src/HOL/Smallcheck.thy
author bulwahn
Fri, 17 Dec 2010 12:14:18 +0100
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adding exhaustive tester instances for numeric types: code_numeral, nat, rat and real
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(* Author: Lukas Bulwahn, TU Muenchen *)
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header {* Another simple counterexample generator *}
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theory Smallcheck
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imports Quickcheck
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uses ("Tools/smallvalue_generators.ML")
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begin
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subsection {* basic operations for generators *}
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definition orelse :: "'a option => 'a option => 'a option" (infixr "orelse" 55)
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where
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  [code_unfold]: "x orelse y = (case x of Some x' => Some x' | None => y)"
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subsection {* small value generator type classes *}
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class small = term_of +
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fixes small :: "('a \<Rightarrow> term list option) \<Rightarrow> code_numeral \<Rightarrow> term list option"
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instantiation unit :: small
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begin
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definition "small f d = f ()"
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instance ..
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end
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instantiation int :: small
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begin
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function small' :: "(int => term list option) => int => int => term list option"
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where "small' f d i = (if d < i then None else (case f i of Some t => Some t | None => small' f d (i + 1)))"
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by pat_completeness auto
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termination 
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  by (relation "measure (%(_, d, i). nat (d + 1 - i))") auto
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definition "small f d = small' f (Code_Numeral.int_of d) (- (Code_Numeral.int_of d))"
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instance ..
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end
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instantiation prod :: (small, small) small
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begin
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definition
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  "small f d = small (%x. small (%y. f (x, y)) d) d"
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instance ..
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end
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subsection {* full small value generator type classes *}
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class full_small = term_of +
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fixes full_small :: "('a * (unit => term) \<Rightarrow> term list option) \<Rightarrow> code_numeral \<Rightarrow> term list option"
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instantiation unit :: full_small
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begin
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definition "full_small f d = f (Code_Evaluation.valtermify ())"
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instance ..
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end
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instantiation code_numeral :: full_small
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begin
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function full_small_code_numeral' :: "(code_numeral * (unit => term) => term list option) => code_numeral => code_numeral => term list option"
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  where "full_small_code_numeral' f d i = (if d < i then None else (case f (i, %_. Code_Evaluation.term_of i) of Some t => Some t | None => full_small_code_numeral' f d (i + 1)))"
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by pat_completeness auto
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termination 
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  by (relation "measure (%(_, d, i). Code_Numeral.nat_of (d + 1 - i))") auto
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definition "full_small f d = full_small_code_numeral' f d 0"
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instance ..
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end
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instantiation nat :: full_small
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begin
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definition "full_small f d = full_small (%(x, xt). f (Code_Numeral.nat_of x, %_. Code_Evaluation.term_of (Code_Numeral.nat_of x))) d"
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instance ..
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end
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instantiation int :: full_small
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begin
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function full_small' :: "(int * (unit => term) => term list option) => int => int => term list option"
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  where "full_small' f d i = (if d < i then None else (case f (i, %_. Code_Evaluation.term_of i) of Some t => Some t | None => full_small' f d (i + 1)))"
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by pat_completeness auto
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termination 
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  by (relation "measure (%(_, d, i). nat (d + 1 - i))") auto
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definition "full_small f d = full_small' f (Code_Numeral.int_of d) (- (Code_Numeral.int_of d))"
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instance ..
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end
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instantiation prod :: (full_small, full_small) full_small
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begin
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definition
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  "full_small f d = full_small (%(x, t1). full_small (%(y, t2). f ((x, y),
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    %u. Code_Evaluation.App (Code_Evaluation.App (Code_Evaluation.term_of (Pair :: 'a => 'b => ('a * 'b))) (t1 ())) (t2 ()))) d) d"
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instance ..
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end
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instantiation "fun" :: ("{equal, full_small}", full_small) full_small
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begin
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fun full_small_fun' :: "(('a => 'b) * (unit => term) => term list option) => code_numeral => code_numeral => term list option"
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where
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  "full_small_fun' f i d = (if i > 1 then
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    full_small (%(a, at). full_small (%(b, bt).
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      full_small_fun' (%(g, gt). f (g(a := b),
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        (%_. let T1 = (Typerep.typerep (TYPE('a)));
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                 T2 = (Typerep.typerep (TYPE('b)))
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             in
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               Code_Evaluation.App (Code_Evaluation.App (Code_Evaluation.App
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                 (Code_Evaluation.Const (STR ''Fun.fun_upd'')
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                    (Typerep.Typerep (STR ''fun'') [Typerep.Typerep (STR ''fun'') [T1, T2],
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                       Typerep.Typerep (STR ''fun'') [T1, Typerep.Typerep (STR ''fun'') [T2, Typerep.Typerep (STR ''fun'') [T1, T2]]]]))
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               (gt ())) (at ())) (bt ())))) (i - 1) d) d) d
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  else (if i > 0 then
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    full_small (%(b, t). f (%_. b, %_. Code_Evaluation.Abs (STR ''x'') (Typerep.typerep TYPE('a)) (t ()))) d else None))"
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definition full_small_fun :: "(('a => 'b) * (unit => term) => term list option) => code_numeral => term list option"
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where
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  "full_small_fun f d = full_small_fun' f d d" 
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instance ..
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end
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subsubsection {* A smarter enumeration scheme for functions over finite datatypes *}
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class check_all = enum + term_of +
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  fixes check_all :: "('a * (unit \<Rightarrow> term) \<Rightarrow> term list option) \<Rightarrow> term list option"
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  fixes enum_term_of :: "'a itself \<Rightarrow> unit \<Rightarrow> term list"
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fun check_all_n_lists :: "(('a :: check_all) list * (unit \<Rightarrow> term list) \<Rightarrow> term list option) \<Rightarrow> code_numeral \<Rightarrow> term list option"
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where
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  "check_all_n_lists f n =
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     (if n = 0 then f ([], (%_. [])) else check_all (%(x, xt). check_all_n_lists (%(xs, xst). f ((x # xs), (%_. (xt () # xst ())))) (n - 1)))"
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definition mk_map_term :: " (unit \<Rightarrow> typerep) \<Rightarrow> (unit \<Rightarrow> typerep) \<Rightarrow> (unit \<Rightarrow> term list) \<Rightarrow> (unit \<Rightarrow> term list) \<Rightarrow> unit \<Rightarrow> term"
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where
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  "mk_map_term T1 T2 domm rng =
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     (%_. let T1 = T1 ();
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              T2 = T2 ();
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              update_term = (%g (a, b).
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                Code_Evaluation.App (Code_Evaluation.App (Code_Evaluation.App
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                 (Code_Evaluation.Const (STR ''Fun.fun_upd'')
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                   (Typerep.Typerep (STR ''fun'') [Typerep.Typerep (STR ''fun'') [T1, T2],
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                      Typerep.Typerep (STR ''fun'') [T1,
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                        Typerep.Typerep (STR ''fun'') [T2, Typerep.Typerep (STR ''fun'') [T1, T2]]]]))
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                        g) a) b)
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          in
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             List.foldl update_term (Code_Evaluation.Abs (STR ''x'') T1 (Code_Evaluation.Const (STR ''HOL.undefined'') T2)) (zip (domm ()) (rng ())))"
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instantiation "fun" :: ("{equal, check_all}", check_all) check_all
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begin
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definition
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  "check_all f =
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    (let
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      mk_term = mk_map_term (%_. Typerep.typerep (TYPE('a))) (%_. Typerep.typerep (TYPE('b))) (enum_term_of (TYPE('a)));
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      enum = (Enum.enum :: 'a list)
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    in check_all_n_lists (\<lambda>(ys, yst). f (the o map_of (zip enum ys), mk_term yst)) (Code_Numeral.of_nat (length enum)))"
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definition enum_term_of_fun :: "('a => 'b) itself => unit => term list"
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where
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  "enum_term_of_fun = (%_ _. let
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    enum_term_of_a = enum_term_of (TYPE('a));
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    mk_term = mk_map_term (%_. Typerep.typerep (TYPE('a))) (%_. Typerep.typerep (TYPE('b))) enum_term_of_a
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  in map (%ys. mk_term (%_. ys) ()) (Enum.n_lists (length (enum_term_of_a ())) (enum_term_of (TYPE('b)) ())))"
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instance ..
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end
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instantiation unit :: check_all
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begin
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definition
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  "check_all f = f (Code_Evaluation.valtermify ())"
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definition enum_term_of_unit :: "unit itself => unit => term list"
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where
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  "enum_term_of_unit = (%_ _. [Code_Evaluation.term_of ()])"
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instance ..
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end
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instantiation bool :: check_all
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begin
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definition
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  "check_all f = (case f (Code_Evaluation.valtermify False) of Some x' \<Rightarrow> Some x' | None \<Rightarrow> f (Code_Evaluation.valtermify True))"
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definition enum_term_of_bool :: "bool itself => unit => term list"
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where
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  "enum_term_of_bool = (%_ _. map Code_Evaluation.term_of (Enum.enum :: bool list))"
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instance ..
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end
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instantiation prod :: (check_all, check_all) check_all
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begin
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definition
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  "check_all f = check_all (%(x, t1). check_all (%(y, t2). f ((x, y), %_. Code_Evaluation.App (Code_Evaluation.App (Code_Evaluation.term_of (Pair :: 'a => 'b => ('a * 'b))) (t1 ())) (t2 ()))))"
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definition enum_term_of_prod :: "('a * 'b) itself => unit => term list"
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where
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  "enum_term_of_prod = (%_ _. map (%(x, y). Code_Evaluation.App (Code_Evaluation.App (Code_Evaluation.term_of (Pair :: 'a => 'b => ('a * 'b))) x) y) (Enum.product (enum_term_of (TYPE('a)) ()) (enum_term_of (TYPE('b)) ())))"
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instance ..
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end
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instantiation sum :: (check_all, check_all) check_all
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begin
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definition
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  "check_all f = (case check_all (%(a, t). f (Inl a, %_. Code_Evaluation.App (Code_Evaluation.term_of (Inl :: 'a => 'a + 'b)) (t ()))) of Some x' => Some x'
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             | None => check_all (%(b, t). f (Inr b, %_. Code_Evaluation.App (Code_Evaluation.term_of (Inr :: 'b => 'a + 'b)) (t ()))))"
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definition enum_term_of_sum :: "('a + 'b) itself => unit => term list"
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where
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  "enum_term_of_sum = (%_ _. map (Code_Evaluation.App (Code_Evaluation.term_of (Inl :: 'a => ('a + 'b)))) (enum_term_of (TYPE('a)) ()) @
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     map (Code_Evaluation.App (Code_Evaluation.term_of (Inr :: 'b => ('a + 'b)))) (enum_term_of (TYPE('b)) ()))"
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instance ..
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end
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instantiation nibble :: check_all
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begin
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definition
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  "check_all f =
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    f (Code_Evaluation.valtermify Nibble0) orelse
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    f (Code_Evaluation.valtermify Nibble1) orelse
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    f (Code_Evaluation.valtermify Nibble2) orelse
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    f (Code_Evaluation.valtermify Nibble3) orelse
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    f (Code_Evaluation.valtermify Nibble4) orelse
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    f (Code_Evaluation.valtermify Nibble5) orelse
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    f (Code_Evaluation.valtermify Nibble6) orelse
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    f (Code_Evaluation.valtermify Nibble7) orelse
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    f (Code_Evaluation.valtermify Nibble8) orelse
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    f (Code_Evaluation.valtermify Nibble9) orelse
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    f (Code_Evaluation.valtermify NibbleA) orelse
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    f (Code_Evaluation.valtermify NibbleB) orelse
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    f (Code_Evaluation.valtermify NibbleC) orelse
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    f (Code_Evaluation.valtermify NibbleD) orelse
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    f (Code_Evaluation.valtermify NibbleE) orelse
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    f (Code_Evaluation.valtermify NibbleF)"
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definition enum_term_of_nibble :: "nibble itself => unit => term list"
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where
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  "enum_term_of_nibble = (%_ _. map Code_Evaluation.term_of (Enum.enum :: nibble list))"
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instance ..
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end
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instantiation char :: check_all
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begin
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definition
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  "check_all f = check_all (%(x, t1). check_all (%(y, t2). f (Char x y, %_. Code_Evaluation.App (Code_Evaluation.App (Code_Evaluation.term_of Char) (t1 ())) (t2 ()))))"
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definition enum_term_of_char :: "char itself => unit => term list"
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where
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  "enum_term_of_char = (%_ _. map Code_Evaluation.term_of (Enum.enum :: char list))"
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instance ..
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end
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instantiation option :: (check_all) check_all
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begin
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definition
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  "check_all f = f (Code_Evaluation.valtermify (None :: 'a option)) orelse check_all (%(x, t). f (Some x, %_. Code_Evaluation.App
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    (Code_Evaluation.Const (STR ''Option.option.Some'')
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      (Typerep.Typerep (STR ''fun'') [Typerep.typerep TYPE('a),  Typerep.Typerep (STR ''Option.option'') [Typerep.typerep TYPE('a)]])) (t ())))"
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definition enum_term_of_option :: "'a option itself => unit => term list"
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where
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  "enum_term_of_option = (% _ _. (Code_Evaluation.term_of (None :: 'a option)) # (map (Code_Evaluation.App (Code_Evaluation.term_of (Some :: 'a => 'a option))) (enum_term_of (TYPE('a)) ())))"
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instance ..
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end
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instantiation Enum.finite_1 :: check_all
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begin
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definition
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  "check_all f = f (Code_Evaluation.valtermify Enum.finite_1.a\<^isub>1)"
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definition enum_term_of_finite_1 :: "Enum.finite_1 itself => unit => term list"
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where
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  "enum_term_of_finite_1 = (%_ _. [Code_Evaluation.term_of Enum.finite_1.a\<^isub>1])"
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instance ..
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end
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instantiation Enum.finite_2 :: check_all
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begin
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definition
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  "check_all f = (case f (Code_Evaluation.valtermify Enum.finite_2.a\<^isub>1) of Some x' \<Rightarrow> Some x' | None \<Rightarrow> f (Code_Evaluation.valtermify Enum.finite_2.a\<^isub>2))"
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definition enum_term_of_finite_2 :: "Enum.finite_2 itself => unit => term list"
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where
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  "enum_term_of_finite_2 = (%_ _. map Code_Evaluation.term_of (Enum.enum :: Enum.finite_2 list))"
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instance ..
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end
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instantiation Enum.finite_3 :: check_all
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begin
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definition
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  "check_all f = (case f (Code_Evaluation.valtermify Enum.finite_3.a\<^isub>1) of Some x' \<Rightarrow> Some x' | None \<Rightarrow> (case f (Code_Evaluation.valtermify Enum.finite_3.a\<^isub>2) of Some x' \<Rightarrow> Some x' | None \<Rightarrow> f (Code_Evaluation.valtermify Enum.finite_3.a\<^isub>3)))"
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definition enum_term_of_finite_3 :: "Enum.finite_3 itself => unit => term list"
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where
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  "enum_term_of_finite_3 = (%_ _. map Code_Evaluation.term_of (Enum.enum :: Enum.finite_3 list))"
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instance ..
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end
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subsection {* Defining combinators for any first-order data type *}
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definition catch_match :: "term list option => term list option => term list option"
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where
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  [code del]: "catch_match t1 t2 = (SOME t. t = t1 \<or> t = t2)"
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code_const catch_match 
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  (SML "(_) handle Match => _")
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use "Tools/smallvalue_generators.ML"
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setup {* Smallvalue_Generators.setup *}
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declare [[quickcheck_tester = exhaustive]]
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hide_fact orelse_def catch_match_def
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no_notation orelse (infixr "orelse" 55)
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hide_const (open) orelse catch_match mk_map_term check_all_n_lists
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end