src/HOL/Tools/Sledgehammer/sledgehammer_proof_reconstruct.ML
author blanchet
Thu Apr 22 10:54:56 2010 +0200 (2010-04-22)
changeset 36285 d868b34d604c
parent 36283 25e69e93954d
child 36287 96f45c5ffb36
permissions -rw-r--r--
Isar proof reconstruction: type variables introduced by the ATP should be treated as type parameters for type inference purposes;
this solves the unification exception that consistently was thrown for Cezary's "FSet3" theory
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(*  Title:      HOL/Tools/Sledgehammer/sledgehammer_proof_reconstruct.ML
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    Author:     Lawrence C Paulson and Claire Quigley, Cambridge University Computer Laboratory
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Transfer of proofs from external provers.
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*)
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signature SLEDGEHAMMER_PROOF_RECONSTRUCT =
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sig
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  type minimize_command = string list -> string
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  val chained_hint: string
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  val invert_const: string -> string
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  val invert_type_const: string -> string
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  val num_typargs: theory -> string -> int
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  val make_tvar: string -> typ
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  val strip_prefix: string -> string -> string option
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  val is_proof_well_formed: string -> bool
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  val metis_line: int -> int -> string list -> string
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  val metis_proof_text:
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    minimize_command -> string -> string vector -> thm -> int
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    -> string * string list
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  val isar_proof_text:
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    bool -> int -> bool -> Proof.context -> minimize_command -> string
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    -> string vector -> thm -> int -> string * string list
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  val proof_text:
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    bool -> bool -> int -> bool -> Proof.context -> minimize_command -> string
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    -> string vector -> thm -> int -> string * string list
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end;
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structure Sledgehammer_Proof_Reconstruct : SLEDGEHAMMER_PROOF_RECONSTRUCT =
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struct
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open Sledgehammer_FOL_Clause
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open Sledgehammer_Fact_Preprocessor
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type minimize_command = string list -> string
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val trace_proof_path = Path.basic "atp_trace";
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fun trace_proof_msg f =
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  if !trace then File.append (File.tmp_path trace_proof_path) (f ()) else ();
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fun string_of_thm ctxt = PrintMode.setmp [] (Display.string_of_thm ctxt);
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(**** PARSING OF TSTP FORMAT ****)
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(*Syntax trees, either termlist or formulae*)
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datatype stree = Int of int | Br of string * stree list;
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fun atom x = Br(x,[]);
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fun scons (x,y) = Br("cons", [x,y]);
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val listof = List.foldl scons (atom "nil");
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(*Strings enclosed in single quotes, e.g. filenames*)
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val quoted = $$"'" |-- Scan.repeat (~$$"'") --| $$"'" >> implode;
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(*Intended for $true and $false*)
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fun tf s = "c_" ^ str (Char.toUpper (String.sub(s,0))) ^ String.extract(s,1,NONE);
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val truefalse = $$"$" |-- Symbol.scan_id >> (atom o tf);
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(*Integer constants, typically proof line numbers*)
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fun is_digit s = Char.isDigit (String.sub(s,0));
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val integer = Scan.many1 is_digit >> (the o Int.fromString o implode);
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(*Generalized FO terms, which include filenames, numbers, etc.*)
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fun termlist x = (term ::: Scan.repeat ($$"," |-- term)) x
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and term x = (quoted >> atom || integer>>Int || truefalse ||
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              Symbol.scan_id -- Scan.optional ($$"(" |-- termlist --| $$")") [] >> Br ||
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              $$"(" |-- term --| $$")" ||
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              $$"[" |-- Scan.optional termlist [] --| $$"]" >> listof) x;
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fun negate t = Br("c_Not", [t]);
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fun equate (t1,t2) = Br("c_equal", [t1,t2]);
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(*Apply equal or not-equal to a term*)
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fun syn_equal (t, NONE) = t
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  | syn_equal (t1, SOME (NONE, t2)) = equate (t1,t2)
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  | syn_equal (t1, SOME (SOME _, t2)) = negate (equate (t1,t2));
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(*Literals can involve negation, = and !=.*)
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fun literal x = ($$"~" |-- literal >> negate ||
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                 (term -- Scan.option (Scan.option ($$"!") --| $$"=" -- term) >> syn_equal)) x;
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val literals = literal ::: Scan.repeat ($$"|" |-- literal);
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(*Clause: a list of literals separated by the disjunction sign*)
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val clause = $$"(" |-- literals --| $$")" || Scan.single literal;
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val annotations = $$"," |-- term -- Scan.option ($$"," |-- termlist);
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(*<cnf_annotated> ::= cnf(<name>,<formula_role>,<cnf_formula><annotations>).
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  The <name> could be an identifier, but we assume integers.*)
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val tstp_line = (Scan.this_string "cnf" -- $$"(") |--
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                integer --| $$"," -- Symbol.scan_id --| $$"," --
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                clause -- Scan.option annotations --| $$ ")";
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(**** INTERPRETATION OF TSTP SYNTAX TREES ****)
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exception STREE of stree;
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(*If string s has the prefix s1, return the result of deleting it.*)
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fun strip_prefix s1 s =
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  if String.isPrefix s1 s
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  then SOME (undo_ascii_of (String.extract (s, size s1, NONE)))
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  else NONE;
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(*Invert the table of translations between Isabelle and ATPs*)
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val type_const_trans_table_inv =
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      Symtab.make (map swap (Symtab.dest type_const_trans_table));
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fun invert_type_const c =
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    case Symtab.lookup type_const_trans_table_inv c of
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        SOME c' => c'
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      | NONE => c;
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fun make_tvar s = TVar (("'" ^ s, 0), HOLogic.typeS);
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fun make_tparam s = TypeInfer.param 0 (s, HOLogic.typeS)
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fun make_var (b,T) = Var((b,0),T);
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(*Type variables are given the basic sort, HOL.type. Some will later be constrained
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  by information from type literals, or by type inference.*)
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fun type_of_stree t =
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  case t of
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      Int _ => raise STREE t
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    | Br (a,ts) =>
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        let val Ts = map type_of_stree ts
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        in
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          case strip_prefix tconst_prefix a of
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              SOME b => Type(invert_type_const b, Ts)
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            | NONE =>
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                if not (null ts) then raise STREE t  (*only tconsts have type arguments*)
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                else
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                case strip_prefix tfree_prefix a of
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                    SOME b => TFree("'" ^ b, HOLogic.typeS)
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                  | NONE =>
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                case strip_prefix tvar_prefix a of
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                    SOME b => make_tvar b
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                  | NONE => make_tparam a  (* Variable from the ATP, say "X1" *)
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        end;
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(*Invert the table of translations between Isabelle and ATPs*)
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val const_trans_table_inv =
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      Symtab.update ("fequal", "op =")
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        (Symtab.make (map swap (Symtab.dest const_trans_table)));
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fun invert_const c =
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    case Symtab.lookup const_trans_table_inv c of
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        SOME c' => c'
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      | NONE => c;
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(*The number of type arguments of a constant, zero if it's monomorphic*)
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fun num_typargs thy s = length (Sign.const_typargs thy (s, Sign.the_const_type thy s));
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(*Generates a constant, given its type arguments*)
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fun const_of thy (a,Ts) = Const(a, Sign.const_instance thy (a,Ts));
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(*First-order translation. No types are known for variables. HOLogic.typeT should allow
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  them to be inferred.*)
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fun term_of_stree args thy t =
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  case t of
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      Int _ => raise STREE t
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    | Br ("hBOOL",[t]) => term_of_stree [] thy t  (*ignore hBOOL*)
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    | Br ("hAPP",[t,u]) => term_of_stree (u::args) thy t
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    | Br (a,ts) =>
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        case strip_prefix const_prefix a of
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            SOME "equal" =>
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              list_comb(Const (@{const_name "op ="}, HOLogic.typeT), List.map (term_of_stree [] thy) ts)
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          | SOME b =>
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              let val c = invert_const b
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                  val nterms = length ts - num_typargs thy c
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                  val us = List.map (term_of_stree [] thy) (List.take(ts,nterms) @ args)
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                  (*Extra args from hAPP come AFTER any arguments given directly to the
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                    constant.*)
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                  val Ts = List.map type_of_stree (List.drop(ts,nterms))
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              in  list_comb(const_of thy (c, Ts), us)  end
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          | NONE => (*a variable, not a constant*)
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              let val T = HOLogic.typeT
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                  val opr = (*a Free variable is typically a Skolem function*)
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                    case strip_prefix fixed_var_prefix a of
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                        SOME b => Free(b,T)
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                      | NONE =>
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                    case strip_prefix schematic_var_prefix a of
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                        SOME b => make_var (b,T)
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                      | NONE => make_var (a,T)    (*Variable from the ATP, say X1*)
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              in  list_comb (opr, List.map (term_of_stree [] thy) (ts@args))  end;
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(*Type class literal applied to a type. Returns triple of polarity, class, type.*)
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fun constraint_of_stree pol (Br("c_Not",[t])) = constraint_of_stree (not pol) t
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  | constraint_of_stree pol t = case t of
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        Int _ => raise STREE t
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      | Br (a,ts) =>
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            (case (strip_prefix class_prefix a, map type_of_stree ts) of
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                 (SOME b, [T]) => (pol, b, T)
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               | _ => raise STREE t);
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(** Accumulate type constraints in a clause: negative type literals **)
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fun addix (key,z)  = Vartab.map_default (key,[]) (cons z);
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fun add_constraint ((false, cl, TFree(a,_)), vt) = addix ((a,~1),cl) vt
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  | add_constraint ((false, cl, TVar(ix,_)), vt) = addix (ix,cl) vt
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  | add_constraint (_, vt) = vt;
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(*False literals (which E includes in its proofs) are deleted*)
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val nofalses = filter (not o equal HOLogic.false_const);
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(*Final treatment of the list of "real" literals from a clause.*)
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fun finish [] = HOLogic.true_const  (*No "real" literals means only type information*)
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  | finish lits =
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      case nofalses lits of
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          [] => HOLogic.false_const  (*The empty clause, since we started with real literals*)
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        | xs => foldr1 HOLogic.mk_disj (rev xs);
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(*Accumulate sort constraints in vt, with "real" literals in lits.*)
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fun lits_of_strees _ (vt, lits) [] = (vt, finish lits)
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  | lits_of_strees ctxt (vt, lits) (t::ts) =
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      lits_of_strees ctxt (add_constraint (constraint_of_stree true t, vt), lits) ts
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      handle STREE _ =>
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      lits_of_strees ctxt (vt, term_of_stree [] (ProofContext.theory_of ctxt) t :: lits) ts;
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(*Update TVars/TFrees with detected sort constraints.*)
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fun fix_sorts vt =
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  let fun tysubst (Type (a, Ts)) = Type (a, map tysubst Ts)
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        | tysubst (TVar (xi, s)) = TVar (xi, the_default s (Vartab.lookup vt xi))
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        | tysubst (TFree (x, s)) = TFree (x, the_default s (Vartab.lookup vt (x, ~1)))
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      fun tmsubst (Const (a, T)) = Const (a, tysubst T)
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        | tmsubst (Free (a, T)) = Free (a, tysubst T)
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        | tmsubst (Var (xi, T)) = Var (xi, tysubst T)
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        | tmsubst (t as Bound _) = t
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        | tmsubst (Abs (a, T, t)) = Abs (a, tysubst T, tmsubst t)
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        | tmsubst (t $ u) = tmsubst t $ tmsubst u;
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  in not (Vartab.is_empty vt) ? tmsubst end;
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(*Interpret a list of syntax trees as a clause, given by "real" literals and sort constraints.
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  vt0 holds the initial sort constraints, from the conjecture clauses.*)
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fun clause_of_strees ctxt vt0 ts =
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  let val (vt, dt) = lits_of_strees ctxt (vt0,[]) ts in
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    singleton (Syntax.check_terms ctxt) (TypeInfer.constrain HOLogic.boolT (fix_sorts vt dt))
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  end
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fun gen_all_vars t = fold_rev Logic.all (OldTerm.term_vars t) t;
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fun ints_of_stree_aux (Int n, ns) = n::ns
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  | ints_of_stree_aux (Br(_,ts), ns) = List.foldl ints_of_stree_aux ns ts;
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fun ints_of_stree t = ints_of_stree_aux (t, []);
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fun decode_tstp vt0 (name, role, ts, annots) ctxt =
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  let val deps = case annots of NONE => [] | SOME (source,_) => ints_of_stree source
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      val cl = clause_of_strees ctxt vt0 ts
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  in  ((name, role, cl, deps), fold Variable.declare_term (OldTerm.term_frees cl) ctxt)  end;
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fun dest_tstp ((((name, role), ts), annots), chs) =
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  case chs of
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          "."::_ => (name, role, ts, annots)
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        | _ => error ("TSTP line not terminated by \".\": " ^ implode chs);
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(** Global sort constraints on TFrees (from tfree_tcs) are positive unit clauses. **)
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fun add_tfree_constraint ((true, cl, TFree(a,_)), vt) = addix ((a,~1),cl) vt
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  | add_tfree_constraint (_, vt) = vt;
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fun tfree_constraints_of_clauses vt [] = vt
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  | tfree_constraints_of_clauses vt ([lit]::tss) =
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      (tfree_constraints_of_clauses (add_tfree_constraint (constraint_of_stree true lit, vt)) tss
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       handle STREE _ => (*not a positive type constraint: ignore*)
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       tfree_constraints_of_clauses vt tss)
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  | tfree_constraints_of_clauses vt (_::tss) = tfree_constraints_of_clauses vt tss;
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(**** Translation of TSTP files to Isar Proofs ****)
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fun decode_tstp_list ctxt tuples =
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  let val vt0 = tfree_constraints_of_clauses Vartab.empty (map #3 tuples)
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  in  #1 (fold_map (decode_tstp vt0) tuples ctxt) end;
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(** Finding a matching assumption. The literals may be permuted, and variable names
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    may disagree. We have to try all combinations of literals (quadratic!) and
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    match up the variable names consistently. **)
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fun strip_alls_aux n (Const(@{const_name all}, _)$Abs(a,T,t))  =
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      strip_alls_aux (n+1) (subst_bound (Var ((a,n), T), t))
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  | strip_alls_aux _ t  =  t;
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val strip_alls = strip_alls_aux 0;
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exception MATCH_LITERAL;
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(*Ignore types: they are not to be trusted...*)
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fun match_literal (t1$u1) (t2$u2) env =
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      match_literal t1 t2 (match_literal u1 u2 env)
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  | match_literal (Abs (_,_,t1)) (Abs (_,_,t2)) env =
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      match_literal t1 t2 env
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  | match_literal (Bound i1) (Bound i2) env =
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      if i1=i2 then env else raise MATCH_LITERAL
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  | match_literal (Const(a1,_)) (Const(a2,_)) env =
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   300
      if a1=a2 then env else raise MATCH_LITERAL
immler@31038
   301
  | match_literal (Free(a1,_)) (Free(a2,_)) env =
paulson@23519
   302
      if a1=a2 then env else raise MATCH_LITERAL
paulson@23519
   303
  | match_literal (Var(ix1,_)) (Var(ix2,_)) env = insert (op =) (ix1,ix2) env
wenzelm@32994
   304
  | match_literal _ _ _ = raise MATCH_LITERAL;
paulson@23519
   305
paulson@23519
   306
(*Checking that all variable associations are unique. The list env contains no
paulson@23519
   307
  repetitions, but does it contain say (x,y) and (y,y)? *)
immler@31038
   308
fun good env =
paulson@23519
   309
  let val (xs,ys) = ListPair.unzip env
paulson@23519
   310
  in  not (has_duplicates (op=) xs orelse has_duplicates (op=) ys)  end;
paulson@23519
   311
paulson@23519
   312
(*Match one list of literals against another, ignoring types and the order of
paulson@23519
   313
  literals. Sorting is unreliable because we don't have types or variable names.*)
paulson@23519
   314
fun matches_aux _ [] [] = true
paulson@23519
   315
  | matches_aux env (lit::lits) ts =
paulson@23519
   316
      let fun match1 us [] = false
paulson@23519
   317
            | match1 us (t::ts) =
paulson@23519
   318
                let val env' = match_literal lit t env
immler@31038
   319
                in  (good env' andalso matches_aux env' lits (us@ts)) orelse
immler@31038
   320
                    match1 (t::us) ts
paulson@23519
   321
                end
paulson@23519
   322
                handle MATCH_LITERAL => match1 (t::us) ts
immler@31038
   323
      in  match1 [] ts  end;
paulson@23519
   324
paulson@23519
   325
(*Is this length test useful?*)
immler@31038
   326
fun matches (lits1,lits2) =
immler@31038
   327
  length lits1 = length lits2  andalso
paulson@23519
   328
  matches_aux [] (map Envir.eta_contract lits1) (map Envir.eta_contract lits2);
paulson@21999
   329
paulson@21999
   330
fun permuted_clause t =
paulson@24958
   331
  let val lits = HOLogic.disjuncts t
paulson@21999
   332
      fun perm [] = NONE
wenzelm@23139
   333
        | perm (ctm::ctms) =
paulson@24958
   334
            if matches (lits, HOLogic.disjuncts (HOLogic.dest_Trueprop (strip_alls ctm)))
paulson@23519
   335
            then SOME ctm else perm ctms
paulson@21999
   336
  in perm end;
paulson@21999
   337
paulson@21999
   338
(*ctms is a list of conjecture clauses as yielded by Isabelle. Those returned by the
paulson@21999
   339
  ATP may have their literals reordered.*)
blanchet@36064
   340
fun isar_proof_body ctxt sorts ctms =
blanchet@35869
   341
  let
blanchet@35869
   342
    val _ = trace_proof_msg (K "\n\nisar_proof_body: start\n")
blanchet@36064
   343
    val string_of_term = 
blanchet@36064
   344
      PrintMode.setmp (filter (curry (op =) Symbol.xsymbolsN)
blanchet@36064
   345
                              (print_mode_value ()))
blanchet@36064
   346
                      (Syntax.string_of_term ctxt)
blanchet@35966
   347
    fun have_or_show "show" _ = "  show \""
blanchet@35966
   348
      | have_or_show have lname = "  " ^ have ^ " " ^ lname ^ ": \""
blanchet@35869
   349
    fun do_line _ (lname, t, []) =
blanchet@36285
   350
       (* No depedencies: it's a conjecture clause, with no proof. *)
blanchet@35869
   351
       (case permuted_clause t ctms of
blanchet@35966
   352
          SOME u => "  assume " ^ lname ^ ": \"" ^ string_of_term u ^ "\"\n"
blanchet@35869
   353
        | NONE => raise TERM ("Sledgehammer_Proof_Reconstruct.isar_proof_body",
blanchet@35869
   354
                              [t]))
blanchet@35869
   355
      | do_line have (lname, t, deps) =
blanchet@35869
   356
        have_or_show have lname ^
blanchet@35869
   357
        string_of_term (gen_all_vars (HOLogic.mk_Trueprop t)) ^
blanchet@35966
   358
        "\"\n    by (metis " ^ space_implode " " deps ^ ")\n"
blanchet@35869
   359
    fun do_lines [(lname, t, deps)] = [do_line "show" (lname, t, deps)]
blanchet@35869
   360
      | do_lines ((lname, t, deps) :: lines) =
blanchet@35869
   361
        do_line "have" (lname, t, deps) :: do_lines lines
blanchet@36064
   362
  in setmp_CRITICAL show_sorts sorts do_lines end;
paulson@21978
   363
blanchet@35869
   364
fun unequal t (_, t', _) = not (t aconv t');
paulson@21978
   365
paulson@22491
   366
(*No "real" literals means only type information*)
paulson@23519
   367
fun eq_types t = t aconv HOLogic.true_const;
paulson@21978
   368
paulson@22731
   369
fun replace_dep (old:int, new) dep = if dep=old then new else [dep];
paulson@21978
   370
wenzelm@23139
   371
fun replace_deps (old:int, new) (lno, t, deps) =
haftmann@33042
   372
      (lno, t, List.foldl (uncurry (union (op =))) [] (map (replace_dep (old, new)) deps));
paulson@21978
   373
paulson@22491
   374
(*Discard axioms; consolidate adjacent lines that prove the same clause, since they differ
paulson@22491
   375
  only in type information.*)
paulson@21978
   376
fun add_prfline ((lno, "axiom", t, []), lines) =  (*axioms are not proof lines*)
paulson@22491
   377
      if eq_types t (*must be clsrel/clsarity: type information, so delete refs to it*)
wenzelm@23139
   378
      then map (replace_deps (lno, [])) lines
paulson@22470
   379
      else
blanchet@35869
   380
       (case take_prefix (unequal t) lines of
paulson@22470
   381
           (_,[]) => lines                  (*no repetition of proof line*)
wenzelm@32994
   382
         | (pre, (lno', _, _) :: post) =>   (*repetition: replace later line by earlier one*)
paulson@22470
   383
             pre @ map (replace_deps (lno', [lno])) post)
wenzelm@32994
   384
  | add_prfline ((lno, _, t, []), lines) =  (*no deps: conjecture clause*)
paulson@22470
   385
      (lno, t, []) :: lines
wenzelm@32994
   386
  | add_prfline ((lno, _, t, deps), lines) =
paulson@22491
   387
      if eq_types t then (lno, t, deps) :: lines
paulson@22491
   388
      (*Type information will be deleted later; skip repetition test.*)
paulson@22491
   389
      else (*FIXME: Doesn't this code risk conflating proofs involving different types??*)
blanchet@35869
   390
      case take_prefix (unequal t) lines of
paulson@22044
   391
         (_,[]) => (lno, t, deps) :: lines  (*no repetition of proof line*)
wenzelm@32994
   392
       | (pre, (lno', t', _) :: post) =>
paulson@22044
   393
           (lno, t', deps) ::               (*repetition: replace later line by earlier one*)
paulson@22044
   394
           (pre @ map (replace_deps (lno', [lno])) post);
paulson@22044
   395
paulson@22470
   396
(*Recursively delete empty lines (type information) from the proof.*)
paulson@22470
   397
fun add_nonnull_prfline ((lno, t, []), lines) = (*no dependencies, so a conjecture clause*)
paulson@22491
   398
     if eq_types t (*must be type information, tfree_tcs, clsrel, clsarity: delete refs to it*)
wenzelm@23139
   399
     then delete_dep lno lines
wenzelm@23139
   400
     else (lno, t, []) :: lines
paulson@22470
   401
  | add_nonnull_prfline ((lno, t, deps), lines) = (lno, t, deps) :: lines
wenzelm@30190
   402
and delete_dep lno lines = List.foldr add_nonnull_prfline [] (map (replace_deps (lno, [])) lines);
paulson@22470
   403
blanchet@35865
   404
fun bad_free (Free (a,_)) = String.isPrefix skolem_prefix a
paulson@22731
   405
  | bad_free _ = false;
paulson@22731
   406
wenzelm@23139
   407
(*TVars are forbidden in goals. Also, we don't want lines with <2 dependencies.
paulson@22491
   408
  To further compress proofs, setting modulus:=n deletes every nth line, and nlines
paulson@22491
   409
  counts the number of proof lines processed so far.
paulson@22491
   410
  Deleted lines are replaced by their own dependencies. Note that the "add_nonnull_prfline"
paulson@22044
   411
  phase may delete some dependencies, hence this phase comes later.*)
blanchet@36064
   412
fun add_wanted_prfline ctxt _ ((lno, t, []), (nlines, lines)) =
paulson@22491
   413
      (nlines, (lno, t, []) :: lines)   (*conjecture clauses must be kept*)
blanchet@36064
   414
  | add_wanted_prfline ctxt modulus ((lno, t, deps), (nlines, lines)) =
wenzelm@29272
   415
      if eq_types t orelse not (null (Term.add_tvars t [])) orelse
wenzelm@29268
   416
         exists_subterm bad_free t orelse
paulson@24937
   417
         (not (null lines) andalso   (*final line can't be deleted for these reasons*)
blanchet@36064
   418
          (length deps < 2 orelse nlines mod modulus <> 0))
paulson@22491
   419
      then (nlines+1, map (replace_deps (lno, deps)) lines) (*Delete line*)
paulson@22491
   420
      else (nlines+1, (lno, t, deps) :: lines);
paulson@21978
   421
paulson@21999
   422
(*Replace numeric proof lines by strings, either from thm_names or sequential line numbers*)
paulson@21978
   423
fun stringify_deps thm_names deps_map [] = []
paulson@21978
   424
  | stringify_deps thm_names deps_map ((lno, t, deps) :: lines) =
paulson@21978
   425
      if lno <= Vector.length thm_names  (*axiom*)
wenzelm@23139
   426
      then (Vector.sub(thm_names,lno-1), t, []) :: stringify_deps thm_names deps_map lines
paulson@21979
   427
      else let val lname = Int.toString (length deps_map)
wenzelm@23139
   428
               fun fix lno = if lno <= Vector.length thm_names
paulson@21978
   429
                             then SOME(Vector.sub(thm_names,lno-1))
paulson@21978
   430
                             else AList.lookup op= deps_map lno;
wenzelm@32952
   431
           in  (lname, t, map_filter fix (distinct (op=) deps)) ::
paulson@21978
   432
               stringify_deps thm_names ((lno,lname)::deps_map) lines
paulson@21978
   433
           end;
paulson@21978
   434
blanchet@36063
   435
fun isar_proof_start i =
blanchet@36063
   436
  (if i = 1 then "" else "prefer " ^ string_of_int i ^ "\n") ^
blanchet@36063
   437
  "proof (neg_clausify)\n";
blanchet@36063
   438
fun isar_fixes [] = ""
blanchet@36063
   439
  | isar_fixes ts = "  fix " ^ space_implode " " ts ^ "\n";
blanchet@36063
   440
fun isar_proof_end 1 = "qed"
blanchet@36063
   441
  | isar_proof_end _ = "next"
paulson@21979
   442
blanchet@36064
   443
fun isar_proof_from_tstp_file cnfs modulus sorts ctxt goal i thm_names =
blanchet@35868
   444
  let
blanchet@35868
   445
    val _ = trace_proof_msg (K "\nisar_proof_from_tstp_file: start\n")
blanchet@35868
   446
    val tuples = map (dest_tstp o tstp_line o explode) cnfs
blanchet@35868
   447
    val _ = trace_proof_msg (fn () =>
blanchet@35868
   448
      Int.toString (length tuples) ^ " tuples extracted\n")
blanchet@35868
   449
    val ctxt = ProofContext.set_mode ProofContext.mode_schematic ctxt
blanchet@35868
   450
    val raw_lines = List.foldr add_prfline [] (decode_tstp_list ctxt tuples)
blanchet@35868
   451
    val _ = trace_proof_msg (fn () =>
blanchet@35868
   452
      Int.toString (length raw_lines) ^ " raw_lines extracted\n")
blanchet@35868
   453
    val nonnull_lines = List.foldr add_nonnull_prfline [] raw_lines
blanchet@35868
   454
    val _ = trace_proof_msg (fn () =>
blanchet@35868
   455
      Int.toString (length nonnull_lines) ^ " nonnull_lines extracted\n")
blanchet@36064
   456
    val (_, lines) = List.foldr (add_wanted_prfline ctxt modulus) (0,[]) nonnull_lines
blanchet@35868
   457
    val _ = trace_proof_msg (fn () =>
blanchet@35868
   458
      Int.toString (length lines) ^ " lines extracted\n")
blanchet@36063
   459
    val (ccls, fixes) = neg_conjecture_clauses ctxt goal i
blanchet@35868
   460
    val _ = trace_proof_msg (fn () =>
blanchet@35868
   461
      Int.toString (length ccls) ^ " conjecture clauses\n")
blanchet@35868
   462
    val ccls = map forall_intr_vars ccls
blanchet@35868
   463
    val _ = app (fn th => trace_proof_msg
blanchet@35868
   464
                              (fn () => "\nccl: " ^ string_of_thm ctxt th)) ccls
blanchet@36064
   465
    val body = isar_proof_body ctxt sorts (map prop_of ccls)
blanchet@35869
   466
                               (stringify_deps thm_names [] lines)
blanchet@36063
   467
    val n = Logic.count_prems (prop_of goal)
blanchet@35868
   468
    val _ = trace_proof_msg (K "\nisar_proof_from_tstp_file: finishing\n")
blanchet@36063
   469
  in
blanchet@36063
   470
    isar_proof_start i ^ isar_fixes (map #1 fixes) ^ implode body ^
blanchet@36063
   471
    isar_proof_end n ^ "\n"
blanchet@36063
   472
  end
blanchet@35868
   473
  handle STREE _ => error "Could not extract proof (ATP output malformed?)";
paulson@21978
   474
paulson@21978
   475
wenzelm@33310
   476
(*=== EXTRACTING PROOF-TEXT === *)
immler@31866
   477
blanchet@35865
   478
val begin_proof_strs = ["# SZS output start CNFRefutation.",
wenzelm@33310
   479
  "=========== Refutation ==========",
immler@31866
   480
  "Here is a proof"];
wenzelm@33310
   481
blanchet@35865
   482
val end_proof_strs = ["# SZS output end CNFRefutation",
wenzelm@33310
   483
  "======= End of refutation =======",
immler@31866
   484
  "Formulae used in the proof"];
wenzelm@33310
   485
wenzelm@33310
   486
fun get_proof_extract proof =
wenzelm@33310
   487
  let
immler@31866
   488
    (*splits to_split by the first possible of a list of splitters*)
immler@31866
   489
    val (begin_string, end_string) =
blanchet@35865
   490
      (find_first (fn s => String.isSubstring s proof) begin_proof_strs,
blanchet@35865
   491
      find_first (fn s => String.isSubstring s proof) end_proof_strs)
wenzelm@33310
   492
  in
wenzelm@33310
   493
    if is_none begin_string orelse is_none end_string
wenzelm@33310
   494
    then error "Could not extract proof (no substring indicating a proof)"
wenzelm@33310
   495
    else proof |> first_field (the begin_string) |> the |> snd
wenzelm@33310
   496
               |> first_field (the end_string) |> the |> fst
wenzelm@33310
   497
  end;
immler@31866
   498
blanchet@35865
   499
(* ==== CHECK IF PROOF WAS SUCCESSFUL === *)
immler@31866
   500
blanchet@35865
   501
fun is_proof_well_formed proof =
blanchet@35865
   502
  exists (fn s => String.isSubstring s proof) begin_proof_strs andalso
blanchet@35865
   503
  exists (fn s => String.isSubstring s proof) end_proof_strs
immler@31866
   504
wenzelm@33310
   505
(* === EXTRACTING LEMMAS === *)
blanchet@36223
   506
(* A list consisting of the first number in each line is returned.
blanchet@36223
   507
   TPTP: Interesting lines have the form "cnf(108, axiom, ...)", where the
blanchet@36223
   508
   number (108) is extracted.
blanchet@36223
   509
   DFG: Lines have the form "108[0:Inp] ...", where the first number (108) is
blanchet@36223
   510
   extracted. *)
blanchet@36223
   511
fun get_step_nums proof_extract =
blanchet@35865
   512
  let
blanchet@35865
   513
    val toks = String.tokens (not o Char.isAlphaNum)
blanchet@35865
   514
    fun inputno ("cnf" :: ntok :: "axiom" :: _) = Int.fromString ntok
blanchet@35865
   515
      | inputno ("cnf" :: ntok :: "negated" :: "conjecture" :: _) =
blanchet@35865
   516
        Int.fromString ntok
blanchet@36223
   517
      | inputno (ntok::"0"::"Inp"::_) = Int.fromString ntok (* DFG *)
blanchet@35865
   518
      | inputno _ = NONE
blanchet@36223
   519
    val lines = split_lines proof_extract
blanchet@35865
   520
  in map_filter (inputno o toks) lines end
wenzelm@33310
   521
  
wenzelm@33310
   522
(*Used to label theorems chained into the sledgehammer call*)
wenzelm@33310
   523
val chained_hint = "CHAINED";
blanchet@35865
   524
val kill_chained = filter_out (curry (op =) chained_hint)
blanchet@35865
   525
blanchet@36063
   526
fun apply_command _ 1 = "by "
blanchet@36063
   527
  | apply_command 1 _ = "apply "
blanchet@36063
   528
  | apply_command i _ = "prefer " ^ string_of_int i ^ " apply "
blanchet@36063
   529
fun metis_command i n [] =
blanchet@36063
   530
    apply_command i n ^ "metis"
blanchet@36063
   531
  | metis_command i n xs =
blanchet@36063
   532
    apply_command i n ^ "(metis " ^ space_implode " " xs ^ ")"
blanchet@36063
   533
fun metis_line i n xs =
blanchet@36063
   534
  "Try this command: " ^
blanchet@36063
   535
  Markup.markup Markup.sendback (metis_command i n xs) ^ ".\n" 
blanchet@36281
   536
fun minimize_line _ [] = ""
blanchet@36281
   537
  | minimize_line minimize_command facts =
blanchet@36281
   538
    case minimize_command facts of
blanchet@36281
   539
      "" => ""
blanchet@36281
   540
    | command =>
blanchet@36065
   541
      "To minimize the number of lemmas, try this command: " ^
blanchet@36281
   542
      Markup.markup Markup.sendback command ^ ".\n"
immler@31840
   543
blanchet@36281
   544
fun metis_proof_text minimize_command proof thm_names goal i =
blanchet@36063
   545
  let
blanchet@36231
   546
    val lemmas =
blanchet@36231
   547
      proof |> get_proof_extract
blanchet@36231
   548
            |> get_step_nums
blanchet@36231
   549
            |> filter (fn i => i <= Vector.length thm_names)
blanchet@36231
   550
            |> map (fn i => Vector.sub (thm_names, i - 1))
blanchet@36231
   551
            |> filter (fn x => x <> "??.unknown")
blanchet@36231
   552
            |> sort_distinct string_ord
blanchet@36063
   553
    val n = Logic.count_prems (prop_of goal)
blanchet@36063
   554
    val xs = kill_chained lemmas
blanchet@36063
   555
  in
blanchet@36281
   556
    (metis_line i n xs ^ minimize_line minimize_command xs, kill_chained lemmas)
blanchet@36223
   557
  end
immler@31037
   558
blanchet@36283
   559
fun isar_proof_text debug modulus sorts ctxt minimize_command proof thm_names
blanchet@36283
   560
                    goal i =
wenzelm@33310
   561
  let
blanchet@36064
   562
    (* We could use "split_lines", but it can return blank lines. *)
blanchet@35865
   563
    val lines = String.tokens (equal #"\n");
blanchet@35868
   564
    val kill_spaces =
blanchet@35868
   565
      String.translate (fn c => if Char.isSpace c then "" else str c)
blanchet@35865
   566
    val extract = get_proof_extract proof
blanchet@35865
   567
    val cnfs = filter (String.isPrefix "cnf(") (map kill_spaces (lines extract))
blanchet@36223
   568
    val (one_line_proof, lemma_names) =
blanchet@36281
   569
      metis_proof_text minimize_command proof thm_names goal i
blanchet@35868
   570
    val tokens = String.tokens (fn c => c = #" ") one_line_proof
blanchet@36283
   571
    fun isar_proof_for () =
blanchet@36283
   572
      case isar_proof_from_tstp_file cnfs modulus sorts ctxt goal i thm_names of
blanchet@36283
   573
        "" => ""
blanchet@36285
   574
      | isar_proof =>
blanchet@36285
   575
        "\nStructured proof:\n" ^ Markup.markup Markup.sendback isar_proof
blanchet@35868
   576
    val isar_proof =
blanchet@36283
   577
      if member (op =) tokens chained_hint then
blanchet@36283
   578
        ""
blanchet@36283
   579
      else if debug then
blanchet@36283
   580
        isar_proof_for ()
blanchet@36283
   581
      else
blanchet@36283
   582
        try isar_proof_for ()
blanchet@36283
   583
        |> the_default "Error: The Isar proof reconstruction failed."
blanchet@36283
   584
  in (one_line_proof ^ isar_proof, lemma_names) end
paulson@21978
   585
blanchet@36283
   586
fun proof_text isar_proof debug modulus sorts ctxt =
blanchet@36283
   587
  if isar_proof then isar_proof_text debug modulus sorts ctxt
blanchet@36283
   588
  else metis_proof_text
blanchet@36223
   589
immler@31038
   590
end;