author  bulwahn 
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permissions  rwrr 
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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 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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(* static options *) 
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val define_foundationally = false 
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(** general term functions **) 
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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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fun mk_undefined T = Const(@{const_name undefined}, T) 
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(** abstract syntax **) 
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fun termifyT T = HOLogic.mk_prodT (T, @{typ "unit => Code_Evaluation.term"}); 
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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", termifyT 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 "Smallcheck.orelse"}, T > T > T) 
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$ x $ y 
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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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val full_smallN = "full_small"; 
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fun full_smallT T = (termifyT T > @{typ "Code_Evaluation.term list option"}) 
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> @{typ code_numeral} > @{typ "Code_Evaluation.term list option"} 
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fun mk_equations thy descr vs tycos smalls (Ts, Us) = 
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let 
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fun mk_small_call T = 
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let 
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val small = Const (@{const_name "Smallcheck.full_small_class.full_small"}, full_smallT T) 
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in 
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(T, (fn t => small $ 
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(HOLogic.split_const (T, @{typ "unit => Code_Evaluation.term"}, @{typ "Code_Evaluation.term list option"}) 
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$ absdummy (T, absdummy (@{typ "unit => Code_Evaluation.term"}, 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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(T, (fn t => small $ 
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(HOLogic.split_const (T, @{typ "unit => Code_Evaluation.term"}, @{typ "Code_Evaluation.term list option"}) 
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$ absdummy (T, absdummy (@{typ "unit => Code_Evaluation.term"}, 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 (fn x => Bound (2 * x + 1)) (((length xs)  1) downto 0) 
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val term_bounds = map (fn x => Bound (2 * x)) (((length xs)  1) downto 0) 
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val Eval_App = Const ("Code_Evaluation.App", HOLogic.termT > HOLogic.termT > HOLogic.termT) 
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val Eval_Const = Const ("Code_Evaluation.Const", HOLogic.literalT > @{typ typerep} > HOLogic.termT) 
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val term = fold (fn u => fn t => Eval_App $ t $ (u $ @{term "()"})) 
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bounds (Eval_Const $ HOLogic.mk_literal c $ HOLogic.mk_typerep (Ts > simpleT)) 
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val start_term = test_function simpleT $ 
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(HOLogic.pair_const simpleT @{typ "unit => Code_Evaluation.term"} 
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$ (list_comb (constr, bounds)) $ absdummy (@{typ unit}, term)) 
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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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eqs 
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end 
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(* foundational definition with the function package *) 
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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 mk_single_measure T = HOLogic.mk_comp (@{term "Code_Numeral.nat_of"}, 
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Const (@{const_name "Product_Type.snd"}, T > @{typ "code_numeral"})) 
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fun mk_termination_measure T = 
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let 
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val T' = fst (HOLogic.dest_prodT (HOLogic.dest_setT T)) 
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in 
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mk_measure (mk_sumcases @{typ nat} mk_single_measure T') 
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end 
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fun termination_tac ctxt = 
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Function_Relation.relation_tac ctxt mk_termination_measure 1 
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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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(* creating the instances *) 
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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 smallsN = map (prefix (full_smallN ^ "_")) (names @ auxnames); 
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in 
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thy 
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> Class.instantiation (tycos, vs, @{sort full_small}) 
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> (if define_foundationally then 
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let 
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val smalls = map2 (fn name => fn T => Free (name, full_smallT T)) smallsN (Ts @ Us) 
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val eqs = mk_equations thy descr vs tycos smalls (Ts, Us) 
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in 
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Function.add_function 
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(map (fn (name, T) => 
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Syntax.no_syn (Binding.conceal (Binding.name name), SOME (full_smallT T))) 
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(smallsN ~~ (Ts @ Us))) 
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(map (pair (apfst Binding.conceal Attrib.empty_binding)) 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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end 
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else 
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fold_map (fn (name, T) => Local_Theory.define 
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((Binding.conceal (Binding.name name), NoSyn), 
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(apfst Binding.conceal Attrib.empty_binding, mk_undefined (full_smallT T))) 
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#> apfst fst) (smallsN ~~ (Ts @ Us)) 
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#> (fn (smalls, lthy) => 
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let 
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val eqs_t = mk_equations thy descr vs tycos smalls (Ts, Us) 
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val eqs = map (fn eq => Goal.prove lthy ["f", "i"] [] eq 
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(fn _ => Skip_Proof.cheat_tac (ProofContext.theory_of lthy))) eqs_t 
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in 
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fold (fn (name, eq) => Local_Theory.note 
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((Binding.conceal (Binding.qualify true prfx 
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(Binding.qualify true name (Binding.name "simps"))), 
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Code.add_default_eqn_attrib :: map (Attrib.internal o K) 
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[Simplifier.simp_add, Nitpick_Simps.add]), [eq]) #> snd) (smallsN ~~ eqs) lthy 
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end)) 
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> Class.prove_instantiation_exit (K (Class.intro_classes_tac [])) 
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end 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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(** 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_index (fn (i, ty) => 
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(2 * (bound_max  i) + 1, 2 * (bound_max  i), 2 * i, ty)) Ts; 
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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 = 
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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"} $ (@{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 (_, _, i, T) t = 
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Const (@{const_name "Smallcheck.full_small_class.full_small"}, full_smallT T) 
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$ (HOLogic.split_const (T, @{typ "unit => term"}, @{typ "term list option"}) 
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$ absdummy (T, absdummy (@{typ "unit => term"}, t))) $ Bound i 
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in Abs ("d", @{typ code_numeral}, fold_rev mk_small_closure bounds 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 Config.get ctxt Quickcheck.report 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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(** setup **) 
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val setup = 
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Datatype.interpretation 
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(Quickcheck_Generators.ensure_sort_datatype (@{sort full_small}, instantiate_smallvalue_datatype)) 
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#> Context.theory_map 
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(Quickcheck.add_generator ("small", compile_generator_expr)); 
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end; 