author  bulwahn 
Mon, 08 Nov 2010 09:25:43 +0100  
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child 40639  f1f0e6adca0a 
permissions  rwrr 
40420
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(* Title: HOL/Tools/smallvalue_generators.ML 
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Author: Lukas Bulwahn, TU Muenchen 
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Generators for small values for various types. 
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*) 
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signature SMALLVALUE_GENERATORS = 
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sig 
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val ensure_smallvalue_datatype: Datatype.config > string list > theory > theory 
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val compile_generator_expr: 
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Proof.context > term > int > term list option * (bool list * bool) 
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val put_counterexample: (unit > int > term list option) 
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> Proof.context > Proof.context 
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val setup: theory > theory 
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end; 
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structure Smallvalue_Generators : SMALLVALUE_GENERATORS = 
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struct 
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(** general term functions **) 
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fun dest_funT (Type ("fun",[S, T])) = (S, T) 
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 dest_funT T = raise TYPE ("dest_funT", [T], []) 
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fun mk_fun_comp (t, u) = 
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let 
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val (_, B) = dest_funT (fastype_of t) 
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val (C, A) = dest_funT (fastype_of u) 
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in 
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Const(@{const_name "Fun.comp"}, (A > B) > (C > A) > C > B) $ t $ u 
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end; 
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fun mk_measure f = 
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let 
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val Type ("fun", [T, @{typ nat}]) = fastype_of f 
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in 
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Const (@{const_name Wellfounded.measure}, 
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(T > @{typ nat}) > HOLogic.mk_prodT (T, T) > @{typ bool}) 
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$ f 
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end 
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fun mk_sumcases rT f (Type (@{type_name Sum_Type.sum}, [TL, TR])) = 
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let 
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val lt = mk_sumcases rT f TL 
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val rt = mk_sumcases rT f TR 
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in 
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SumTree.mk_sumcase TL TR rT lt rt 
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end 
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 mk_sumcases _ f T = f T 
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(** abstract syntax **) 
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val size = @{term "i :: code_numeral"} 
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val size_pred = @{term "(i :: code_numeral)  1"} 
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val size_ge_zero = @{term "(i :: code_numeral) > 0"} 
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fun test_function T = Free ("f", T > @{typ "term list option"}) 
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fun mk_none_continuation (x, y) = 
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let 
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val (T as Type(@{type_name "option"}, [T'])) = fastype_of x 
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in 
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Const (@{const_name Option.option_case}, T > (T' > T) > T > T) 
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$ y $ Const (@{const_name Some}, T' > T) $ x 
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end 
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(** datatypes **) 
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(* constructing smallvalue generator instances on datatypes *) 
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exception FUNCTION_TYPE; 
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val smallN = "small"; 
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fun smallT T = (T > @{typ "Code_Evaluation.term list option"}) > @{typ code_numeral} 
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> @{typ "Code_Evaluation.term list option"} 
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fun mk_equations thy descr vs tycos (names, auxnames) (Ts, Us) = 
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let 
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val smallsN = map (prefix (smallN ^ "_")) (names @ auxnames); 
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val smalls = map2 (fn name => fn T => Free (name, smallT T)) 
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smallsN (Ts @ Us) 
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fun mk_small_call T = 
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let 
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val small = Const (@{const_name "Smallcheck.small_class.small"}, smallT T) 
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in 
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(T, (fn t => small $ absdummy (T, t) $ size_pred)) 
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end 
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fun mk_small_aux_call fTs (k, _) (tyco, Ts) = 
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let 
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val T = Type (tyco, Ts) 
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val _ = if not (null fTs) then raise FUNCTION_TYPE else () 
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val small = nth smalls k 
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in 
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(T, (fn t => small $ absdummy (T, t) $ size_pred)) 
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end 
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fun mk_consexpr simpleT (c, xs) = 
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let 
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val (Ts, fns) = split_list xs 
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val constr = Const (c, Ts > simpleT) 
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val bounds = map Bound (((length xs)  1) downto 0) 
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val start_term = test_function simpleT $ (list_comb (constr, bounds)) 
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in fold_rev (fn f => fn t => f t) fns start_term end 
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fun mk_rhs exprs = 
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@{term "If :: bool => term list option => term list option => term list option"} 
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$ size_ge_zero $ (foldr1 mk_none_continuation exprs) $ @{term "None :: term list option"} 
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val rhss = 
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Datatype_Aux.interpret_construction descr vs 
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{ atyp = mk_small_call, dtyp = mk_small_aux_call } 
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> (map o apfst) Type 
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> map (fn (T, cs) => map (mk_consexpr T) cs) 
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> map mk_rhs 
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val lhss = map2 (fn t => fn T => t $ test_function T $ size) smalls (Ts @ Us); 
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val eqs = map (HOLogic.mk_Trueprop o HOLogic.mk_eq) (lhss ~~ rhss) 
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in 
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(Ts @ Us ~~ (smallsN ~~ eqs)) 
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end 
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val less_int_pred = @{lemma "i > 0 ==> Code_Numeral.nat_of ((i :: code_numeral)  1) < Code_Numeral.nat_of i" by auto} 
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fun gen_inst_state_tac ctxt rel st = 
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case Term.add_vars (prop_of st) [] of 
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[v as (_, T)] => 
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let 
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val cert = Thm.cterm_of (ProofContext.theory_of ctxt) 
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val rel' = cert rel 
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val st' = Thm.incr_indexes (#maxidx (Thm.rep_cterm rel') + 1) st (*FIXME??*) 
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in 
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PRIMITIVE (Drule.cterm_instantiate [(cert (Var v), rel')]) st' 
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end 
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 _ => Seq.empty; 
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fun instantiate_smallvalue_datatype config descr vs tycos prfx (names, auxnames) (Ts, Us) thy = 
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let 
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val _ = Datatype_Aux.message config "Creating smallvalue generators ..."; 
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val eqs = mk_equations thy descr vs tycos (names, auxnames) (Ts, Us) 
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fun my_relation_tac ctxt st = 
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let 
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val ((_ $ (_ $ rel)) :: tl) = prems_of st 
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val domT = (HOLogic.dest_setT (fastype_of rel)) 
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fun mk_single_measure T = mk_fun_comp (@{term "Code_Numeral.nat_of"}, 
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Const (@{const_name "Product_Type.snd"}, T > @{typ "code_numeral"})) 
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val measure = mk_measure (mk_sumcases @{typ nat} mk_single_measure domT) 
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in 
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(Function_Common.apply_termination_rule ctxt 1 
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THEN gen_inst_state_tac ctxt measure) st 
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end 
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fun termination_tac ctxt = 
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my_relation_tac ctxt 
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THEN rtac @{thm wf_measure} 1 
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THEN (REPEAT_DETERM (Simplifier.asm_full_simp_tac 
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(HOL_basic_ss addsimps [@{thm in_measure}, @{thm o_def}, @{thm snd_conv}, 
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@{thm nat_mono_iff}, less_int_pred] @ @{thms sum.cases}) 1)) 
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fun pat_completeness_auto ctxt = 
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Pat_Completeness.pat_completeness_tac ctxt 1 
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THEN auto_tac (clasimpset_of ctxt) 
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in 
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thy 
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> Class.instantiation (tycos, vs, @{sort small}) 
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> Function.add_function 
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(map (fn (T, (name, _)) => 
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Syntax.no_syn (Binding.conceal (Binding.name name), SOME (smallT T))) eqs) 
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(map (pair (apfst Binding.conceal Attrib.empty_binding) o snd o snd) eqs) 
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Function_Common.default_config pat_completeness_auto 
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> snd 
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> Local_Theory.restore 
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> (fn lthy => Function.prove_termination NONE (termination_tac lthy) lthy) 
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> snd 
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> Class.prove_instantiation_exit (K (Class.intro_classes_tac [])) 
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end; 
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fun ensure_smallvalue_datatype config raw_tycos thy = 
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let 
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val algebra = Sign.classes_of thy; 
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val (descr, raw_vs, tycos, prfx, (names, auxnames), raw_TUs) = 
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Datatype.the_descr thy raw_tycos; 
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val typerep_vs = (map o apsnd) 
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(curry (Sorts.inter_sort algebra) @{sort typerep}) raw_vs; 
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val smallvalue_insts = (map (rpair @{sort small}) o flat o maps snd o maps snd) 
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(Datatype_Aux.interpret_construction descr typerep_vs 
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{ atyp = single, dtyp = (K o K o K) [] }); 
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(*val term_of_insts = (map (rpair @{sort term_of}) o flat o maps snd o maps snd) 
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(Datatype_Aux.interpret_construction descr typerep_vs 
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{ atyp = K [], dtyp = K o K });*) 
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val has_inst = exists (fn tyco => 
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can (Sorts.mg_domain algebra tyco) @{sort small}) tycos; 
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in if has_inst then thy 
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else case Quickcheck_Generators.perhaps_constrain thy smallvalue_insts typerep_vs 
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of SOME constrain => (instantiate_smallvalue_datatype config descr 
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(map constrain typerep_vs) tycos prfx (names, auxnames) 
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((pairself o map o map_atyps) (fn TFree v => TFree (constrain v)) raw_TUs) thy 
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handle FUNCTION_TYPE => 
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(Datatype_Aux.message config 
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"Creation of smallvalue generators failed because the datatype contains a function type"; 
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thy)) 
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 NONE => thy 
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end; 
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(** building and compiling generator expressions **) 
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structure Counterexample = Proof_Data ( 
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type T = unit > int > term list option 
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fun init _ () = error "Counterexample" 
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); 
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val put_counterexample = Counterexample.put; 
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val target = "Quickcheck"; 
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fun mk_generator_expr thy prop Ts = 
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let 
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val bound_max = length Ts  1; 
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val bounds = map Bound (bound_max downto 0) 
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val result = list_comb (prop, bounds); 
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val terms = HOLogic.mk_list @{typ term} (map2 HOLogic.mk_term_of Ts bounds); 
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val check = 
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@{term "Smallcheck.catch_match :: term list option => term list option => term list option"} $ 
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(@{term "If :: bool => term list option => term list option => term list option"} 
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$ result $ @{term "None :: term list option"} 
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$ (@{term "Some :: term list => term list option"} $ terms)) 
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$ @{term "None :: term list option"}; 
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fun mk_small_closure (depth, T) t = 
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Const (@{const_name "Smallcheck.small_class.small"}, smallT T) 
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$ absdummy (T, t) $ depth 
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in Abs ("d", @{typ code_numeral}, fold_rev mk_small_closure (rev bounds ~~ Ts) check) end 
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fun compile_generator_expr ctxt t = 
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let 
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val Ts = (map snd o fst o strip_abs) t; 
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val thy = ProofContext.theory_of ctxt 
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in if Quickcheck.report ctxt then 
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error "Compilation with reporting facility is not supported" 
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else 
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let 
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val t' = mk_generator_expr thy t Ts; 
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val compile = Code_Runtime.dynamic_value_strict 
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(Counterexample.get, put_counterexample, "Smallvalue_Generators.put_counterexample") 
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thy (SOME target) (fn proc => fn g => g #> (Option.map o map) proc) t' []; 
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val dummy_report = ([], false) 
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in compile #> rpair dummy_report end 
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end; 
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241 

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(** setup **) 
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val setup = 
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Datatype.interpretation ensure_smallvalue_datatype 
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#> Context.theory_map 
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(Quickcheck.add_generator ("small", compile_generator_expr)); 
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248 

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end; 