--- a/src/HOL/Tools/exhaustive_generators.ML Fri Mar 11 15:21:13 2011 +0100
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,405 +0,0 @@
-(* Title: HOL/Tools/exhaustive_generators.ML
- Author: Lukas Bulwahn, TU Muenchen
-
-Exhaustive generators for various types.
-*)
-
-signature EXHAUSTIVE_GENERATORS =
-sig
- val compile_generator_expr:
- Proof.context -> term -> int -> term list option * Quickcheck.report option
- val compile_generator_exprs:
- Proof.context -> term list -> (int -> term list option) list
- val put_counterexample: (unit -> int -> term list option)
- -> Proof.context -> Proof.context
- val put_counterexample_batch: (unit -> (int -> term list option) list)
- -> Proof.context -> Proof.context
- val smart_quantifier : bool Config.T;
- val quickcheck_pretty : bool Config.T;
- val setup: theory -> theory
-end;
-
-structure Exhaustive_Generators : EXHAUSTIVE_GENERATORS =
-struct
-
-(* static options *)
-
-val define_foundationally = false
-
-(* dynamic options *)
-
-val (smart_quantifier, setup_smart_quantifier) =
- Attrib.config_bool "quickcheck_smart_quantifier" (K true)
-
-val (quickcheck_pretty, setup_quickcheck_pretty) =
- Attrib.config_bool "quickcheck_pretty" (K true)
-
-(** general term functions **)
-
-fun mk_measure f =
- let
- val Type ("fun", [T, @{typ nat}]) = fastype_of f
- in
- Const (@{const_name Wellfounded.measure},
- (T --> @{typ nat}) --> HOLogic.mk_prodT (T, T) --> @{typ bool})
- $ f
- end
-
-fun mk_sumcases rT f (Type (@{type_name Sum_Type.sum}, [TL, TR])) =
- let
- val lt = mk_sumcases rT f TL
- val rt = mk_sumcases rT f TR
- in
- SumTree.mk_sumcase TL TR rT lt rt
- end
- | mk_sumcases _ f T = f T
-
-fun mk_undefined T = Const(@{const_name undefined}, T)
-
-
-(** abstract syntax **)
-
-fun termifyT T = HOLogic.mk_prodT (T, @{typ "unit => Code_Evaluation.term"});
-
-val size = @{term "i :: code_numeral"}
-val size_pred = @{term "(i :: code_numeral) - 1"}
-val size_ge_zero = @{term "(i :: code_numeral) > 0"}
-fun test_function T = Free ("f", termifyT T --> @{typ "term list option"})
-
-fun mk_none_continuation (x, y) =
- let
- val (T as Type(@{type_name "option"}, [T'])) = fastype_of x
- in
- Const (@{const_name "Quickcheck_Exhaustive.orelse"}, T --> T --> T)
- $ x $ y
- end
-
-(** datatypes **)
-
-(* constructing exhaustive generator instances on datatypes *)
-
-exception FUNCTION_TYPE;
-val exhaustiveN = "exhaustive";
-
-fun exhaustiveT T = (termifyT T --> @{typ "Code_Evaluation.term list option"})
- --> @{typ code_numeral} --> @{typ "Code_Evaluation.term list option"}
-
-fun check_allT T = (termifyT T --> @{typ "Code_Evaluation.term list option"})
- --> @{typ "Code_Evaluation.term list option"}
-
-fun mk_equations thy descr vs tycos exhaustives (Ts, Us) =
- let
- fun mk_call T =
- let
- val exhaustive = Const (@{const_name "Quickcheck_Exhaustive.exhaustive_class.exhaustive"}, exhaustiveT T)
- in
- (T, (fn t => exhaustive $
- (HOLogic.split_const (T, @{typ "unit => Code_Evaluation.term"}, @{typ "Code_Evaluation.term list option"})
- $ absdummy (T, absdummy (@{typ "unit => Code_Evaluation.term"}, t))) $ size_pred))
- end
- fun mk_aux_call fTs (k, _) (tyco, Ts) =
- let
- val T = Type (tyco, Ts)
- val _ = if not (null fTs) then raise FUNCTION_TYPE else ()
- in
- (T, (fn t => nth exhaustives k $
- (HOLogic.split_const (T, @{typ "unit => Code_Evaluation.term"}, @{typ "Code_Evaluation.term list option"})
- $ absdummy (T, absdummy (@{typ "unit => Code_Evaluation.term"}, t))) $ size_pred))
- end
- fun mk_consexpr simpleT (c, xs) =
- let
- val (Ts, fns) = split_list xs
- val constr = Const (c, Ts ---> simpleT)
- val bounds = map (fn x => Bound (2 * x + 1)) (((length xs) - 1) downto 0)
- val term_bounds = map (fn x => Bound (2 * x)) (((length xs) - 1) downto 0)
- val Eval_App = Const ("Code_Evaluation.App", HOLogic.termT --> HOLogic.termT --> HOLogic.termT)
- val Eval_Const = Const ("Code_Evaluation.Const", HOLogic.literalT --> @{typ typerep} --> HOLogic.termT)
- val term = fold (fn u => fn t => Eval_App $ t $ (u $ @{term "()"}))
- bounds (Eval_Const $ HOLogic.mk_literal c $ HOLogic.mk_typerep (Ts ---> simpleT))
- val start_term = test_function simpleT $
- (HOLogic.pair_const simpleT @{typ "unit => Code_Evaluation.term"}
- $ (list_comb (constr, bounds)) $ absdummy (@{typ unit}, term))
- in fold_rev (fn f => fn t => f t) fns start_term end
- fun mk_rhs exprs =
- @{term "If :: bool => term list option => term list option => term list option"}
- $ size_ge_zero $ (foldr1 mk_none_continuation exprs) $ @{term "None :: term list option"}
- val rhss =
- Datatype_Aux.interpret_construction descr vs
- { atyp = mk_call, dtyp = mk_aux_call }
- |> (map o apfst) Type
- |> map (fn (T, cs) => map (mk_consexpr T) cs)
- |> map mk_rhs
- val lhss = map2 (fn t => fn T => t $ test_function T $ size) exhaustives (Ts @ Us);
- val eqs = map (HOLogic.mk_Trueprop o HOLogic.mk_eq) (lhss ~~ rhss)
- in
- eqs
- end
-
-(* foundational definition with the function package *)
-
-val less_int_pred = @{lemma "i > 0 ==> Code_Numeral.nat_of ((i :: code_numeral) - 1) < Code_Numeral.nat_of i" by auto}
-
-fun mk_single_measure T = HOLogic.mk_comp (@{term "Code_Numeral.nat_of"},
- Const (@{const_name "Product_Type.snd"}, T --> @{typ "code_numeral"}))
-
-fun mk_termination_measure T =
- let
- val T' = fst (HOLogic.dest_prodT (HOLogic.dest_setT T))
- in
- mk_measure (mk_sumcases @{typ nat} mk_single_measure T')
- end
-
-fun termination_tac ctxt =
- Function_Relation.relation_tac ctxt mk_termination_measure 1
- THEN rtac @{thm wf_measure} 1
- THEN (REPEAT_DETERM (Simplifier.asm_full_simp_tac
- (HOL_basic_ss addsimps [@{thm in_measure}, @{thm o_def}, @{thm snd_conv},
- @{thm nat_mono_iff}, less_int_pred] @ @{thms sum.cases}) 1))
-
-fun pat_completeness_auto ctxt =
- Pat_Completeness.pat_completeness_tac ctxt 1
- THEN auto_tac (clasimpset_of ctxt)
-
-
-(* creating the instances *)
-
-fun instantiate_exhaustive_datatype config descr vs tycos prfx (names, auxnames) (Ts, Us) thy =
- let
- val _ = Datatype_Aux.message config "Creating exhaustive generators ...";
- val exhaustivesN = map (prefix (exhaustiveN ^ "_")) (names @ auxnames);
- in
- thy
- |> Class.instantiation (tycos, vs, @{sort exhaustive})
- |> (if define_foundationally then
- let
- val exhaustives = map2 (fn name => fn T => Free (name, exhaustiveT T)) exhaustivesN (Ts @ Us)
- val eqs = mk_equations thy descr vs tycos exhaustives (Ts, Us)
- in
- Function.add_function
- (map (fn (name, T) =>
- Syntax.no_syn (Binding.conceal (Binding.name name), SOME (exhaustiveT T)))
- (exhaustivesN ~~ (Ts @ Us)))
- (map (pair (apfst Binding.conceal Attrib.empty_binding)) eqs)
- Function_Common.default_config pat_completeness_auto
- #> snd
- #> Local_Theory.restore
- #> (fn lthy => Function.prove_termination NONE (termination_tac lthy) lthy)
- #> snd
- end
- else
- fold_map (fn (name, T) => Local_Theory.define
- ((Binding.conceal (Binding.name name), NoSyn),
- (apfst Binding.conceal Attrib.empty_binding, mk_undefined (exhaustiveT T)))
- #> apfst fst) (exhaustivesN ~~ (Ts @ Us))
- #> (fn (exhaustives, lthy) =>
- let
- val eqs_t = mk_equations thy descr vs tycos exhaustives (Ts, Us)
- val eqs = map (fn eq => Goal.prove lthy ["f", "i"] [] eq
- (fn _ => Skip_Proof.cheat_tac (ProofContext.theory_of lthy))) eqs_t
- in
- fold (fn (name, eq) => Local_Theory.note
- ((Binding.conceal (Binding.qualify true prfx
- (Binding.qualify true name (Binding.name "simps"))),
- Code.add_default_eqn_attrib :: map (Attrib.internal o K)
- [Simplifier.simp_add, Nitpick_Simps.add]), [eq]) #> snd) (exhaustivesN ~~ eqs) lthy
- end))
- |> Class.prove_instantiation_exit (K (Class.intro_classes_tac []))
- end handle FUNCTION_TYPE =>
- (Datatype_Aux.message config
- "Creation of exhaustivevalue generators failed because the datatype contains a function type";
- thy)
-
-(** building and compiling generator expressions **)
-
-structure Counterexample = Proof_Data
-(
- type T = unit -> int -> term list option
- (* FIXME avoid user error with non-user text *)
- fun init _ () = error "Counterexample"
-);
-val put_counterexample = Counterexample.put;
-
-structure Counterexample_Batch = Proof_Data
-(
- type T = unit -> (int -> term list option) list
- (* FIXME avoid user error with non-user text *)
- fun init _ () = error "Counterexample"
-);
-val put_counterexample_batch = Counterexample_Batch.put;
-
-val target = "Quickcheck";
-
-fun mk_smart_generator_expr ctxt t =
- let
- val thy = ProofContext.theory_of ctxt
- val ((vnames, Ts), t') = apfst split_list (strip_abs t)
- val ([depth_name], ctxt') = Variable.variant_fixes ["depth"] ctxt
- val (names, ctxt'') = Variable.variant_fixes vnames ctxt'
- val (term_names, ctxt''') = Variable.variant_fixes (map (prefix "t_") vnames) ctxt''
- val depth = Free (depth_name, @{typ code_numeral})
- val frees = map2 (curry Free) names Ts
- val term_vars = map (fn n => Free (n, @{typ "unit => term"})) term_names
- fun strip_imp (Const(@{const_name HOL.implies},_) $ A $ B) = apfst (cons A) (strip_imp B)
- | strip_imp A = ([], A)
- val (assms, concl) = strip_imp (subst_bounds (rev frees, t'))
- val terms = HOLogic.mk_list @{typ term} (map (fn v => v $ @{term "()"}) term_vars)
- fun mk_exhaustive_closure (free as Free (_, T), term_var) t =
- if Sign.of_sort thy (T, @{sort enum}) then
- Const (@{const_name "Quickcheck_Exhaustive.check_all_class.check_all"}, check_allT T)
- $ (HOLogic.split_const (T, @{typ "unit => term"}, @{typ "term list option"})
- $ lambda free (lambda term_var t))
- else
- Const (@{const_name "Quickcheck_Exhaustive.exhaustive_class.exhaustive"}, exhaustiveT T)
- $ (HOLogic.split_const (T, @{typ "unit => term"}, @{typ "term list option"})
- $ lambda free (lambda term_var t)) $ depth
- fun lookup v = the (AList.lookup (op =) (names ~~ (frees ~~ term_vars)) v)
- val none_t = @{term "None :: term list option"}
- fun mk_safe_if (cond, then_t, else_t) =
- @{term "Quickcheck_Exhaustive.catch_match :: term list option => term list option => term list option"} $
- (@{term "If :: bool => term list option => term list option => term list option"}
- $ cond $ then_t $ else_t) $ none_t;
- fun mk_test_term bound_vars assms =
- let
- fun vars_of t = subtract (op =) bound_vars (Term.add_free_names t [])
- val (vars, check) =
- case assms of [] =>
- (vars_of concl, (concl, none_t, @{term "Some :: term list => term list option"} $ terms))
- | assm :: assms =>
- (vars_of assm, (assm, mk_test_term (union (op =) (vars_of assm) bound_vars) assms, none_t))
- in
- fold_rev mk_exhaustive_closure (map lookup vars) (mk_safe_if check)
- end
- in lambda depth (mk_test_term [] assms) end
-
-fun mk_generator_expr ctxt t =
- let
- val Ts = (map snd o fst o strip_abs) t;
- val thy = ProofContext.theory_of ctxt
- val bound_max = length Ts - 1;
- val bounds = map_index (fn (i, ty) =>
- (2 * (bound_max - i) + 1, 2 * (bound_max - i), 2 * i, ty)) Ts;
- val result = list_comb (t, map (fn (i, _, _, _) => Bound i) bounds);
- val terms = HOLogic.mk_list @{typ term} (map (fn (_, i, _, _) => Bound i $ @{term "()"}) bounds);
- val check =
- @{term "Quickcheck_Exhaustive.catch_match :: term list option => term list option => term list option"} $
- (@{term "If :: bool => term list option => term list option => term list option"}
- $ result $ @{term "None :: term list option"} $ (@{term "Some :: term list => term list option"} $ terms))
- $ @{term "None :: term list option"};
- fun mk_exhaustive_closure (_, _, i, T) t =
- Const (@{const_name "Quickcheck_Exhaustive.exhaustive_class.exhaustive"}, exhaustiveT T)
- $ (HOLogic.split_const (T, @{typ "unit => term"}, @{typ "term list option"})
- $ absdummy (T, absdummy (@{typ "unit => term"}, t))) $ Bound i
- in Abs ("d", @{typ code_numeral}, fold_rev mk_exhaustive_closure bounds check) end
-
-(** post-processing of function terms **)
-
-fun dest_fun_upd (Const (@{const_name fun_upd}, _) $ t0 $ t1 $ t2) = (t0, (t1, t2))
- | dest_fun_upd t = raise TERM ("dest_fun_upd", [t])
-
-fun mk_fun_upd T1 T2 (t1, t2) t =
- Const (@{const_name fun_upd}, (T1 --> T2) --> T1 --> T2 --> T1 --> T2) $ t $ t1 $ t2
-
-fun dest_fun_upds t =
- case try dest_fun_upd t of
- NONE =>
- (case t of
- Abs (_, _, _) => ([], t)
- | _ => raise TERM ("dest_fun_upds", [t]))
- | SOME (t0, (t1, t2)) => apfst (cons (t1, t2)) (dest_fun_upds t0)
-
-fun make_fun_upds T1 T2 (tps, t) = fold_rev (mk_fun_upd T1 T2) tps t
-
-fun make_set T1 [] = Const (@{const_abbrev Set.empty}, T1 --> @{typ bool})
- | make_set T1 ((_, @{const False}) :: tps) = make_set T1 tps
- | make_set T1 ((t1, @{const True}) :: tps) =
- Const (@{const_name insert}, T1 --> (T1 --> @{typ bool}) --> T1 --> @{typ bool})
- $ t1 $ (make_set T1 tps)
- | make_set T1 ((_, t) :: tps) = raise TERM ("make_set", [t])
-
-fun make_coset T [] = Const (@{const_abbrev UNIV}, T --> @{typ bool})
- | make_coset T tps =
- let
- val U = T --> @{typ bool}
- fun invert @{const False} = @{const True}
- | invert @{const True} = @{const False}
- in
- Const (@{const_name "Groups.minus_class.minus"}, U --> U --> U)
- $ Const (@{const_abbrev UNIV}, U) $ make_set T (map (apsnd invert) tps)
- end
-
-fun make_map T1 T2 [] = Const (@{const_abbrev Map.empty}, T1 --> T2)
- | make_map T1 T2 ((_, Const (@{const_name None}, _)) :: tps) = make_map T1 T2 tps
- | make_map T1 T2 ((t1, t2) :: tps) = mk_fun_upd T1 T2 (t1, t2) (make_map T1 T2 tps)
-
-fun post_process_term t =
- let
- fun map_Abs f t =
- case t of Abs (x, T, t') => Abs (x, T, f t') | _ => raise TERM ("map_Abs", [t])
- fun process_args t = case strip_comb t of
- (c as Const (_, _), ts) => list_comb (c, map post_process_term ts)
- in
- case fastype_of t of
- Type (@{type_name fun}, [T1, T2]) =>
- (case try dest_fun_upds t of
- SOME (tps, t) =>
- (map (pairself post_process_term) tps, map_Abs post_process_term t)
- |> (case T2 of
- @{typ bool} =>
- (case t of
- Abs(_, _, @{const True}) => fst #> rev #> make_set T1
- | Abs(_, _, @{const False}) => fst #> rev #> make_coset T1
- | Abs(_, _, Const (@{const_name undefined}, _)) => fst #> rev #> make_set T1
- | _ => raise TERM ("post_process_term", [t]))
- | Type (@{type_name option}, _) =>
- (case t of
- Abs(_, _, Const(@{const_name None}, _)) => fst #> make_map T1 T2
- | Abs(_, _, Const (@{const_name undefined}, _)) => fst #> make_map T1 T2
- | _ => make_fun_upds T1 T2)
- | _ => make_fun_upds T1 T2)
- | NONE => process_args t)
- | _ => process_args t
- end
-
-(** generator compiliation **)
-
-fun compile_generator_expr ctxt t =
- let
- val thy = ProofContext.theory_of ctxt
- val t' =
- (if Config.get ctxt smart_quantifier then mk_smart_generator_expr else mk_generator_expr)
- ctxt t;
- val compile = Code_Runtime.dynamic_value_strict
- (Counterexample.get, put_counterexample, "Exhaustive_Generators.put_counterexample")
- thy (SOME target) (fn proc => fn g => g #> (Option.map o map) proc) t' [];
- in
- fn size => rpair NONE (compile size |>
- (if Config.get ctxt quickcheck_pretty then Option.map (map post_process_term) else I))
- end;
-
-fun compile_generator_exprs ctxt ts =
- let
- val thy = ProofContext.theory_of ctxt
- val mk_generator_expr =
- if Config.get ctxt smart_quantifier then mk_smart_generator_expr else mk_generator_expr
- val ts' = map (mk_generator_expr ctxt) ts;
- val compiles = Code_Runtime.dynamic_value_strict
- (Counterexample_Batch.get, put_counterexample_batch,
- "Exhaustive_Generators.put_counterexample_batch")
- thy (SOME target) (fn proc => map (fn g => g #> (Option.map o map) proc))
- (HOLogic.mk_list @{typ "code_numeral => term list option"} ts') [];
- in
- map (fn compile => fn size => compile size |> Option.map (map post_process_term)) compiles
- end;
-
-
-(** setup **)
-
-val setup =
- Datatype.interpretation
- (Quickcheck_Generators.ensure_sort_datatype (@{sort exhaustive}, instantiate_exhaustive_datatype))
- #> setup_smart_quantifier
- #> setup_quickcheck_pretty
- #> Context.theory_map (Quickcheck.add_generator ("exhaustive", compile_generator_expr))
- #> Context.theory_map (Quickcheck.add_batch_generator ("exhaustive", compile_generator_exprs));
-
-end;