src/HOL/Tools/Nitpick/nitpick_rep.ML

+(*  Title:      HOL/Nitpick/Tools/nitpick_rep.ML
+    Author:     Jasmin Blanchette, TU Muenchen
+    Copyright   2008, 2009
+
+Kodkod representations of Nitpick terms.
+*)
+
+signature NITPICK_REP =
+sig
+  type polarity = NitpickUtil.polarity
+  type scope = NitpickScope.scope
+
+  datatype rep =
+    Any |
+    Formula of polarity |
+    Unit |
+    Atom of int * int |
+    Struct of rep list |
+    Vect of int * rep |
+    Func of rep * rep |
+    Opt of rep
+
+  exception REP of string * rep list
+
+  val string_for_polarity : polarity -> string
+  val string_for_rep : rep -> string
+  val is_Func : rep -> bool
+  val is_Opt : rep -> bool
+  val is_opt_rep : rep -> bool
+  val flip_rep_polarity : rep -> rep
+  val card_of_rep : rep -> int
+  val arity_of_rep : rep -> int
+  val min_univ_card_of_rep : rep -> int
+  val is_one_rep : rep -> bool
+  val is_lone_rep : rep -> bool
+  val dest_Func : rep -> rep * rep
+  val smart_range_rep : int Typtab.table -> typ -> (unit -> int) -> rep -> rep
+  val binder_reps : rep -> rep list
+  val body_rep : rep -> rep
+  val one_rep : int Typtab.table -> typ -> rep -> rep
+  val optable_rep : int Typtab.table -> typ -> rep -> rep
+  val opt_rep : int Typtab.table -> typ -> rep -> rep
+  val unopt_rep : rep -> rep
+  val min_rep : rep -> rep -> rep
+  val min_reps : rep list -> rep list -> rep list
+  val card_of_domain_from_rep : int -> rep -> int
+  val rep_to_binary_rel_rep : int Typtab.table -> typ -> rep -> rep
+  val best_one_rep_for_type : scope -> typ -> rep
+  val best_opt_set_rep_for_type : scope -> typ -> rep
+  val best_non_opt_set_rep_for_type : scope -> typ -> rep
+  val best_set_rep_for_type : scope -> typ -> rep
+  val best_non_opt_symmetric_reps_for_fun_type : scope -> typ -> rep * rep
+  val atom_schema_of_rep : rep -> (int * int) list
+  val atom_schema_of_reps : rep list -> (int * int) list
+  val type_schema_of_rep : typ -> rep -> typ list
+  val type_schema_of_reps : typ list -> rep list -> typ list
+  val all_combinations_for_rep : rep -> int list list
+  val all_combinations_for_reps : rep list -> int list list
+end;
+
+structure NitpickRep : NITPICK_REP =
+struct
+
+open NitpickUtil
+open NitpickHOL
+open NitpickScope
+
+datatype rep =
+  Any |
+  Formula of polarity |
+  Unit |
+  Atom of int * int |
+  Struct of rep list |
+  Vect of int * rep |
+  Func of rep * rep |
+  Opt of rep
+
+exception REP of string * rep list
+
+(* polarity -> string *)
+fun string_for_polarity Pos = "+"
+  | string_for_polarity Neg = "-"
+  | string_for_polarity Neut = "="
+
+(* rep -> string *)
+fun atomic_string_for_rep rep =
+  let val s = string_for_rep rep in
+    if String.isPrefix "[" s orelse not (is_substring_of " " s) then s
+    else "(" ^ s ^ ")"
+  end
+(* rep -> string *)
+and string_for_rep Any = "X"
+  | string_for_rep (Formula polar) = "F" ^ string_for_polarity polar
+  | string_for_rep Unit = "U"
+  | string_for_rep (Atom (k, j0)) =
+    "A" ^ string_of_int k ^ (if j0 = 0 then "" else "@" ^ string_of_int j0)
+  | string_for_rep (Struct rs) = "[" ^ commas (map string_for_rep rs) ^ "]"
+  | string_for_rep (Vect (k, R)) =
+    string_of_int k ^ " x " ^ atomic_string_for_rep R
+  | string_for_rep (Func (R1, R2)) =
+    atomic_string_for_rep R1 ^ " => " ^ string_for_rep R2
+  | string_for_rep (Opt R) = atomic_string_for_rep R ^ "?"
+
+(* rep -> bool *)
+fun is_Func (Func _) = true
+  | is_Func _ = false
+fun is_Opt (Opt _) = true
+  | is_Opt _ = false
+fun is_opt_rep (Func (_, R2)) = is_opt_rep R2
+  | is_opt_rep (Opt _) = true
+  | is_opt_rep _ = false
+
+(* rep -> int *)
+fun card_of_rep Any = raise REP ("NitpickRep.card_of_rep", [Any])
+  | card_of_rep (Formula _) = 2
+  | card_of_rep Unit = 1
+  | card_of_rep (Atom (k, _)) = k
+  | card_of_rep (Struct rs) = Integer.prod (map card_of_rep rs)
+  | card_of_rep (Vect (k, R)) = reasonable_power (card_of_rep R) k
+  | card_of_rep (Func (R1, R2)) =
+    reasonable_power (card_of_rep R2) (card_of_rep R1)
+  | card_of_rep (Opt R) = card_of_rep R
+fun arity_of_rep Any = raise REP ("NitpickRep.arity_of_rep", [Any])
+  | arity_of_rep (Formula _) = 0
+  | arity_of_rep Unit = 0
+  | arity_of_rep (Atom _) = 1
+  | arity_of_rep (Struct Rs) = Integer.sum (map arity_of_rep Rs)
+  | arity_of_rep (Vect (k, R)) = k * arity_of_rep R
+  | arity_of_rep (Func (R1, R2)) = arity_of_rep R1 + arity_of_rep R2
+  | arity_of_rep (Opt R) = arity_of_rep R
+fun min_univ_card_of_rep Any =
+    raise REP ("NitpickRep.min_univ_card_of_rep", [Any])
+  | min_univ_card_of_rep (Formula _) = 0
+  | min_univ_card_of_rep Unit = 0
+  | min_univ_card_of_rep (Atom (k, j0)) = k + j0 + 1
+  | min_univ_card_of_rep (Struct Rs) =
+    fold Integer.max (map min_univ_card_of_rep Rs) 0
+  | min_univ_card_of_rep (Vect (_, R)) = min_univ_card_of_rep R
+  | min_univ_card_of_rep (Func (R1, R2)) =
+    Int.max (min_univ_card_of_rep R1, min_univ_card_of_rep R2)
+  | min_univ_card_of_rep (Opt R) = min_univ_card_of_rep R
+
+(* rep -> bool *)
+fun is_one_rep Unit = true
+  | is_one_rep (Atom _) = true
+  | is_one_rep (Struct _) = true
+  | is_one_rep (Vect _) = true
+  | is_one_rep _ = false
+fun is_lone_rep (Opt R) = is_one_rep R
+  | is_lone_rep R = is_one_rep R
+
+(* rep -> rep * rep *)
+fun dest_Func (Func z) = z
+  | dest_Func R = raise REP ("NitpickRep.dest_Func", [R])
+(* int Typtab.table -> typ -> (unit -> int) -> rep -> rep *)
+fun smart_range_rep _ _ _ Unit = Unit
+  | smart_range_rep _ _ _ (Vect (_, R)) = R
+  | smart_range_rep _ _ _ (Func (_, R2)) = R2
+  | smart_range_rep ofs T ran_card (Opt R) =
+    Opt (smart_range_rep ofs T ran_card R)
+  | smart_range_rep ofs (Type ("fun", [_, T2])) _ (Atom (1, _)) =
+    Atom (1, offset_of_type ofs T2)
+  | smart_range_rep ofs (Type ("fun", [_, T2])) ran_card (Atom _) =
+    Atom (ran_card (), offset_of_type ofs T2)
+  | smart_range_rep _ _ _ R = raise REP ("NitpickRep.smart_range_rep", [R])
+
+(* rep -> rep list *)
+fun binder_reps (Func (R1, R2)) = R1 :: binder_reps R2
+  | binder_reps R = []
+(* rep -> rep *)
+fun body_rep (Func (_, R2)) = body_rep R2
+  | body_rep R = R
+
+(* rep -> rep *)
+fun flip_rep_polarity (Formula polar) = Formula (flip_polarity polar)
+  | flip_rep_polarity (Func (R1, R2)) = Func (R1, flip_rep_polarity R2)
+  | flip_rep_polarity R = R
+
+(* int Typtab.table -> rep -> rep *)
+fun one_rep _ _ Any = raise REP ("NitpickRep.one_rep", [Any])
+  | one_rep _ _ (Atom x) = Atom x
+  | one_rep _ _ (Struct Rs) = Struct Rs
+  | one_rep _ _ (Vect z) = Vect z
+  | one_rep ofs T (Opt R) = one_rep ofs T R
+  | one_rep ofs T R = Atom (card_of_rep R, offset_of_type ofs T)
+fun optable_rep ofs (Type ("fun", [_, T2])) (Func (R1, R2)) =
+    Func (R1, optable_rep ofs T2 R2)
+  | optable_rep ofs T R = one_rep ofs T R
+fun opt_rep ofs (Type ("fun", [_, T2])) (Func (R1, R2)) =
+    Func (R1, opt_rep ofs T2 R2)
+  | opt_rep ofs T R = Opt (optable_rep ofs T R)
+(* rep -> rep *)
+fun unopt_rep (Func (R1, R2)) = Func (R1, unopt_rep R2)
+  | unopt_rep (Opt R) = R
+  | unopt_rep R = R
+
+(* polarity -> polarity -> polarity *)
+fun min_polarity polar1 polar2 =
+  if polar1 = polar2 then
+    polar1
+  else if polar1 = Neut then
+    polar2
+  else if polar2 = Neut then
+    polar1
+  else
+    raise ARG ("NitpickRep.min_polarity",
+               commas (map (quote o string_for_polarity) [polar1, polar2]))
+
+(* It's important that Func is before Vect, because if the range is Opt we
+   could lose information by converting a Func to a Vect. *)
+(* rep -> rep -> rep *)
+fun min_rep (Opt R1) (Opt R2) = Opt (min_rep R1 R2)
+  | min_rep (Opt R) _ = Opt R
+  | min_rep _ (Opt R) = Opt R
+  | min_rep (Formula polar1) (Formula polar2) =
+    Formula (min_polarity polar1 polar2)
+  | min_rep (Formula polar) _ = Formula polar
+  | min_rep _ (Formula polar) = Formula polar
+  | min_rep Unit _ = Unit
+  | min_rep _ Unit = Unit
+  | min_rep (Atom x) _ = Atom x
+  | min_rep _ (Atom x) = Atom x
+  | min_rep (Struct Rs1) (Struct Rs2) = Struct (min_reps Rs1 Rs2)
+  | min_rep (Struct Rs) _ = Struct Rs
+  | min_rep _ (Struct Rs) = Struct Rs
+  | min_rep (R1 as Func (R11, R12)) (R2 as Func (R21, R22)) =
+    (case pairself is_opt_rep (R12, R22) of
+       (true, false) => R1
+     | (false, true) => R2
+     | _ => if R11 = R21 then Func (R11, min_rep R12 R22)
+            else if min_rep R11 R21 = R11 then R1
+            else R2)
+  | min_rep (Func z) _ = Func z
+  | min_rep _ (Func z) = Func z
+  | min_rep (Vect (k1, R1)) (Vect (k2, R2)) =
+    if k1 < k2 then Vect (k1, R1)
+    else if k1 > k2 then Vect (k2, R2)
+    else Vect (k1, min_rep R1 R2)
+  | min_rep R1 R2 = raise REP ("NitpickRep.min_rep", [R1, R2])
+(* rep list -> rep list -> rep list *)
+and min_reps [] _ = []
+  | min_reps _ [] = []
+  | min_reps (R1 :: Rs1) (R2 :: Rs2) =
+    if R1 = R2 then R1 :: min_reps Rs1 Rs2
+    else if min_rep R1 R2 = R1 then R1 :: Rs1
+    else R2 :: Rs2
+
+(* int -> rep -> int *)
+fun card_of_domain_from_rep ran_card R =
+  case R of
+    Unit => 1
+  | Atom (k, _) => exact_log ran_card k
+  | Vect (k, _) => k
+  | Func (R1, _) => card_of_rep R1
+  | Opt R => card_of_domain_from_rep ran_card R
+  | _ => raise REP ("NitpickRep.card_of_domain_from_rep", [R])
+
+(* int Typtab.table -> typ -> rep -> rep *)
+fun rep_to_binary_rel_rep ofs T R =
+  let
+    val k = exact_root 2 (card_of_domain_from_rep 2 R)
+    val j0 = offset_of_type ofs (fst (HOLogic.dest_prodT (domain_type T)))
+  in Func (Struct [Atom (k, j0), Atom (k, j0)], Formula Neut) end
+
+(* scope -> typ -> rep *)
+fun best_one_rep_for_type (scope as {card_assigns, ...} : scope)
+                          (Type ("fun", [T1, T2])) =
+    (case best_one_rep_for_type scope T2 of
+       Unit => Unit
+     | R2 => Vect (card_of_type card_assigns T1, R2))
+  | best_one_rep_for_type scope (Type ("*", [T1, T2])) =
+    (case (best_one_rep_for_type scope T1, best_one_rep_for_type scope T2) of
+       (Unit, Unit) => Unit
+     | (R1, R2) => Struct [R1, R2])
+  | best_one_rep_for_type (scope as {card_assigns, datatypes, ofs, ...}) T =
+    (case card_of_type card_assigns T of
+       1 => if is_some (datatype_spec datatypes T)
+               orelse is_fp_iterator_type T then
+              Atom (1, offset_of_type ofs T)
+            else
+              Unit
+     | k => Atom (k, offset_of_type ofs T))
+
+(* Datatypes are never represented by Unit, because it would confuse
+   "nfa_transitions_for_ctor". *)
+(* scope -> typ -> rep *)
+fun best_opt_set_rep_for_type scope (Type ("fun", [T1, T2])) =
+    Func (best_one_rep_for_type scope T1, best_opt_set_rep_for_type scope T2)
+  | best_opt_set_rep_for_type (scope as {ofs, ...}) T =
+    opt_rep ofs T (best_one_rep_for_type scope T)
+fun best_non_opt_set_rep_for_type (scope as {ofs, ...})
+                                  (Type ("fun", [T1, T2])) =
+    (case (best_one_rep_for_type scope T1,
+           best_non_opt_set_rep_for_type scope T2) of
+       (_, Unit) => Unit
+     | (Unit, Atom (2, _)) =>
+       Func (Atom (1, offset_of_type ofs T1), Formula Neut)
+     | (R1, Atom (2, _)) => Func (R1, Formula Neut)
+     | z => Func z)
+  | best_non_opt_set_rep_for_type scope T = best_one_rep_for_type scope T
+fun best_set_rep_for_type (scope as {datatypes, ...}) T =
+  (if is_precise_type datatypes T then best_non_opt_set_rep_for_type
+   else best_opt_set_rep_for_type) scope T
+fun best_non_opt_symmetric_reps_for_fun_type (scope as {ofs, ...})
+                                             (Type ("fun", [T1, T2])) =
+    (optable_rep ofs T1 (best_one_rep_for_type scope T1),
+     optable_rep ofs T2 (best_one_rep_for_type scope T2))
+  | best_non_opt_symmetric_reps_for_fun_type _ T =
+    raise TYPE ("NitpickRep.best_non_opt_symmetric_reps_for_fun_type", [T], [])
+
+(* rep -> (int * int) list *)
+fun atom_schema_of_rep Any = raise REP ("NitpickRep.atom_schema_of_rep", [Any])
+  | atom_schema_of_rep (Formula _) = []
+  | atom_schema_of_rep Unit = []
+  | atom_schema_of_rep (Atom x) = [x]
+  | atom_schema_of_rep (Struct Rs) = atom_schema_of_reps Rs
+  | atom_schema_of_rep (Vect (k, R)) = replicate_list k (atom_schema_of_rep R)
+  | atom_schema_of_rep (Func (R1, R2)) =
+    atom_schema_of_rep R1 @ atom_schema_of_rep R2
+  | atom_schema_of_rep (Opt R) = atom_schema_of_rep R
+(* rep list -> (int * int) list *)
+and atom_schema_of_reps Rs = maps atom_schema_of_rep Rs
+
+(* typ -> rep -> typ list *)
+fun type_schema_of_rep _ (Formula _) = []
+  | type_schema_of_rep _ Unit = []
+  | type_schema_of_rep T (Atom _) = [T]
+  | type_schema_of_rep (Type ("*", [T1, T2])) (Struct [R1, R2]) =
+    type_schema_of_reps [T1, T2] [R1, R2]
+  | type_schema_of_rep (Type ("fun", [_, T2])) (Vect (k, R)) =
+    replicate_list k (type_schema_of_rep T2 R)
+  | type_schema_of_rep (Type ("fun", [T1, T2])) (Func (R1, R2)) =
+    type_schema_of_rep T1 R1 @ type_schema_of_rep T2 R2
+  | type_schema_of_rep T (Opt R) = type_schema_of_rep T R
+  | type_schema_of_rep T R = raise REP ("NitpickRep.type_schema_of_rep", [R])
+(* typ list -> rep list -> typ list *)
+and type_schema_of_reps Ts Rs = flat (map2 type_schema_of_rep Ts Rs)
+
+(* rep -> int list list *)
+val all_combinations_for_rep = all_combinations o atom_schema_of_rep
+(* rep list -> int list list *)
+val all_combinations_for_reps = all_combinations o atom_schema_of_reps
+
+end;