src/HOL/Library/Quickcheck.thy
 changeset 31179 ced817160283 parent 31153 6b31b143f18b
```--- a/src/HOL/Library/Quickcheck.thy	Fri May 15 16:39:15 2009 +0200
+++ b/src/HOL/Library/Quickcheck.thy	Fri May 15 16:39:16 2009 +0200
@@ -3,43 +3,22 @@
header {* A simple counterexample generator *}

theory Quickcheck
-imports Random Code_Eval Map
+imports Main Real Random
begin

+notation fcomp (infixl "o>" 60)
+notation scomp (infixl "o\<rightarrow>" 60)
+
+
subsection {* The @{text random} class *}

class random = typerep +
-  fixes random :: "index \<Rightarrow> seed \<Rightarrow> ('a \<times> (unit \<Rightarrow> term)) \<times> seed"
-
-text {* Type @{typ "'a itself"} *}
-
-instantiation itself :: ("{type, typerep}") random
-begin
-
-definition
-  "random _ = Pair (TYPE('a), \<lambda>u. Code_Eval.Const (STR ''TYPE'') TYPEREP('a))"
-
-instance ..
-
-end
+  fixes random :: "index \<Rightarrow> Random.seed \<Rightarrow> ('a \<times> (unit \<Rightarrow> term)) \<times> Random.seed"

subsection {* Quickcheck generator *}

ML {*
-structure StateMonad =
-struct
-
-fun liftT T sT = sT --> HOLogic.mk_prodT (T, sT);
-fun liftT' sT = sT --> sT;
-
-fun return T sT x = Const (@{const_name Pair}, T --> liftT T sT) \$ x;
-
-fun scomp T1 T2 sT f g = Const (@{const_name scomp},
-  liftT T1 sT --> (T1 --> liftT T2 sT) --> liftT T2 sT) \$ f \$ g;
-
-end;
-
structure Quickcheck =
struct

@@ -58,24 +37,26 @@
val terms = HOLogic.mk_list @{typ term} (map (fn (_, i, _, _) => Bound i \$ @{term "()"}) bounds);
val check = @{term "If \<Colon> bool \<Rightarrow> term list option \<Rightarrow> term list option \<Rightarrow> term list option"}
\$ result \$ @{term "None \<Colon> term list option"} \$ (@{term "Some \<Colon> term list \<Rightarrow> term list option "} \$ terms);
-    val return = @{term "Pair \<Colon> term list option \<Rightarrow> seed \<Rightarrow> term list option \<times> seed"};
+    val return = @{term "Pair \<Colon> term list option \<Rightarrow> Random.seed \<Rightarrow> term list option \<times> Random.seed"};
+    fun liftT T sT = sT --> HOLogic.mk_prodT (T, sT);
fun mk_termtyp ty = HOLogic.mk_prodT (ty, @{typ "unit \<Rightarrow> term"});
+    fun mk_scomp T1 T2 sT f g = Const (@{const_name scomp},
+      liftT T1 sT --> (T1 --> liftT T2 sT) --> liftT T2 sT) \$ f \$ g;
fun mk_split ty = Sign.mk_const thy
-      (@{const_name split}, [ty, @{typ "unit \<Rightarrow> term"}, StateMonad.liftT @{typ "term list option"} @{typ seed}]);
+      (@{const_name split}, [ty, @{typ "unit \<Rightarrow> term"}, liftT @{typ "term list option"} @{typ Random.seed}]);
fun mk_scomp_split ty t t' =
-      StateMonad.scomp (mk_termtyp ty) @{typ "term list option"} @{typ seed} t (*FIXME*)
+      mk_scomp (mk_termtyp ty) @{typ "term list option"} @{typ Random.seed} t
(mk_split ty \$ Abs ("", ty, Abs ("", @{typ "unit \<Rightarrow> term"}, t')));
fun mk_bindclause (_, _, i, ty) = mk_scomp_split ty
-      (Sign.mk_const thy (@{const_name random}, [ty]) \$ Bound i)
-    val t = fold_rev mk_bindclause bounds (return \$ check);
-  in Abs ("n", @{typ index}, t) end;
+      (Sign.mk_const thy (@{const_name random}, [ty]) \$ Bound i);
+  in Abs ("n", @{typ index}, fold_rev mk_bindclause bounds (return \$ check)) end;

fun compile_generator_expr thy t =
let
val tys = (map snd o fst o strip_abs) t;
val t' = mk_generator_expr thy t tys;
val f = Code_ML.eval (SOME target) ("Quickcheck.eval_ref", eval_ref)
-      (fn proc => fn g => fn s => g (s + 1) #>> (Option.map o map) proc) thy t' [];
+      (fn proc => fn g => fn s => g s #>> (Option.map o map) proc) thy t' [];
in f #> Random_Engine.run end;

end
@@ -87,7 +68,35 @@
*}

-subsection {* Type @{typ "'a \<Rightarrow> 'b"} *}
+subsection {* Fundamental types*}
+
+definition (in term_syntax)
+  "termify_bool b = (if b then termify True else termify False)"
+
+instantiation bool :: random
+begin
+
+definition
+  "random i = Random.range i o\<rightarrow> (\<lambda>k. Pair (termify_bool (k div 2 = 0)))"
+
+instance ..
+
+end
+
+definition (in term_syntax)
+  "termify_itself TYPE('a\<Colon>typerep) = termify TYPE('a)"
+
+instantiation itself :: (typerep) random
+begin
+
+definition random_itself :: "index \<Rightarrow> Random.seed \<Rightarrow> ('a itself \<times> (unit \<Rightarrow> term)) \<times> Random.seed" where
+  "random_itself _ = Pair (termify_itself TYPE('a))"
+
+instance ..
+
+end
+
+text {* Type @{typ "'a \<Rightarrow> 'b"} *}

ML {*
structure Random_Engine =
@@ -123,10 +132,9 @@
end
*}

-axiomatization
-  random_fun_aux :: "typerep \<Rightarrow> typerep \<Rightarrow> ('a \<Rightarrow> 'a \<Rightarrow> bool) \<Rightarrow> ('a \<Rightarrow> term)
-    \<Rightarrow> (seed \<Rightarrow> ('b \<times> (unit \<Rightarrow> term)) \<times> seed) \<Rightarrow> (seed \<Rightarrow> seed \<times> seed)
-    \<Rightarrow> seed \<Rightarrow> (('a \<Rightarrow> 'b) \<times> (unit \<Rightarrow> term)) \<times> seed"
+axiomatization random_fun_aux :: "typerep \<Rightarrow> typerep \<Rightarrow> ('a \<Rightarrow> 'a \<Rightarrow> bool) \<Rightarrow> ('a \<Rightarrow> term)
+  \<Rightarrow> (Random.seed \<Rightarrow> ('b \<times> (unit \<Rightarrow> term)) \<times> Random.seed) \<Rightarrow> (Random.seed \<Rightarrow> Random.seed \<times> Random.seed)
+  \<Rightarrow> Random.seed \<Rightarrow> (('a \<Rightarrow> 'b) \<times> (unit \<Rightarrow> term)) \<times> Random.seed"

code_const random_fun_aux (Quickcheck "Random'_Engine.random'_fun")
-- {* With enough criminal energy this can be abused to derive @{prop False};
@@ -136,8 +144,8 @@
instantiation "fun" :: ("{eq, term_of}", "{type, random}") random
begin

-definition random_fun :: "index \<Rightarrow> seed \<Rightarrow> (('a \<Rightarrow> 'b) \<times> (unit \<Rightarrow> term)) \<times> seed" where
-  "random n = random_fun_aux TYPEREP('a) TYPEREP('b) (op =) Code_Eval.term_of (random n) split_seed"
+definition random_fun :: "index \<Rightarrow> Random.seed \<Rightarrow> (('a \<Rightarrow> 'b) \<times> (unit \<Rightarrow> term)) \<times> Random.seed" where
+  "random n = random_fun_aux TYPEREP('a) TYPEREP('b) (op =) Code_Eval.term_of (random n) Random.split_seed"

instance ..

@@ -145,4 +153,80 @@

code_reserved Quickcheck Random_Engine

+
+subsection {* Numeric types *}
+
+function (in term_syntax) termify_numeral :: "index \<Rightarrow> int \<times> (unit \<Rightarrow> term)" where
+  "termify_numeral k = (if k = 0 then termify Int.Pls
+    else (if k mod 2 = 0 then termify Int.Bit0 else termify Int.Bit1) <\<cdot>> termify_numeral (k div 2))"
+  by pat_completeness auto
+
+declare (in term_syntax) termify_numeral.psimps [simp del]
+
+termination termify_numeral by (relation "measure Code_Index.nat_of")
+  (simp_all add: index)
+
+definition (in term_syntax) termify_int_number :: "index \<Rightarrow> int \<times> (unit \<Rightarrow> term)" where
+  "termify_int_number k = termify number_of <\<cdot>> termify_numeral k"
+
+definition (in term_syntax) termify_nat_number :: "index \<Rightarrow> nat \<times> (unit \<Rightarrow> term)" where
+  "termify_nat_number k = (nat \<circ> number_of, snd (termify (number_of :: int \<Rightarrow> nat))) <\<cdot>> termify_numeral k"
+
+declare termify_nat_number_def [simplified snd_conv, code]
+
+instantiation nat :: random
+begin
+
+definition random_nat :: "index \<Rightarrow> Random.seed \<Rightarrow> (nat \<times> (unit \<Rightarrow> term)) \<times> Random.seed" where
+  "random_nat i = Random.range (i + 1) o\<rightarrow> (\<lambda>k. Pair (termify_nat_number k))"
+
+instance ..
+
end
+
+definition (in term_syntax) term_uminus :: "int \<times> (unit \<Rightarrow> term) \<Rightarrow> int \<times> (unit \<Rightarrow> term)" where
+  [code inline]: "term_uminus k = termify uminus <\<cdot>> k"
+
+instantiation int :: random
+begin
+
+definition
+  "random i = Random.range (2 * i + 1) o\<rightarrow> (\<lambda>k. Pair (if k \<ge> i
+     then let j = k - i in termify_int_number j
+     else let j = i - k in term_uminus (termify_int_number j)))"
+
+instance ..
+
+end
+
+definition (in term_syntax) term_fract :: "int \<times> (unit \<Rightarrow> term) \<Rightarrow> int \<times> (unit \<Rightarrow> term) \<Rightarrow> rat \<times> (unit \<Rightarrow> term)" where
+  [code inline]: "term_fract k l = termify Fract <\<cdot>> k <\<cdot>> l"
+
+instantiation rat :: random
+begin
+
+definition
+  "random i = random i o\<rightarrow> (\<lambda>num. Random.range (i + 1) o\<rightarrow> (\<lambda>denom. Pair (term_fract num (termify_int_number denom))))"
+
+instance ..
+
+end
+
+definition (in term_syntax) term_ratreal :: "rat \<times> (unit \<Rightarrow> term) \<Rightarrow> real \<times> (unit \<Rightarrow> term)" where
+  [code inline]: "term_ratreal k = termify Ratreal <\<cdot>> k"
+
+instantiation real :: random
+begin
+
+definition
+  "random i = random i o\<rightarrow> (\<lambda>r. Pair (term_ratreal r))"
+
+instance ..
+
+end
+
+
+no_notation fcomp (infixl "o>" 60)
+no_notation scomp (infixl "o\<rightarrow>" 60)
+
+end```