author  bulwahn 
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permissions  rwrr 
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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 {* 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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section {* 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 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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ML {* @{const_name "Pair"} *} 
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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))); T2 = (Typerep.typerep (TYPE('b))) in 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], 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 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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subsection {* Defining combinators for any firstorder 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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(* We do not activate smallcheck yet. 
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setup {* Smallvalue_Generators.setup *} 
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*) 
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hide_fact catch_match_def 
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hide_const (open) catch_match 
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end 