--- a/src/HOL/ex/Quickcheck.thy Tue Dec 16 21:18:53 2008 -0800
+++ b/src/HOL/ex/Quickcheck.thy Wed Dec 17 12:10:38 2008 +0100
@@ -1,11 +1,9 @@
-(* ID: $Id$
- Author: Florian Haftmann, TU Muenchen
-*)
+(* Author: Florian Haftmann, TU Muenchen *)
header {* A simple counterexample generator *}
theory Quickcheck
-imports Random Code_Eval
+imports Random Code_Eval Map
begin
subsection {* The @{text random} class *}
@@ -25,166 +23,6 @@
end
-text {* Datatypes *}
-
-definition
- collapse :: "('a \<Rightarrow> ('a \<Rightarrow> 'b \<times> 'a) \<times> 'a) \<Rightarrow> 'a \<Rightarrow> 'b \<times> 'a" where
- "collapse f = (do g \<leftarrow> f; g done)"
-
-ML {*
-structure StateMonad =
-struct
-
-fun liftT T sT = sT --> HOLogic.mk_prodT (T, sT);
-fun liftT' sT = sT --> sT;
-
-fun return T sT x = Const (@{const_name return}, T --> liftT T sT) $ x;
-
-fun scomp T1 T2 sT f g = Const (@{const_name scomp},
- liftT T1 sT --> (T1 --> liftT T2 sT) --> liftT T2 sT) $ f $ g;
-
-end;
-*}
-
-lemma random'_if:
- fixes random' :: "index \<Rightarrow> index \<Rightarrow> seed \<Rightarrow> ('a \<times> (unit \<Rightarrow> term)) \<times> seed"
- assumes "random' 0 j = (\<lambda>s. undefined)"
- and "\<And>i. random' (Suc_index i) j = rhs2 i"
- shows "random' i j s = (if i = 0 then undefined else rhs2 (i - 1) s)"
- by (cases i rule: index.exhaust) (insert assms, simp_all)
-
-setup {*
-let
- exception REC of string;
- fun mk_collapse thy ty = Sign.mk_const thy
- (@{const_name collapse}, [@{typ seed}, ty]);
- fun term_ty ty = HOLogic.mk_prodT (ty, @{typ "unit \<Rightarrow> term"});
- fun mk_split thy ty ty' = Sign.mk_const thy
- (@{const_name split}, [ty, @{typ "unit \<Rightarrow> term"}, StateMonad.liftT (term_ty ty') @{typ seed}]);
- fun mk_scomp_split thy ty ty' t t' =
- StateMonad.scomp (term_ty ty) (term_ty ty') @{typ seed} t
- (mk_split thy ty ty' $ Abs ("", ty, Abs ("", @{typ "unit \<Rightarrow> term"}, t')))
- fun mk_cons thy this_ty (c, args) =
- let
- val tys = map (fst o fst) args;
- val c_ty = tys ---> this_ty;
- val c = Const (c, tys ---> this_ty);
- val t_indices = map (curry ( op * ) 2) (length tys - 1 downto 0);
- val c_indices = map (curry ( op + ) 1) t_indices;
- val c_t = list_comb (c, map Bound c_indices);
- val t_t = Abs ("", @{typ unit}, Eval.mk_term Free Typerep.typerep
- (list_comb (c, map (fn k => Bound (k + 1)) t_indices))
- |> map_aterms (fn t as Bound _ => t $ @{term "()"} | t => t));
- val return = StateMonad.return (term_ty this_ty) @{typ seed}
- (HOLogic.mk_prod (c_t, t_t));
- val t = fold_rev (fn ((ty, _), random) =>
- mk_scomp_split thy ty this_ty random)
- args return;
- val is_rec = exists (snd o fst) args;
- in (is_rec, t) end;
- fun mk_conss thy ty [] = NONE
- | mk_conss thy ty [(_, t)] = SOME t
- | mk_conss thy ty ts = SOME (mk_collapse thy (term_ty ty) $
- (Sign.mk_const thy (@{const_name select}, [StateMonad.liftT (term_ty ty) @{typ seed}]) $
- HOLogic.mk_list (StateMonad.liftT (term_ty ty) @{typ seed}) (map snd ts)));
- fun mk_clauses thy ty (tyco, (ts_rec, ts_atom)) =
- let
- val SOME t_atom = mk_conss thy ty ts_atom;
- in case mk_conss thy ty ts_rec
- of SOME t_rec => mk_collapse thy (term_ty ty) $
- (Sign.mk_const thy (@{const_name select_default}, [StateMonad.liftT (term_ty ty) @{typ seed}]) $
- @{term "i\<Colon>index"} $ t_rec $ t_atom)
- | NONE => t_atom
- end;
- fun mk_random_eqs thy vs tycos =
- let
- val this_ty = Type (hd tycos, map TFree vs);
- val this_ty' = StateMonad.liftT (term_ty this_ty) @{typ seed};
- val random_name = NameSpace.base @{const_name random};
- val random'_name = random_name ^ "_" ^ Class.type_name (hd tycos) ^ "'";
- fun random ty = Sign.mk_const thy (@{const_name random}, [ty]);
- val random' = Free (random'_name,
- @{typ index} --> @{typ index} --> this_ty');
- fun atom ty = ((ty, false), random ty $ @{term "j\<Colon>index"});
- fun dtyp tyco = ((this_ty, true), random' $ @{term "i\<Colon>index"} $ @{term "j\<Colon>index"});
- fun rtyp tyco tys = raise REC
- ("Will not generate random elements for mutual recursive type " ^ quote (hd tycos));
- val rhss = DatatypePackage.construction_interpretation thy
- { atom = atom, dtyp = dtyp, rtyp = rtyp } vs tycos
- |> (map o apsnd o map) (mk_cons thy this_ty)
- |> (map o apsnd) (List.partition fst)
- |> map (mk_clauses thy this_ty)
- val eqss = map ((apsnd o map) (HOLogic.mk_Trueprop o HOLogic.mk_eq) o (fn rhs => ((this_ty, random'), [
- (random' $ @{term "0\<Colon>index"} $ @{term "j\<Colon>index"}, Abs ("s", @{typ seed},
- Const (@{const_name undefined}, HOLogic.mk_prodT (term_ty this_ty, @{typ seed})))),
- (random' $ @{term "Suc_index i"} $ @{term "j\<Colon>index"}, rhs)
- ]))) rhss;
- in eqss end;
- fun random_inst [tyco] thy =
- let
- val (raw_vs, _) = DatatypePackage.the_datatype_spec thy tyco;
- val vs = (map o apsnd)
- (curry (Sorts.inter_sort (Sign.classes_of thy)) @{sort random}) raw_vs;
- val { descr, index, ... } = DatatypePackage.the_datatype thy tyco;
- val ((this_ty, random'), eqs') = singleton (mk_random_eqs thy vs) tyco;
- val eq = (HOLogic.mk_Trueprop o HOLogic.mk_eq)
- (Sign.mk_const thy (@{const_name random}, [this_ty]) $ @{term "i\<Colon>index"},
- random' $ @{term "i\<Colon>index"} $ @{term "i\<Colon>index"})
- val del_func = Attrib.internal (fn _ => Thm.declaration_attribute
- (fn thm => Context.mapping (Code.del_eqn thm) I));
- fun add_code simps lthy =
- let
- val thy = ProofContext.theory_of lthy;
- val thm = @{thm random'_if}
- |> Drule.instantiate' [SOME (Thm.ctyp_of thy this_ty)] [SOME (Thm.cterm_of thy random')]
- |> (fn thm => thm OF simps)
- |> singleton (ProofContext.export lthy (ProofContext.init thy));
- val c = (fst o dest_Const o fst o strip_comb o fst
- o HOLogic.dest_eq o HOLogic.dest_Trueprop o Thm.prop_of) thm;
- in
- lthy
- |> LocalTheory.theory (Code.del_eqns c
- #> PureThy.add_thm ((fst (dest_Free random') ^ "_code", thm), [Thm.kind_internal])
- #-> Code.add_eqn)
- end;
- in
- thy
- |> TheoryTarget.instantiation ([tyco], vs, @{sort random})
- |> PrimrecPackage.add_primrec
- [(Binding.name (fst (dest_Free random')), SOME (snd (dest_Free random')), NoSyn)]
- (map (fn eq => ((Binding.empty, [del_func]), eq)) eqs')
- |-> add_code
- |> `(fn lthy => Syntax.check_term lthy eq)
- |-> (fn eq => Specification.definition (NONE, (Attrib.empty_binding, eq)))
- |> snd
- |> Class.prove_instantiation_instance (K (Class.intro_classes_tac []))
- |> LocalTheory.exit_global
- end
- | random_inst tycos thy = raise REC
- ("Will not generate random elements for mutual recursive type(s) " ^ commas (map quote tycos));
- fun add_random_inst tycos thy = random_inst tycos thy
- handle REC msg => (warning msg; thy);
-in DatatypePackage.interpretation add_random_inst end
-*}
-
-text {* Type @{typ int} *}
-
-instantiation int :: random
-begin
-
-definition
- "random n = (do
- (b, _) \<leftarrow> random n;
- (m, t) \<leftarrow> random n;
- return (if b then (int m, \<lambda>u. Code_Eval.App (Code_Eval.Const (STR ''Int.int'') TYPEREP(nat \<Rightarrow> int)) (t ()))
- else (- int m, \<lambda>u. Code_Eval.App (Code_Eval.Const (STR ''HOL.uminus_class.uminus'') TYPEREP(int \<Rightarrow> int))
- (Code_Eval.App (Code_Eval.Const (STR ''Int.int'') TYPEREP(nat \<Rightarrow> int)) (t ()))))
- done)"
-
-instance ..
-
-end
-
text {* Type @{typ "'a \<Rightarrow> 'b"} *}
ML {*
@@ -240,6 +78,170 @@
code_reserved SML Random_Engine
+text {* Datatypes *}
+
+definition
+ collapse :: "('a \<Rightarrow> ('a \<Rightarrow> 'b \<times> 'a) \<times> 'a) \<Rightarrow> 'a \<Rightarrow> 'b \<times> 'a" where
+ "collapse f = (do g \<leftarrow> f; g done)"
+
+ML {*
+structure StateMonad =
+struct
+
+fun liftT T sT = sT --> HOLogic.mk_prodT (T, sT);
+fun liftT' sT = sT --> sT;
+
+fun return T sT x = Const (@{const_name return}, T --> liftT T sT) $ x;
+
+fun scomp T1 T2 sT f g = Const (@{const_name scomp},
+ liftT T1 sT --> (T1 --> liftT T2 sT) --> liftT T2 sT) $ f $ g;
+
+end;
+*}
+
+lemma random'_if:
+ fixes random' :: "index \<Rightarrow> index \<Rightarrow> seed \<Rightarrow> ('a \<times> (unit \<Rightarrow> term)) \<times> seed"
+ assumes "random' 0 j = (\<lambda>s. undefined)"
+ and "\<And>i. random' (Suc_index i) j = rhs2 i"
+ shows "random' i j s = (if i = 0 then undefined else rhs2 (i - 1) s)"
+ by (cases i rule: index.exhaust) (insert assms, simp_all)
+
+setup {*
+let
+ exception REC of string;
+ exception TYP of string;
+ fun mk_collapse thy ty = Sign.mk_const thy
+ (@{const_name collapse}, [@{typ seed}, ty]);
+ fun term_ty ty = HOLogic.mk_prodT (ty, @{typ "unit \<Rightarrow> term"});
+ fun mk_split thy ty ty' = Sign.mk_const thy
+ (@{const_name split}, [ty, @{typ "unit \<Rightarrow> term"}, StateMonad.liftT (term_ty ty') @{typ seed}]);
+ fun mk_scomp_split thy ty ty' t t' =
+ StateMonad.scomp (term_ty ty) (term_ty ty') @{typ seed} t
+ (mk_split thy ty ty' $ Abs ("", ty, Abs ("", @{typ "unit \<Rightarrow> term"}, t')))
+ fun mk_cons thy this_ty (c, args) =
+ let
+ val tys = map (fst o fst) args;
+ val c_ty = tys ---> this_ty;
+ val c = Const (c, tys ---> this_ty);
+ val t_indices = map (curry ( op * ) 2) (length tys - 1 downto 0);
+ val c_indices = map (curry ( op + ) 1) t_indices;
+ val c_t = list_comb (c, map Bound c_indices);
+ val t_t = Abs ("", @{typ unit}, Eval.mk_term Free Typerep.typerep
+ (list_comb (c, map (fn k => Bound (k + 1)) t_indices))
+ |> map_aterms (fn t as Bound _ => t $ @{term "()"} | t => t));
+ val return = StateMonad.return (term_ty this_ty) @{typ seed}
+ (HOLogic.mk_prod (c_t, t_t));
+ val t = fold_rev (fn ((ty, _), random) =>
+ mk_scomp_split thy ty this_ty random)
+ args return;
+ val is_rec = exists (snd o fst) args;
+ in (is_rec, t) end;
+ fun mk_conss thy ty [] = NONE
+ | mk_conss thy ty [(_, t)] = SOME t
+ | mk_conss thy ty ts = SOME (mk_collapse thy (term_ty ty) $
+ (Sign.mk_const thy (@{const_name select}, [StateMonad.liftT (term_ty ty) @{typ seed}]) $
+ HOLogic.mk_list (StateMonad.liftT (term_ty ty) @{typ seed}) (map snd ts)));
+ fun mk_clauses thy ty (tyco, (ts_rec, ts_atom)) =
+ let
+ val SOME t_atom = mk_conss thy ty ts_atom;
+ in case mk_conss thy ty ts_rec
+ of SOME t_rec => mk_collapse thy (term_ty ty) $
+ (Sign.mk_const thy (@{const_name select_default}, [StateMonad.liftT (term_ty ty) @{typ seed}]) $
+ @{term "i\<Colon>index"} $ t_rec $ t_atom)
+ | NONE => t_atom
+ end;
+ fun mk_random_eqs thy vs tycos =
+ let
+ val this_ty = Type (hd tycos, map TFree vs);
+ val this_ty' = StateMonad.liftT (term_ty this_ty) @{typ seed};
+ val random_name = NameSpace.base @{const_name random};
+ val random'_name = random_name ^ "_" ^ Class.type_name (hd tycos) ^ "'";
+ fun random ty = Sign.mk_const thy (@{const_name random}, [ty]);
+ val random' = Free (random'_name,
+ @{typ index} --> @{typ index} --> this_ty');
+ fun atom ty = if Sign.of_sort thy (ty, @{sort random})
+ then ((ty, false), random ty $ @{term "j\<Colon>index"})
+ else raise TYP
+ ("Will not generate random elements for type(s) " ^ quote (hd tycos));
+ fun dtyp tyco = ((this_ty, true), random' $ @{term "i\<Colon>index"} $ @{term "j\<Colon>index"});
+ fun rtyp tyco tys = raise REC
+ ("Will not generate random elements for mutual recursive type " ^ quote (hd tycos));
+ val rhss = DatatypePackage.construction_interpretation thy
+ { atom = atom, dtyp = dtyp, rtyp = rtyp } vs tycos
+ |> (map o apsnd o map) (mk_cons thy this_ty)
+ |> (map o apsnd) (List.partition fst)
+ |> map (mk_clauses thy this_ty)
+ val eqss = map ((apsnd o map) (HOLogic.mk_Trueprop o HOLogic.mk_eq) o (fn rhs => ((this_ty, random'), [
+ (random' $ @{term "0\<Colon>index"} $ @{term "j\<Colon>index"}, Abs ("s", @{typ seed},
+ Const (@{const_name undefined}, HOLogic.mk_prodT (term_ty this_ty, @{typ seed})))),
+ (random' $ @{term "Suc_index i"} $ @{term "j\<Colon>index"}, rhs)
+ ]))) rhss;
+ in eqss end;
+ fun random_inst [tyco] thy =
+ let
+ val (raw_vs, _) = DatatypePackage.the_datatype_spec thy tyco;
+ val vs = (map o apsnd)
+ (curry (Sorts.inter_sort (Sign.classes_of thy)) @{sort random}) raw_vs;
+ val ((this_ty, random'), eqs') = singleton (mk_random_eqs thy vs) tyco;
+ val eq = (HOLogic.mk_Trueprop o HOLogic.mk_eq)
+ (Sign.mk_const thy (@{const_name random}, [this_ty]) $ @{term "i\<Colon>index"},
+ random' $ @{term "i\<Colon>index"} $ @{term "i\<Colon>index"})
+ val del_func = Attrib.internal (fn _ => Thm.declaration_attribute
+ (fn thm => Context.mapping (Code.del_eqn thm) I));
+ fun add_code simps lthy =
+ let
+ val thy = ProofContext.theory_of lthy;
+ val thm = @{thm random'_if}
+ |> Drule.instantiate' [SOME (Thm.ctyp_of thy this_ty)] [SOME (Thm.cterm_of thy random')]
+ |> (fn thm => thm OF simps)
+ |> singleton (ProofContext.export lthy (ProofContext.init thy));
+ val c = (fst o dest_Const o fst o strip_comb o fst
+ o HOLogic.dest_eq o HOLogic.dest_Trueprop o Thm.prop_of) thm;
+ in
+ lthy
+ |> LocalTheory.theory (Code.del_eqns c
+ #> PureThy.add_thm ((fst (dest_Free random') ^ "_code", thm), [Thm.kind_internal])
+ #-> Code.add_eqn)
+ end;
+ in
+ thy
+ |> TheoryTarget.instantiation ([tyco], vs, @{sort random})
+ |> PrimrecPackage.add_primrec
+ [(Binding.name (fst (dest_Free random')), SOME (snd (dest_Free random')), NoSyn)]
+ (map (fn eq => ((Binding.empty, [del_func]), eq)) eqs')
+ |-> add_code
+ |> `(fn lthy => Syntax.check_term lthy eq)
+ |-> (fn eq => Specification.definition (NONE, (Attrib.empty_binding, eq)))
+ |> snd
+ |> Class.prove_instantiation_instance (K (Class.intro_classes_tac []))
+ |> LocalTheory.exit_global
+ end
+ | random_inst tycos thy = raise REC
+ ("Will not generate random elements for mutual recursive type(s) " ^ commas (map quote tycos));
+ fun add_random_inst tycos thy = random_inst tycos thy
+ handle REC msg => (warning msg; thy)
+ | TYP msg => (warning msg; thy)
+in DatatypePackage.interpretation add_random_inst end
+*}
+
+text {* Type @{typ int} *}
+
+instantiation int :: random
+begin
+
+definition
+ "random n = (do
+ (b, _) \<leftarrow> random n;
+ (m, t) \<leftarrow> random n;
+ return (if b then (int m, \<lambda>u. Code_Eval.App (Code_Eval.Const (STR ''Int.int'') TYPEREP(nat \<Rightarrow> int)) (t ()))
+ else (- int m, \<lambda>u. Code_Eval.App (Code_Eval.Const (STR ''HOL.uminus_class.uminus'') TYPEREP(int \<Rightarrow> int))
+ (Code_Eval.App (Code_Eval.Const (STR ''Int.int'') TYPEREP(nat \<Rightarrow> int)) (t ()))))
+ done)"
+
+instance ..
+
+end
+
subsection {* Quickcheck generator *}