--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Quickcheck_Exhaustive.thy Fri Mar 11 15:21:12 2011 +0100
@@ -0,0 +1,420 @@
+(* Author: Lukas Bulwahn, TU Muenchen *)
+
+header {* Another simple counterexample generator *}
+
+theory Smallcheck
+imports Quickcheck
+uses ("Tools/smallvalue_generators.ML")
+begin
+
+subsection {* basic operations for generators *}
+
+definition orelse :: "'a option => 'a option => 'a option" (infixr "orelse" 55)
+where
+ [code_unfold]: "x orelse y = (case x of Some x' => Some x' | None => y)"
+
+subsection {* small value generator type classes *}
+
+class small = term_of +
+fixes small :: "('a \<Rightarrow> term list option) \<Rightarrow> code_numeral \<Rightarrow> term list option"
+
+instantiation unit :: small
+begin
+
+definition "small f d = f ()"
+
+instance ..
+
+end
+
+instantiation int :: small
+begin
+
+function small' :: "(int => term list option) => int => int => term list option"
+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)))"
+by pat_completeness auto
+
+termination
+ by (relation "measure (%(_, d, i). nat (d + 1 - i))") auto
+
+definition "small f d = small' f (Code_Numeral.int_of d) (- (Code_Numeral.int_of d))"
+
+instance ..
+
+end
+
+instantiation prod :: (small, small) small
+begin
+
+definition
+ "small f d = small (%x. small (%y. f (x, y)) d) d"
+
+instance ..
+
+end
+
+subsection {* full small value generator type classes *}
+
+class full_small = term_of +
+fixes full_small :: "('a * (unit => term) \<Rightarrow> term list option) \<Rightarrow> code_numeral \<Rightarrow> term list option"
+
+instantiation unit :: full_small
+begin
+
+definition "full_small f d = f (Code_Evaluation.valtermify ())"
+
+instance ..
+
+end
+
+instantiation code_numeral :: full_small
+begin
+
+function full_small_code_numeral' :: "(code_numeral * (unit => term) => term list option) => code_numeral => code_numeral => term list option"
+ 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)))"
+by pat_completeness auto
+
+termination
+ by (relation "measure (%(_, d, i). Code_Numeral.nat_of (d + 1 - i))") auto
+
+definition "full_small f d = full_small_code_numeral' f d 0"
+
+instance ..
+
+end
+
+instantiation nat :: full_small
+begin
+
+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"
+
+instance ..
+
+end
+
+instantiation int :: full_small
+begin
+
+function full_small' :: "(int * (unit => term) => term list option) => int => int => term list option"
+ 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)))"
+by pat_completeness auto
+
+termination
+ by (relation "measure (%(_, d, i). nat (d + 1 - i))") auto
+
+definition "full_small f d = full_small' f (Code_Numeral.int_of d) (- (Code_Numeral.int_of d))"
+
+instance ..
+
+end
+
+instantiation prod :: (full_small, full_small) full_small
+begin
+
+definition
+ "full_small f d = full_small (%(x, t1). full_small (%(y, t2). f ((x, y),
+ %u. let T1 = (Typerep.typerep (TYPE('a)));
+ T2 = (Typerep.typerep (TYPE('b)))
+ in Code_Evaluation.App (Code_Evaluation.App (
+ Code_Evaluation.Const (STR ''Product_Type.Pair'')
+ (Typerep.Typerep (STR ''fun'') [T1, Typerep.Typerep (STR ''fun'') [T2, Typerep.Typerep (STR ''Product_Type.prod'') [T1, T2]]]))
+ (t1 ())) (t2 ()))) d) d"
+
+instance ..
+
+end
+
+instantiation "fun" :: ("{equal, full_small}", full_small) full_small
+begin
+
+fun full_small_fun' :: "(('a => 'b) * (unit => term) => term list option) => code_numeral => code_numeral => term list option"
+where
+ "full_small_fun' f i d = (if i > 1 then
+ full_small (%(a, at). full_small (%(b, bt).
+ full_small_fun' (%(g, gt). f (g(a := b),
+ (%_. let T1 = (Typerep.typerep (TYPE('a)));
+ T2 = (Typerep.typerep (TYPE('b)))
+ in
+ Code_Evaluation.App (Code_Evaluation.App (Code_Evaluation.App
+ (Code_Evaluation.Const (STR ''Fun.fun_upd'')
+ (Typerep.Typerep (STR ''fun'') [Typerep.Typerep (STR ''fun'') [T1, T2],
+ Typerep.Typerep (STR ''fun'') [T1, Typerep.Typerep (STR ''fun'') [T2, Typerep.Typerep (STR ''fun'') [T1, T2]]]]))
+ (gt ())) (at ())) (bt ())))) (i - 1) d) d) d
+ else (if i > 0 then
+ full_small (%(b, t). f (%_. b, %_. Code_Evaluation.Abs (STR ''x'') (Typerep.typerep TYPE('a)) (t ()))) d else None))"
+
+definition full_small_fun :: "(('a => 'b) * (unit => term) => term list option) => code_numeral => term list option"
+where
+ "full_small_fun f d = full_small_fun' f d d"
+
+instance ..
+
+end
+
+subsubsection {* A smarter enumeration scheme for functions over finite datatypes *}
+
+
+class check_all = enum + term_of +
+ fixes check_all :: "('a * (unit \<Rightarrow> term) \<Rightarrow> term list option) \<Rightarrow> term list option"
+ fixes enum_term_of :: "'a itself \<Rightarrow> unit \<Rightarrow> term list"
+
+fun check_all_n_lists :: "(('a :: check_all) list * (unit \<Rightarrow> term list) \<Rightarrow> term list option) \<Rightarrow> code_numeral \<Rightarrow> term list option"
+where
+ "check_all_n_lists f n =
+ (if n = 0 then f ([], (%_. [])) else check_all (%(x, xt). check_all_n_lists (%(xs, xst). f ((x # xs), (%_. (xt () # xst ())))) (n - 1)))"
+
+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"
+where
+ "mk_map_term T1 T2 domm rng =
+ (%_. let T1 = T1 ();
+ T2 = T2 ();
+ update_term = (%g (a, b).
+ Code_Evaluation.App (Code_Evaluation.App (Code_Evaluation.App
+ (Code_Evaluation.Const (STR ''Fun.fun_upd'')
+ (Typerep.Typerep (STR ''fun'') [Typerep.Typerep (STR ''fun'') [T1, T2],
+ Typerep.Typerep (STR ''fun'') [T1,
+ Typerep.Typerep (STR ''fun'') [T2, Typerep.Typerep (STR ''fun'') [T1, T2]]]]))
+ g) a) b)
+ in
+ List.foldl update_term (Code_Evaluation.Abs (STR ''x'') T1 (Code_Evaluation.Const (STR ''HOL.undefined'') T2)) (zip (domm ()) (rng ())))"
+
+instantiation "fun" :: ("{equal, check_all}", check_all) check_all
+begin
+
+definition
+ "check_all f =
+ (let
+ mk_term = mk_map_term (%_. Typerep.typerep (TYPE('a))) (%_. Typerep.typerep (TYPE('b))) (enum_term_of (TYPE('a)));
+ enum = (Enum.enum :: 'a list)
+ 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)))"
+
+definition enum_term_of_fun :: "('a => 'b) itself => unit => term list"
+where
+ "enum_term_of_fun = (%_ _. let
+ enum_term_of_a = enum_term_of (TYPE('a));
+ mk_term = mk_map_term (%_. Typerep.typerep (TYPE('a))) (%_. Typerep.typerep (TYPE('b))) enum_term_of_a
+ in map (%ys. mk_term (%_. ys) ()) (Enum.n_lists (length (enum_term_of_a ())) (enum_term_of (TYPE('b)) ())))"
+
+instance ..
+
+end
+
+
+instantiation unit :: check_all
+begin
+
+definition
+ "check_all f = f (Code_Evaluation.valtermify ())"
+
+definition enum_term_of_unit :: "unit itself => unit => term list"
+where
+ "enum_term_of_unit = (%_ _. [Code_Evaluation.term_of ()])"
+
+instance ..
+
+end
+
+
+instantiation bool :: check_all
+begin
+
+definition
+ "check_all f = (case f (Code_Evaluation.valtermify False) of Some x' \<Rightarrow> Some x' | None \<Rightarrow> f (Code_Evaluation.valtermify True))"
+
+definition enum_term_of_bool :: "bool itself => unit => term list"
+where
+ "enum_term_of_bool = (%_ _. map Code_Evaluation.term_of (Enum.enum :: bool list))"
+
+instance ..
+
+end
+
+
+instantiation prod :: (check_all, check_all) check_all
+begin
+
+definition
+ "check_all f = check_all (%(x, t1). check_all (%(y, t2). f ((x, y),
+ %u. let T1 = (Typerep.typerep (TYPE('a)));
+ T2 = (Typerep.typerep (TYPE('b)))
+ in Code_Evaluation.App (Code_Evaluation.App (
+ Code_Evaluation.Const (STR ''Product_Type.Pair'')
+ (Typerep.Typerep (STR ''fun'') [T1, Typerep.Typerep (STR ''fun'') [T2, Typerep.Typerep (STR ''Product_Type.prod'') [T1, T2]]]))
+ (t1 ())) (t2 ()))))"
+
+definition enum_term_of_prod :: "('a * 'b) itself => unit => term list"
+where
+ "enum_term_of_prod = (%_ _. map (%(x, y).
+ let T1 = (Typerep.typerep (TYPE('a)));
+ T2 = (Typerep.typerep (TYPE('b)))
+ in Code_Evaluation.App (Code_Evaluation.App (
+ Code_Evaluation.Const (STR ''Product_Type.Pair'')
+ (Typerep.Typerep (STR ''fun'') [T1, Typerep.Typerep (STR ''fun'') [T2, Typerep.Typerep (STR ''Product_Type.prod'') [T1, T2]]])) x) y)
+ (Enum.product (enum_term_of (TYPE('a)) ()) (enum_term_of (TYPE('b)) ()))) "
+
+instance ..
+
+end
+
+
+instantiation sum :: (check_all, check_all) check_all
+begin
+
+definition
+ "check_all f = (case check_all (%(a, t). f (Inl a, %_.
+ let T1 = (Typerep.typerep (TYPE('a)));
+ T2 = (Typerep.typerep (TYPE('b)))
+ in Code_Evaluation.App (Code_Evaluation.Const (STR ''Sum_Type.Inl'')
+ (Typerep.Typerep (STR ''fun'') [T1, Typerep.Typerep (STR ''Sum_Type.sum'') [T1, T2]])) (t ()))) of Some x' => Some x'
+ | None => check_all (%(b, t). f (Inr b, %_. let
+ T1 = (Typerep.typerep (TYPE('a)));
+ T2 = (Typerep.typerep (TYPE('b)))
+ in Code_Evaluation.App (Code_Evaluation.Const (STR ''Sum_Type.Inr'')
+ (Typerep.Typerep (STR ''fun'') [T2, Typerep.Typerep (STR ''Sum_Type.sum'') [T1, T2]])) (t ()))))"
+
+definition enum_term_of_sum :: "('a + 'b) itself => unit => term list"
+where
+ "enum_term_of_sum = (%_ _.
+ let
+ T1 = (Typerep.typerep (TYPE('a)));
+ T2 = (Typerep.typerep (TYPE('b)))
+ in
+ map (Code_Evaluation.App (Code_Evaluation.Const (STR ''Sum_Type.Inl'')
+ (Typerep.Typerep (STR ''fun'') [T1, Typerep.Typerep (STR ''Sum_Type.sum'') [T1, T2]])))
+ (enum_term_of (TYPE('a)) ()) @
+ map (Code_Evaluation.App (Code_Evaluation.Const (STR ''Sum_Type.Inr'')
+ (Typerep.Typerep (STR ''fun'') [T2, Typerep.Typerep (STR ''Sum_Type.sum'') [T1, T2]])))
+ (enum_term_of (TYPE('b)) ()))"
+
+instance ..
+
+end
+
+instantiation nibble :: check_all
+begin
+
+definition
+ "check_all f =
+ f (Code_Evaluation.valtermify Nibble0) orelse
+ f (Code_Evaluation.valtermify Nibble1) orelse
+ f (Code_Evaluation.valtermify Nibble2) orelse
+ f (Code_Evaluation.valtermify Nibble3) orelse
+ f (Code_Evaluation.valtermify Nibble4) orelse
+ f (Code_Evaluation.valtermify Nibble5) orelse
+ f (Code_Evaluation.valtermify Nibble6) orelse
+ f (Code_Evaluation.valtermify Nibble7) orelse
+ f (Code_Evaluation.valtermify Nibble8) orelse
+ f (Code_Evaluation.valtermify Nibble9) orelse
+ f (Code_Evaluation.valtermify NibbleA) orelse
+ f (Code_Evaluation.valtermify NibbleB) orelse
+ f (Code_Evaluation.valtermify NibbleC) orelse
+ f (Code_Evaluation.valtermify NibbleD) orelse
+ f (Code_Evaluation.valtermify NibbleE) orelse
+ f (Code_Evaluation.valtermify NibbleF)"
+
+definition enum_term_of_nibble :: "nibble itself => unit => term list"
+where
+ "enum_term_of_nibble = (%_ _. map Code_Evaluation.term_of (Enum.enum :: nibble list))"
+
+instance ..
+
+end
+
+
+instantiation char :: check_all
+begin
+
+definition
+ "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 ()))))"
+
+definition enum_term_of_char :: "char itself => unit => term list"
+where
+ "enum_term_of_char = (%_ _. map Code_Evaluation.term_of (Enum.enum :: char list))"
+
+instance ..
+
+end
+
+
+instantiation option :: (check_all) check_all
+begin
+
+definition
+ "check_all f = f (Code_Evaluation.valtermify (None :: 'a option)) orelse check_all (%(x, t). f (Some x, %_. Code_Evaluation.App
+ (Code_Evaluation.Const (STR ''Option.option.Some'')
+ (Typerep.Typerep (STR ''fun'') [Typerep.typerep TYPE('a), Typerep.Typerep (STR ''Option.option'') [Typerep.typerep TYPE('a)]])) (t ())))"
+
+definition enum_term_of_option :: "'a option itself => unit => term list"
+where
+ "enum_term_of_option = (% _ _. (Code_Evaluation.term_of (None :: 'a option)) # (map (Code_Evaluation.App (Code_Evaluation.Const (STR ''Option.option.Some'')
+ (Typerep.Typerep (STR ''fun'') [Typerep.typerep TYPE('a), Typerep.Typerep (STR ''Option.option'') [Typerep.typerep TYPE('a)]]))) (enum_term_of (TYPE('a)) ())))"
+
+instance ..
+
+end
+
+
+instantiation Enum.finite_1 :: check_all
+begin
+
+definition
+ "check_all f = f (Code_Evaluation.valtermify Enum.finite_1.a\<^isub>1)"
+
+definition enum_term_of_finite_1 :: "Enum.finite_1 itself => unit => term list"
+where
+ "enum_term_of_finite_1 = (%_ _. [Code_Evaluation.term_of Enum.finite_1.a\<^isub>1])"
+
+instance ..
+
+end
+
+instantiation Enum.finite_2 :: check_all
+begin
+
+definition
+ "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))"
+
+definition enum_term_of_finite_2 :: "Enum.finite_2 itself => unit => term list"
+where
+ "enum_term_of_finite_2 = (%_ _. map Code_Evaluation.term_of (Enum.enum :: Enum.finite_2 list))"
+
+instance ..
+
+end
+
+instantiation Enum.finite_3 :: check_all
+begin
+
+definition
+ "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)))"
+
+definition enum_term_of_finite_3 :: "Enum.finite_3 itself => unit => term list"
+where
+ "enum_term_of_finite_3 = (%_ _. map Code_Evaluation.term_of (Enum.enum :: Enum.finite_3 list))"
+
+instance ..
+
+end
+
+
+
+subsection {* Defining combinators for any first-order data type *}
+
+definition catch_match :: "term list option => term list option => term list option"
+where
+ [code del]: "catch_match t1 t2 = (SOME t. t = t1 \<or> t = t2)"
+
+code_const catch_match
+ (SML "(_) handle Match => _")
+
+use "Tools/smallvalue_generators.ML"
+
+setup {* Smallvalue_Generators.setup *}
+
+declare [[quickcheck_tester = exhaustive]]
+
+hide_fact orelse_def catch_match_def
+no_notation orelse (infixr "orelse" 55)
+hide_const (open) orelse catch_match mk_map_term check_all_n_lists
+
+end
\ No newline at end of file
--- a/src/HOL/Smallcheck.thy Fri Mar 11 10:37:45 2011 +0100
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,420 +0,0 @@
-(* Author: Lukas Bulwahn, TU Muenchen *)
-
-header {* Another simple counterexample generator *}
-
-theory Smallcheck
-imports Quickcheck
-uses ("Tools/smallvalue_generators.ML")
-begin
-
-subsection {* basic operations for generators *}
-
-definition orelse :: "'a option => 'a option => 'a option" (infixr "orelse" 55)
-where
- [code_unfold]: "x orelse y = (case x of Some x' => Some x' | None => y)"
-
-subsection {* small value generator type classes *}
-
-class small = term_of +
-fixes small :: "('a \<Rightarrow> term list option) \<Rightarrow> code_numeral \<Rightarrow> term list option"
-
-instantiation unit :: small
-begin
-
-definition "small f d = f ()"
-
-instance ..
-
-end
-
-instantiation int :: small
-begin
-
-function small' :: "(int => term list option) => int => int => term list option"
-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)))"
-by pat_completeness auto
-
-termination
- by (relation "measure (%(_, d, i). nat (d + 1 - i))") auto
-
-definition "small f d = small' f (Code_Numeral.int_of d) (- (Code_Numeral.int_of d))"
-
-instance ..
-
-end
-
-instantiation prod :: (small, small) small
-begin
-
-definition
- "small f d = small (%x. small (%y. f (x, y)) d) d"
-
-instance ..
-
-end
-
-subsection {* full small value generator type classes *}
-
-class full_small = term_of +
-fixes full_small :: "('a * (unit => term) \<Rightarrow> term list option) \<Rightarrow> code_numeral \<Rightarrow> term list option"
-
-instantiation unit :: full_small
-begin
-
-definition "full_small f d = f (Code_Evaluation.valtermify ())"
-
-instance ..
-
-end
-
-instantiation code_numeral :: full_small
-begin
-
-function full_small_code_numeral' :: "(code_numeral * (unit => term) => term list option) => code_numeral => code_numeral => term list option"
- 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)))"
-by pat_completeness auto
-
-termination
- by (relation "measure (%(_, d, i). Code_Numeral.nat_of (d + 1 - i))") auto
-
-definition "full_small f d = full_small_code_numeral' f d 0"
-
-instance ..
-
-end
-
-instantiation nat :: full_small
-begin
-
-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"
-
-instance ..
-
-end
-
-instantiation int :: full_small
-begin
-
-function full_small' :: "(int * (unit => term) => term list option) => int => int => term list option"
- 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)))"
-by pat_completeness auto
-
-termination
- by (relation "measure (%(_, d, i). nat (d + 1 - i))") auto
-
-definition "full_small f d = full_small' f (Code_Numeral.int_of d) (- (Code_Numeral.int_of d))"
-
-instance ..
-
-end
-
-instantiation prod :: (full_small, full_small) full_small
-begin
-
-definition
- "full_small f d = full_small (%(x, t1). full_small (%(y, t2). f ((x, y),
- %u. let T1 = (Typerep.typerep (TYPE('a)));
- T2 = (Typerep.typerep (TYPE('b)))
- in Code_Evaluation.App (Code_Evaluation.App (
- Code_Evaluation.Const (STR ''Product_Type.Pair'')
- (Typerep.Typerep (STR ''fun'') [T1, Typerep.Typerep (STR ''fun'') [T2, Typerep.Typerep (STR ''Product_Type.prod'') [T1, T2]]]))
- (t1 ())) (t2 ()))) d) d"
-
-instance ..
-
-end
-
-instantiation "fun" :: ("{equal, full_small}", full_small) full_small
-begin
-
-fun full_small_fun' :: "(('a => 'b) * (unit => term) => term list option) => code_numeral => code_numeral => term list option"
-where
- "full_small_fun' f i d = (if i > 1 then
- full_small (%(a, at). full_small (%(b, bt).
- full_small_fun' (%(g, gt). f (g(a := b),
- (%_. let T1 = (Typerep.typerep (TYPE('a)));
- T2 = (Typerep.typerep (TYPE('b)))
- in
- Code_Evaluation.App (Code_Evaluation.App (Code_Evaluation.App
- (Code_Evaluation.Const (STR ''Fun.fun_upd'')
- (Typerep.Typerep (STR ''fun'') [Typerep.Typerep (STR ''fun'') [T1, T2],
- Typerep.Typerep (STR ''fun'') [T1, Typerep.Typerep (STR ''fun'') [T2, Typerep.Typerep (STR ''fun'') [T1, T2]]]]))
- (gt ())) (at ())) (bt ())))) (i - 1) d) d) d
- else (if i > 0 then
- full_small (%(b, t). f (%_. b, %_. Code_Evaluation.Abs (STR ''x'') (Typerep.typerep TYPE('a)) (t ()))) d else None))"
-
-definition full_small_fun :: "(('a => 'b) * (unit => term) => term list option) => code_numeral => term list option"
-where
- "full_small_fun f d = full_small_fun' f d d"
-
-instance ..
-
-end
-
-subsubsection {* A smarter enumeration scheme for functions over finite datatypes *}
-
-
-class check_all = enum + term_of +
- fixes check_all :: "('a * (unit \<Rightarrow> term) \<Rightarrow> term list option) \<Rightarrow> term list option"
- fixes enum_term_of :: "'a itself \<Rightarrow> unit \<Rightarrow> term list"
-
-fun check_all_n_lists :: "(('a :: check_all) list * (unit \<Rightarrow> term list) \<Rightarrow> term list option) \<Rightarrow> code_numeral \<Rightarrow> term list option"
-where
- "check_all_n_lists f n =
- (if n = 0 then f ([], (%_. [])) else check_all (%(x, xt). check_all_n_lists (%(xs, xst). f ((x # xs), (%_. (xt () # xst ())))) (n - 1)))"
-
-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"
-where
- "mk_map_term T1 T2 domm rng =
- (%_. let T1 = T1 ();
- T2 = T2 ();
- update_term = (%g (a, b).
- Code_Evaluation.App (Code_Evaluation.App (Code_Evaluation.App
- (Code_Evaluation.Const (STR ''Fun.fun_upd'')
- (Typerep.Typerep (STR ''fun'') [Typerep.Typerep (STR ''fun'') [T1, T2],
- Typerep.Typerep (STR ''fun'') [T1,
- Typerep.Typerep (STR ''fun'') [T2, Typerep.Typerep (STR ''fun'') [T1, T2]]]]))
- g) a) b)
- in
- List.foldl update_term (Code_Evaluation.Abs (STR ''x'') T1 (Code_Evaluation.Const (STR ''HOL.undefined'') T2)) (zip (domm ()) (rng ())))"
-
-instantiation "fun" :: ("{equal, check_all}", check_all) check_all
-begin
-
-definition
- "check_all f =
- (let
- mk_term = mk_map_term (%_. Typerep.typerep (TYPE('a))) (%_. Typerep.typerep (TYPE('b))) (enum_term_of (TYPE('a)));
- enum = (Enum.enum :: 'a list)
- 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)))"
-
-definition enum_term_of_fun :: "('a => 'b) itself => unit => term list"
-where
- "enum_term_of_fun = (%_ _. let
- enum_term_of_a = enum_term_of (TYPE('a));
- mk_term = mk_map_term (%_. Typerep.typerep (TYPE('a))) (%_. Typerep.typerep (TYPE('b))) enum_term_of_a
- in map (%ys. mk_term (%_. ys) ()) (Enum.n_lists (length (enum_term_of_a ())) (enum_term_of (TYPE('b)) ())))"
-
-instance ..
-
-end
-
-
-instantiation unit :: check_all
-begin
-
-definition
- "check_all f = f (Code_Evaluation.valtermify ())"
-
-definition enum_term_of_unit :: "unit itself => unit => term list"
-where
- "enum_term_of_unit = (%_ _. [Code_Evaluation.term_of ()])"
-
-instance ..
-
-end
-
-
-instantiation bool :: check_all
-begin
-
-definition
- "check_all f = (case f (Code_Evaluation.valtermify False) of Some x' \<Rightarrow> Some x' | None \<Rightarrow> f (Code_Evaluation.valtermify True))"
-
-definition enum_term_of_bool :: "bool itself => unit => term list"
-where
- "enum_term_of_bool = (%_ _. map Code_Evaluation.term_of (Enum.enum :: bool list))"
-
-instance ..
-
-end
-
-
-instantiation prod :: (check_all, check_all) check_all
-begin
-
-definition
- "check_all f = check_all (%(x, t1). check_all (%(y, t2). f ((x, y),
- %u. let T1 = (Typerep.typerep (TYPE('a)));
- T2 = (Typerep.typerep (TYPE('b)))
- in Code_Evaluation.App (Code_Evaluation.App (
- Code_Evaluation.Const (STR ''Product_Type.Pair'')
- (Typerep.Typerep (STR ''fun'') [T1, Typerep.Typerep (STR ''fun'') [T2, Typerep.Typerep (STR ''Product_Type.prod'') [T1, T2]]]))
- (t1 ())) (t2 ()))))"
-
-definition enum_term_of_prod :: "('a * 'b) itself => unit => term list"
-where
- "enum_term_of_prod = (%_ _. map (%(x, y).
- let T1 = (Typerep.typerep (TYPE('a)));
- T2 = (Typerep.typerep (TYPE('b)))
- in Code_Evaluation.App (Code_Evaluation.App (
- Code_Evaluation.Const (STR ''Product_Type.Pair'')
- (Typerep.Typerep (STR ''fun'') [T1, Typerep.Typerep (STR ''fun'') [T2, Typerep.Typerep (STR ''Product_Type.prod'') [T1, T2]]])) x) y)
- (Enum.product (enum_term_of (TYPE('a)) ()) (enum_term_of (TYPE('b)) ()))) "
-
-instance ..
-
-end
-
-
-instantiation sum :: (check_all, check_all) check_all
-begin
-
-definition
- "check_all f = (case check_all (%(a, t). f (Inl a, %_.
- let T1 = (Typerep.typerep (TYPE('a)));
- T2 = (Typerep.typerep (TYPE('b)))
- in Code_Evaluation.App (Code_Evaluation.Const (STR ''Sum_Type.Inl'')
- (Typerep.Typerep (STR ''fun'') [T1, Typerep.Typerep (STR ''Sum_Type.sum'') [T1, T2]])) (t ()))) of Some x' => Some x'
- | None => check_all (%(b, t). f (Inr b, %_. let
- T1 = (Typerep.typerep (TYPE('a)));
- T2 = (Typerep.typerep (TYPE('b)))
- in Code_Evaluation.App (Code_Evaluation.Const (STR ''Sum_Type.Inr'')
- (Typerep.Typerep (STR ''fun'') [T2, Typerep.Typerep (STR ''Sum_Type.sum'') [T1, T2]])) (t ()))))"
-
-definition enum_term_of_sum :: "('a + 'b) itself => unit => term list"
-where
- "enum_term_of_sum = (%_ _.
- let
- T1 = (Typerep.typerep (TYPE('a)));
- T2 = (Typerep.typerep (TYPE('b)))
- in
- map (Code_Evaluation.App (Code_Evaluation.Const (STR ''Sum_Type.Inl'')
- (Typerep.Typerep (STR ''fun'') [T1, Typerep.Typerep (STR ''Sum_Type.sum'') [T1, T2]])))
- (enum_term_of (TYPE('a)) ()) @
- map (Code_Evaluation.App (Code_Evaluation.Const (STR ''Sum_Type.Inr'')
- (Typerep.Typerep (STR ''fun'') [T2, Typerep.Typerep (STR ''Sum_Type.sum'') [T1, T2]])))
- (enum_term_of (TYPE('b)) ()))"
-
-instance ..
-
-end
-
-instantiation nibble :: check_all
-begin
-
-definition
- "check_all f =
- f (Code_Evaluation.valtermify Nibble0) orelse
- f (Code_Evaluation.valtermify Nibble1) orelse
- f (Code_Evaluation.valtermify Nibble2) orelse
- f (Code_Evaluation.valtermify Nibble3) orelse
- f (Code_Evaluation.valtermify Nibble4) orelse
- f (Code_Evaluation.valtermify Nibble5) orelse
- f (Code_Evaluation.valtermify Nibble6) orelse
- f (Code_Evaluation.valtermify Nibble7) orelse
- f (Code_Evaluation.valtermify Nibble8) orelse
- f (Code_Evaluation.valtermify Nibble9) orelse
- f (Code_Evaluation.valtermify NibbleA) orelse
- f (Code_Evaluation.valtermify NibbleB) orelse
- f (Code_Evaluation.valtermify NibbleC) orelse
- f (Code_Evaluation.valtermify NibbleD) orelse
- f (Code_Evaluation.valtermify NibbleE) orelse
- f (Code_Evaluation.valtermify NibbleF)"
-
-definition enum_term_of_nibble :: "nibble itself => unit => term list"
-where
- "enum_term_of_nibble = (%_ _. map Code_Evaluation.term_of (Enum.enum :: nibble list))"
-
-instance ..
-
-end
-
-
-instantiation char :: check_all
-begin
-
-definition
- "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 ()))))"
-
-definition enum_term_of_char :: "char itself => unit => term list"
-where
- "enum_term_of_char = (%_ _. map Code_Evaluation.term_of (Enum.enum :: char list))"
-
-instance ..
-
-end
-
-
-instantiation option :: (check_all) check_all
-begin
-
-definition
- "check_all f = f (Code_Evaluation.valtermify (None :: 'a option)) orelse check_all (%(x, t). f (Some x, %_. Code_Evaluation.App
- (Code_Evaluation.Const (STR ''Option.option.Some'')
- (Typerep.Typerep (STR ''fun'') [Typerep.typerep TYPE('a), Typerep.Typerep (STR ''Option.option'') [Typerep.typerep TYPE('a)]])) (t ())))"
-
-definition enum_term_of_option :: "'a option itself => unit => term list"
-where
- "enum_term_of_option = (% _ _. (Code_Evaluation.term_of (None :: 'a option)) # (map (Code_Evaluation.App (Code_Evaluation.Const (STR ''Option.option.Some'')
- (Typerep.Typerep (STR ''fun'') [Typerep.typerep TYPE('a), Typerep.Typerep (STR ''Option.option'') [Typerep.typerep TYPE('a)]]))) (enum_term_of (TYPE('a)) ())))"
-
-instance ..
-
-end
-
-
-instantiation Enum.finite_1 :: check_all
-begin
-
-definition
- "check_all f = f (Code_Evaluation.valtermify Enum.finite_1.a\<^isub>1)"
-
-definition enum_term_of_finite_1 :: "Enum.finite_1 itself => unit => term list"
-where
- "enum_term_of_finite_1 = (%_ _. [Code_Evaluation.term_of Enum.finite_1.a\<^isub>1])"
-
-instance ..
-
-end
-
-instantiation Enum.finite_2 :: check_all
-begin
-
-definition
- "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))"
-
-definition enum_term_of_finite_2 :: "Enum.finite_2 itself => unit => term list"
-where
- "enum_term_of_finite_2 = (%_ _. map Code_Evaluation.term_of (Enum.enum :: Enum.finite_2 list))"
-
-instance ..
-
-end
-
-instantiation Enum.finite_3 :: check_all
-begin
-
-definition
- "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)))"
-
-definition enum_term_of_finite_3 :: "Enum.finite_3 itself => unit => term list"
-where
- "enum_term_of_finite_3 = (%_ _. map Code_Evaluation.term_of (Enum.enum :: Enum.finite_3 list))"
-
-instance ..
-
-end
-
-
-
-subsection {* Defining combinators for any first-order data type *}
-
-definition catch_match :: "term list option => term list option => term list option"
-where
- [code del]: "catch_match t1 t2 = (SOME t. t = t1 \<or> t = t2)"
-
-code_const catch_match
- (SML "(_) handle Match => _")
-
-use "Tools/smallvalue_generators.ML"
-
-setup {* Smallvalue_Generators.setup *}
-
-declare [[quickcheck_tester = exhaustive]]
-
-hide_fact orelse_def catch_match_def
-no_notation orelse (infixr "orelse" 55)
-hide_const (open) orelse catch_match mk_map_term check_all_n_lists
-
-end
\ No newline at end of file