author  haftmann 
Fri, 15 May 2009 16:39:16 +0200  
changeset 31179  ced817160283 
parent 31153  6b31b143f18b 
permissions  rwrr 
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(* Author: Florian Haftmann, TU Muenchen *) 
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header {* A simple counterexample generator *} 

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theory Quickcheck 

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imports Main Real Random 
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begin 
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notation fcomp (infixl "o>" 60) 
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notation scomp (infixl "o\<rightarrow>" 60) 

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subsection {* The @{text random} class *} 
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class random = typerep + 
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fixes random :: "index \<Rightarrow> Random.seed \<Rightarrow> ('a \<times> (unit \<Rightarrow> term)) \<times> Random.seed" 
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subsection {* Quickcheck generator *} 
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ML {* 

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structure Quickcheck = 
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struct 

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open Quickcheck; 
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val eval_ref : (unit > int > int * int > term list option * (int * int)) option ref = ref NONE; 
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val target = "Quickcheck"; 
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fun mk_generator_expr thy prop tys = 
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let 
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val bound_max = length tys  1; 
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val bounds = map_index (fn (i, ty) => 

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(2 * (bound_max  i) + 1, 2 * (bound_max  i), 2 * i, ty)) tys; 

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val result = list_comb (prop, map (fn (i, _, _, _) => Bound i) bounds); 

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val terms = HOLogic.mk_list @{typ term} (map (fn (_, i, _, _) => Bound i $ @{term "()"}) bounds); 

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val check = @{term "If \<Colon> bool \<Rightarrow> term list option \<Rightarrow> term list option \<Rightarrow> term list option"} 
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$ result $ @{term "None \<Colon> term list option"} $ (@{term "Some \<Colon> term list \<Rightarrow> term list option "} $ terms); 
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val return = @{term "Pair \<Colon> term list option \<Rightarrow> Random.seed \<Rightarrow> term list option \<times> Random.seed"}; 
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fun liftT T sT = sT > HOLogic.mk_prodT (T, sT); 

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fun mk_termtyp ty = HOLogic.mk_prodT (ty, @{typ "unit \<Rightarrow> term"}); 
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fun mk_scomp T1 T2 sT f g = Const (@{const_name scomp}, 
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liftT T1 sT > (T1 > liftT T2 sT) > liftT T2 sT) $ f $ g; 

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fun mk_split ty = Sign.mk_const thy 
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(@{const_name split}, [ty, @{typ "unit \<Rightarrow> term"}, liftT @{typ "term list option"} @{typ Random.seed}]); 
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fun mk_scomp_split ty t t' = 
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mk_scomp (mk_termtyp ty) @{typ "term list option"} @{typ Random.seed} t 
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(mk_split ty $ Abs ("", ty, Abs ("", @{typ "unit \<Rightarrow> term"}, t'))); 
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fun mk_bindclause (_, _, i, ty) = mk_scomp_split ty 
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(Sign.mk_const thy (@{const_name random}, [ty]) $ Bound i); 
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in Abs ("n", @{typ index}, fold_rev mk_bindclause bounds (return $ check)) end; 

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fun compile_generator_expr thy t = 
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let 
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val tys = (map snd o fst o strip_abs) t; 
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val t' = mk_generator_expr thy t tys; 

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val f = Code_ML.eval (SOME target) ("Quickcheck.eval_ref", eval_ref) 
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(fn proc => fn g => fn s => g s #>> (Option.map o map) proc) thy t' []; 
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in f #> Random_Engine.run end; 
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end 

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*} 

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setup {* 
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Code_Target.extend_target (Quickcheck.target, (Code_ML.target_Eval, K I)) 
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#> Quickcheck.add_generator ("code", Quickcheck.compile_generator_expr o ProofContext.theory_of) 

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*} 
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subsection {* Fundamental types*} 
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definition (in term_syntax) 

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"termify_bool b = (if b then termify True else termify False)" 

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instantiation bool :: random 

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begin 

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definition 

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"random i = Random.range i o\<rightarrow> (\<lambda>k. Pair (termify_bool (k div 2 = 0)))" 

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instance .. 

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end 

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definition (in term_syntax) 

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"termify_itself TYPE('a\<Colon>typerep) = termify TYPE('a)" 

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instantiation itself :: (typerep) random 

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begin 

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definition random_itself :: "index \<Rightarrow> Random.seed \<Rightarrow> ('a itself \<times> (unit \<Rightarrow> term)) \<times> Random.seed" where 

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"random_itself _ = Pair (termify_itself TYPE('a))" 

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instance .. 

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end 

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text {* Type @{typ "'a \<Rightarrow> 'b"} *} 

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ML {* 

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structure Random_Engine = 

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struct 

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open Random_Engine; 

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fun random_fun (T1 : typ) (T2 : typ) (eq : 'a > 'a > bool) (term_of : 'a > term) 

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(random : Random_Engine.seed > ('b * (unit > term)) * Random_Engine.seed) 

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(random_split : Random_Engine.seed > Random_Engine.seed * Random_Engine.seed) 

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(seed : Random_Engine.seed) = 

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let 

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val (seed', seed'') = random_split seed; 

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val state = ref (seed', [], Const (@{const_name undefined}, T1 > T2)); 

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val fun_upd = Const (@{const_name fun_upd}, 

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(T1 > T2) > T1 > T2 > T1 > T2); 

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fun random_fun' x = 

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let 

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val (seed, fun_map, f_t) = ! state; 

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in case AList.lookup (uncurry eq) fun_map x 

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of SOME y => y 

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 NONE => let 

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val t1 = term_of x; 

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val ((y, t2), seed') = random seed; 

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val fun_map' = (x, y) :: fun_map; 

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val f_t' = fun_upd $ f_t $ t1 $ t2 (); 

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val _ = state := (seed', fun_map', f_t'); 

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in y end 

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end; 

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fun term_fun' () = #3 (! state); 

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in ((random_fun', term_fun'), seed'') end; 

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

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\<Rightarrow> Random.seed \<Rightarrow> (('a \<Rightarrow> 'b) \<times> (unit \<Rightarrow> term)) \<times> Random.seed" 

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code_const random_fun_aux (Quickcheck "Random'_Engine.random'_fun") 

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 {* With enough criminal energy this can be abused to derive @{prop False}; 

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for this reason we use a distinguished target @{text Quickcheck} 

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not spoiling the regular trusted code generation *} 

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instantiation "fun" :: ("{eq, term_of}", "{type, random}") random 

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begin 

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

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instance .. 

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end 

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code_reserved Quickcheck Random_Engine 

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subsection {* Numeric types *} 

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function (in term_syntax) termify_numeral :: "index \<Rightarrow> int \<times> (unit \<Rightarrow> term)" where 

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"termify_numeral k = (if k = 0 then termify Int.Pls 

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else (if k mod 2 = 0 then termify Int.Bit0 else termify Int.Bit1) <\<cdot>> termify_numeral (k div 2))" 

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by pat_completeness auto 

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declare (in term_syntax) termify_numeral.psimps [simp del] 

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termination termify_numeral by (relation "measure Code_Index.nat_of") 

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(simp_all add: index) 

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definition (in term_syntax) termify_int_number :: "index \<Rightarrow> int \<times> (unit \<Rightarrow> term)" where 

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"termify_int_number k = termify number_of <\<cdot>> termify_numeral k" 

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definition (in term_syntax) termify_nat_number :: "index \<Rightarrow> nat \<times> (unit \<Rightarrow> term)" where 

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"termify_nat_number k = (nat \<circ> number_of, snd (termify (number_of :: int \<Rightarrow> nat))) <\<cdot>> termify_numeral k" 

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declare termify_nat_number_def [simplified snd_conv, code] 

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instantiation nat :: random 

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begin 

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definition random_nat :: "index \<Rightarrow> Random.seed \<Rightarrow> (nat \<times> (unit \<Rightarrow> term)) \<times> Random.seed" where 

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"random_nat i = Random.range (i + 1) o\<rightarrow> (\<lambda>k. Pair (termify_nat_number k))" 

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instance .. 

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end 
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definition (in term_syntax) term_uminus :: "int \<times> (unit \<Rightarrow> term) \<Rightarrow> int \<times> (unit \<Rightarrow> term)" where 

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[code inline]: "term_uminus k = termify uminus <\<cdot>> k" 

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instantiation int :: random 

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begin 

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definition 

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"random i = Random.range (2 * i + 1) o\<rightarrow> (\<lambda>k. Pair (if k \<ge> i 

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then let j = k  i in termify_int_number j 

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else let j = i  k in term_uminus (termify_int_number j)))" 

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instance .. 

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end 

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definition (in term_syntax) term_fract :: "int \<times> (unit \<Rightarrow> term) \<Rightarrow> int \<times> (unit \<Rightarrow> term) \<Rightarrow> rat \<times> (unit \<Rightarrow> term)" where 

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[code inline]: "term_fract k l = termify Fract <\<cdot>> k <\<cdot>> l" 

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instantiation rat :: random 

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begin 

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definition 

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"random i = random i o\<rightarrow> (\<lambda>num. Random.range (i + 1) o\<rightarrow> (\<lambda>denom. Pair (term_fract num (termify_int_number denom))))" 

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instance .. 

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end 

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definition (in term_syntax) term_ratreal :: "rat \<times> (unit \<Rightarrow> term) \<Rightarrow> real \<times> (unit \<Rightarrow> term)" where 

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[code inline]: "term_ratreal k = termify Ratreal <\<cdot>> k" 

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instantiation real :: random 

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begin 

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definition 

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"random i = random i o\<rightarrow> (\<lambda>r. Pair (term_ratreal r))" 

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instance .. 

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end 

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no_notation fcomp (infixl "o>" 60) 

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no_notation scomp (infixl "o\<rightarrow>" 60) 

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end 