(* Author: Florian Haftmann, TU Muenchen *)
header {* A simple counterexample generator *}
theory Quickcheck
imports Random Code_Eval
uses ("Tools/quickcheck_generators.ML")
begin
notation fcomp (infixl "o>" 60)
notation scomp (infixl "o\<rightarrow>" 60)
subsection {* The @{text random} class *}
class random = typerep +
fixes random :: "code_numeral \<Rightarrow> Random.seed \<Rightarrow> ('a \<times> (unit \<Rightarrow> term)) \<times> Random.seed"
subsection {* Fundamental and numeric types*}
instantiation bool :: random
begin
definition
"random i = Random.range i o\<rightarrow>
(\<lambda>k. Pair (if (k div 2 = 0) then Code_Eval.valtermify True else Code_Eval.valtermify False))"
instance ..
end
instantiation itself :: (typerep) random
begin
definition random_itself :: "code_numeral \<Rightarrow> Random.seed \<Rightarrow> ('a itself \<times> (unit \<Rightarrow> term)) \<times> Random.seed" where
"random_itself _ = Pair (Code_Eval.valtermify TYPE('a))"
instance ..
end
instantiation char :: random
begin
definition
"random _ = Random.select chars o\<rightarrow> (\<lambda>c. Pair (c, \<lambda>u. Code_Eval.term_of c))"
instance ..
end
instantiation String.literal :: random
begin
definition
"random _ = Pair (STR [], \<lambda>u. Code_Eval.term_of (STR []))"
instance ..
end
instantiation nat :: random
begin
definition random_nat :: "code_numeral \<Rightarrow> Random.seed \<Rightarrow> (nat \<times> (unit \<Rightarrow> Code_Eval.term)) \<times> Random.seed" where
"random_nat i = Random.range (i + 1) o\<rightarrow> (\<lambda>k. Pair (
let n = Code_Numeral.nat_of k
in (n, \<lambda>_. Code_Eval.term_of n)))"
instance ..
end
instantiation int :: random
begin
definition
"random i = Random.range (2 * i + 1) o\<rightarrow> (\<lambda>k. Pair (
let j = (if k \<ge> i then Code_Numeral.int_of (k - i) else - Code_Numeral.int_of (i - k))
in (j, \<lambda>_. Code_Eval.term_of j)))"
instance ..
end
subsection {* Complex generators *}
text {* Towards @{typ "'a \<Rightarrow> 'b"} *}
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"
definition random_fun_lift :: "(Random.seed \<Rightarrow> ('b \<times> (unit \<Rightarrow> term)) \<times> Random.seed)
\<Rightarrow> Random.seed \<Rightarrow> (('a\<Colon>term_of \<Rightarrow> 'b\<Colon>typerep) \<times> (unit \<Rightarrow> term)) \<times> Random.seed" where
"random_fun_lift f = random_fun_aux TYPEREP('a) TYPEREP('b) (op =) Code_Eval.term_of f Random.split_seed"
instantiation "fun" :: ("{eq, term_of}", "{type, random}") random
begin
definition random_fun :: "code_numeral \<Rightarrow> Random.seed \<Rightarrow> (('a \<Rightarrow> 'b) \<times> (unit \<Rightarrow> term)) \<times> Random.seed" where
"random i = random_fun_lift (random i)"
instance ..
end
text {* Towards type copies and datatypes *}
definition collapse :: "('a \<Rightarrow> ('a \<Rightarrow> 'b \<times> 'a) \<times> 'a) \<Rightarrow> 'a \<Rightarrow> 'b \<times> 'a" where
"collapse f = (f o\<rightarrow> id)"
definition beyond :: "code_numeral \<Rightarrow> code_numeral \<Rightarrow> code_numeral" where
"beyond k l = (if l > k then l else 0)"
lemma beyond_zero:
"beyond k 0 = 0"
by (simp add: beyond_def)
lemma random_aux_rec:
fixes random_aux :: "code_numeral \<Rightarrow> 'a"
assumes "random_aux 0 = rhs 0"
and "\<And>k. random_aux (Suc_code_numeral k) = rhs (Suc_code_numeral k)"
shows "random_aux k = rhs k"
using assms by (rule code_numeral.induct)
use "Tools/quickcheck_generators.ML"
setup {* Quickcheck_Generators.setup *}
code_const random_fun_aux (Quickcheck "Quickcheck'_Generators.random'_fun")
-- {* With enough criminal energy this can be abused to derive @{prop False};
for this reason we use a distinguished target @{text Quickcheck}
not spoiling the regular trusted code generation *}
code_reserved Quickcheck Quickcheck_Generators
hide (open) const random collapse beyond random_fun_aux random_fun_lift
no_notation fcomp (infixl "o>" 60)
no_notation scomp (infixl "o\<rightarrow>" 60)
end