--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/exhaustive_generators.ML Fri Mar 11 15:21:13 2011 +0100
@@ -0,0 +1,412 @@
+(* Title: HOL/Tools/smallvalue_generators.ML
+ Author: Lukas Bulwahn, TU Muenchen
+
+Generators for small values for various types.
+*)
+
+signature SMALLVALUE_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 Smallvalue_Generators : SMALLVALUE_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 "Smallcheck.orelse"}, T --> T --> T)
+ $ x $ y
+ end
+
+(** datatypes **)
+
+(* constructing smallvalue generator instances on datatypes *)
+
+exception FUNCTION_TYPE;
+
+val smallN = "small";
+
+fun smallT T = (T --> @{typ "Code_Evaluation.term list option"}) --> @{typ code_numeral}
+ --> @{typ "Code_Evaluation.term list option"}
+
+val full_smallN = "full_small";
+
+fun full_smallT 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 smalls (Ts, Us) =
+ let
+ fun mk_small_call T =
+ let
+ val small = Const (@{const_name "Smallcheck.full_small_class.full_small"}, full_smallT T)
+ in
+ (T, (fn t => small $
+ (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_small_aux_call fTs (k, _) (tyco, Ts) =
+ let
+ val T = Type (tyco, Ts)
+ val _ = if not (null fTs) then raise FUNCTION_TYPE else ()
+ val small = nth smalls k
+ in
+ (T, (fn t => small $
+ (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_small_call, dtyp = mk_small_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) smalls (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_smallvalue_datatype config descr vs tycos prfx (names, auxnames) (Ts, Us) thy =
+ let
+ val _ = Datatype_Aux.message config "Creating smallvalue generators ...";
+ val smallsN = map (prefix (full_smallN ^ "_")) (names @ auxnames);
+ in
+ thy
+ |> Class.instantiation (tycos, vs, @{sort full_small})
+ |> (if define_foundationally then
+ let
+ val smalls = map2 (fn name => fn T => Free (name, full_smallT T)) smallsN (Ts @ Us)
+ val eqs = mk_equations thy descr vs tycos smalls (Ts, Us)
+ in
+ Function.add_function
+ (map (fn (name, T) =>
+ Syntax.no_syn (Binding.conceal (Binding.name name), SOME (full_smallT T)))
+ (smallsN ~~ (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 (full_smallT T)))
+ #> apfst fst) (smallsN ~~ (Ts @ Us))
+ #> (fn (smalls, lthy) =>
+ let
+ val eqs_t = mk_equations thy descr vs tycos smalls (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) (smallsN ~~ eqs) lthy
+ end))
+ |> Class.prove_instantiation_exit (K (Class.intro_classes_tac []))
+ end handle FUNCTION_TYPE =>
+ (Datatype_Aux.message config
+ "Creation of smallvalue 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_small_closure (free as Free (_, T), term_var) t =
+ if Sign.of_sort thy (T, @{sort enum}) then
+ Const (@{const_name "Smallcheck.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 "Smallcheck.full_small_class.full_small"}, full_smallT 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 "Smallcheck.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_small_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 "Smallcheck.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_small_closure (_, _, i, T) t =
+ Const (@{const_name "Smallcheck.full_small_class.full_small"}, full_smallT 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_small_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, "Smallvalue_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,
+ "Smallvalue_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 full_small}, instantiate_smallvalue_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;