author | bulwahn |
Wed, 15 Dec 2010 17:46:46 +0100 | |
changeset 41177 | 810a885decee |
parent 41176 | ede546773fd6 |
child 41178 | f4d3acf0c4cc |
permissions | -rw-r--r-- |
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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 * Quickcheck.report option |
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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 smart_quantifier : bool Config.T; |
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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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(* dynamic options *) |
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val (smart_quantifier, setup_smart_quantifier) = |
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Attrib.config_bool "quickcheck_smart_quantifier" (K true) |
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||
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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 check_allT T = (termifyT T --> @{typ "Code_Evaluation.term list option"}) |
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--> @{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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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_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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135 |
end |
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136 |
|
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137 |
(* foundational definition with the function package *) |
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138 |
|
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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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140 |
|
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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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143 |
|
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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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150 |
|
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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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157 |
|
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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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161 |
|
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162 |
|
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(* creating the instances *) |
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164 |
|
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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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190 |
((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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198 |
in |
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fold (fn (name, eq) => Local_Theory.note |
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200 |
((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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204 |
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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208 |
"Creation of smallvalue generators failed because the datatype contains a function type"; |
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209 |
thy) |
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210 |
|
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211 |
(** building and compiling generator expressions **) |
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212 |
|
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213 |
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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216 |
); |
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val put_counterexample = Counterexample.put; |
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218 |
|
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val target = "Quickcheck"; |
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220 |
|
40907 | 221 |
fun mk_smart_generator_expr ctxt t = |
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222 |
let |
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223 |
val thy = ProofContext.theory_of ctxt |
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val ((vnames, Ts), t') = apfst split_list (strip_abs t) |
225 |
val ([depth_name], ctxt') = Variable.variant_fixes ["depth"] ctxt |
|
226 |
val (names, ctxt'') = Variable.variant_fixes vnames ctxt' |
|
227 |
val (term_names, ctxt''') = Variable.variant_fixes (map (prefix "t_") vnames) ctxt'' |
|
228 |
val depth = Free (depth_name, @{typ code_numeral}) |
|
229 |
val frees = map2 (curry Free) names Ts |
|
230 |
val term_vars = map (fn n => Free (n, @{typ "unit => term"})) term_names |
|
231 |
fun strip_imp (Const(@{const_name HOL.implies},_) $ A $ B) = apfst (cons A) (strip_imp B) |
|
232 |
| strip_imp A = ([], A) |
|
233 |
val (assms, concl) = strip_imp (subst_bounds (rev frees, t')) |
|
234 |
val terms = HOLogic.mk_list @{typ term} (map (fn v => v $ @{term "()"}) term_vars) |
|
235 |
fun mk_small_closure (free as Free (_, T), term_var) t = |
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236 |
if Sign.of_sort thy (T, @{sort enum}) then |
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237 |
Const (@{const_name "Smallcheck.check_all_class.check_all"}, check_allT T) |
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238 |
$ (HOLogic.split_const (T, @{typ "unit => term"}, @{typ "term list option"}) |
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239 |
$ lambda free (lambda term_var t)) |
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240 |
else |
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241 |
Const (@{const_name "Smallcheck.full_small_class.full_small"}, full_smallT T) |
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242 |
$ (HOLogic.split_const (T, @{typ "unit => term"}, @{typ "term list option"}) |
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243 |
$ lambda free (lambda term_var t)) $ depth |
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fun lookup v = the (AList.lookup (op =) (names ~~ (frees ~~ term_vars)) v) |
245 |
val none_t = @{term "None :: term list option"} |
|
246 |
fun mk_safe_if (cond, then_t, else_t) = |
|
247 |
@{term "Smallcheck.catch_match :: term list option => term list option => term list option"} $ |
|
248 |
(@{term "If :: bool => term list option => term list option => term list option"} |
|
249 |
$ cond $ then_t $ else_t) $ none_t; |
|
250 |
fun mk_test_term bound_vars assms = |
|
251 |
let |
|
252 |
fun vars_of t = subtract (op =) bound_vars (Term.add_free_names t []) |
|
253 |
val (vars, check) = |
|
254 |
case assms of [] => |
|
255 |
(vars_of concl, (concl, none_t, @{term "Some :: term list => term list option"} $ terms)) |
|
256 |
| assm :: assms => |
|
257 |
(vars_of assm, (assm, mk_test_term (union (op =) (vars_of assm) bound_vars) assms, none_t)) |
|
258 |
in |
|
259 |
fold_rev mk_small_closure (map lookup vars) (mk_safe_if check) |
|
260 |
end |
|
261 |
in lambda depth (mk_test_term [] assms) end |
|
262 |
||
263 |
fun mk_generator_expr ctxt t = |
|
264 |
let |
|
265 |
val Ts = (map snd o fst o strip_abs) t; |
|
266 |
val thy = ProofContext.theory_of ctxt |
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267 |
val bound_max = length Ts - 1; |
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268 |
val bounds = map_index (fn (i, ty) => |
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269 |
(2 * (bound_max - i) + 1, 2 * (bound_max - i), 2 * i, ty)) Ts; |
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val result = list_comb (t, 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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|
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fun make_set T1 [] = Const (@{const_abbrev Set.empty}, T1 --> @{typ bool}) |
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| make_set T1 ((t1, @{const False}) :: tps) = make_set T1 tps |
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| make_set T1 ((t1, @{const True}) :: tps) = |
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Const (@{const_name insert}, T1 --> (T1 --> @{typ bool}) --> T1 --> @{typ bool}) |
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$ t1 $ (make_set T1 tps) |
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| make_set T1 ((_, t) :: tps) = raise TERM ("make_set", [t]) |
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|
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fun dest_fun_upd (Const (@{const_name fun_upd}, _) $ t0 $ t1 $ t2) = (t0, (t1, t2)) |
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| dest_fun_upd t = raise TERM ("dest_fun_upd", [t]) |
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|
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fun mk_fun_upd T1 T2 (t1, t2) t = |
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Const (@{const_name fun_upd}, (T1 --> T2) --> T1 --> T2 --> T1 --> T2) $ t $ t1 $ t2 |
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|
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fun dest_plain_fun t = |
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case try dest_fun_upd t of |
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NONE => |
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(case t of |
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(Abs (_, _, Const (@{const_name HOL.undefined}, _))) => [] |
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| _ => raise TERM ("dest_plain_fun", [t])) |
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| SOME (t0, (t1, t2)) => (t1, t2) :: dest_plain_fun t0 |
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|
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fun make_plain_fun T1 T2 tps = |
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fold_rev (mk_fun_upd T1 T2) tps (absdummy (T1, Const ("_", T2))) |
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|
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fun post_process_term t = |
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case fastype_of t of |
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Type (@{type_name fun}, [T1, T2]) => |
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dest_plain_fun t |> map (pairself post_process_term) |> |
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(if T2 = @{typ bool} then rev #> make_set T1 else make_plain_fun T1 T2) |
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| _ => t |
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|
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fun compile_generator_expr ctxt t = |
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let |
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val thy = ProofContext.theory_of ctxt |
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val t' = |
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(if Config.get ctxt smart_quantifier then mk_smart_generator_expr else mk_generator_expr) |
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ctxt t; |
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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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in |
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fn size => rpair NONE (compile size |> Option.map (map post_process_term)) |
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end; |
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|
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(** setup **) |
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|
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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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#> setup_smart_quantifier |
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#> Context.theory_map |
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(Quickcheck.add_generator ("exhaustive", compile_generator_expr)); |
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|
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end; |