src/HOL/Tools/Sledgehammer/metis_clauses.ML
author blanchet
Mon Jul 26 11:21:25 2010 +0200 (2010-07-26)
changeset 37992 7911e78a7122
parent 37926 e6ff246c0cdb
child 37994 b04307085a09
permissions -rw-r--r--
renamed internal function
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(*  Title:      HOL/Tools/Sledgehammer/metis_clauses.ML
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    Author:     Jia Meng, Cambridge University Computer Laboratory
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    Author:     Jasmin Blanchette, TU Muenchen
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Storing/printing FOL clauses and arity clauses.  Typed equality is
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treated differently.
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*)
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signature METIS_CLAUSES =
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sig
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  type name = string * string
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  datatype kind = Axiom | Conjecture
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  datatype type_literal =
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    TyLitVar of name * name |
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    TyLitFree of name * name
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  datatype arLit =
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    TConsLit of name * name * name list |
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    TVarLit of name * name
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  datatype arity_clause = ArityClause of
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   {axiom_name: string, conclLit: arLit, premLits: arLit list}
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  datatype class_rel_clause = ClassRelClause of
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   {axiom_name: string, subclass: name, superclass: name}
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  datatype combtyp =
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    CombTVar of name |
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    CombTFree of name |
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    CombType of name * combtyp list
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  datatype combterm =
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    CombConst of name * combtyp * combtyp list (* Const and Free *) |
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    CombVar of name * combtyp |
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    CombApp of combterm * combterm
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  datatype fol_literal = FOLLiteral of bool * combterm
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  datatype fol_clause =
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    FOLClause of {clause_id: int, axiom_name: string, th: thm, kind: kind,
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                  literals: fol_literal list, ctypes_sorts: typ list}
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  val type_wrapper_name : string
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  val schematic_var_prefix: string
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  val fixed_var_prefix: string
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  val tvar_prefix: string
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  val tfree_prefix: string
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  val const_prefix: string
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  val type_const_prefix: string
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  val class_prefix: string
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  val union_all: ''a list list -> ''a list
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  val invert_const: string -> string
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  val ascii_of: string -> string
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  val undo_ascii_of: string -> string
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  val strip_prefix_and_undo_ascii: string -> string -> string option
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  val make_schematic_var : string * int -> string
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  val make_fixed_var : string -> string
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  val make_schematic_type_var : string * int -> string
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  val make_fixed_type_var : string -> string
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  val make_fixed_const : string -> string
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  val make_fixed_type_const : string -> string
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  val make_type_class : string -> string
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  val skolem_theory_name: string
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  val skolem_prefix: string
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  val skolem_infix: string
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  val is_skolem_const_name: string -> bool
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  val num_type_args: theory -> string -> int
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  val type_literals_for_types : typ list -> type_literal list
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  val make_class_rel_clauses: theory -> class list -> class list -> class_rel_clause list
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  val make_arity_clauses: theory -> string list -> class list -> class list * arity_clause list
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  val type_of_combterm : combterm -> combtyp
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  val strip_combterm_comb : combterm -> combterm * combterm list
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  val literals_of_term : theory -> term -> fol_literal list * typ list
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  val conceal_skolem_terms :
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    int -> (string * term) list -> term -> (string * term) list * term
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  val reveal_skolem_terms : (string * term) list -> term -> term
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  val tfree_classes_of_terms : term list -> string list
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  val tvar_classes_of_terms : term list -> string list
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  val type_consts_of_terms : theory -> term list -> string list
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end
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structure Metis_Clauses : METIS_CLAUSES =
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struct
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val type_wrapper_name = "ti"
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val schematic_var_prefix = "V_";
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val fixed_var_prefix = "v_";
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val tvar_prefix = "T_";
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val tfree_prefix = "t_";
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val class_rel_clause_prefix = "clsrel_";
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val const_prefix = "c_";
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val type_const_prefix = "tc_";
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val class_prefix = "class_";
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fun union_all xss = fold (union (op =)) xss []
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(* Readable names for the more common symbolic functions. Do not mess with the
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   last nine entries of the table unless you know what you are doing. *)
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val const_trans_table =
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  Symtab.make [(@{type_name Product_Type.prod}, "prod"),
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               (@{type_name Sum_Type.sum}, "sum"),
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               (@{const_name "op ="}, "equal"),
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               (@{const_name "op &"}, "and"),
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               (@{const_name "op |"}, "or"),
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               (@{const_name "op -->"}, "implies"),
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               (@{const_name Set.member}, "in"),
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               (@{const_name fequal}, "fequal"),
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               (@{const_name COMBI}, "COMBI"),
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               (@{const_name COMBK}, "COMBK"),
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               (@{const_name COMBB}, "COMBB"),
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               (@{const_name COMBC}, "COMBC"),
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               (@{const_name COMBS}, "COMBS"),
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               (@{const_name True}, "True"),
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               (@{const_name False}, "False"),
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               (@{const_name If}, "If")]
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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", @{const_name "op ="})
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                (Symtab.make (map swap (Symtab.dest const_trans_table)))
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val invert_const = perhaps (Symtab.lookup const_trans_table_inv)
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(*Escaping of special characters.
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  Alphanumeric characters are left unchanged.
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  The character _ goes to __
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  Characters in the range ASCII space to / go to _A to _P, respectively.
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  Other printing characters go to _nnn where nnn is the decimal ASCII code.*)
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val A_minus_space = Char.ord #"A" - Char.ord #" ";
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fun stringN_of_int 0 _ = ""
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  | stringN_of_int k n = stringN_of_int (k-1) (n div 10) ^ Int.toString (n mod 10);
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fun ascii_of_c c =
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  if Char.isAlphaNum c then String.str c
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  else if c = #"_" then "__"
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  else if #" " <= c andalso c <= #"/"
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       then "_" ^ String.str (Char.chr (Char.ord c + A_minus_space))
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  else if Char.isPrint c
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       then ("_" ^ stringN_of_int 3 (Char.ord c))  (*fixed width, in case more digits follow*)
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  else ""
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val ascii_of = String.translate ascii_of_c;
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(** Remove ASCII armouring from names in proof files **)
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(*We don't raise error exceptions because this code can run inside the watcher.
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  Also, the errors are "impossible" (hah!)*)
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fun undo_ascii_aux rcs [] = String.implode(rev rcs)
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  | undo_ascii_aux rcs [#"_"] = undo_ascii_aux (#"_"::rcs) []  (*ERROR*)
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      (*Three types of _ escapes: __, _A to _P, _nnn*)
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  | undo_ascii_aux rcs (#"_" :: #"_" :: cs) = undo_ascii_aux (#"_"::rcs) cs
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  | undo_ascii_aux rcs (#"_" :: c :: cs) =
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      if #"A" <= c andalso c<= #"P"  (*translation of #" " to #"/"*)
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      then undo_ascii_aux (Char.chr(Char.ord c - A_minus_space) :: rcs) cs
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      else
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        let val digits = List.take (c::cs, 3) handle Subscript => []
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        in
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            case Int.fromString (String.implode digits) of
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                NONE => undo_ascii_aux (c:: #"_"::rcs) cs  (*ERROR*)
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              | SOME n => undo_ascii_aux (Char.chr n :: rcs) (List.drop (cs, 2))
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        end
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  | undo_ascii_aux rcs (c::cs) = undo_ascii_aux (c::rcs) cs;
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val undo_ascii_of = undo_ascii_aux [] o String.explode;
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(* If string s has the prefix s1, return the result of deleting it,
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   un-ASCII'd. *)
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fun strip_prefix_and_undo_ascii s1 s =
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  if String.isPrefix s1 s then
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    SOME (undo_ascii_of (String.extract (s, size s1, NONE)))
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  else
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    NONE
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(*Remove the initial ' character from a type variable, if it is present*)
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fun trim_type_var s =
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  if s <> "" andalso String.sub(s,0) = #"'" then String.extract(s,1,NONE)
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  else error ("trim_type: Malformed type variable encountered: " ^ s);
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fun ascii_of_indexname (v,0) = ascii_of v
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  | ascii_of_indexname (v,i) = ascii_of v ^ "_" ^ Int.toString i;
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fun make_schematic_var v = schematic_var_prefix ^ (ascii_of_indexname v);
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fun make_fixed_var x = fixed_var_prefix ^ (ascii_of x);
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fun make_schematic_type_var (x,i) =
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      tvar_prefix ^ (ascii_of_indexname (trim_type_var x,i));
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fun make_fixed_type_var x = tfree_prefix ^ (ascii_of (trim_type_var x));
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fun lookup_const c =
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  case Symtab.lookup const_trans_table c of
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    SOME c' => c'
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  | NONE => ascii_of c
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(* "op =" MUST BE "equal" because it's built into ATPs. *)
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fun make_fixed_const @{const_name "op ="} = "equal"
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  | make_fixed_const c = const_prefix ^ lookup_const c
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fun make_fixed_type_const c = type_const_prefix ^ lookup_const c
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fun make_type_class clas = class_prefix ^ ascii_of clas;
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val skolem_theory_name = "Sledgehammer" ^ Long_Name.separator ^ "Sko"
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val skolem_prefix = "sko_"
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val skolem_infix = "$"
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(* Hack: Could return false positives (e.g., a user happens to declare a
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   constant called "SomeTheory.sko_means_shoe_in_$wedish". *)
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val is_skolem_const_name =
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  Long_Name.base_name
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  #> String.isPrefix skolem_prefix andf String.isSubstring skolem_infix
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(* The number of type arguments of a constant, zero if it's monomorphic. For
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   (instances of) Skolem pseudoconstants, this information is encoded in the
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   constant name. *)
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fun num_type_args thy s =
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  if String.isPrefix skolem_theory_name s then
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    s |> unprefix skolem_theory_name
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      |> space_explode skolem_infix |> hd
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      |> space_explode "_" |> List.last |> Int.fromString |> the
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  else
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    (s, Sign.the_const_type thy s) |> Sign.const_typargs thy |> length
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(**** Definitions and functions for FOL clauses for TPTP format output ****)
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type name = string * string
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datatype kind = Axiom | Conjecture
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(**** Isabelle FOL clauses ****)
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(* The first component is the type class; the second is a TVar or TFree. *)
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datatype type_literal =
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  TyLitVar of name * name |
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  TyLitFree of name * name
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exception CLAUSE of string * term;
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(*Make literals for sorted type variables*)
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fun sorts_on_typs_aux (_, [])   = []
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  | sorts_on_typs_aux ((x,i),  s::ss) =
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      let val sorts = sorts_on_typs_aux ((x,i), ss)
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      in
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          if s = "HOL.type" then sorts
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          else if i = ~1 then TyLitFree (`make_type_class s, `make_fixed_type_var x) :: sorts
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          else TyLitVar (`make_type_class s, (make_schematic_type_var (x,i), x)) :: sorts
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      end;
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fun sorts_on_typs (TFree (a,s)) = sorts_on_typs_aux ((a,~1),s)
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  | sorts_on_typs (TVar (v,s))  = sorts_on_typs_aux (v,s);
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(*Given a list of sorted type variables, return a list of type literals.*)
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fun type_literals_for_types Ts =
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  fold (union (op =)) (map sorts_on_typs Ts) []
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(** make axiom and conjecture clauses. **)
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(**** Isabelle arities ****)
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datatype arLit =
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  TConsLit of name * name * name list |
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  TVarLit of name * name
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datatype arity_clause =
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  ArityClause of {axiom_name: string, conclLit: arLit, premLits: arLit list}
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fun gen_TVars 0 = []
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  | gen_TVars n = ("T_" ^ Int.toString n) :: gen_TVars (n-1);
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fun pack_sort(_,[])  = []
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  | pack_sort(tvar, "HOL.type"::srt) = pack_sort (tvar, srt)   (*IGNORE sort "type"*)
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  | pack_sort(tvar, cls::srt) =
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    (`make_type_class cls, (tvar, tvar)) :: pack_sort (tvar, srt)
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(*Arity of type constructor tcon :: (arg1,...,argN)res*)
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fun make_axiom_arity_clause (tcons, axiom_name, (cls,args)) =
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  let
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    val tvars = gen_TVars (length args)
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    val tvars_srts = ListPair.zip (tvars, args)
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  in
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    ArityClause {axiom_name = axiom_name, 
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                 conclLit = TConsLit (`make_type_class cls,
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                                      `make_fixed_type_const tcons,
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                                      tvars ~~ tvars),
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                 premLits = map TVarLit (union_all (map pack_sort tvars_srts))}
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  end
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(**** Isabelle class relations ****)
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datatype class_rel_clause =
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  ClassRelClause of {axiom_name: string, subclass: name, superclass: name}
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(*Generate all pairs (sub,super) such that sub is a proper subclass of super in theory thy.*)
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fun class_pairs _ [] _ = []
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  | class_pairs thy subs supers =
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      let
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        val class_less = Sorts.class_less (Sign.classes_of thy)
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        fun add_super sub super = class_less (sub, super) ? cons (sub, super)
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        fun add_supers sub = fold (add_super sub) supers
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      in fold add_supers subs [] end
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fun make_class_rel_clause (sub,super) =
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  ClassRelClause {axiom_name = class_rel_clause_prefix ^ ascii_of sub ^ "_" ^
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                               ascii_of super,
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                  subclass = `make_type_class sub,
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                  superclass = `make_type_class super};
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fun make_class_rel_clauses thy subs supers =
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  map make_class_rel_clause (class_pairs thy subs supers);
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(** Isabelle arities **)
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fun arity_clause _ _ (_, []) = []
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  | arity_clause seen n (tcons, ("HOL.type",_)::ars) =  (*ignore*)
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      arity_clause seen n (tcons,ars)
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  | arity_clause seen n (tcons, (ar as (class,_)) :: ars) =
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      if member (op =) seen class then (*multiple arities for the same tycon, class pair*)
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          make_axiom_arity_clause (tcons, lookup_const tcons ^ "_" ^ class ^ "_" ^ Int.toString n, ar) ::
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          arity_clause seen (n+1) (tcons,ars)
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      else
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          make_axiom_arity_clause (tcons, lookup_const tcons ^ "_" ^ class, ar) ::
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          arity_clause (class::seen) n (tcons,ars)
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fun multi_arity_clause [] = []
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  | multi_arity_clause ((tcons, ars) :: tc_arlists) =
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      arity_clause [] 1 (tcons, ars) @ multi_arity_clause tc_arlists
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(*Generate all pairs (tycon,class,sorts) such that tycon belongs to class in theory thy
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  provided its arguments have the corresponding sorts.*)
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fun type_class_pairs thy tycons classes =
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  let val alg = Sign.classes_of thy
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      fun domain_sorts tycon = Sorts.mg_domain alg tycon o single
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      fun add_class tycon class =
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        cons (class, domain_sorts tycon class)
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        handle Sorts.CLASS_ERROR _ => I
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      fun try_classes tycon = (tycon, fold (add_class tycon) classes [])
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  in  map try_classes tycons  end;
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(*Proving one (tycon, class) membership may require proving others, so iterate.*)
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fun iter_type_class_pairs _ _ [] = ([], [])
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  | iter_type_class_pairs thy tycons classes =
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      let val cpairs = type_class_pairs thy tycons classes
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          val newclasses = union_all (union_all (union_all (map (map #2 o #2) cpairs)))
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            |> subtract (op =) classes |> subtract (op =) HOLogic.typeS
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          val (classes', cpairs') = iter_type_class_pairs thy tycons newclasses
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      in (union (op =) classes' classes, union (op =) cpairs' cpairs) end;
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fun make_arity_clauses thy tycons classes =
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  let val (classes', cpairs) = iter_type_class_pairs thy tycons classes
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  in  (classes', multi_arity_clause cpairs)  end;
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datatype combtyp =
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  CombTVar of name |
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  CombTFree of name |
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  CombType of name * combtyp list
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datatype combterm =
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  CombConst of name * combtyp * combtyp list (* Const and Free *) |
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  CombVar of name * combtyp |
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  CombApp of combterm * combterm
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   361
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   362
datatype fol_literal = FOLLiteral of bool * combterm
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datatype fol_clause =
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  FOLClause of {clause_id: int, axiom_name: string, th: thm, kind: kind,
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                literals: fol_literal list, ctypes_sorts: typ list}
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(*********************************************************************)
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(* convert a clause with type Term.term to a clause with type clause *)
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(*********************************************************************)
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(*Result of a function type; no need to check that the argument type matches.*)
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fun result_type (CombType (_, [_, tp2])) = tp2
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  | result_type _ = raise Fail "non-function type"
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   375
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   376
fun type_of_combterm (CombConst (_, tp, _)) = tp
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  | type_of_combterm (CombVar (_, tp)) = tp
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  | type_of_combterm (CombApp (t1, _)) = result_type (type_of_combterm t1)
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   379
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   380
(*gets the head of a combinator application, along with the list of arguments*)
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fun strip_combterm_comb u =
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    let fun stripc (CombApp(t,u), ts) = stripc (t, u::ts)
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        |   stripc  x =  x
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   384
    in stripc(u,[]) end
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   385
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   386
fun type_of (Type (a, Ts)) =
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    let val (folTypes,ts) = types_of Ts in
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   388
      (CombType (`make_fixed_type_const a, folTypes), ts)
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   389
    end
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   390
  | type_of (tp as TFree (a, _)) = (CombTFree (`make_fixed_type_var a), [tp])
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   391
  | type_of (tp as TVar (x, _)) =
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   392
    (CombTVar (make_schematic_type_var x, string_of_indexname x), [tp])
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   393
and types_of Ts =
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   394
    let val (folTyps, ts) = ListPair.unzip (map type_of Ts) in
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   395
      (folTyps, union_all ts)
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   396
    end
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   397
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   398
(* same as above, but no gathering of sort information *)
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   399
fun simp_type_of (Type (a, Ts)) =
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   400
      CombType (`make_fixed_type_const a, map simp_type_of Ts)
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   401
  | simp_type_of (TFree (a, _)) = CombTFree (`make_fixed_type_var a)
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   402
  | simp_type_of (TVar (x, _)) =
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   403
    CombTVar (make_schematic_type_var x, string_of_indexname x)
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   404
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   405
(* convert a Term.term (with combinators) into a combterm, also accummulate sort info *)
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   406
fun combterm_of thy (Const (c, T)) =
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   407
      let
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   408
        val (tp, ts) = type_of T
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   409
        val tvar_list =
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   410
          (if String.isPrefix skolem_theory_name c then
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   411
             [] |> Term.add_tvarsT T |> map TVar
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   412
           else
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   413
             (c, T) |> Sign.const_typargs thy)
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   414
          |> map simp_type_of
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   415
        val c' = CombConst (`make_fixed_const c, tp, tvar_list)
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   416
      in  (c',ts)  end
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   417
  | combterm_of _ (Free(v, T)) =
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   418
      let val (tp,ts) = type_of T
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   419
          val v' = CombConst (`make_fixed_var v, tp, [])
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   420
      in  (v',ts)  end
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   421
  | combterm_of _ (Var(v, T)) =
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   422
      let val (tp,ts) = type_of T
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   423
          val v' = CombVar ((make_schematic_var v, string_of_indexname v), tp)
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   424
      in  (v',ts)  end
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   425
  | combterm_of thy (P $ Q) =
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   426
      let val (P', tsP) = combterm_of thy P
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   427
          val (Q', tsQ) = combterm_of thy Q
blanchet@37577
   428
      in  (CombApp (P', Q'), union (op =) tsP tsQ)  end
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   429
  | combterm_of _ (Abs _) = raise Fail "HOL clause: Abs"
blanchet@37577
   430
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   431
fun predicate_of thy ((@{const Not} $ P), pos) = predicate_of thy (P, not pos)
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   432
  | predicate_of thy (t, pos) = (combterm_of thy (Envir.eta_contract t), pos)
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   433
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   434
fun literals_of_term1 args thy (@{const Trueprop} $ P) =
blanchet@37577
   435
    literals_of_term1 args thy P
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   436
  | literals_of_term1 args thy (@{const "op |"} $ P $ Q) =
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   437
    literals_of_term1 (literals_of_term1 args thy P) thy Q
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   438
  | literals_of_term1 (lits, ts) thy P =
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   439
    let val ((pred, ts'), pol) = predicate_of thy (P, true) in
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   440
      (FOLLiteral (pol, pred) :: lits, union (op =) ts ts')
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   441
    end
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   442
val literals_of_term = literals_of_term1 ([], [])
blanchet@37577
   443
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   444
fun skolem_name i j num_T_args =
blanchet@37577
   445
  skolem_prefix ^ (space_implode "_" (map Int.toString [i, j, num_T_args])) ^
blanchet@37577
   446
  skolem_infix ^ "g"
blanchet@37577
   447
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   448
fun conceal_skolem_terms i skolems t =
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   449
  if exists_Const (curry (op =) @{const_name skolem_id} o fst) t then
blanchet@37577
   450
    let
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   451
      fun aux skolems
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   452
              (t as (Const (@{const_name skolem_id}, Type (_, [_, T])) $ _)) =
blanchet@37577
   453
          let
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   454
            val (skolems, s) =
blanchet@37577
   455
              if i = ~1 then
blanchet@37625
   456
                (skolems, @{const_name undefined})
blanchet@37625
   457
              else case AList.find (op aconv) skolems t of
blanchet@37625
   458
                s :: _ => (skolems, s)
blanchet@37577
   459
              | [] =>
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   460
                let
blanchet@37577
   461
                  val s = skolem_theory_name ^ "." ^
blanchet@37625
   462
                          skolem_name i (length skolems)
blanchet@37577
   463
                                        (length (Term.add_tvarsT T []))
blanchet@37625
   464
                in ((s, t) :: skolems, s) end
blanchet@37625
   465
          in (skolems, Const (s, T)) end
blanchet@37625
   466
        | aux skolems (t1 $ t2) =
blanchet@37577
   467
          let
blanchet@37625
   468
            val (skolems, t1) = aux skolems t1
blanchet@37625
   469
            val (skolems, t2) = aux skolems t2
blanchet@37625
   470
          in (skolems, t1 $ t2) end
blanchet@37625
   471
        | aux skolems (Abs (s, T, t')) =
blanchet@37625
   472
          let val (skolems, t') = aux skolems t' in
blanchet@37625
   473
            (skolems, Abs (s, T, t'))
blanchet@37577
   474
          end
blanchet@37625
   475
        | aux skolems t = (skolems, t)
blanchet@37625
   476
    in aux skolems t end
blanchet@37577
   477
  else
blanchet@37625
   478
    (skolems, t)
blanchet@37577
   479
blanchet@37632
   480
fun reveal_skolem_terms skolems =
blanchet@37632
   481
  map_aterms (fn t as Const (s, _) =>
blanchet@37632
   482
                 if String.isPrefix skolem_theory_name s then
blanchet@37632
   483
                   AList.lookup (op =) skolems s |> the
blanchet@37632
   484
                   |> map_types Type_Infer.paramify_vars
blanchet@37632
   485
                 else
blanchet@37632
   486
                   t
blanchet@37632
   487
               | t => t)
blanchet@37632
   488
blanchet@37577
   489
blanchet@37577
   490
(***************************************************************)
blanchet@37577
   491
(* Type Classes Present in the Axiom or Conjecture Clauses     *)
blanchet@37577
   492
(***************************************************************)
blanchet@37577
   493
blanchet@37577
   494
fun set_insert (x, s) = Symtab.update (x, ()) s
blanchet@37577
   495
blanchet@37577
   496
fun add_classes (sorts, cset) = List.foldl set_insert cset (flat sorts)
blanchet@37577
   497
blanchet@37577
   498
(*Remove this trivial type class*)
blanchet@37577
   499
fun delete_type cset = Symtab.delete_safe (the_single @{sort HOL.type}) cset;
blanchet@37577
   500
blanchet@37577
   501
fun tfree_classes_of_terms ts =
blanchet@37577
   502
  let val sorts_list = map (map #2 o OldTerm.term_tfrees) ts
blanchet@37577
   503
  in  Symtab.keys (delete_type (List.foldl add_classes Symtab.empty sorts_list))  end;
blanchet@37577
   504
blanchet@37577
   505
fun tvar_classes_of_terms ts =
blanchet@37577
   506
  let val sorts_list = map (map #2 o OldTerm.term_tvars) ts
blanchet@37577
   507
  in  Symtab.keys (delete_type (List.foldl add_classes Symtab.empty sorts_list))  end;
blanchet@37577
   508
blanchet@37577
   509
(*fold type constructors*)
blanchet@37577
   510
fun fold_type_consts f (Type (a, Ts)) x = fold (fold_type_consts f) Ts (f (a,x))
blanchet@37577
   511
  | fold_type_consts _ _ x = x;
blanchet@37577
   512
blanchet@37577
   513
(*Type constructors used to instantiate overloaded constants are the only ones needed.*)
blanchet@37577
   514
fun add_type_consts_in_term thy =
blanchet@37577
   515
  let
blanchet@37577
   516
    val const_typargs = Sign.const_typargs thy
blanchet@37577
   517
    fun aux (Const x) = fold (fold_type_consts set_insert) (const_typargs x)
blanchet@37577
   518
      | aux (Abs (_, _, u)) = aux u
blanchet@37577
   519
      | aux (Const (@{const_name skolem_id}, _) $ _) = I
blanchet@37577
   520
      | aux (t $ u) = aux t #> aux u
blanchet@37577
   521
      | aux _ = I
blanchet@37577
   522
  in aux end
blanchet@37577
   523
blanchet@37577
   524
fun type_consts_of_terms thy ts =
blanchet@37577
   525
  Symtab.keys (fold (add_type_consts_in_term thy) ts Symtab.empty);
blanchet@37577
   526
paulson@15347
   527
end;