src/HOL/Tools/Nitpick/nitpick_nut.ML
author blanchet
Thu, 22 Oct 2009 14:51:47 +0200
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permissions -rw-r--r--
added Nitpick's theory and ML files to Isabelle/HOL; the examples and the documentation are on their way.
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(*  Title:      HOL/Nitpick/Tools/nitpick_nut.ML
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    Author:     Jasmin Blanchette, TU Muenchen
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    Copyright   2008, 2009
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Nitpick underlying terms (nuts).
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*)
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signature NITPICK_NUT =
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sig
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  type special_fun = NitpickHOL.special_fun
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  type extended_context = NitpickHOL.extended_context
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  type scope = NitpickScope.scope
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  type name_pool = NitpickPeephole.name_pool
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  type rep = NitpickRep.rep
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  datatype cst =
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    Unity |
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    False |
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    True |
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    Iden |
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    Num of int |
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    Unknown |
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    Unrep |
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    Suc |
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    Add |
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    Subtract |
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    Multiply |
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    Divide |
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    Modulo |
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    Gcd |
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    Lcm |
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    Fracs |
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    NormFrac |
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    NatToInt |
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    IntToNat
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  datatype op1 =
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    Not |
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    Finite |
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    Converse |
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    Closure |
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    SingletonSet |
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    Tha |
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    First |
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    Second |
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    Cast
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  datatype op2 =
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    All |
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    Exist |
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    Or |
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    And |
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    Less |
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    Subset |
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    DefEq |
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    Eq |
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    The |
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    Eps |
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    Triad |
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    Union |
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    SetDifference |
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    Intersect |
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    Composition |
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    Product |
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    Image |
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    Apply |
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    Lambda
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  datatype op3 =
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    Let |
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    If
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  datatype nut =
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    Cst of cst * typ * rep |
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    Op1 of op1 * typ * rep * nut |
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    Op2 of op2 * typ * rep * nut * nut |
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    Op3 of op3 * typ * rep * nut * nut * nut |
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    Tuple of typ * rep * nut list |
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    Construct of nut list * typ * rep * nut list |
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    BoundName of int * typ * rep * string |
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    FreeName of string * typ * rep |
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    ConstName of string * typ * rep |
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    BoundRel of Kodkod.n_ary_index * typ * rep * string |
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    FreeRel of Kodkod.n_ary_index * typ * rep * string |
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    RelReg of int * typ * rep |
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    FormulaReg of int * typ * rep
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  structure NameTable : TABLE
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  exception NUT of string * nut list
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  val string_for_nut : Proof.context -> nut -> string
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  val inline_nut : nut -> bool
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  val type_of : nut -> typ
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  val rep_of : nut -> rep
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  val nickname_of : nut -> string
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  val is_skolem_name : nut -> bool
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  val is_eval_name : nut -> bool
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  val is_Cst : cst -> nut -> bool
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  val fold_nut : (nut -> 'a -> 'a) -> nut -> 'a -> 'a
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  val map_nut : (nut -> nut) -> nut -> nut
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  val untuple : (nut -> 'a) -> nut -> 'a list
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  val add_free_and_const_names :
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    nut -> nut list * nut list -> nut list * nut list
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  val name_ord : (nut * nut) -> order
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  val the_name : 'a NameTable.table -> nut -> 'a
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  val the_rel : nut NameTable.table -> nut -> Kodkod.n_ary_index
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  val nut_from_term : theory -> bool -> special_fun list -> op2 -> term -> nut
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  val choose_reps_for_free_vars :
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    scope -> nut list -> rep NameTable.table -> nut list * rep NameTable.table
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  val choose_reps_for_consts :
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    scope -> bool -> nut list -> rep NameTable.table
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    -> nut list * rep NameTable.table
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  val choose_reps_for_all_sels :
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    scope -> rep NameTable.table -> nut list * rep NameTable.table
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  val choose_reps_in_nut :
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    scope -> bool -> rep NameTable.table -> bool -> nut -> nut
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  val rename_free_vars :
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    nut list -> name_pool -> nut NameTable.table
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    -> nut list * name_pool * nut NameTable.table
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  val rename_vars_in_nut : name_pool -> nut NameTable.table -> nut -> nut
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end;
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structure NitpickNut : NITPICK_NUT =
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struct
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open NitpickUtil
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open NitpickHOL
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open NitpickScope
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open NitpickPeephole
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open NitpickRep
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datatype cst =
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  Unity |
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  False |
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  True |
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  Iden |
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  Num of int |
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  Unknown |
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  Unrep |
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  Suc |
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  Add |
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  Subtract |
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  Multiply |
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  Divide |
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  Modulo |
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  Gcd |
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  Lcm |
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  Fracs |
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  NormFrac |
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  NatToInt |
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  IntToNat
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datatype op1 =
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  Not |
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  Finite |
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  Converse |
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  Closure |
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  SingletonSet |
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  Tha |
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  First |
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  Second |
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  Cast
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datatype op2 =
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  All |
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  Exist |
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  Or |
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  And |
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  Less |
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  Subset |
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  DefEq |
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  Eq |
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  The |
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  Eps |
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  Triad |
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  Union |
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  SetDifference |
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  Intersect |
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  Composition |
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  Product |
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  Image |
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  Apply |
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  Lambda
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datatype op3 =
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  Let |
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  If
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datatype nut =
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  Cst of cst * typ * rep |
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  Op1 of op1 * typ * rep * nut |
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  Op2 of op2 * typ * rep * nut * nut |
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  Op3 of op3 * typ * rep * nut * nut * nut |
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  Tuple of typ * rep * nut list |
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  Construct of nut list * typ * rep * nut list |
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  BoundName of int * typ * rep * string |
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  FreeName of string * typ * rep |
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  ConstName of string * typ * rep |
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  BoundRel of Kodkod.n_ary_index * typ * rep * string |
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  FreeRel of Kodkod.n_ary_index * typ * rep * string |
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  RelReg of int * typ * rep |
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  FormulaReg of int * typ * rep
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exception NUT of string * nut list
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(* cst -> string *)
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fun string_for_cst Unity = "Unity"
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  | string_for_cst False = "False"
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  | string_for_cst True = "True"
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  | string_for_cst Iden = "Iden"
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  | string_for_cst (Num j) = "Num " ^ signed_string_of_int j
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  | string_for_cst Unknown = "Unknown"
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  | string_for_cst Unrep = "Unrep"
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  | string_for_cst Suc = "Suc"
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  | string_for_cst Add = "Add"
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  | string_for_cst Subtract = "Subtract"
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  | string_for_cst Multiply = "Multiply"
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  | string_for_cst Divide = "Divide"
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  | string_for_cst Modulo = "Modulo"
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  | string_for_cst Gcd = "Gcd"
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  | string_for_cst Lcm = "Lcm"
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  | string_for_cst Fracs = "Fracs"
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  | string_for_cst NormFrac = "NormFrac"
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  | string_for_cst NatToInt = "NatToInt"
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  | string_for_cst IntToNat = "IntToNat"
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(* op1 -> string *)
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fun string_for_op1 Not = "Not"
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  | string_for_op1 Finite = "Finite"
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  | string_for_op1 Converse = "Converse"
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  | string_for_op1 Closure = "Closure"
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  | string_for_op1 SingletonSet = "SingletonSet"
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  | string_for_op1 Tha = "Tha"
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  | string_for_op1 First = "First"
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  | string_for_op1 Second = "Second"
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  | string_for_op1 Cast = "Cast"
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(* op2 -> string *)
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fun string_for_op2 All = "All"
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  | string_for_op2 Exist = "Exist"
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  | string_for_op2 Or = "Or"
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  | string_for_op2 And = "And"
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  | string_for_op2 Less = "Less"
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  | string_for_op2 Subset = "Subset"
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  | string_for_op2 DefEq = "DefEq"
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  | string_for_op2 Eq = "Eq"
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  | string_for_op2 The = "The"
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  | string_for_op2 Eps = "Eps"
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  | string_for_op2 Triad = "Triad"
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  | string_for_op2 Union = "Union"
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  | string_for_op2 SetDifference = "SetDifference"
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  | string_for_op2 Intersect = "Intersect"
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  | string_for_op2 Composition = "Composition"
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  | string_for_op2 Product = "Product"
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  | string_for_op2 Image = "Image"
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  | string_for_op2 Apply = "Apply"
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  | string_for_op2 Lambda = "Lambda"
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(* op3 -> string *)
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fun string_for_op3 Let = "Let"
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  | string_for_op3 If = "If"
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(* int -> Proof.context -> nut -> string *)
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fun basic_string_for_nut indent ctxt u =
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  let
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    (* nut -> string *)
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    val sub = basic_string_for_nut (indent + 1) ctxt
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  in
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    (if indent = 0 then "" else "\n" ^ implode (replicate (2 * indent) " ")) ^
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    "(" ^
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    (case u of
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       Cst (c, T, R) =>
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       "Cst " ^ string_for_cst c ^ " " ^ Syntax.string_of_typ ctxt T ^ " " ^
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       string_for_rep R
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     | Op1 (oper, T, R, u1) =>
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       "Op1 " ^ string_for_op1 oper ^ " " ^ Syntax.string_of_typ ctxt T ^ " " ^
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       string_for_rep R ^ " " ^ sub u1
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     | Op2 (oper, T, R, u1, u2) =>
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       "Op2 " ^ string_for_op2 oper ^ " " ^ Syntax.string_of_typ ctxt T ^ " " ^
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       string_for_rep R ^ " " ^ sub u1 ^ " " ^ sub u2
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     | Op3 (oper, T, R, u1, u2, u3) =>
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       "Op3 " ^ string_for_op3 oper ^ " " ^ Syntax.string_of_typ ctxt T ^ " " ^
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       string_for_rep R ^ " " ^ sub u1 ^ " " ^ sub u2 ^ " " ^ sub u3
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     | Tuple (T, R, us) =>
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       "Tuple " ^ Syntax.string_of_typ ctxt T ^ " " ^ string_for_rep R ^
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       implode (map sub us)
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     | Construct (us', T, R, us) =>
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       "Construct " ^ implode (map sub us') ^ Syntax.string_of_typ ctxt T ^
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       " " ^ string_for_rep R ^ " " ^ implode (map sub us)
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     | BoundName (j, T, R, nick) =>
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       "BoundName " ^ signed_string_of_int j ^ " " ^
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       Syntax.string_of_typ ctxt T ^ " " ^ string_for_rep R ^ " " ^ nick
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     | FreeName (s, T, R) =>
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       "FreeName " ^ s ^ " " ^ Syntax.string_of_typ ctxt T ^ " " ^
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       string_for_rep R
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     | ConstName (s, T, R) =>
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       "ConstName " ^ s ^ " " ^ Syntax.string_of_typ ctxt T ^ " " ^
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       string_for_rep R
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     | BoundRel ((n, j), T, R, nick) =>
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       "BoundRel " ^ string_of_int n ^ "." ^ signed_string_of_int j ^ " " ^
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   302
       Syntax.string_of_typ ctxt T ^ " " ^ string_for_rep R ^ " " ^ nick
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   303
     | FreeRel ((n, j), T, R, nick) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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parents:
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   304
       "FreeRel " ^ string_of_int n ^ "." ^ signed_string_of_int j ^ " " ^
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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parents:
diff changeset
   305
       Syntax.string_of_typ ctxt T ^ " " ^ string_for_rep R ^ " " ^ nick
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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   306
     | RelReg (j, T, R) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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parents:
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   307
       "RelReg " ^ signed_string_of_int j ^ " " ^ Syntax.string_of_typ ctxt T ^
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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parents:
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   308
       " " ^ string_for_rep R
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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parents:
diff changeset
   309
     | FormulaReg (j, T, R) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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parents:
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   310
       "FormulaReg " ^ signed_string_of_int j ^ " " ^
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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parents:
diff changeset
   311
       Syntax.string_of_typ ctxt T ^ " " ^ string_for_rep R) ^
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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   312
    ")"
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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parents:
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   313
  end
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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   314
(* Proof.context -> nut -> string *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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parents:
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   315
val string_for_nut = basic_string_for_nut 0
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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   316
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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parents:
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   317
(* nut -> bool *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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parents:
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   318
fun inline_nut (Op1 _) = false
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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   319
  | inline_nut (Op2 _) = false
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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   320
  | inline_nut (Op3 _) = false
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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parents:
diff changeset
   321
  | inline_nut (Tuple (_, _, us)) = forall inline_nut us
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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   322
  | inline_nut _ = true
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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parents:
diff changeset
   323
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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parents:
diff changeset
   324
(* nut -> typ *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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parents:
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   325
fun type_of (Cst (_, T, _)) = T
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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parents:
diff changeset
   326
  | type_of (Op1 (_, T, _, _)) = T
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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parents:
diff changeset
   327
  | type_of (Op2 (_, T, _, _, _)) = T
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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parents:
diff changeset
   328
  | type_of (Op3 (_, T, _, _, _, _)) = T
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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parents:
diff changeset
   329
  | type_of (Tuple (T, _, _)) = T
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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parents:
diff changeset
   330
  | type_of (Construct (_, T, _, _)) = T
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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parents:
diff changeset
   331
  | type_of (BoundName (_, T, _, _)) = T
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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parents:
diff changeset
   332
  | type_of (FreeName (_, T, _)) = T
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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parents:
diff changeset
   333
  | type_of (ConstName (_, T, _)) = T
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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parents:
diff changeset
   334
  | type_of (BoundRel (_, T, _, _)) = T
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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parents:
diff changeset
   335
  | type_of (FreeRel (_, T, _, _)) = T
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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parents:
diff changeset
   336
  | type_of (RelReg (_, T, _)) = T
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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parents:
diff changeset
   337
  | type_of (FormulaReg (_, T, _)) = T
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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parents:
diff changeset
   338
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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parents:
diff changeset
   339
(* nut -> rep *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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parents:
diff changeset
   340
fun rep_of (Cst (_, _, R)) = R
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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parents:
diff changeset
   341
  | rep_of (Op1 (_, _, R, _)) = R
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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parents:
diff changeset
   342
  | rep_of (Op2 (_, _, R, _, _)) = R
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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parents:
diff changeset
   343
  | rep_of (Op3 (_, _, R, _, _, _)) = R
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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parents:
diff changeset
   344
  | rep_of (Tuple (_, R, _)) = R
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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parents:
diff changeset
   345
  | rep_of (Construct (_, _, R, _)) = R
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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parents:
diff changeset
   346
  | rep_of (BoundName (_, _, R, _)) = R
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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parents:
diff changeset
   347
  | rep_of (FreeName (_, _, R)) = R
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   348
  | rep_of (ConstName (_, _, R)) = R
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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parents:
diff changeset
   349
  | rep_of (BoundRel (_, _, R, _)) = R
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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parents:
diff changeset
   350
  | rep_of (FreeRel (_, _, R, _)) = R
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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parents:
diff changeset
   351
  | rep_of (RelReg (_, _, R)) = R
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   352
  | rep_of (FormulaReg (_, _, R)) = R
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   353
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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parents:
diff changeset
   354
(* nut -> string *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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parents:
diff changeset
   355
fun nickname_of (BoundName (_, _, _, nick)) = nick
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   356
  | nickname_of (FreeName (s, _, _)) = s
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   357
  | nickname_of (ConstName (s, _, _)) = s
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   358
  | nickname_of (BoundRel (_, _, _, nick)) = nick
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   359
  | nickname_of (FreeRel (_, _, _, nick)) = nick
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   360
  | nickname_of u = raise NUT ("NitpickNut.nickname_of", [u])
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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parents:
diff changeset
   361
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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parents:
diff changeset
   362
(* nut -> bool *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   363
fun is_skolem_name u =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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parents:
diff changeset
   364
  space_explode name_sep (nickname_of u)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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parents:
diff changeset
   365
  |> exists (String.isPrefix skolem_prefix)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   366
  handle NUT ("NitpickNut.nickname_of", _) => false
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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parents:
diff changeset
   367
fun is_eval_name u =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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parents:
diff changeset
   368
  String.isPrefix eval_prefix (nickname_of u)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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parents:
diff changeset
   369
  handle NUT ("NitpickNut.nickname_of", _) => false
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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parents:
diff changeset
   370
(* cst -> nut -> bool *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   371
fun is_Cst cst (Cst (cst', _, _)) = (cst = cst')
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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parents:
diff changeset
   372
  | is_Cst _ _ = false
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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parents:
diff changeset
   373
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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parents:
diff changeset
   374
(* (nut -> 'a -> 'a) -> nut -> 'a -> 'a *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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parents:
diff changeset
   375
fun fold_nut f u =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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parents:
diff changeset
   376
  case u of
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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parents:
diff changeset
   377
    Op1 (_, _, _, u1) => fold_nut f u1
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   378
  | Op2 (_, _, _, u1, u2) => fold_nut f u1 #> fold_nut f u2
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   379
  | Op3 (_, _, _, u1, u2, u3) => fold_nut f u1 #> fold_nut f u2 #> fold_nut f u3
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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parents:
diff changeset
   380
  | Tuple (_, _, us) => fold (fold_nut f) us
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   381
  | Construct (us', _, _, us) => fold (fold_nut f) us #> fold (fold_nut f) us'
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
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parents:
diff changeset
   382
  | _ => f u
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   383
(* (nut -> nut) -> nut -> nut *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   384
fun map_nut f u =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   385
  case u of
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   386
    Op1 (oper, T, R, u1) => Op1 (oper, T, R, map_nut f u1)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   387
  | Op2 (oper, T, R, u1, u2) => Op2 (oper, T, R, map_nut f u1, map_nut f u2)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   388
  | Op3 (oper, T, R, u1, u2, u3) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   389
    Op3 (oper, T, R, map_nut f u1, map_nut f u2, map_nut f u3)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   390
  | Tuple (T, R, us) => Tuple (T, R, map (map_nut f) us)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   391
  | Construct (us', T, R, us) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   392
    Construct (map (map_nut f) us', T, R, map (map_nut f) us)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   393
  | _ => f u
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   394
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   395
(* nut * nut -> order *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   396
fun name_ord (BoundName (j1, _, _, _), BoundName (j2, _, _, _)) =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   397
    int_ord (j1, j2)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   398
  | name_ord (BoundName _, _) = LESS
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   399
  | name_ord (_, BoundName _) = GREATER
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   400
  | name_ord (FreeName (s1, T1, _), FreeName (s2, T2, _)) =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   401
    (case fast_string_ord (s1, s2) of
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   402
       EQUAL => TermOrd.typ_ord (T1, T2)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   403
     | ord => ord)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   404
  | name_ord (FreeName _, _) = LESS
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   405
  | name_ord (_, FreeName _) = GREATER
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   406
  | name_ord (ConstName (s1, T1, _), ConstName (s2, T2, _)) =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   407
    (case fast_string_ord (s1, s2) of
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   408
       EQUAL => TermOrd.typ_ord (T1, T2)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   409
     | ord => ord)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   410
  | name_ord (u1, u2) = raise NUT ("NitpickNut.name_ord", [u1, u2])
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   411
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   412
(* nut -> nut -> int *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   413
fun num_occs_in_nut needle_u stack_u =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   414
  fold_nut (fn u => if u = needle_u then Integer.add 1 else I) stack_u 0
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   415
(* nut -> nut -> bool *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   416
val is_subterm_of = not_equal 0 oo num_occs_in_nut
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   417
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   418
(* nut -> nut -> nut -> nut *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   419
fun substitute_in_nut needle_u needle_u' =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   420
  map_nut (fn u => if u = needle_u then needle_u' else u)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   421
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   422
(* nut -> nut list * nut list -> nut list * nut list *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   423
val add_free_and_const_names =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   424
  fold_nut (fn u => case u of
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   425
                      FreeName _ => apfst (insert (op =) u)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   426
                    | ConstName _ => apsnd (insert (op =) u)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   427
                    | _ => I)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   428
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   429
(* nut -> rep -> nut *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   430
fun modify_name_rep (BoundName (j, T, _, nick)) R = BoundName (j, T, R, nick)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   431
  | modify_name_rep (FreeName (s, T, _)) R = FreeName (s, T, R)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   432
  | modify_name_rep (ConstName (s, T, _)) R = ConstName (s, T, R)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   433
  | modify_name_rep u _ = raise NUT ("NitpickNut.modify_name_rep", [u])
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   434
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   435
structure NameTable = Table(type key = nut val ord = name_ord)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   436
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   437
(* 'a NameTable.table -> nut -> 'a *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   438
fun the_name table name =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   439
  case NameTable.lookup table name of
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   440
    SOME u => u
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   441
  | NONE => raise NUT ("NitpickNut.the_name", [name])
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   442
(* nut NameTable.table -> nut -> Kodkod.n_ary_index *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   443
fun the_rel table name =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   444
  case the_name table name of
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   445
    FreeRel (x, _, _, _) => x
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   446
  | u => raise NUT ("NitpickNut.the_rel", [u])
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   447
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   448
(* typ * term -> typ * term *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   449
fun mk_fst (_, Const (@{const_name Pair}, T) $ t1 $ _) = (domain_type T, t1)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   450
  | mk_fst (T, t) =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   451
    let val res_T = fst (HOLogic.dest_prodT T) in
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   452
      (res_T, Const (@{const_name fst}, T --> res_T) $ t)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   453
    end
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   454
fun mk_snd (_, Const (@{const_name Pair}, T) $ _ $ t2) =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   455
    (domain_type (range_type T), t2)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   456
  | mk_snd (T, t) =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   457
    let val res_T = snd (HOLogic.dest_prodT T) in
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   458
      (res_T, Const (@{const_name snd}, T --> res_T) $ t)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   459
    end
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   460
(* typ * term -> (typ * term) list *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   461
fun factorize (z as (Type ("*", _), _)) = maps factorize [mk_fst z, mk_snd z]
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   462
  | factorize z = [z]
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   463
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   464
(* theory -> bool -> special_fun list -> op2 -> term -> nut *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   465
fun nut_from_term thy fast_descrs special_funs eq =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   466
  let
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   467
    (* string list -> typ list -> term -> nut *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   468
    fun aux eq ss Ts t =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   469
      let
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   470
        (* term -> nut *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   471
        val sub = aux Eq ss Ts
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   472
        val sub' = aux eq ss Ts
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   473
        (* string -> typ -> term -> nut *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   474
        fun sub_abs s T = aux eq (s :: ss) (T :: Ts)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   475
        (* typ -> term -> term -> nut *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   476
        fun sub_equals T t1 t2 =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   477
          let
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   478
            val (binder_Ts, body_T) = strip_type (domain_type T)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   479
            val n = length binder_Ts
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   480
          in
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   481
            if eq = Eq andalso n > 0 then
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   482
              let
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   483
                val t1 = incr_boundvars n t1
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   484
                val t2 = incr_boundvars n t2
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   485
                val xs = map Bound (n - 1 downto 0)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   486
                val equation = Const (@{const_name "op ="},
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   487
                                      body_T --> body_T --> bool_T)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   488
                                   $ betapplys (t1, xs) $ betapplys (t2, xs)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   489
                val t =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   490
                  fold_rev (fn T => fn (t, j) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   491
                               (Const (@{const_name All}, T --> bool_T)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   492
                                $ Abs ("x" ^ nat_subscript j, T, t), j - 1))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   493
                           binder_Ts (equation, n) |> fst
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   494
              in sub' t end
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   495
            else
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   496
              Op2 (eq, bool_T, Any, aux Eq ss Ts t1, aux Eq ss Ts t2)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   497
          end
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   498
        (* op2 -> string -> typ -> term -> nut *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   499
        fun do_quantifier quant s T t1 =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   500
          let
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   501
            val bound_u = BoundName (length Ts, T, Any, s)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   502
            val body_u = sub_abs s T t1
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   503
          in
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   504
            if is_subterm_of bound_u body_u then
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   505
              Op2 (quant, bool_T, Any, bound_u, body_u)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   506
            else
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   507
              body_u
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   508
          end
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   509
        (* term -> term list -> nut *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   510
        fun do_apply t0 ts =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   511
          let
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   512
            val (ts', t2) = split_last ts
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   513
            val t1 = list_comb (t0, ts')
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   514
            val T1 = fastype_of1 (Ts, t1)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   515
          in Op2 (Apply, range_type T1, Any, sub t1, sub t2) end
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   516
      in
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   517
        case strip_comb t of
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   518
          (Const (@{const_name all}, _), [Abs (s, T, t1)]) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   519
          do_quantifier All s T t1
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   520
        | (t0 as Const (@{const_name all}, T), [t1]) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   521
          sub' (t0 $ eta_expand Ts t1 1)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   522
        | (Const (@{const_name "=="}, T), [t1, t2]) => sub_equals T t1 t2
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   523
        | (Const (@{const_name "==>"}, _), [t1, t2]) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   524
          Op2 (Or, prop_T, Any, Op1 (Not, prop_T, Any, sub t1), sub' t2)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   525
        | (Const (@{const_name Pure.conjunction}, _), [t1, t2]) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   526
          Op2 (And, prop_T, Any, sub' t1, sub' t2)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   527
        | (Const (@{const_name Trueprop}, _), [t1]) => sub' t1
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   528
        | (Const (@{const_name Not}, _), [t1]) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   529
          (case sub t1 of
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   530
             Op1 (Not, _, _, u11) => u11
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   531
           | u1 => Op1 (Not, bool_T, Any, u1))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   532
        | (Const (@{const_name False}, T), []) => Cst (False, T, Any)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   533
        | (Const (@{const_name True}, T), []) => Cst (True, T, Any)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   534
        | (Const (@{const_name All}, _), [Abs (s, T, t1)]) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   535
          do_quantifier All s T t1
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   536
        | (t0 as Const (@{const_name All}, T), [t1]) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   537
          sub' (t0 $ eta_expand Ts t1 1)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   538
        | (Const (@{const_name Ex}, _), [Abs (s, T, t1)]) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   539
          do_quantifier Exist s T t1
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   540
        | (t0 as Const (@{const_name Ex}, T), [t1]) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   541
          sub' (t0 $ eta_expand Ts t1 1)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   542
        | (t0 as Const (@{const_name The}, T), [t1]) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   543
          if fast_descrs then
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   544
            Op2 (The, range_type T, Any, sub t1,
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   545
                 sub (Const (@{const_name undefined_fast_The}, range_type T)))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   546
          else
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   547
            do_apply t0 [t1]
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   548
        | (t0 as Const (@{const_name Eps}, T), [t1]) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   549
          if fast_descrs then
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   550
            Op2 (Eps, range_type T, Any, sub t1,
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   551
                 sub (Const (@{const_name undefined_fast_Eps}, range_type T)))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   552
          else
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   553
            do_apply t0 [t1]
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   554
        | (Const (@{const_name "op ="}, T), [t1, t2]) => sub_equals T t1 t2
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   555
        | (Const (@{const_name "op &"}, _), [t1, t2]) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   556
          Op2 (And, bool_T, Any, sub' t1, sub' t2)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   557
        | (Const (@{const_name "op |"}, _), [t1, t2]) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   558
          Op2 (Or, bool_T, Any, sub t1, sub t2)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   559
        | (Const (@{const_name "op -->"}, _), [t1, t2]) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   560
          Op2 (Or, bool_T, Any, Op1 (Not, bool_T, Any, sub t1), sub' t2)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   561
        | (Const (@{const_name If}, T), [t1, t2, t3]) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   562
          Op3 (If, nth_range_type 3 T, Any, sub t1, sub t2, sub t3)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   563
        | (Const (@{const_name Let}, T), [t1, Abs (s, T', t2)]) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   564
          Op3 (Let, nth_range_type 2 T, Any, BoundName (length Ts, T', Any, s),
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   565
               sub t1, sub_abs s T' t2)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   566
        | (t0 as Const (@{const_name Let}, T), [t1, t2]) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   567
          sub (t0 $ t1 $ eta_expand Ts t2 1)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   568
        | (Const (@{const_name unknown}, T), []) => Cst (Unknown, T, Any)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   569
        | (@{const Unity}, []) => Cst (Unity, @{typ unit}, Any)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   570
        | (Const (@{const_name Pair}, T), [t1, t2]) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   571
          Tuple (nth_range_type 2 T, Any, map sub [t1, t2])
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   572
        | (Const (@{const_name fst}, T), [t1]) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   573
          Op1 (First, range_type T, Any, sub t1)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   574
        | (Const (@{const_name snd}, T), [t1]) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   575
          Op1 (Second, range_type T, Any, sub t1)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   576
        | (Const (@{const_name Id}, T), []) => Cst (Iden, T, Any)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   577
        | (Const (@{const_name insert}, T), [t1, t2]) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   578
          (case t2 of
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   579
             Abs (_, _, @{const False}) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   580
             Op1 (SingletonSet, nth_range_type 2 T, Any, sub t1)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   581
           | _ =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   582
             Op2 (Union, nth_range_type 2 T, Any,
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   583
                  Op1 (SingletonSet, nth_range_type 2 T, Any, sub t1), sub t2))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   584
        | (Const (@{const_name converse}, T), [t1]) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   585
          Op1 (Converse, range_type T, Any, sub t1)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   586
        | (Const (@{const_name trancl}, T), [t1]) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   587
          Op1 (Closure, range_type T, Any, sub t1)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   588
        | (Const (@{const_name rel_comp}, T), [t1, t2]) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   589
          Op2 (Composition, nth_range_type 2 T, Any, sub t1, sub t2)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   590
        | (Const (@{const_name Sigma}, T), [t1, Abs (s, T', t2')]) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   591
          Op2 (Product, nth_range_type 2 T, Any, sub t1, sub_abs s T' t2')
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   592
        | (Const (@{const_name image}, T), [t1, t2]) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   593
          Op2 (Image, nth_range_type 2 T, Any, sub t1, sub t2)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   594
        | (Const (@{const_name Suc}, T), []) => Cst (Suc, T, Any)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   595
        | (Const (@{const_name finite}, T), [t1]) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   596
          Op1 (Finite, bool_T, Any, sub t1)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   597
        | (Const (@{const_name nat}, T), []) => Cst (IntToNat, T, Any)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   598
        | (Const (@{const_name zero_nat_inst.zero_nat}, T), []) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   599
          Cst (Num 0, T, Any)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   600
        | (Const (@{const_name one_nat_inst.one_nat}, T), []) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   601
          Cst (Num 1, T, Any)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   602
        | (Const (@{const_name plus_nat_inst.plus_nat}, T), []) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   603
          Cst (Add, T, Any)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   604
        | (Const (@{const_name minus_nat_inst.minus_nat}, T), []) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   605
          Cst (Subtract, T, Any)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   606
        | (Const (@{const_name times_nat_inst.times_nat}, T), []) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   607
          Cst (Multiply, T, Any)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   608
        | (Const (@{const_name div_nat_inst.div_nat}, T), []) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   609
          Cst (Divide, T, Any)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   610
        | (Const (@{const_name div_nat_inst.mod_nat}, T), []) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   611
          Cst (Modulo, T, Any)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   612
        | (Const (@{const_name ord_nat_inst.less_nat}, T), [t1, t2]) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   613
          Op2 (Less, bool_T, Any, sub t1, sub t2)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   614
        | (Const (@{const_name ord_nat_inst.less_eq_nat}, T), [t1, t2]) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   615
          Op1 (Not, bool_T, Any, Op2 (Less, bool_T, Any, sub t2, sub t1))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   616
        | (Const (@{const_name nat_gcd}, T), []) => Cst (Gcd, T, Any)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   617
        | (Const (@{const_name nat_lcm}, T), []) => Cst (Lcm, T, Any)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   618
        | (Const (@{const_name zero_int_inst.zero_int}, T), []) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   619
          Cst (Num 0, T, Any)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   620
        | (Const (@{const_name one_int_inst.one_int}, T), []) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   621
          Cst (Num 1, T, Any)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   622
        | (Const (@{const_name plus_int_inst.plus_int}, T), []) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   623
          Cst (Add, T, Any)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   624
        | (Const (@{const_name minus_int_inst.minus_int}, T), []) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   625
          Cst (Subtract, T, Any)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   626
        | (Const (@{const_name times_int_inst.times_int}, T), []) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   627
          Cst (Multiply, T, Any)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   628
        | (Const (@{const_name div_int_inst.div_int}, T), []) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   629
          Cst (Divide, T, Any)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   630
        | (Const (@{const_name div_int_inst.mod_int}, T), []) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   631
          Cst (Modulo, T, Any)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   632
        | (Const (@{const_name uminus_int_inst.uminus_int}, T), []) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   633
          Op2 (Apply, int_T --> int_T, Any,
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   634
               Cst (Subtract, [int_T, int_T] ---> int_T, Any),
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   635
               Cst (Num 0, int_T, Any))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   636
        | (Const (@{const_name ord_int_inst.less_int}, T), [t1, t2]) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   637
          Op2 (Less, bool_T, Any, sub t1, sub t2)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   638
        | (Const (@{const_name ord_int_inst.less_eq_int}, T), [t1, t2]) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   639
          Op1 (Not, bool_T, Any, Op2 (Less, bool_T, Any, sub t2, sub t1))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   640
        | (Const (@{const_name Tha}, Type ("fun", [_, T2])), [t1]) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   641
          Op1 (Tha, T2, Any, sub t1)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   642
        | (Const (@{const_name Frac}, T), []) => Cst (Fracs, T, Any)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   643
        | (Const (@{const_name norm_frac}, T), []) => Cst (NormFrac, T, Any)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   644
        | (Const (@{const_name of_nat}, T as @{typ "nat => int"}), []) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   645
          Cst (NatToInt, T, Any)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   646
        | (Const (@{const_name lower_semilattice_fun_inst.inf_fun}, T),
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   647
                  [t1, t2]) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   648
          Op2 (Intersect, nth_range_type 2 T, Any, sub t1, sub t2)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   649
        | (Const (@{const_name upper_semilattice_fun_inst.sup_fun}, T),
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   650
                  [t1, t2]) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   651
          Op2 (Union, nth_range_type 2 T, Any, sub t1, sub t2)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   652
        | (t0 as Const (@{const_name minus_fun_inst.minus_fun}, T), [t1, t2]) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   653
          Op2 (SetDifference, nth_range_type 2 T, Any, sub t1, sub t2)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   654
        | (t0 as Const (@{const_name ord_fun_inst.less_eq_fun}, T), [t1, t2]) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   655
          Op2 (Subset, bool_T, Any, sub t1, sub t2)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   656
        | (t0 as Const (x as (s, T)), ts) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   657
          if is_constr thy x then
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   658
            case num_binder_types T - length ts of
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   659
              0 => Construct (map ((fn (s, T) => ConstName (s, T, Any))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   660
                                    o nth_sel_for_constr x)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   661
                                  (~1 upto num_sels_for_constr_type T - 1),
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   662
                              body_type T, Any,
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   663
                              ts |> map (`(curry fastype_of1 Ts))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   664
                                 |> maps factorize |> map (sub o snd))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   665
            | k => sub (eta_expand Ts t k)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   666
          else if String.isPrefix numeral_prefix s then
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   667
            Cst (Num (the (Int.fromString (unprefix numeral_prefix s))), T, Any)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   668
          else
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   669
            (case arity_of_built_in_const fast_descrs x of
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   670
               SOME n =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   671
               (case n - length ts of
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   672
                  0 => raise TERM ("NitpickNut.nut_from_term.aux", [t])
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   673
                | k => if k > 0 then sub (eta_expand Ts t k)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   674
                       else do_apply t0 ts)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   675
             | NONE => if null ts then ConstName (s, T, Any)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   676
                       else do_apply t0 ts)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   677
        | (Free (s, T), []) => FreeName (s, T, Any)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   678
        | (Var _, []) => raise TERM ("NitpickNut.nut_from_term", [t])
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   679
        | (Bound j, []) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   680
          BoundName (length Ts - j - 1, nth Ts j, Any, nth ss j)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   681
        | (Abs (s, T, t1), []) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   682
          Op2 (Lambda, T --> fastype_of1 (T :: Ts, t1), Any,
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   683
               BoundName (length Ts, T, Any, s), sub_abs s T t1)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   684
        | (t0, ts) => do_apply t0 ts
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   685
      end
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   686
  in aux eq [] [] end
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   687
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   688
(* scope -> typ -> rep *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   689
fun rep_for_abs_fun scope T =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   690
  let val (R1, R2) = best_non_opt_symmetric_reps_for_fun_type scope T in
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   691
    Func (R1, (card_of_rep R1 <> card_of_rep R2 ? Opt) R2)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   692
  end
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   693
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   694
(* scope -> nut -> nut list * rep NameTable.table
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   695
   -> nut list * rep NameTable.table *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   696
fun choose_rep_for_free_var scope v (vs, table) =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   697
  let
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   698
    val R = best_non_opt_set_rep_for_type scope (type_of v)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   699
    val v = modify_name_rep v R
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   700
  in (v :: vs, NameTable.update (v, R) table) end
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   701
(* scope -> bool -> nut -> nut list * rep NameTable.table
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   702
   -> nut list * rep NameTable.table *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   703
fun choose_rep_for_const (scope as {ext_ctxt as {thy, ctxt, ...}, datatypes,
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   704
                                    ofs, ...}) all_precise v (vs, table) =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   705
  let
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   706
    val x as (s, T) = (nickname_of v, type_of v)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   707
    val R = (if is_abs_fun thy x then
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   708
               rep_for_abs_fun
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   709
             else if is_rep_fun thy x then
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   710
               Func oo best_non_opt_symmetric_reps_for_fun_type
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   711
             else if all_precise orelse is_skolem_name v
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   712
                     orelse s mem [@{const_name undefined_fast_The},
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   713
                                   @{const_name undefined_fast_Eps},
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   714
                                   @{const_name bisim}] then
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   715
               best_non_opt_set_rep_for_type
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   716
             else if original_name s
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   717
                     mem [@{const_name set}, @{const_name distinct},
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   718
                          @{const_name ord_class.less},
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   719
                          @{const_name ord_class.less_eq},
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   720
                          @{const_name bisim_iterator_max}] then
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   721
               best_set_rep_for_type
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   722
             else
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   723
               best_opt_set_rep_for_type) scope T
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   724
    val v = modify_name_rep v R
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   725
  in (v :: vs, NameTable.update (v, R) table) end
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   726
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   727
(* scope -> nut list -> rep NameTable.table -> nut list * rep NameTable.table *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   728
fun choose_reps_for_free_vars scope vs table =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   729
  fold (choose_rep_for_free_var scope) vs ([], table)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   730
(* scope -> bool -> nut list -> rep NameTable.table
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   731
   -> nut list * rep NameTable.table *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   732
fun choose_reps_for_consts scope all_precise vs table =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   733
  fold (choose_rep_for_const scope all_precise) vs ([], table)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   734
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   735
(* scope -> styp -> int -> nut list * rep NameTable.table
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   736
   -> nut list * rep NameTable.table *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   737
fun choose_rep_for_nth_sel_for_constr (scope as {ext_ctxt, ...}) x n
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   738
                                      (vs, table) =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   739
  let
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   740
    val (s', T') = boxed_nth_sel_for_constr ext_ctxt x n
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   741
    val R' = if n = ~1 then best_non_opt_set_rep_for_type scope T'
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   742
             else best_opt_set_rep_for_type scope T' |> unopt_rep
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   743
    val v = ConstName (s', T', R')
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   744
  in (v :: vs, NameTable.update (v, R') table) end
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   745
(* scope -> styp -> nut list * rep NameTable.table
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   746
   -> nut list * rep NameTable.table *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   747
fun choose_rep_for_sels_for_constr scope (x as (_, T)) =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   748
  fold_rev (choose_rep_for_nth_sel_for_constr scope x)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   749
           (~1 upto num_sels_for_constr_type T - 1)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   750
(* scope -> dtype_spec -> nut list * rep NameTable.table
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   751
   -> nut list * rep NameTable.table *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   752
fun choose_rep_for_sels_of_datatype scope ({constrs, ...} : dtype_spec) =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   753
  fold_rev (choose_rep_for_sels_for_constr scope o #const) constrs
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   754
(* scope -> rep NameTable.table -> nut list * rep NameTable.table *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   755
fun choose_reps_for_all_sels (scope as {datatypes, ...}) =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   756
  fold (choose_rep_for_sels_of_datatype scope) datatypes o pair []
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   757
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   758
(* scope -> nut -> rep NameTable.table -> rep NameTable.table *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   759
fun choose_rep_for_bound_var scope v table =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   760
  let val R = best_one_rep_for_type scope (type_of v) in
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   761
    NameTable.update (v, R) table
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   762
  end
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   763
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   764
(* A nut is said to be constructive if whenever it evaluates to unknown in our
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   765
   three-valued logic, it would evaluate to a unrepresentable value ("unrep")
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   766
   according to the HOL semantics. For example, "Suc n" is
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   767
   constructive if "n" is representable or "Unrep", because unknown implies
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   768
   unrep. *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   769
(* nut -> bool *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   770
fun is_constructive u =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   771
  is_Cst Unrep u orelse
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   772
  (not (is_fun_type (type_of u)) andalso not (is_opt_rep (rep_of u))) orelse
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   773
  case u of
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   774
    Cst (Num _, _, _) => true
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   775
  | Cst (cst, T, _) => cst = Suc orelse (body_type T = nat_T andalso cst = Add)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   776
  | Op2 (Apply, _, _, u1, u2) => forall is_constructive [u1, u2]
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   777
  | Op3 (If, _, _, u1, u2, u3) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   778
    not (is_opt_rep (rep_of u1)) andalso forall is_constructive [u2, u3]
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   779
  | Tuple (_, _, us) => forall is_constructive us
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   780
  | Construct (_, _, _, us) => forall is_constructive us
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   781
  | _ => false
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   782
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   783
(* nut -> nut *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   784
fun optimize_unit u =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   785
  if rep_of u = Unit then Cst (Unity, type_of u, Unit) else u
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   786
(* typ -> rep -> nut *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   787
fun unknown_boolean T R =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   788
  Cst (case R of
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   789
         Formula Pos => False
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   790
       | Formula Neg => True
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   791
       | _ => Unknown, T, R)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   792
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   793
(* op1 -> typ -> rep -> nut -> nut *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   794
fun s_op1 oper T R u1 =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   795
  ((if oper = Not then
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   796
      if is_Cst True u1 then Cst (False, T, R)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   797
      else if is_Cst False u1 then Cst (True, T, R)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   798
      else raise SAME ()
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   799
    else
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   800
      raise SAME ())
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   801
   handle SAME () => Op1 (oper, T, R, u1))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   802
  |> optimize_unit
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   803
(* op2 -> typ -> rep -> nut -> nut -> nut *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   804
fun s_op2 oper T R u1 u2 =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   805
  ((case oper of
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   806
      Or =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   807
      if exists (is_Cst True) [u1, u2] then Cst (True, T, unopt_rep R)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   808
      else if is_Cst False u1 then u2
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   809
      else if is_Cst False u2 then u1
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   810
      else raise SAME ()
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   811
    | And =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   812
      if exists (is_Cst False) [u1, u2] then Cst (False, T, unopt_rep R)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   813
      else if is_Cst True u1 then u2
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   814
      else if is_Cst True u2 then u1
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   815
      else raise SAME ()
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   816
    | Eq =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   817
      (case pairself (is_Cst Unrep) (u1, u2) of
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   818
         (true, true) => unknown_boolean T R
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   819
       | (false, false) => raise SAME ()
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   820
       | _ => if forall (is_opt_rep o rep_of) [u1, u2] then raise SAME ()
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   821
              else Cst (False, T, Formula Neut))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   822
    | Triad =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   823
      if is_Cst True u1 then u1
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   824
      else if is_Cst False u2 then u2
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   825
      else raise SAME ()
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   826
    | Apply =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   827
      if is_Cst Unrep u1 then
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   828
        Cst (Unrep, T, R)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   829
      else if is_Cst Unrep u2 then
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   830
        if is_constructive u1 then
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   831
          Cst (Unrep, T, R)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   832
        else if is_boolean_type T andalso not (is_opt_rep (rep_of u1)) then
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   833
          (* Selectors are an unfortunate exception to the rule that non-"Opt"
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   834
             predicates return "False" for unrepresentable domain values. *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   835
          case u1 of
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   836
             ConstName (s, _, _) => if is_sel s then unknown_boolean T R
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   837
                                    else Cst (False, T, Formula Neut)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   838
           | _ => Cst (False, T, Formula Neut)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   839
        else case u1 of
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   840
          Op2 (Apply, _, _, ConstName (@{const_name List.append}, _, _), _) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   841
          Cst (Unrep, T, R)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   842
        | _ => raise SAME ()
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   843
      else
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   844
        raise SAME ()
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   845
    | _ => raise SAME ())
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   846
   handle SAME () => Op2 (oper, T, R, u1, u2))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   847
  |> optimize_unit
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   848
(* op3 -> typ -> rep -> nut -> nut -> nut -> nut *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   849
fun s_op3 oper T R u1 u2 u3 =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   850
  ((case oper of
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   851
      Let =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   852
      if inline_nut u2 orelse num_occs_in_nut u1 u3 < 2 then
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   853
        substitute_in_nut u1 u2 u3
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   854
      else
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   855
        raise SAME ()
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   856
    | _ => raise SAME ())
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   857
   handle SAME () => Op3 (oper, T, R, u1, u2, u3))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   858
  |> optimize_unit
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   859
(* typ -> rep -> nut list -> nut *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   860
fun s_tuple T R us =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   861
  (if exists (is_Cst Unrep) us then Cst (Unrep, T, R) else Tuple (T, R, us))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   862
  |> optimize_unit
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   863
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   864
(* theory -> nut -> nut *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   865
fun optimize_nut u =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   866
  case u of
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   867
    Op1 (oper, T, R, u1) => s_op1 oper T R (optimize_nut u1)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   868
  | Op2 (oper, T, R, u1, u2) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   869
    s_op2 oper T R (optimize_nut u1) (optimize_nut u2)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   870
  | Op3 (oper, T, R, u1, u2, u3) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   871
    s_op3 oper T R (optimize_nut u1) (optimize_nut u2) (optimize_nut u3)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   872
  | Tuple (T, R, us) => s_tuple T R (map optimize_nut us)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   873
  | Construct (us', T, R, us) => Construct (us', T, R, map optimize_nut us)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   874
  | _ => optimize_unit u
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   875
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   876
(* (nut -> 'a) -> nut -> 'a list *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   877
fun untuple f (Tuple (_, _, us)) = maps (untuple f) us
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   878
  | untuple f u = if rep_of u = Unit then [] else [f u]
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   879
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   880
(* scope -> bool -> rep NameTable.table -> bool -> nut -> nut *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   881
fun choose_reps_in_nut (scope as {ext_ctxt as {thy, ctxt, ...}, card_assigns,
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   882
                                  datatypes, ofs, ...}) liberal table def =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   883
  let
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   884
    val bool_atom_R = Atom (2, offset_of_type ofs bool_T)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   885
    (* polarity -> bool -> rep *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   886
    fun bool_rep polar opt =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   887
      if polar = Neut andalso opt then Opt bool_atom_R else Formula polar
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   888
    (* nut -> nut -> nut *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   889
    fun triad u1 u2 = s_op2 Triad (type_of u1) (Opt bool_atom_R) u1 u2
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   890
    (* (polarity -> nut) -> nut *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   891
    fun triad_fn f = triad (f Pos) (f Neg)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   892
    (* rep NameTable.table -> bool -> polarity -> nut -> nut -> nut *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   893
    fun unrepify_nut_in_nut table def polar needle_u =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   894
      let val needle_T = type_of needle_u in
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   895
        substitute_in_nut needle_u (Cst (if is_fun_type needle_T then Unknown
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   896
                                         else Unrep, needle_T, Any))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   897
        #> aux table def polar
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   898
      end
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   899
    (* rep NameTable.table -> bool -> polarity -> nut -> nut *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   900
    and aux table def polar u =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   901
      let
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   902
        (* bool -> polarity -> nut -> nut *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   903
        val gsub = aux table
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   904
        (* nut -> nut *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   905
        val sub = gsub false Neut
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   906
      in
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   907
        case u of
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   908
          Cst (False, T, _) => Cst (False, T, Formula Neut)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   909
        | Cst (True, T, _) => Cst (True, T, Formula Neut)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   910
        | Cst (Num j, T, _) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   911
          (case spec_of_type scope T of
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   912
             (1, j0) => if j = 0 then Cst (Unity, T, Unit)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   913
                        else Cst (Unrep, T, Opt (Atom (1, j0)))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   914
           | (k, j0) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   915
             let
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   916
               val ok = (if T = int_T then atom_for_int (k, j0) j <> ~1
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   917
                         else j < k)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   918
             in
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   919
               if ok then Cst (Num j, T, Atom (k, j0))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   920
               else Cst (Unrep, T, Opt (Atom (k, j0)))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   921
             end)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   922
        | Cst (Suc, T as Type ("fun", [T1, _]), _) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   923
          let val R = Atom (spec_of_type scope T1) in
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   924
            Cst (Suc, T, Func (R, Opt R))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   925
          end
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   926
        | Cst (Fracs, T, _) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   927
          Cst (Fracs, T, best_non_opt_set_rep_for_type scope T)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   928
        | Cst (NormFrac, T, _) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   929
          let val R1 = Atom (spec_of_type scope (domain_type T)) in
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   930
            Cst (NormFrac, T, Func (R1, Func (R1, Opt (Struct [R1, R1]))))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   931
          end
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   932
        | Cst (cst, T, _) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   933
          if cst mem [Unknown, Unrep] then
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   934
            case (is_boolean_type T, polar) of
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   935
              (true, Pos) => Cst (False, T, Formula Pos)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   936
            | (true, Neg) => Cst (True, T, Formula Neg)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   937
            | _ => Cst (cst, T, best_opt_set_rep_for_type scope T)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   938
          else if cst mem [Add, Subtract, Multiply, Divide, Modulo, Gcd,
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   939
                           Lcm] then
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   940
            let
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   941
              val T1 = domain_type T
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   942
              val R1 = Atom (spec_of_type scope T1)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   943
              val total =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   944
                T1 = nat_T andalso cst mem [Subtract, Divide, Modulo, Gcd]
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   945
            in Cst (cst, T, Func (R1, Func (R1, (not total ? Opt) R1))) end
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   946
          else if cst mem [NatToInt, IntToNat] then
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   947
            let
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   948
              val (nat_card, nat_j0) = spec_of_type scope nat_T
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   949
              val (int_card, int_j0) = spec_of_type scope int_T
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   950
            in
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   951
              if cst = NatToInt then
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   952
                let val total = (max_int_for_card int_card >= nat_card + 1) in
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   953
                  Cst (cst, T,
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   954
                       Func (Atom (nat_card, nat_j0),
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   955
                             (not total ? Opt) (Atom (int_card, int_j0))))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   956
                end
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   957
              else
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   958
                let val total = (max_int_for_card int_card < nat_card) in
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   959
                  Cst (cst, T, Func (Atom (int_card, int_j0),
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   960
                       Atom (nat_card, nat_j0)) |> not total ? Opt)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   961
                end
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   962
            end
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   963
          else
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   964
            Cst (cst, T, best_set_rep_for_type scope T)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   965
        | Op1 (Not, T, _, u1) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   966
          (case gsub def (flip_polarity polar) u1 of
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   967
             Op2 (Triad, T, R, u11, u12) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   968
             triad (s_op1 Not T (Formula Pos) u12)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   969
                   (s_op1 Not T (Formula Neg) u11)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   970
           | u1' => s_op1 Not T (flip_rep_polarity (rep_of u1')) u1')
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   971
        | Op1 (oper, T, _, u1) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   972
          let
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   973
            val u1 = sub u1
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   974
            val R1 = rep_of u1
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   975
            val R = case oper of
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   976
                      Finite => bool_rep polar (is_opt_rep R1)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   977
                    | _ => (if is_opt_rep R1 then best_opt_set_rep_for_type
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   978
                            else best_non_opt_set_rep_for_type) scope T
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   979
          in s_op1 oper T R u1 end
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   980
        | Op2 (Less, T, _, u1, u2) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   981
          let
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   982
            val u1 = sub u1
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   983
            val u2 = sub u2
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   984
            val R = bool_rep polar (exists (is_opt_rep o rep_of) [u1, u2])
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   985
          in s_op2 Less T R u1 u2 end
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   986
        | Op2 (Subset, T, _, u1, u2) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   987
          let
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   988
            val u1 = sub u1
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   989
            val u2 = sub u2
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   990
            val opt = exists (is_opt_rep o rep_of) [u1, u2]
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   991
            val R = bool_rep polar opt
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   992
          in
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   993
            if is_opt_rep R then
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   994
              triad_fn (fn polar => s_op2 Subset T (Formula polar) u1 u2)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   995
            else if opt andalso polar = Pos andalso
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   996
                    not (is_fully_comparable_type datatypes (type_of u1)) then
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   997
              Cst (False, T, Formula Pos)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   998
            else
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
   999
              s_op2 Subset T R u1 u2
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1000
          end
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1001
        | Op2 (DefEq, T, _, u1, u2) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1002
          s_op2 DefEq T (Formula Neut) (sub u1) (sub u2)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1003
        | Op2 (Eq, T, _, u1, u2) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1004
          let
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1005
            val u1' = sub u1
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1006
            val u2' = sub u2
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1007
            (* unit -> nut *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1008
            fun non_opt_case () = s_op2 Eq T (Formula polar) u1' u2'
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1009
            (* unit -> nut *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1010
            fun opt_opt_case () =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1011
              if polar = Neut then
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1012
                triad_fn (fn polar => s_op2 Eq T (Formula polar) u1' u2')
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1013
              else
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1014
                non_opt_case ()
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1015
            (* nut -> nut *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1016
            fun hybrid_case u =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1017
              (* hackish optimization *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1018
              if is_constructive u then s_op2 Eq T (Formula Neut) u1' u2'
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1019
              else opt_opt_case ()
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1020
          in
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1021
            if liberal orelse polar = Neg
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1022
               orelse is_fully_comparable_type datatypes (type_of u1) then
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1023
              case (is_opt_rep (rep_of u1'), is_opt_rep (rep_of u2')) of
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1024
                (true, true) => opt_opt_case ()
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1025
              | (true, false) => hybrid_case u1'
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1026
              | (false, true) => hybrid_case u2'
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1027
              | (false, false) => non_opt_case ()
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1028
            else
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1029
              Cst (False, T, Formula Pos)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1030
              |> polar = Neut ? (fn pos_u => triad pos_u (gsub def Neg u))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1031
          end
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1032
        | Op2 (Image, T, _, u1, u2) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1033
          let
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1034
            val u1' = sub u1
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1035
            val u2' = sub u2
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1036
          in
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1037
            (case (rep_of u1', rep_of u2') of
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1038
               (Func (R11, R12), Func (R21, Formula Neut)) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1039
               if R21 = R11 andalso is_lone_rep R12 then
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1040
                 let
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1041
                   val R =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1042
                     best_non_opt_set_rep_for_type scope T
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1043
                     |> exists (is_opt_rep o rep_of) [u1', u2'] ? opt_rep ofs T
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1044
                 in s_op2 Image T R u1' u2' end
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1045
               else
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1046
                 raise SAME ()
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1047
             | _ => raise SAME ())
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1048
            handle SAME () =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1049
                   let
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1050
                     val T1 = type_of u1
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1051
                     val dom_T = domain_type T1
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1052
                     val ran_T = range_type T1
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1053
                     val x_u = BoundName (~1, dom_T, Any, "image.x")
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1054
                     val y_u = BoundName (~2, ran_T, Any, "image.y")
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1055
                   in
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1056
                     Op2 (Lambda, T, Any, y_u,
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1057
                          Op2 (Exist, bool_T, Any, x_u,
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1058
                               Op2 (And, bool_T, Any,
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1059
                                    case u2 of
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1060
                                      Op2 (Lambda, _, _, u21, u22) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1061
                                      if num_occs_in_nut u21 u22 = 0 then (* FIXME: move to s_op2 *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1062
                                        u22
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1063
                                      else
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1064
                                        Op2 (Apply, bool_T, Any, u2, x_u)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1065
                                    | _ => Op2 (Apply, bool_T, Any, u2, x_u),
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1066
                                    Op2 (Eq, bool_T, Any, y_u,
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1067
                                         Op2 (Apply, ran_T, Any, u1, x_u)))))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1068
                     |> sub
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1069
                   end
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1070
          end
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1071
        | Op2 (Apply, T, _, u1, u2) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1072
          let
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1073
            val u1 = sub u1
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1074
            val u2 = sub u2
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1075
            val T1 = type_of u1
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1076
            val R1 = rep_of u1
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1077
            val R2 = rep_of u2
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1078
            val opt =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1079
              case (u1, is_opt_rep R2) of
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1080
                (ConstName (@{const_name set}, _, _), false) => false
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1081
              | _ => exists is_opt_rep [R1, R2]
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1082
            val ran_R =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1083
              if is_boolean_type T then
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1084
                bool_rep polar opt
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1085
              else
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1086
                smart_range_rep ofs T1 (fn () => card_of_type card_assigns T)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1087
                                (unopt_rep R1)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1088
                |> opt ? opt_rep ofs T
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1089
          in s_op2 Apply T ran_R u1 u2 end
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1090
        | Op2 (Lambda, T, _, u1, u2) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1091
          (case best_set_rep_for_type scope T of
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1092
             Unit => Cst (Unity, T, Unit)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1093
           | R as Func (R1, _) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1094
             let
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1095
               val table' = NameTable.update (u1, R1) table
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1096
               val u1' = aux table' false Neut u1
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1097
               val u2' = aux table' false Neut u2
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1098
               val R =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1099
                 if is_opt_rep (rep_of u2')
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1100
                    orelse (range_type T = bool_T andalso
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1101
                            not (is_Cst False
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1102
                                        (unrepify_nut_in_nut table false Neut
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1103
                                                             u1 u2
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1104
                                         |> optimize_nut))) then
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1105
                   opt_rep ofs T R
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1106
                 else
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1107
                   unopt_rep R
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1108
             in s_op2 Lambda T R u1' u2' end
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1109
           | R => raise NUT ("NitpickNut.aux.choose_reps_in_nut", [u]))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1110
        | Op2 (oper, T, _, u1, u2) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1111
          if oper mem [All, Exist] then
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1112
            let
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1113
              val table' = fold (choose_rep_for_bound_var scope) (untuple I u1)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1114
                                table
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1115
              val u1' = aux table' def polar u1
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1116
              val u2' = aux table' def polar u2
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1117
            in
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1118
              if polar = Neut andalso is_opt_rep (rep_of u2') then
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1119
                triad_fn (fn polar => gsub def polar u)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1120
              else
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1121
                let val quant_u = s_op2 oper T (Formula polar) u1' u2' in
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1122
                  if def
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1123
                     orelse (liberal andalso (polar = Pos) = (oper = All))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1124
                     orelse is_precise_type datatypes (type_of u1) then
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1125
                    quant_u
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1126
                  else
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1127
                    let
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1128
                      val connective = if oper = All then And else Or
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1129
                      val unrepified_u = unrepify_nut_in_nut table def polar
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1130
                                                             u1 u2
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1131
                    in
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1132
                      s_op2 connective T
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1133
                            (min_rep (rep_of quant_u) (rep_of unrepified_u))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1134
                            quant_u unrepified_u
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1135
                    end
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1136
                end
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1137
            end
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1138
          else if oper mem [Or, And] then
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1139
            let
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1140
              val u1' = gsub def polar u1
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1141
              val u2' = gsub def polar u2
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1142
            in
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1143
              (if polar = Neut then
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1144
                 case (is_opt_rep (rep_of u1'), is_opt_rep (rep_of u2')) of
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1145
                   (true, true) => triad_fn (fn polar => gsub def polar u)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1146
                 | (true, false) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1147
                   s_op2 oper T (Opt bool_atom_R)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1148
                         (triad_fn (fn polar => gsub def polar u1)) u2'
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1149
                 | (false, true) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1150
                   s_op2 oper T (Opt bool_atom_R)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1151
                         u1' (triad_fn (fn polar => gsub def polar u2))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1152
                 | (false, false) => raise SAME ()
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1153
               else
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1154
                 raise SAME ())
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1155
              handle SAME () => s_op2 oper T (Formula polar) u1' u2'
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1156
            end
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1157
          else if oper mem [The, Eps] then
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1158
            let
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1159
              val u1' = sub u1
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1160
              val opt1 = is_opt_rep (rep_of u1')
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1161
              val unopt_R = best_one_rep_for_type scope T |> optable_rep ofs T
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1162
              val R = unopt_R |> (oper = Eps orelse opt1) ? opt_rep ofs T
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1163
              val u = Op2 (oper, T, R, u1', sub u2)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1164
            in
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1165
              if is_precise_type datatypes T orelse not opt1 then
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1166
                u
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1167
              else
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1168
                let
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1169
                  val x_u = BoundName (~1, T, unopt_R, "descr.x")
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1170
                  val R = R |> opt_rep ofs T
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1171
                in
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1172
                  Op3 (If, T, R,
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1173
                       Op2 (Exist, bool_T, Formula Pos, x_u,
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1174
                            s_op2 Apply bool_T (Formula Pos) (gsub false Pos u1)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1175
                                  x_u), u, Cst (Unknown, T, R))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1176
                end
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1177
            end
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1178
          else
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1179
            let
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1180
              val u1 = sub u1
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1181
              val u2 = sub u2
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1182
              val R =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1183
                best_non_opt_set_rep_for_type scope T
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1184
                |> exists (is_opt_rep o rep_of) [u1, u2] ? opt_rep ofs T
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1185
            in s_op2 oper T R u1 u2 end
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1186
        | Op3 (Let, T, _, u1, u2, u3) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1187
          let
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1188
            val u2 = sub u2
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1189
            val R2 = rep_of u2
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1190
            val table' = NameTable.update (u1, R2) table
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1191
            val u1 = modify_name_rep u1 R2
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1192
            val u3 = aux table' false polar u3
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1193
          in s_op3 Let T (rep_of u3) u1 u2 u3 end
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1194
        | Op3 (If, T, _, u1, u2, u3) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1195
          let
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1196
            val u1 = sub u1
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1197
            val u2 = gsub def polar u2
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1198
            val u3 = gsub def polar u3
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1199
            val min_R = min_rep (rep_of u2) (rep_of u3)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1200
            val R = min_R |> is_opt_rep (rep_of u1) ? opt_rep ofs T
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1201
          in s_op3 If T R u1 u2 u3 end
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1202
        | Tuple (T, _, us) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1203
          let
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1204
            val Rs = map (best_one_rep_for_type scope o type_of) us
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1205
            val us = map sub us
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1206
            val R = if forall (equal Unit) Rs then Unit else Struct Rs
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1207
            val R' = (exists (is_opt_rep o rep_of) us ? opt_rep ofs T) R
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1208
          in s_tuple T R' us end
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1209
        | Construct (us', T, _, us) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1210
          let
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1211
            val us = map sub us
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1212
            val Rs = map rep_of us
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1213
            val R = best_one_rep_for_type scope T
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1214
            val {total, ...} =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1215
              constr_spec datatypes (original_name (nickname_of (hd us')), T)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1216
            val opt = exists is_opt_rep Rs orelse not total
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1217
          in Construct (map sub us', T, R |> opt ? Opt, us) end
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1218
        | _ =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1219
          let val u = modify_name_rep u (the_name table u) in
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1220
            if polar = Neut orelse not (is_boolean_type (type_of u))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1221
               orelse not (is_opt_rep (rep_of u)) then
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1222
              u
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1223
            else
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1224
              s_op1 Cast (type_of u) (Formula polar) u
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1225
          end
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1226
      end
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1227
      |> optimize_unit
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1228
  in aux table def Pos end
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1229
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1230
(* int -> Kodkod.n_ary_index list -> Kodkod.n_ary_index list
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1231
   -> int * Kodkod.n_ary_index list *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1232
fun fresh_n_ary_index n [] ys = (0, (n, 1) :: ys)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1233
  | fresh_n_ary_index n ((m, j) :: xs) ys =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1234
    if m = n then (j, ys @ ((m, j + 1) :: xs))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1235
    else fresh_n_ary_index n xs ((m, j) :: ys)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1236
(* int -> name_pool -> int * name_pool *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1237
fun fresh_rel n {rels, vars, formula_reg, rel_reg} =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1238
  let val (j, rels') = fresh_n_ary_index n rels [] in
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1239
    (j, {rels = rels', vars = vars, formula_reg = formula_reg,
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1240
         rel_reg = rel_reg})
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1241
  end
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1242
(* int -> name_pool -> int * name_pool *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1243
fun fresh_var n {rels, vars, formula_reg, rel_reg} =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1244
  let val (j, vars') = fresh_n_ary_index n vars [] in
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1245
    (j, {rels = rels, vars = vars', formula_reg = formula_reg,
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1246
         rel_reg = rel_reg})
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1247
  end
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1248
(* int -> name_pool -> int * name_pool *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1249
fun fresh_formula_reg {rels, vars, formula_reg, rel_reg} =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1250
  (formula_reg, {rels = rels, vars = vars, formula_reg = formula_reg + 1,
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1251
                 rel_reg = rel_reg})
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1252
(* int -> name_pool -> int * name_pool *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1253
fun fresh_rel_reg {rels, vars, formula_reg, rel_reg} =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1254
  (rel_reg, {rels = rels, vars = vars, formula_reg = formula_reg,
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1255
             rel_reg = rel_reg + 1})
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1256
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1257
(* nut -> nut list * name_pool * nut NameTable.table
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1258
   -> nut list * name_pool * nut NameTable.table *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1259
fun rename_plain_var v (ws, pool, table) =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1260
  let
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1261
    val is_formula = (rep_of v = Formula Neut)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1262
    val fresh = if is_formula then fresh_formula_reg else fresh_rel_reg
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1263
    val (j, pool) = fresh pool
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1264
    val constr = if is_formula then FormulaReg else RelReg
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1265
    val w = constr (j, type_of v, rep_of v)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1266
  in (w :: ws, pool, NameTable.update (v, w) table) end
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1267
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1268
(* typ -> rep -> nut list -> nut *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1269
fun shape_tuple (T as Type ("*", [T1, T2])) (R as Struct [R1, R2]) us =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1270
    let val arity1 = arity_of_rep R1 in
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1271
      Tuple (T, R, [shape_tuple T1 R1 (List.take (us, arity1)),
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1272
                    shape_tuple T2 R2 (List.drop (us, arity1))])
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1273
    end
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1274
  | shape_tuple (T as Type ("fun", [_, T2])) (R as Vect (k, R')) us =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1275
    Tuple (T, R, map (shape_tuple T2 R') (batch_list (length us div k) us))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1276
  | shape_tuple T R [u] =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1277
    if type_of u = T then u else raise NUT ("NitpickNut.shape_tuple", [u])
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1278
  | shape_tuple T Unit [] = Cst (Unity, T, Unit)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1279
  | shape_tuple _ _ us = raise NUT ("NitpickNut.shape_tuple", us)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1280
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1281
(* bool -> nut -> nut list * name_pool * nut NameTable.table
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1282
   -> nut list * name_pool * nut NameTable.table *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1283
fun rename_n_ary_var rename_free v (ws, pool, table) =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1284
  let
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1285
    val T = type_of v
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1286
    val R = rep_of v
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1287
    val arity = arity_of_rep R
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1288
    val nick = nickname_of v
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1289
    val (constr, fresh) = if rename_free then (FreeRel, fresh_rel)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1290
                          else (BoundRel, fresh_var)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1291
  in
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1292
    if not rename_free andalso arity > 1 then
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1293
      let
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1294
        val atom_schema = atom_schema_of_rep R
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1295
        val type_schema = type_schema_of_rep T R
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1296
        val (js, pool) = funpow arity (fn (js, pool) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1297
                                          let val (j, pool) = fresh 1 pool in
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1298
                                            (j :: js, pool)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1299
                                          end)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1300
                                ([], pool)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1301
        val ws' = map3 (fn j => fn x => fn T =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1302
                           constr ((1, j), T, Atom x,
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1303
                                   nick ^ " [" ^ string_of_int j ^ "]"))
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1304
                       (rev js) atom_schema type_schema
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1305
      in (ws' @ ws, pool, NameTable.update (v, shape_tuple T R ws') table) end
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1306
    else
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1307
      let
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1308
        val (j, pool) = fresh arity pool
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1309
        val w = constr ((arity, j), T, R, nick)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1310
      in (w :: ws, pool, NameTable.update (v, w) table) end
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1311
  end
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1312
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1313
(* nut list -> name_pool -> nut NameTable.table
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1314
  -> nut list * name_pool * nut NameTable.table *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1315
fun rename_free_vars vs pool table =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1316
  let
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1317
    val vs = filter (not_equal Unit o rep_of) vs
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1318
    val (vs, pool, table) = fold (rename_n_ary_var true) vs ([], pool, table)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1319
  in (rev vs, pool, table) end
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1320
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1321
(* name_pool -> nut NameTable.table -> nut -> nut *)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1322
fun rename_vars_in_nut pool table u =
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1323
  case u of
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1324
    Cst _ => u
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1325
  | Op1 (oper, T, R, u1) => Op1 (oper, T, R, rename_vars_in_nut pool table u1)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1326
  | Op2 (oper, T, R, u1, u2) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1327
    if oper mem [All, Exist, Lambda] then
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1328
      let
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1329
        val (_, pool, table) = fold (rename_n_ary_var false) (untuple I u1)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1330
                                    ([], pool, table)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1331
      in
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1332
        Op2 (oper, T, R, rename_vars_in_nut pool table u1,
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1333
             rename_vars_in_nut pool table u2)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1334
      end
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1335
    else
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1336
      Op2 (oper, T, R, rename_vars_in_nut pool table u1,
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1337
           rename_vars_in_nut pool table u2)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1338
  | Op3 (Let, T, R, u1, u2, u3) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1339
    if rep_of u2 = Unit orelse inline_nut u2 then
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1340
      let
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1341
        val u2 = rename_vars_in_nut pool table u2
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1342
        val table = NameTable.update (u1, u2) table
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1343
      in rename_vars_in_nut pool table u3 end
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1344
    else
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1345
      let
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1346
        val bs = untuple I u1
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1347
        val (_, pool, table') = fold rename_plain_var bs ([], pool, table)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1348
        val u11 = rename_vars_in_nut pool table' u1
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1349
      in
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1350
        Op3 (Let, T, R, rename_vars_in_nut pool table' u1,
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1351
             rename_vars_in_nut pool table u2,
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1352
             rename_vars_in_nut pool table' u3)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1353
      end
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1354
  | Op3 (oper, T, R, u1, u2, u3) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1355
    Op3 (oper, T, R, rename_vars_in_nut pool table u1,
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1356
         rename_vars_in_nut pool table u2, rename_vars_in_nut pool table u3)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1357
  | Tuple (T, R, us) => Tuple (T, R, map (rename_vars_in_nut pool table) us)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1358
  | Construct (us', T, R, us) =>
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1359
    Construct (map (rename_vars_in_nut pool table) us', T, R,
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1360
               map (rename_vars_in_nut pool table) us)
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1361
  | _ => the_name table u
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1362
08a39a957ed7 added Nitpick's theory and ML files to Isabelle/HOL;
blanchet
parents:
diff changeset
  1363
end;