conflating proofs involving different
blanchet@36486:          types?? *)
blanchet@36486:        (_, []) => Inference (num, t, deps) :: lines
blanchet@36486:      | (pre, Inference (num', t', _) :: post) =>
blanchet@36486:        Inference (num, t', deps) ::
blanchet@36486:        pre @ map (replace_deps_in_line (num', [num])) post
paulson@22044: 
blanchet@36486: (* Recursively delete empty lines (type information) from the proof. *)
blanchet@36486: fun add_nontrivial_line (Inference (num, t, [])) lines =
blanchet@36486:     if is_only_type_information t then delete_dep num lines
blanchet@36486:     else Inference (num, t, []) :: lines
blanchet@36486:   | add_nontrivial_line line lines = line :: lines
blanchet@36395: and delete_dep num lines =
blanchet@36486:   fold_rev add_nontrivial_line (map (replace_deps_in_line (num, [])) lines) []
blanchet@36486: 
blanchet@36560: (* ATPs sometimes reuse free variable names in the strangest ways. Surprisingly,
blanchet@36560:    removing the offending lines often does the trick. *)
blanchet@36560: fun is_bad_free frees (Free x) = not (member (op =) frees x)
blanchet@36560:   | is_bad_free _ _ = false
paulson@22470: 
blanchet@36570: (* Vampire is keen on producing these. *)
blanchet@36570: fun is_trivial_formula (@{const Not} $ (Const (@{const_name "op ="}, _)
blanchet@36570:                                         $ t1 $ t2)) = (t1 aconv t2)
blanchet@36570:   | is_trivial_formula t = false
blanchet@36570: 
blanchet@36570: fun add_desired_line _ _ _ _ _ (line as Definition _) (j, lines) =
blanchet@36560:     (j, line :: lines)
blanchet@36924:   | add_desired_line ctxt isar_shrink_factor conjecture_shape thm_names frees
blanchet@36570:                      (Inference (num, t, deps)) (j, lines) =
blanchet@36402:     (j + 1,
blanchet@36570:      if is_axiom_clause_number thm_names num orelse
blanchet@36570:         is_conjecture_clause_number conjecture_shape num orelse
blanchet@36570:         (not (is_only_type_information t) andalso
blanchet@36570:          null (Term.add_tvars t []) andalso
blanchet@36570:          not (exists_subterm (is_bad_free frees) t) andalso
blanchet@36570:          not (is_trivial_formula t) andalso
blanchet@36570:          (null lines orelse (* last line must be kept *)
blanchet@36924:           (length deps >= 2 andalso j mod isar_shrink_factor = 0))) then
blanchet@36570:        Inference (num, t, deps) :: lines  (* keep line *)
blanchet@36402:      else
blanchet@36570:        map (replace_deps_in_line (num, deps)) lines)  (* drop line *)
paulson@21978: 
blanchet@36402: (** EXTRACTING LEMMAS **)
paulson@21979: 
blanchet@36223: (* A list consisting of the first number in each line is returned.
blanchet@36395:    TSTP: Interesting lines have the form "cnf(108, axiom, ...)", where the
blanchet@36223:    number (108) is extracted.
blanchet@36395:    SPASS: Lines have the form "108[0:Inp] ...", where the first number (108) is
blanchet@36223:    extracted. *)
blanchet@36402: fun extract_clause_numbers_in_atp_proof atp_proof =
blanchet@35865:   let
blanchet@36395:     val tokens_of = String.tokens (not o is_ident_char)
blanchet@36402:     fun extract_num ("cnf" :: num :: "axiom" :: _) = Int.fromString num
blanchet@36395:       | extract_num (num :: "0" :: "Inp" :: _) = Int.fromString num
blanchet@36395:       | extract_num _ = NONE
blanchet@36402:   in atp_proof |> split_lines |> map_filter (extract_num o tokens_of) end
wenzelm@33310:   
blanchet@36968: (* Used to label theorems chained into the goal. *)
blanchet@36395: val chained_hint = "sledgehammer_chained"
blanchet@35865: 
blanchet@36063: fun apply_command _ 1 = "by "
blanchet@36063:   | apply_command 1 _ = "apply "
blanchet@36063:   | apply_command i _ = "prefer " ^ string_of_int i ^ " apply "
blanchet@36570: fun metis_command i n [] = apply_command i n ^ "metis"
blanchet@36570:   | metis_command i n ss =
blanchet@36570:     apply_command i n ^ "(metis " ^ space_implode " " ss ^ ")"
blanchet@36063: fun metis_line i n xs =
blanchet@36063:   "Try this command: " ^
blanchet@36063:   Markup.markup Markup.sendback (metis_command i n xs) ^ ".\n" 
blanchet@36281: fun minimize_line _ [] = ""
blanchet@36281:   | minimize_line minimize_command facts =
blanchet@36281:     case minimize_command facts of
blanchet@36281:       "" => ""
blanchet@36281:     | command =>
blanchet@36065:       "To minimize the number of lemmas, try this command: " ^
blanchet@36281:       Markup.markup Markup.sendback command ^ ".\n"
immler@31840: 
krauss@36606: fun metis_proof_text (minimize_command, atp_proof, thm_names, goal, i) =
blanchet@36063:   let
blanchet@36231:     val lemmas =
blanchet@36402:       atp_proof |> extract_clause_numbers_in_atp_proof
blanchet@36402:                 |> filter (is_axiom_clause_number thm_names)
blanchet@36402:                 |> map (fn i => Vector.sub (thm_names, i - 1))
blanchet@36402:                 |> filter_out (fn s => s = "??.unknown" orelse s = chained_hint)
blanchet@36402:                 |> sort_distinct string_ord
blanchet@36063:     val n = Logic.count_prems (prop_of goal)
blanchet@36395:   in (metis_line i n lemmas ^ minimize_line minimize_command lemmas, lemmas) end
immler@31037: 
blanchet@36486: (** Isar proof construction and manipulation **)
blanchet@36486: 
blanchet@36486: fun merge_fact_sets (ls1, ss1) (ls2, ss2) =
blanchet@36486:   (union (op =) ls1 ls2, union (op =) ss1 ss2)
blanchet@36402: 
blanchet@36402: type label = string * int
blanchet@36402: type facts = label list * string list
blanchet@36402: 
blanchet@36402: datatype qualifier = Show | Then | Moreover | Ultimately
blanchet@36291: 
blanchet@36402: datatype step =
blanchet@36478:   Fix of (string * typ) list |
blanchet@36486:   Let of term * term |
blanchet@36402:   Assume of label * term |
blanchet@36402:   Have of qualifier list * label * term * byline
blanchet@36402: and byline =
blanchet@36564:   ByMetis of facts |
blanchet@36402:   CaseSplit of step list list * facts
blanchet@36402: 
blanchet@36574: fun smart_case_split [] facts = ByMetis facts
blanchet@36574:   | smart_case_split proofs facts = CaseSplit (proofs, facts)
blanchet@36574: 
blanchet@36402: val raw_prefix = "X"
blanchet@36402: val assum_prefix = "A"
blanchet@36402: val fact_prefix = "F"
blanchet@36402: 
blanchet@36570: fun string_for_label (s, num) = s ^ string_of_int num
blanchet@36570: 
blanchet@36475: fun add_fact_from_dep thm_names num =
blanchet@36475:   if is_axiom_clause_number thm_names num then
blanchet@36480:     apsnd (insert (op =) (Vector.sub (thm_names, num - 1)))
blanchet@36475:   else
blanchet@36480:     apfst (insert (op =) (raw_prefix, num))
blanchet@36402: 
blanchet@36491: fun forall_vars t = fold_rev forall_of (map Var (Term.add_vars t [])) t
blanchet@36491: 
blanchet@36486: fun step_for_line _ _ (Definition (num, t1, t2)) = Let (t1, t2)
blanchet@36486:   | step_for_line _ _ (Inference (num, t, [])) = Assume ((raw_prefix, num), t)
blanchet@36486:   | step_for_line thm_names j (Inference (num, t, deps)) =
blanchet@36486:     Have (if j = 1 then [Show] else [], (raw_prefix, num),
blanchet@36491:           forall_vars t,
blanchet@36564:           ByMetis (fold (add_fact_from_dep thm_names) deps ([], [])))
blanchet@36291: 
blanchet@36967: fun proof_from_atp_proof pool ctxt full_types tfrees isar_shrink_factor
blanchet@36967:                          atp_proof conjecture_shape thm_names params frees =
blanchet@36402:   let
blanchet@36486:     val lines =
blanchet@36574:       atp_proof ^ "$" (* the $ sign acts as a sentinel *)
blanchet@36548:       |> parse_proof pool
blanchet@36967:       |> decode_lines ctxt full_types tfrees
blanchet@36551:       |> rpair [] |-> fold_rev (add_line conjecture_shape thm_names)
blanchet@36486:       |> rpair [] |-> fold_rev add_nontrivial_line
blanchet@36924:       |> rpair (0, []) |-> fold_rev (add_desired_line ctxt isar_shrink_factor
blanchet@36570:                                                conjecture_shape thm_names frees)
blanchet@36486:       |> snd
blanchet@36402:   in
blanchet@36909:     (if null params then [] else [Fix params]) @
blanchet@36486:     map2 (step_for_line thm_names) (length lines downto 1) lines
blanchet@36402:   end
blanchet@36402: 
blanchet@36402: val indent_size = 2
blanchet@36402: val no_label = ("", ~1)
blanchet@36402: 
blanchet@36402: fun no_show qs = not (member (op =) qs Show)
blanchet@36402: 
blanchet@36402: (* When redirecting proofs, we keep information about the labels seen so far in
blanchet@36402:    the "backpatches" data structure. The first component indicates which facts
blanchet@36402:    should be associated with forthcoming proof steps. The second component is a
blanchet@36402:    pair ("keep_ls", "drop_ls"), where "keep_ls" are the labels to keep and
blanchet@36402:    "drop_ls" are those that should be dropped in a case split. *)
blanchet@36402: type backpatches = (label * facts) list * (label list * label list)
blanchet@36402: 
blanchet@36556: fun used_labels_of_step (Have (_, _, _, by)) =
blanchet@36402:     (case by of
blanchet@36564:        ByMetis (ls, _) => ls
blanchet@36556:      | CaseSplit (proofs, (ls, _)) =>
blanchet@36556:        fold (union (op =) o used_labels_of) proofs ls)
blanchet@36556:   | used_labels_of_step _ = []
blanchet@36556: and used_labels_of proof = fold (union (op =) o used_labels_of_step) proof []
blanchet@36402: 
blanchet@36402: fun new_labels_of_step (Fix _) = []
blanchet@36486:   | new_labels_of_step (Let _) = []
blanchet@36402:   | new_labels_of_step (Assume (l, _)) = [l]
blanchet@36402:   | new_labels_of_step (Have (_, l, _, _)) = [l]
blanchet@36402: val new_labels_of = maps new_labels_of_step
blanchet@36402: 
blanchet@36402: val join_proofs =
blanchet@36402:   let
blanchet@36402:     fun aux _ [] = NONE
blanchet@36402:       | aux proof_tail (proofs as (proof1 :: _)) =
blanchet@36402:         if exists null proofs then
blanchet@36402:           NONE
blanchet@36402:         else if forall (curry (op =) (hd proof1) o hd) (tl proofs) then
blanchet@36402:           aux (hd proof1 :: proof_tail) (map tl proofs)
blanchet@36402:         else case hd proof1 of
blanchet@36402:           Have ([], l, t, by) =>
blanchet@36402:           if forall (fn Have ([], l', t', _) :: _ => (l, t) = (l', t')
blanchet@36402:                       | _ => false) (tl proofs) andalso
blanchet@36402:              not (exists (member (op =) (maps new_labels_of proofs))
blanchet@36556:                          (used_labels_of proof_tail)) then
blanchet@36402:             SOME (l, t, map rev proofs, proof_tail)
blanchet@36402:           else
blanchet@36402:             NONE
blanchet@36402:         | _ => NONE
blanchet@36402:   in aux [] o map rev end
blanchet@36402: 
blanchet@36402: fun case_split_qualifiers proofs =
blanchet@36402:   case length proofs of
blanchet@36402:     0 => []
blanchet@36402:   | 1 => [Then]
blanchet@36402:   | _ => [Ultimately]
blanchet@36402: 
blanchet@36491: fun redirect_proof thy conjecture_shape hyp_ts concl_t proof =
wenzelm@33310:   let
blanchet@36402:     val concl_ls = map (pair raw_prefix) (List.last conjecture_shape)
blanchet@36551:     fun find_hyp num = nth hyp_ts (index_in_shape num conjecture_shape)
blanchet@36402:     fun first_pass ([], contra) = ([], contra)
blanchet@36491:       | first_pass ((step as Fix _) :: proof, contra) =
blanchet@36491:         first_pass (proof, contra) |>> cons step
blanchet@36491:       | first_pass ((step as Let _) :: proof, contra) =
blanchet@36491:         first_pass (proof, contra) |>> cons step
blanchet@36551:       | first_pass ((step as Assume (l as (_, num), t)) :: proof, contra) =
blanchet@36402:         if member (op =) concl_ls l then
blanchet@36491:           first_pass (proof, contra ||> cons step)
blanchet@36402:         else
blanchet@36551:           first_pass (proof, contra) |>> cons (Assume (l, find_hyp num))
blanchet@36564:       | first_pass ((step as Have (qs, l, t, ByMetis (ls, ss))) :: proof,
blanchet@36491:                     contra) =
blanchet@36402:         if exists (member (op =) (fst contra)) ls then
blanchet@36491:           first_pass (proof, contra |>> cons l ||> cons step)
blanchet@36402:         else
blanchet@36491:           first_pass (proof, contra) |>> cons step
blanchet@36402:       | first_pass _ = raise Fail "malformed proof"
blanchet@36402:     val (proof_top, (contra_ls, contra_proof)) =
blanchet@36402:       first_pass (proof, (concl_ls, []))
blanchet@36402:     val backpatch_label = the_default ([], []) oo AList.lookup (op =) o fst
blanchet@36402:     fun backpatch_labels patches ls =
blanchet@36402:       fold merge_fact_sets (map (backpatch_label patches) ls) ([], [])
blanchet@36402:     fun second_pass end_qs ([], assums, patches) =
blanchet@36402:         ([Have (end_qs, no_label,
blanchet@36402:                 if length assums < length concl_ls then
blanchet@36491:                   clause_for_literals thy (map (negate_term thy o fst) assums)
blanchet@36402:                 else
blanchet@36402:                   concl_t,
blanchet@36564:                 ByMetis (backpatch_labels patches (map snd assums)))], patches)
blanchet@36402:       | second_pass end_qs (Assume (l, t) :: proof, assums, patches) =
blanchet@36402:         second_pass end_qs (proof, (t, l) :: assums, patches)
blanchet@36564:       | second_pass end_qs (Have (qs, l, t, ByMetis (ls, ss)) :: proof, assums,
blanchet@36402:                             patches) =
blanchet@36402:         if member (op =) (snd (snd patches)) l andalso
blanchet@36402:            not (AList.defined (op =) (fst patches) l) then
blanchet@36402:           second_pass end_qs (proof, assums, patches ||> apsnd (append ls))
blanchet@36402:         else
blanchet@36402:           (case List.partition (member (op =) contra_ls) ls of
blanchet@36402:              ([contra_l], co_ls) =>
blanchet@36402:              if no_show qs then
blanchet@36402:                second_pass end_qs
blanchet@36402:                            (proof, assums,
blanchet@36402:                             patches |>> cons (contra_l, (l :: co_ls, ss)))
blanchet@36402:                |>> cons (if member (op =) (fst (snd patches)) l then
blanchet@36491:                            Assume (l, negate_term thy t)
blanchet@36402:                          else
blanchet@36491:                            Have (qs, l, negate_term thy t,
blanchet@36564:                                  ByMetis (backpatch_label patches l)))
blanchet@36402:              else
blanchet@36402:                second_pass end_qs (proof, assums,
blanchet@36402:                                    patches |>> cons (contra_l, (co_ls, ss)))
blanchet@36402:            | (contra_ls as _ :: _, co_ls) =>
blanchet@36402:              let
blanchet@36402:                val proofs =
blanchet@36402:                  map_filter
blanchet@36402:                      (fn l =>
blanchet@36402:                          if member (op =) concl_ls l then
blanchet@36402:                            NONE
blanchet@36402:                          else
blanchet@36402:                            let
blanchet@36402:                              val drop_ls = filter (curry (op <>) l) contra_ls
blanchet@36402:                            in
blanchet@36402:                              second_pass []
blanchet@36402:                                  (proof, assums,
blanchet@36402:                                   patches ||> apfst (insert (op =) l)
blanchet@36402:                                           ||> apsnd (union (op =) drop_ls))
blanchet@36402:                              |> fst |> SOME
blanchet@36402:                            end) contra_ls
blanchet@36402:                val facts = (co_ls, [])
blanchet@36402:              in
blanchet@36402:                (case join_proofs proofs of
blanchet@36402:                   SOME (l, t, proofs, proof_tail) =>
blanchet@36402:                   Have (case_split_qualifiers proofs @
blanchet@36402:                         (if null proof_tail then end_qs else []), l, t,
blanchet@36574:                         smart_case_split proofs facts) :: proof_tail
blanchet@36402:                 | NONE =>
blanchet@36402:                   [Have (case_split_qualifiers proofs @ end_qs, no_label,
blanchet@36574:                          concl_t, smart_case_split proofs facts)],
blanchet@36402:                 patches)
blanchet@36402:              end
blanchet@36402:            | _ => raise Fail "malformed proof")
blanchet@36402:        | second_pass _ _ = raise Fail "malformed proof"
blanchet@36486:     val proof_bottom =
blanchet@36486:       second_pass [Show] (contra_proof, [], ([], ([], []))) |> fst
blanchet@36402:   in proof_top @ proof_bottom end
blanchet@36402: 
blanchet@36402: val kill_duplicate_assumptions_in_proof =
blanchet@36402:   let
blanchet@36402:     fun relabel_facts subst =
blanchet@36402:       apfst (map (fn l => AList.lookup (op =) subst l |> the_default l))
blanchet@36491:     fun do_step (step as Assume (l, t)) (proof, subst, assums) =
blanchet@36402:         (case AList.lookup (op aconv) assums t of
blanchet@36967:            SOME l' => (proof, (l, l') :: subst, assums)
blanchet@36491:          | NONE => (step :: proof, subst, (t, l) :: assums))
blanchet@36402:       | do_step (Have (qs, l, t, by)) (proof, subst, assums) =
blanchet@36402:         (Have (qs, l, t,
blanchet@36402:                case by of
blanchet@36564:                  ByMetis facts => ByMetis (relabel_facts subst facts)
blanchet@36402:                | CaseSplit (proofs, facts) =>
blanchet@36402:                  CaseSplit (map do_proof proofs, relabel_facts subst facts)) ::
blanchet@36402:          proof, subst, assums)
blanchet@36491:       | do_step step (proof, subst, assums) = (step :: proof, subst, assums)
blanchet@36402:     and do_proof proof = fold do_step proof ([], [], []) |> #1 |> rev
blanchet@36402:   in do_proof end
blanchet@36402: 
blanchet@36402: val then_chain_proof =
blanchet@36402:   let
blanchet@36402:     fun aux _ [] = []
blanchet@36491:       | aux _ ((step as Assume (l, _)) :: proof) = step :: aux l proof
blanchet@36402:       | aux l' (Have (qs, l, t, by) :: proof) =
blanchet@36402:         (case by of
blanchet@36564:            ByMetis (ls, ss) =>
blanchet@36402:            Have (if member (op =) ls l' then
blanchet@36402:                    (Then :: qs, l, t,
blanchet@36564:                     ByMetis (filter_out (curry (op =) l') ls, ss))
blanchet@36402:                  else
blanchet@36564:                    (qs, l, t, ByMetis (ls, ss)))
blanchet@36402:          | CaseSplit (proofs, facts) =>
blanchet@36402:            Have (qs, l, t, CaseSplit (map (aux no_label) proofs, facts))) ::
blanchet@36402:         aux l proof
blanchet@36491:       | aux _ (step :: proof) = step :: aux no_label proof
blanchet@36402:   in aux no_label end
blanchet@36402: 
blanchet@36402: fun kill_useless_labels_in_proof proof =
blanchet@36402:   let
blanchet@36556:     val used_ls = used_labels_of proof
blanchet@36402:     fun do_label l = if member (op =) used_ls l then l else no_label
blanchet@36556:     fun do_step (Assume (l, t)) = Assume (do_label l, t)
blanchet@36556:       | do_step (Have (qs, l, t, by)) =
blanchet@36402:         Have (qs, do_label l, t,
blanchet@36402:               case by of
blanchet@36402:                 CaseSplit (proofs, facts) =>
blanchet@36556:                 CaseSplit (map (map do_step) proofs, facts)
blanchet@36402:               | _ => by)
blanchet@36556:       | do_step step = step
blanchet@36556:   in map do_step proof end
blanchet@36402: 
blanchet@36402: fun prefix_for_depth n = replicate_string (n + 1)
blanchet@36402: 
blanchet@36402: val relabel_proof =
blanchet@36402:   let
blanchet@36402:     fun aux _ _ _ [] = []
blanchet@36402:       | aux subst depth (next_assum, next_fact) (Assume (l, t) :: proof) =
blanchet@36402:         if l = no_label then
blanchet@36402:           Assume (l, t) :: aux subst depth (next_assum, next_fact) proof
blanchet@36402:         else
blanchet@36402:           let val l' = (prefix_for_depth depth assum_prefix, next_assum) in
blanchet@36402:             Assume (l', t) ::
blanchet@36402:             aux ((l, l') :: subst) depth (next_assum + 1, next_fact) proof
blanchet@36402:           end
blanchet@36402:       | aux subst depth (next_assum, next_fact) (Have (qs, l, t, by) :: proof) =
blanchet@36402:         let
blanchet@36402:           val (l', subst, next_fact) =
blanchet@36402:             if l = no_label then
blanchet@36402:               (l, subst, next_fact)
blanchet@36402:             else
blanchet@36402:               let
blanchet@36402:                 val l' = (prefix_for_depth depth fact_prefix, next_fact)
blanchet@36402:               in (l', (l, l') :: subst, next_fact + 1) end
blanchet@36570:           val relabel_facts =
blanchet@36570:             apfst (map (fn l =>
blanchet@36570:                            case AList.lookup (op =) subst l of
blanchet@36570:                              SOME l' => l'
blanchet@36570:                            | NONE => raise Fail ("unknown label " ^
blanchet@36570:                                                  quote (string_for_label l))))
blanchet@36402:           val by =
blanchet@36402:             case by of
blanchet@36564:               ByMetis facts => ByMetis (relabel_facts facts)
blanchet@36402:             | CaseSplit (proofs, facts) =>
blanchet@36402:               CaseSplit (map (aux subst (depth + 1) (1, 1)) proofs,
blanchet@36402:                          relabel_facts facts)
blanchet@36402:         in
blanchet@36402:           Have (qs, l', t, by) ::
blanchet@36402:           aux subst depth (next_assum, next_fact) proof
blanchet@36402:         end
blanchet@36491:       | aux subst depth nextp (step :: proof) =
blanchet@36491:         step :: aux subst depth nextp proof
blanchet@36402:   in aux [] 0 (1, 1) end
blanchet@36402: 
blanchet@36488: fun string_for_proof ctxt i n =
blanchet@36402:   let
blanchet@36478:     fun fix_print_mode f =
wenzelm@37146:       Print_Mode.setmp (filter (curry (op =) Symbol.xsymbolsN)
blanchet@36478:                       (print_mode_value ())) f
blanchet@36402:     fun do_indent ind = replicate_string (ind * indent_size) " "
blanchet@36478:     fun do_free (s, T) =
blanchet@36478:       maybe_quote s ^ " :: " ^
blanchet@36478:       maybe_quote (fix_print_mode (Syntax.string_of_typ ctxt) T)
blanchet@36570:     fun do_label l = if l = no_label then "" else string_for_label l ^ ": "
blanchet@36402:     fun do_have qs =
blanchet@36402:       (if member (op =) qs Moreover then "moreover " else "") ^
blanchet@36402:       (if member (op =) qs Ultimately then "ultimately " else "") ^
blanchet@36402:       (if member (op =) qs Then then
blanchet@36402:          if member (op =) qs Show then "thus" else "hence"
blanchet@36402:        else
blanchet@36402:          if member (op =) qs Show then "show" else "have")
blanchet@36478:     val do_term = maybe_quote o fix_print_mode (Syntax.string_of_term ctxt)
blanchet@36570:     fun do_facts (ls, ss) =
blanchet@36570:       let
blanchet@36570:         val ls = ls |> sort_distinct (prod_ord string_ord int_ord)
blanchet@36570:         val ss = ss |> sort_distinct string_ord
blanchet@36570:       in metis_command 1 1 (map string_for_label ls @ ss) end
blanchet@36478:     and do_step ind (Fix xs) =
blanchet@36478:         do_indent ind ^ "fix " ^ space_implode " and " (map do_free xs) ^ "\n"
blanchet@36486:       | do_step ind (Let (t1, t2)) =
blanchet@36486:         do_indent ind ^ "let " ^ do_term t1 ^ " = " ^ do_term t2 ^ "\n"
blanchet@36402:       | do_step ind (Assume (l, t)) =
blanchet@36402:         do_indent ind ^ "assume " ^ do_label l ^ do_term t ^ "\n"
blanchet@36564:       | do_step ind (Have (qs, l, t, ByMetis facts)) =
blanchet@36402:         do_indent ind ^ do_have qs ^ " " ^
blanchet@36479:         do_label l ^ do_term t ^ " " ^ do_facts facts ^ "\n"
blanchet@36402:       | do_step ind (Have (qs, l, t, CaseSplit (proofs, facts))) =
blanchet@36402:         space_implode (do_indent ind ^ "moreover\n")
blanchet@36402:                       (map (do_block ind) proofs) ^
blanchet@36479:         do_indent ind ^ do_have qs ^ " " ^ do_label l ^ do_term t ^ " " ^
blanchet@36478:         do_facts facts ^ "\n"
blanchet@36402:     and do_steps prefix suffix ind steps =
blanchet@36402:       let val s = implode (map (do_step ind) steps) in
blanchet@36402:         replicate_string (ind * indent_size - size prefix) " " ^ prefix ^
blanchet@36402:         String.extract (s, ind * indent_size,
blanchet@36402:                         SOME (size s - ind * indent_size - 1)) ^
blanchet@36402:         suffix ^ "\n"
blanchet@36402:       end
blanchet@36402:     and do_block ind proof = do_steps "{ " " }" (ind + 1) proof
blanchet@36564:     (* One-step proofs are pointless; better use the Metis one-liner
blanchet@36564:        directly. *)
blanchet@36564:     and do_proof [Have (_, _, _, ByMetis _)] = ""
blanchet@36564:       | do_proof proof =
blanchet@36480:         (if i <> 1 then "prefer " ^ string_of_int i ^ "\n" else "") ^
blanchet@36480:         do_indent 0 ^ "proof -\n" ^
blanchet@36480:         do_steps "" "" 1 proof ^
blanchet@36480:         do_indent 0 ^ (if n <> 1 then "next" else "qed") ^ "\n"
blanchet@36488:   in do_proof end
blanchet@36402: 
blanchet@36924: fun isar_proof_text (pool, debug, full_types, isar_shrink_factor, ctxt,
blanchet@36909:                      conjecture_shape)
krauss@36606:                     (minimize_command, atp_proof, thm_names, goal, i) =
blanchet@36402:   let
blanchet@36402:     val thy = ProofContext.theory_of ctxt
blanchet@36909:     val (params, hyp_ts, concl_t) = strip_subgoal goal i
blanchet@36909:     val frees = fold Term.add_frees (concl_t :: hyp_ts) []
blanchet@36967:     val tfrees = fold Term.add_tfrees (concl_t :: hyp_ts) []
blanchet@36402:     val n = Logic.count_prems (prop_of goal)
blanchet@36223:     val (one_line_proof, lemma_names) =
blanchet@36402:       metis_proof_text (minimize_command, atp_proof, thm_names, goal, i)
blanchet@36283:     fun isar_proof_for () =
blanchet@36967:       case proof_from_atp_proof pool ctxt full_types tfrees isar_shrink_factor
blanchet@36924:                                 atp_proof conjecture_shape thm_names params
blanchet@36924:                                 frees
blanchet@36491:            |> redirect_proof thy conjecture_shape hyp_ts concl_t
blanchet@36402:            |> kill_duplicate_assumptions_in_proof
blanchet@36402:            |> then_chain_proof
blanchet@36402:            |> kill_useless_labels_in_proof
blanchet@36402:            |> relabel_proof
blanchet@36488:            |> string_for_proof ctxt i n of
blanchet@36283:         "" => ""
blanchet@36402:       | proof => "\nStructured proof:\n" ^ Markup.markup Markup.sendback proof
blanchet@35868:     val isar_proof =
blanchet@36402:       if debug then
blanchet@36283:         isar_proof_for ()
blanchet@36283:       else
blanchet@36283:         try isar_proof_for ()
blanchet@36287:         |> the_default "Warning: The Isar proof construction failed.\n"
blanchet@36283:   in (one_line_proof ^ isar_proof, lemma_names) end
paulson@21978: 
blanchet@36557: fun proof_text isar_proof isar_params other_params =
blanchet@36557:   (if isar_proof then isar_proof_text isar_params else metis_proof_text)
blanchet@36557:       other_params
blanchet@36223: 
immler@31038: end;