src/HOL/Tools/Quickcheck/exhaustive_generators.ML

sketch & explore: recover from duplicate fixed variables in Isar proofs

(*  Title:      HOL/Tools/Quickcheck/exhaustive_generators.ML
    Author:     Lukas Bulwahn, TU Muenchen

Exhaustive generators for various types.
*)

signature EXHAUSTIVE_GENERATORS =
sig
  val compile_generator_expr: Proof.context -> (term * term list) list -> bool -> int list ->
    (bool * term list) option * Quickcheck.report option
  val compile_generator_exprs: Proof.context -> term list -> (int -> term list option) list
  val compile_validator_exprs: Proof.context -> term list -> (int -> bool) list
  val put_counterexample:
    (unit -> Code_Numeral.natural -> bool -> Code_Numeral.natural -> (bool * term list) option) ->
      Proof.context -> Proof.context
  val put_counterexample_batch: (unit -> (Code_Numeral.natural -> term list option) list) ->
    Proof.context -> Proof.context
  val put_validator_batch: (unit -> (Code_Numeral.natural -> bool) list) ->
    Proof.context -> Proof.context
  exception Counterexample of term list
  val smart_quantifier : bool Config.T
  val optimise_equality : bool Config.T
  val quickcheck_pretty : bool Config.T
  val setup_exhaustive_datatype_interpretation : theory -> theory
  val setup_bounded_forall_datatype_interpretation : theory -> theory
  val instantiate_full_exhaustive_datatype : Old_Datatype_Aux.config -> Old_Datatype_Aux.descr ->
    (string * sort) list -> string list -> string -> string list * string list ->
    typ list * typ list -> theory -> theory
  val instantiate_exhaustive_datatype : Old_Datatype_Aux.config -> Old_Datatype_Aux.descr ->
    (string * sort) list -> string list -> string -> string list * string list ->
    typ list * typ list -> theory -> theory
end

structure Exhaustive_Generators : EXHAUSTIVE_GENERATORS =
struct

(* basics *)

(** dynamic options **)

val smart_quantifier = Attrib.setup_config_bool \<^binding>\<open>quickcheck_smart_quantifier\<close> (K true)
val optimise_equality = Attrib.setup_config_bool \<^binding>\<open>quickcheck_optimise_equality\<close> (K true)

val fast = Attrib.setup_config_bool \<^binding>\<open>quickcheck_fast\<close> (K false)
val bounded_forall = Attrib.setup_config_bool \<^binding>\<open>quickcheck_bounded_forall\<close> (K false)
val full_support = Attrib.setup_config_bool \<^binding>\<open>quickcheck_full_support\<close> (K true)
val quickcheck_pretty = Attrib.setup_config_bool \<^binding>\<open>quickcheck_pretty\<close> (K true)


(** abstract syntax **)

fun termifyT T = HOLogic.mk_prodT (T, \<^typ>\<open>unit \<Rightarrow> Code_Evaluation.term\<close>)

val size = \<^term>\<open>i :: natural\<close>
val size_pred = \<^term>\<open>(i :: natural) - 1\<close>
val size_ge_zero = \<^term>\<open>(i :: natural) > 0\<close>

fun mk_none_continuation (x, y) =
  let val (T as Type (\<^type_name>\<open>option\<close>, _)) = fastype_of x
  in Const (\<^const_name>\<open>orelse\<close>, T --> T --> T) $ x $ y end

fun mk_if (b, t, e) =
  let val T = fastype_of t
  in Const (\<^const_name>\<open>If\<close>, \<^typ>\<open>bool\<close> --> T --> T --> T) $ b $ t $ e end


(* handling inductive datatypes *)

(** constructing generator instances **)

exception FUNCTION_TYPE

exception Counterexample of term list

val resultT = \<^typ>\<open>(bool \<times> term list) option\<close>

val exhaustiveN = "exhaustive"
val full_exhaustiveN = "full_exhaustive"
val bounded_forallN = "bounded_forall"

fun fast_exhaustiveT T = (T --> \<^typ>\<open>unit\<close>) --> \<^typ>\<open>natural\<close> --> \<^typ>\<open>unit\<close>

fun exhaustiveT T = (T --> resultT) --> \<^typ>\<open>natural\<close> --> resultT

fun bounded_forallT T = (T --> \<^typ>\<open>bool\<close>) --> \<^typ>\<open>natural\<close> --> \<^typ>\<open>bool\<close>

fun full_exhaustiveT T = (termifyT T --> resultT) --> \<^typ>\<open>natural\<close> --> resultT

fun check_allT T = (termifyT T --> resultT) --> resultT

fun mk_equation_terms generics (descr, vs, Ts) =
  let
    val (mk_call, mk_aux_call, mk_consexpr, mk_rhs, test_function, exhaustives) = generics
    val rhss =
      Old_Datatype_Aux.interpret_construction descr vs
        { atyp = mk_call, dtyp = mk_aux_call }
      |> (map o apfst) Type
      |> map (fn (T, cs) => map (mk_consexpr T) cs)
      |> map mk_rhs
    val lhss = map2 (fn t => fn T => t $ test_function T $ size) exhaustives Ts
  in map (HOLogic.mk_Trueprop o HOLogic.mk_eq) (lhss ~~ rhss) end

fun gen_mk_call c T =  (T, fn t => c T $ absdummy T t $ size_pred)

fun gen_mk_aux_call functerms fTs (k, _) (tyco, Ts) =
  let
    val T = Type (tyco, Ts)
    val _ = if not (null fTs) then raise FUNCTION_TYPE else ()
  in (T, fn t => nth functerms k $ absdummy T t $ size_pred) end

fun gen_mk_consexpr test_function simpleT (c, xs) =
  let
    val (Ts, fns) = split_list xs
    val constr = Const (c, Ts ---> simpleT)
    val bounds = map Bound (((length xs) - 1) downto 0)
    val start_term = test_function simpleT $ list_comb (constr, bounds)
  in fold_rev (fn f => fn t => f t) fns start_term end

fun mk_equations functerms =
  let
    fun test_function T = Free ("f", T --> resultT)
    val mk_call = gen_mk_call (fn T => Const (\<^const_name>\<open>exhaustive\<close>, exhaustiveT T))
    val mk_aux_call = gen_mk_aux_call functerms
    val mk_consexpr = gen_mk_consexpr test_function
    fun mk_rhs exprs =
      mk_if (size_ge_zero, foldr1 mk_none_continuation exprs, Const (\<^const_name>\<open>None\<close>, resultT))
  in mk_equation_terms (mk_call, mk_aux_call, mk_consexpr, mk_rhs, test_function, functerms) end

fun mk_bounded_forall_equations functerms =
  let
    fun test_function T = Free ("P", T --> \<^typ>\<open>bool\<close>)
    val mk_call = gen_mk_call (fn T => Const (\<^const_name>\<open>bounded_forall\<close>, bounded_forallT T))
    val mk_aux_call = gen_mk_aux_call functerms
    val mk_consexpr = gen_mk_consexpr test_function
    fun mk_rhs exprs = mk_if (size_ge_zero, foldr1 HOLogic.mk_conj exprs, \<^term>\<open>True\<close>)
  in mk_equation_terms (mk_call, mk_aux_call, mk_consexpr, mk_rhs, test_function, functerms) end

fun mk_full_equations functerms =
  let
    fun test_function T = Free ("f", termifyT T --> resultT)
    fun case_prod_const T =
      HOLogic.case_prod_const (T, \<^typ>\<open>unit \<Rightarrow> Code_Evaluation.term\<close>, resultT)
    fun mk_call T =
      let
        val full_exhaustive = Const (\<^const_name>\<open>full_exhaustive\<close>, full_exhaustiveT T)
      in
        (T,
          fn t =>
            full_exhaustive $
              (case_prod_const T $ absdummy T (absdummy \<^typ>\<open>unit \<Rightarrow> Code_Evaluation.term\<close> t)) $
              size_pred)
      end
    fun mk_aux_call fTs (k, _) (tyco, Ts) =
      let
        val T = Type (tyco, Ts)
        val _ = if not (null fTs) then raise FUNCTION_TYPE else ()
      in
        (T,
          fn t =>
            nth functerms k $
              (case_prod_const T $ absdummy T (absdummy \<^typ>\<open>unit \<Rightarrow> Code_Evaluation.term\<close> t)) $
              size_pred)
      end
    fun mk_consexpr simpleT (c, xs) =
      let
        val (Ts, fns) = split_list xs
        val constr = Const (c, Ts ---> simpleT)
        val bounds = map (fn x => Bound (2 * x + 1)) (((length xs) - 1) downto 0)
        val Eval_App =
          Const (\<^const_name>\<open>Code_Evaluation.App\<close>,
            HOLogic.termT --> HOLogic.termT --> HOLogic.termT)
        val Eval_Const =
          Const (\<^const_name>\<open>Code_Evaluation.Const\<close>,
            HOLogic.literalT --> \<^typ>\<open>typerep\<close> --> HOLogic.termT)
        val term =
          fold (fn u => fn t => Eval_App $ t $ (u $ \<^term>\<open>()\<close>))
            bounds (Eval_Const $ HOLogic.mk_literal c $ HOLogic.mk_typerep (Ts ---> simpleT))
        val start_term =
          test_function simpleT $
            (HOLogic.pair_const simpleT \<^typ>\<open>unit \<Rightarrow> Code_Evaluation.term\<close> $
              (list_comb (constr, bounds)) $ absdummy \<^typ>\<open>unit\<close> term)
      in fold_rev (fn f => fn t => f t) fns start_term end
    fun mk_rhs exprs =
      mk_if (size_ge_zero, foldr1 mk_none_continuation exprs, Const (\<^const_name>\<open>None\<close>, resultT))
  in mk_equation_terms (mk_call, mk_aux_call, mk_consexpr, mk_rhs, test_function, functerms) end


(** instantiating generator classes **)

fun contains_recursive_type_under_function_types xs =
  exists (fn (_, (_, _, cs)) => cs |> exists (snd #> exists (fn dT =>
    (case Old_Datatype_Aux.strip_dtyp dT of (_ :: _, Old_Datatype_Aux.DtRec _) => true | _ => false)))) xs

fun instantiate_datatype (name, constprfx, sort, mk_equations, mk_T, argnames)
    config descr vs tycos prfx (names, auxnames) (Ts, Us) thy =
  if not (contains_recursive_type_under_function_types descr) then
    let
      val _ = Old_Datatype_Aux.message config ("Creating " ^ name ^ "...")
      val fullnames = map (prefix (constprfx ^ "_")) (names @ auxnames)
    in
      thy
      |> Class.instantiation (tycos, vs, sort)
      |> Quickcheck_Common.define_functions
          (fn functerms => mk_equations functerms (descr, vs, Ts @ Us), NONE)
          prfx argnames fullnames (map mk_T (Ts @ Us))
      |> Class.prove_instantiation_exit (fn ctxt => Class.intro_classes_tac ctxt [])
    end
  else
    (Old_Datatype_Aux.message config
      ("Creation of " ^ name ^ " failed because the datatype is recursive under a function type");
    thy)

val instantiate_bounded_forall_datatype =
  instantiate_datatype
    ("bounded universal quantifiers", bounded_forallN, \<^sort>\<open>bounded_forall\<close>,
      mk_bounded_forall_equations, bounded_forallT, ["P", "i"])

val instantiate_exhaustive_datatype =
  instantiate_datatype
    ("exhaustive generators", exhaustiveN, \<^sort>\<open>exhaustive\<close>,
      mk_equations, exhaustiveT, ["f", "i"])

val instantiate_full_exhaustive_datatype =
  instantiate_datatype
    ("full exhaustive generators", full_exhaustiveN, \<^sort>\<open>full_exhaustive\<close>,
      mk_full_equations, full_exhaustiveT, ["f", "i"])


(* building and compiling generator expressions *)

fun mk_let_expr (x, t, e) genuine =
  let val (T1, T2) = (fastype_of x, fastype_of (e genuine))
  in Const (\<^const_name>\<open>Let\<close>, T1 --> (T1 --> T2) --> T2) $ t $ lambda x (e genuine) end

fun mk_safe_let_expr genuine_only none safe (x, t, e) genuine =
  let
    val (T1, T2) = (fastype_of x, fastype_of (e genuine))
    val if_t = Const (\<^const_name>\<open>If\<close>, \<^typ>\<open>bool\<close> --> T2 --> T2 --> T2)
  in
    Const (\<^const_name>\<open>Quickcheck_Random.catch_match\<close>, T2 --> T2 --> T2) $
      (Const (\<^const_name>\<open>Let\<close>, T1 --> (T1 --> T2) --> T2) $ t $ lambda x (e genuine)) $
      (if_t $ genuine_only $ none $ safe false)
  end

fun mk_test_term lookup mk_closure mk_if mk_let none_t return ctxt =
  let
    val cnstrs =
      flat (maps
        (map (fn (_, (Tname, _, cs)) => map (apsnd (rpair Tname o length)) cs) o #descr o snd)
        (Symtab.dest
          (BNF_LFP_Compat.get_all (Proof_Context.theory_of ctxt) Quickcheck_Common.compat_prefs)))
    fun is_constrt (Const (s, T), ts) =
          (case (AList.lookup (op =) cnstrs s, body_type T) of
            (SOME (i, Tname), Type (Tname', _)) => length ts = i andalso Tname = Tname'
          | _ => false)
      | is_constrt _ = false
    fun mk_naive_test_term t =
      fold_rev mk_closure (map lookup (Term.add_free_names t [])) (mk_if (t, none_t, return) true)
    fun mk_test (vars, check) = fold_rev mk_closure (map lookup vars) check
    fun mk_smart_test_term' concl bound_vars assms genuine =
      let
        fun vars_of t = subtract (op =) bound_vars (Term.add_free_names t [])
        fun mk_equality_term (lhs, f as Free (x, _)) c (assm, assms) =
              if member (op =) (Term.add_free_names lhs bound_vars) x then
                c (assm, assms)
              else
                let
                   val rec_call = mk_smart_test_term' concl (union (op =) (vars_of assm) bound_vars) assms
                   fun safe genuine =
                     the_default I (Option.map mk_closure (try lookup x)) (rec_call genuine)
                in
                  mk_test (remove (op =) x (vars_of assm),
                    mk_let safe f (try lookup x) lhs
                      (mk_smart_test_term' concl (union (op =) (vars_of assm) bound_vars) assms) genuine)
    
                end
          | mk_equality_term (lhs, t) c (assm, assms) =
              if is_constrt (strip_comb t) then
                let
                  val (constr, args) = strip_comb t
                  val T = fastype_of t
                  val vars =
                    map Free
                      (Variable.variant_frees ctxt (concl :: assms)
                        (map (fn t => ("x", fastype_of t)) args))
                  val varnames = map (fst o dest_Free) vars
                  val dummy_var =
                    Free (singleton
                      (Variable.variant_frees ctxt (concl :: assms @ vars)) ("dummy", T))
                  val new_assms = map HOLogic.mk_eq (vars ~~ args)
                  val bound_vars' = union (op =) (vars_of lhs) (union (op =) varnames bound_vars)
                  val cont_t = mk_smart_test_term' concl bound_vars' (new_assms @ assms) genuine
                in
                  mk_test (vars_of lhs,
                    Case_Translation.make_case ctxt Case_Translation.Quiet Name.context lhs
                      [(list_comb (constr, vars), cont_t), (dummy_var, none_t)])
                end
              else c (assm, assms)
        fun default (assm, assms) =
          mk_test
            (vars_of assm,
              mk_if (HOLogic.mk_not assm, none_t,
                mk_smart_test_term' concl (union (op =) (vars_of assm) bound_vars) assms) genuine)
      in
        (case assms of
          [] => mk_test (vars_of concl, mk_if (concl, none_t, return) genuine)
        | assm :: assms =>
            if Config.get ctxt optimise_equality then
              (case try HOLogic.dest_eq assm of
                SOME (lhs, rhs) =>
                  mk_equality_term (lhs, rhs) (mk_equality_term (rhs, lhs) default) (assm, assms)
              | NONE => default (assm, assms))
            else default (assm, assms))
      end
    val mk_smart_test_term =
      Quickcheck_Common.strip_imp #> (fn (assms, concl) => mk_smart_test_term' concl [] assms true)
  in if Config.get ctxt smart_quantifier then mk_smart_test_term else mk_naive_test_term end

fun mk_fast_generator_expr ctxt (t, eval_terms) =
  let
    val ctxt' = Proof_Context.augment t ctxt
    val names = Term.add_free_names t []
    val frees = map Free (Term.add_frees t [])
    fun lookup v = the (AList.lookup (op =) (names ~~ frees) v)
    val ([depth_name], _) = Variable.variant_fixes ["depth"] ctxt'
    val depth = Free (depth_name, \<^typ>\<open>natural\<close>)
    fun return _ =
      \<^term>\<open>throw_Counterexample :: term list \<Rightarrow> unit\<close> $
        (HOLogic.mk_list \<^typ>\<open>term\<close>
          (map (fn t => HOLogic.mk_term_of (fastype_of t) t) (frees @ eval_terms)))
    fun mk_exhaustive_closure (free as Free (_, T)) t =
      Const (\<^const_name>\<open>fast_exhaustive\<close>, fast_exhaustiveT T) $ lambda free t $ depth
    val none_t = \<^term>\<open>()\<close>
    fun mk_safe_if (cond, then_t, else_t) genuine = mk_if (cond, then_t, else_t genuine)
    fun mk_let _ def v_opt t e = mk_let_expr (the_default def v_opt, t, e)
    val mk_test_term =
      mk_test_term lookup mk_exhaustive_closure mk_safe_if mk_let none_t return ctxt
  in lambda depth (\<^term>\<open>catch_Counterexample :: unit => term list option\<close> $ mk_test_term t) end

fun mk_unknown_term T =
  HOLogic.reflect_term (Const (\<^const_name>\<open>unknown\<close>, T))

fun mk_safe_term t =
  \<^term>\<open>Quickcheck_Random.catch_match :: term \<Rightarrow> term \<Rightarrow> term\<close> $
    (HOLogic.mk_term_of (fastype_of t) t) $ mk_unknown_term (fastype_of t)

fun mk_return t genuine =
  \<^term>\<open>Some :: bool \<times> term list \<Rightarrow> (bool \<times> term list) option\<close> $
    (HOLogic.pair_const \<^typ>\<open>bool\<close> \<^typ>\<open>term list\<close> $
      Quickcheck_Common.reflect_bool genuine $ t)

fun mk_generator_expr ctxt (t, eval_terms) =
  let
    val ctxt' = Proof_Context.augment t ctxt
    val names = Term.add_free_names t []
    val frees = map Free (Term.add_frees t [])
    fun lookup v = the (AList.lookup (op =) (names ~~ frees) v)
    val ([depth_name, genuine_only_name], _) =
      Variable.variant_fixes ["depth", "genuine_only"] ctxt'
    val depth = Free (depth_name, \<^typ>\<open>natural\<close>)
    val genuine_only = Free (genuine_only_name, \<^typ>\<open>bool\<close>)
    val return =
      mk_return (HOLogic.mk_list \<^typ>\<open>term\<close>
        (map (fn t => HOLogic.mk_term_of (fastype_of t) t) frees @ map mk_safe_term eval_terms))
    fun mk_exhaustive_closure (free as Free (_, T)) t =
      Const (\<^const_name>\<open>exhaustive\<close>, exhaustiveT T) $ lambda free t $ depth
    val none_t = Const (\<^const_name>\<open>None\<close>, resultT)
    val mk_if = Quickcheck_Common.mk_safe_if genuine_only none_t
    fun mk_let safe def v_opt t e =
      mk_safe_let_expr genuine_only none_t safe (the_default def v_opt, t, e)
    val mk_test_term = mk_test_term lookup mk_exhaustive_closure mk_if mk_let none_t return ctxt
  in lambda genuine_only (lambda depth (mk_test_term t)) end

fun mk_full_generator_expr ctxt (t, eval_terms) =
  let
    val thy = Proof_Context.theory_of ctxt
    val ctxt' = Proof_Context.augment t ctxt
    val names = Term.add_free_names t []
    val frees = map Free (Term.add_frees t [])
    val ([depth_name, genuine_only_name], ctxt'') =
      Variable.variant_fixes ["depth", "genuine_only"] ctxt'
    val (term_names, _) = Variable.variant_fixes (map (prefix "t_") names) ctxt''
    val depth = Free (depth_name, \<^typ>\<open>natural\<close>)
    val genuine_only = Free (genuine_only_name, \<^typ>\<open>bool\<close>)
    val term_vars = map (fn n => Free (n, \<^typ>\<open>unit \<Rightarrow> term\<close>)) term_names
    fun lookup v = the (AList.lookup (op =) (names ~~ (frees ~~ term_vars)) v)
    val return =
      mk_return
        (HOLogic.mk_list \<^typ>\<open>term\<close>
          (map (fn v => v $ \<^term>\<open>()\<close>) term_vars @ map mk_safe_term eval_terms))
    fun mk_exhaustive_closure (free as Free (_, T), term_var) t =
      if Sign.of_sort thy (T, \<^sort>\<open>check_all\<close>) then
        Const (\<^const_name>\<open>check_all\<close>, check_allT T) $
          (HOLogic.case_prod_const (T, \<^typ>\<open>unit \<Rightarrow> term\<close>, resultT) $
            lambda free (lambda term_var t))
      else
        Const (\<^const_name>\<open>full_exhaustive\<close>, full_exhaustiveT T) $
          (HOLogic.case_prod_const (T, \<^typ>\<open>unit \<Rightarrow> term\<close>, resultT) $
            lambda free (lambda term_var t)) $ depth
    val none_t = Const (\<^const_name>\<open>None\<close>, resultT)
    val mk_if = Quickcheck_Common.mk_safe_if genuine_only none_t
    fun mk_let safe _ (SOME (v, term_var)) t e =
          mk_safe_let_expr genuine_only none_t safe (v, t,
            e #> subst_free [(term_var, absdummy \<^typ>\<open>unit\<close> (mk_safe_term t))])
      | mk_let safe v NONE t e = mk_safe_let_expr genuine_only none_t safe (v, t, e)
    val mk_test_term = mk_test_term lookup mk_exhaustive_closure mk_if mk_let none_t return ctxt
  in lambda genuine_only (lambda depth (mk_test_term t)) end

fun mk_parametric_generator_expr mk_generator_expr =
  Quickcheck_Common.gen_mk_parametric_generator_expr
    ((mk_generator_expr,
      absdummy \<^typ>\<open>bool\<close> (absdummy \<^typ>\<open>natural\<close> (Const (\<^const_name>\<open>None\<close>, resultT)))),
      \<^typ>\<open>bool\<close> --> \<^typ>\<open>natural\<close> --> resultT)

fun mk_validator_expr ctxt t =
  let
    fun bounded_forallT T = (T --> \<^typ>\<open>bool\<close>) --> \<^typ>\<open>natural\<close> --> \<^typ>\<open>bool\<close>
    val ctxt' = Proof_Context.augment t ctxt
    val names = Term.add_free_names t []
    val frees = map Free (Term.add_frees t [])
    fun lookup v = the (AList.lookup (op =) (names ~~ frees) v)
    val ([depth_name], _) = Variable.variant_fixes ["depth"] ctxt'
    val depth = Free (depth_name, \<^typ>\<open>natural\<close>)
    fun mk_bounded_forall (Free (s, T)) t =
      Const (\<^const_name>\<open>bounded_forall\<close>, bounded_forallT T) $ lambda (Free (s, T)) t $ depth
    fun mk_safe_if (cond, then_t, else_t) genuine = mk_if (cond, then_t, else_t genuine)
    fun mk_let _ def v_opt t e = mk_let_expr (the_default def v_opt, t, e)
    val mk_test_term =
      mk_test_term lookup mk_bounded_forall mk_safe_if mk_let \<^term>\<open>True\<close> (K \<^term>\<open>False\<close>) ctxt
  in lambda depth (mk_test_term t) end

fun mk_bounded_forall_generator_expr ctxt (t, eval_terms) =
  let
    val frees = Term.add_free_names t []
    val dummy_term =
      \<^term>\<open>Code_Evaluation.Const (STR ''Pure.dummy_pattern'') (Typerep.Typerep (STR ''dummy'') [])\<close>
    val return =
      \<^term>\<open>Some :: term list => term list option\<close> $
        (HOLogic.mk_list \<^typ>\<open>term\<close> (replicate (length frees + length eval_terms) dummy_term))
    val wrap = absdummy \<^typ>\<open>bool\<close>
      (\<^term>\<open>If :: bool \<Rightarrow> term list option \<Rightarrow> term list option \<Rightarrow> term list option\<close> $
        Bound 0 $ \<^term>\<open>None :: term list option\<close> $ return)
  in HOLogic.mk_comp (wrap, mk_validator_expr ctxt t) end


(** generator compilation **)

structure Data = Proof_Data
(
  type T =
    (unit -> Code_Numeral.natural -> bool -> Code_Numeral.natural -> (bool * term list) option) *
    (unit -> (Code_Numeral.natural -> term list option) list) *
    (unit -> (Code_Numeral.natural -> bool) list)
  val empty: T =
   (fn () => raise Fail "counterexample",
    fn () => raise Fail "counterexample_batch",
    fn () => raise Fail "validator_batch")
  fun init _ = empty
)

val get_counterexample = #1 o Data.get
val get_counterexample_batch = #2 o Data.get
val get_validator_batch = #3 o Data.get

val put_counterexample = Data.map o @{apply 3(1)} o K
val put_counterexample_batch = Data.map o @{apply 3(2)} o K
val put_validator_batch = Data.map o @{apply 3(3)} o K

val target = "Quickcheck"

fun compile_generator_expr_raw ctxt ts =
  let
    val mk_generator_expr =
      if Config.get ctxt fast then mk_fast_generator_expr
      else if Config.get ctxt bounded_forall then mk_bounded_forall_generator_expr
      else if Config.get ctxt full_support then mk_full_generator_expr else mk_generator_expr
    val t' = mk_parametric_generator_expr mk_generator_expr ctxt ts
    val compile =
      Code_Runtime.dynamic_value_strict
        (get_counterexample, put_counterexample, "Exhaustive_Generators.put_counterexample")
        ctxt (SOME target)
        (fn proc => fn g => fn card => fn genuine_only => fn size =>
          g card genuine_only size
          |> (Option.map o apsnd o map) proc) t' []
  in
    fn genuine_only => fn [card, size] =>
      rpair NONE (compile card genuine_only size
      |> (if Config.get ctxt quickcheck_pretty then
          Option.map (apsnd (map Quickcheck_Common.post_process_term)) else I))
  end

fun compile_generator_expr ctxt ts =
  let val compiled = compile_generator_expr_raw ctxt ts in
    fn genuine_only => fn [card, size] =>
      compiled genuine_only
        [Code_Numeral.natural_of_integer card, Code_Numeral.natural_of_integer size]
  end

fun compile_generator_exprs_raw ctxt ts =
  let
    val ts' = map (fn t => mk_generator_expr ctxt (t, [])) ts
    val compiles =
      Code_Runtime.dynamic_value_strict
        (get_counterexample_batch, put_counterexample_batch,
          "Exhaustive_Generators.put_counterexample_batch")
        ctxt (SOME target) (fn proc => map (fn g => g #> (Option.map o map) proc))
        (HOLogic.mk_list \<^typ>\<open>natural \<Rightarrow> term list option\<close> ts') []
  in
    map (fn compile => fn size =>
      compile size |> (Option.map o map) Quickcheck_Common.post_process_term) compiles
  end

fun compile_generator_exprs ctxt ts =
  compile_generator_exprs_raw ctxt ts
  |> map (fn f => fn size => f (Code_Numeral.natural_of_integer size))

fun compile_validator_exprs_raw ctxt ts =
  let val ts' = map (mk_validator_expr ctxt) ts in
    Code_Runtime.dynamic_value_strict
      (get_validator_batch, put_validator_batch, "Exhaustive_Generators.put_validator_batch")
      ctxt (SOME target) (K I) (HOLogic.mk_list \<^typ>\<open>natural \<Rightarrow> bool\<close> ts') []
  end

fun compile_validator_exprs ctxt ts =
  compile_validator_exprs_raw ctxt ts
  |> map (fn f => fn size => f (Code_Numeral.natural_of_integer size))

fun size_matters_for thy Ts = not (forall (fn T => Sign.of_sort thy (T, \<^sort>\<open>check_all\<close>)) Ts)

val test_goals =
  Quickcheck_Common.generator_test_goal_terms
    ("exhaustive", (size_matters_for, compile_generator_expr))


(* setup *)

val setup_exhaustive_datatype_interpretation =
  Quickcheck_Common.datatype_interpretation \<^plugin>\<open>quickcheck_exhaustive\<close>
    (\<^sort>\<open>exhaustive\<close>, instantiate_exhaustive_datatype)

val setup_bounded_forall_datatype_interpretation =
  BNF_LFP_Compat.interpretation \<^plugin>\<open>quickcheck_bounded_forall\<close> Quickcheck_Common.compat_prefs
    (Quickcheck_Common.ensure_sort
       (((\<^sort>\<open>type\<close>, \<^sort>\<open>type\<close>), \<^sort>\<open>bounded_forall\<close>),
       (fn thy => BNF_LFP_Compat.the_descr thy Quickcheck_Common.compat_prefs,
        instantiate_bounded_forall_datatype)))

val active = Attrib.setup_config_bool \<^binding>\<open>quickcheck_exhaustive_active\<close> (K true)

val _ =
  Theory.setup
   (Quickcheck_Common.datatype_interpretation \<^plugin>\<open>quickcheck_full_exhaustive\<close>
      (\<^sort>\<open>full_exhaustive\<close>, instantiate_full_exhaustive_datatype)
    #> Context.theory_map (Quickcheck.add_tester ("exhaustive", (active, test_goals)))
    #> Context.theory_map (Quickcheck.add_batch_generator ("exhaustive", compile_generator_exprs))
    #> Context.theory_map (Quickcheck.add_batch_validator ("exhaustive", compile_validator_exprs)))

end