--- a/src/HOL/ex/Quickcheck_Generators.thy Wed Jun 10 21:04:36 2009 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,274 +0,0 @@
-(* Author: Florian Haftmann, TU Muenchen *)
-
-header {* Experimental counterexample generators *}
-
-theory Quickcheck_Generators
-imports Quickcheck State_Monad
-begin
-
-subsection {* 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)"
-
-lemma random'_if:
- fixes random' :: "code_numeral \<Rightarrow> code_numeral \<Rightarrow> Random.seed \<Rightarrow> ('a \<times> (unit \<Rightarrow> term)) \<times> Random.seed"
- assumes "random' 0 j = (\<lambda>s. undefined)"
- and "\<And>i. random' (Suc_code_numeral i) j = rhs2 i"
- shows "random' i j s = (if i = 0 then undefined else rhs2 (i - 1) s)"
- by (cases i rule: code_numeral.exhaust) (insert assms, simp_all)
-
-setup {*
-let
- fun liftT T sT = sT --> HOLogic.mk_prodT (T, sT);
- fun scomp T1 T2 sT f g = Const (@{const_name scomp},
- liftT T1 sT --> (T1 --> liftT T2 sT) --> liftT T2 sT) $ f $ g;
- exception REC of string;
- exception TYP of string;
- fun mk_collapse thy ty = Sign.mk_const thy
- (@{const_name collapse}, [@{typ Random.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"}, liftT (term_ty ty') @{typ Random.seed}]);
- fun mk_scomp_split thy ty ty' t t' =
- scomp (term_ty ty) (term_ty ty') @{typ Random.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}, HOLogic.reflect_term
- (list_comb (c, map (fn k => Bound (k + 1)) t_indices))
- |> map_aterms (fn t as Bound _ => t $ @{term "()"} | t => t));
- val return = HOLogic.mk_return (term_ty this_ty) @{typ Random.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 Random.select}, [liftT (term_ty ty) @{typ Random.seed}]) $
- HOLogic.mk_list (liftT (term_ty ty) @{typ Random.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 Random.select_default}, [liftT (term_ty ty) @{typ Random.seed}]) $
- @{term "i\<Colon>code_numeral"} $ 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' = liftT (term_ty this_ty) @{typ Random.seed};
- val random_name = Long_Name.base_name @{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 code_numeral} --> @{typ code_numeral} --> this_ty');
- fun atom ty = if Sign.of_sort thy (ty, @{sort random})
- then ((ty, false), random ty $ @{term "j\<Colon>code_numeral"})
- else raise TYP
- ("Will not generate random elements for type(s) " ^ quote (hd tycos));
- fun dtyp tyco = ((this_ty, true), random' $ @{term "i\<Colon>code_numeral"} $ @{term "j\<Colon>code_numeral"});
- fun rtyp (tyco, Ts) _ = 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
- |> fst
- |> (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>code_numeral"} $ @{term "j\<Colon>code_numeral"}, Abs ("s", @{typ Random.seed},
- Const (@{const_name undefined}, HOLogic.mk_prodT (term_ty this_ty, @{typ Random.seed})))),
- (random' $ @{term "Suc_code_numeral i"} $ @{term "j\<Colon>code_numeral"}, 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>code_numeral"},
- random' $ @{term "max (i\<Colon>code_numeral) 1"} $ @{term "i\<Colon>code_numeral"})
- 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 ((Binding.name (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 [@{type_name bool}] thy = thy
- | add_random_inst [@{type_name nat}] thy = thy
- | add_random_inst [@{type_name char}] thy = thy
- | add_random_inst [@{type_name String.literal}] thy = thy
- | 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
-*}
-
-
-subsection {* Examples *}
-
-theorem "map g (map f xs) = map (g o f) xs"
- quickcheck [generator = code]
- by (induct xs) simp_all
-
-theorem "map g (map f xs) = map (f o g) xs"
- quickcheck [generator = code]
- oops
-
-theorem "rev (xs @ ys) = rev ys @ rev xs"
- quickcheck [generator = code]
- by simp
-
-theorem "rev (xs @ ys) = rev xs @ rev ys"
- quickcheck [generator = code]
- oops
-
-theorem "rev (rev xs) = xs"
- quickcheck [generator = code]
- by simp
-
-theorem "rev xs = xs"
- quickcheck [generator = code]
- oops
-
-primrec app :: "('a \<Rightarrow> 'a) list \<Rightarrow> 'a \<Rightarrow> 'a" where
- "app [] x = x"
- | "app (f # fs) x = app fs (f x)"
-
-lemma "app (fs @ gs) x = app gs (app fs x)"
- quickcheck [generator = code]
- by (induct fs arbitrary: x) simp_all
-
-lemma "app (fs @ gs) x = app fs (app gs x)"
- quickcheck [generator = code]
- oops
-
-primrec occurs :: "'a \<Rightarrow> 'a list \<Rightarrow> nat" where
- "occurs a [] = 0"
- | "occurs a (x#xs) = (if (x=a) then Suc(occurs a xs) else occurs a xs)"
-
-primrec del1 :: "'a \<Rightarrow> 'a list \<Rightarrow> 'a list" where
- "del1 a [] = []"
- | "del1 a (x#xs) = (if (x=a) then xs else (x#del1 a xs))"
-
-lemma "Suc (occurs a (del1 a xs)) = occurs a xs"
- -- {* Wrong. Precondition needed.*}
- quickcheck [generator = code]
- oops
-
-lemma "xs ~= [] \<longrightarrow> Suc (occurs a (del1 a xs)) = occurs a xs"
- quickcheck [generator = code]
- -- {* Also wrong.*}
- oops
-
-lemma "0 < occurs a xs \<longrightarrow> Suc (occurs a (del1 a xs)) = occurs a xs"
- quickcheck [generator = code]
- by (induct xs) auto
-
-primrec replace :: "'a \<Rightarrow> 'a \<Rightarrow> 'a list \<Rightarrow> 'a list" where
- "replace a b [] = []"
- | "replace a b (x#xs) = (if (x=a) then (b#(replace a b xs))
- else (x#(replace a b xs)))"
-
-lemma "occurs a xs = occurs b (replace a b xs)"
- quickcheck [generator = code]
- -- {* Wrong. Precondition needed.*}
- oops
-
-lemma "occurs b xs = 0 \<or> a=b \<longrightarrow> occurs a xs = occurs b (replace a b xs)"
- quickcheck [generator = code]
- by (induct xs) simp_all
-
-
-subsection {* Trees *}
-
-datatype 'a tree = Twig | Leaf 'a | Branch "'a tree" "'a tree"
-
-primrec leaves :: "'a tree \<Rightarrow> 'a list" where
- "leaves Twig = []"
- | "leaves (Leaf a) = [a]"
- | "leaves (Branch l r) = (leaves l) @ (leaves r)"
-
-primrec plant :: "'a list \<Rightarrow> 'a tree" where
- "plant [] = Twig "
- | "plant (x#xs) = Branch (Leaf x) (plant xs)"
-
-primrec mirror :: "'a tree \<Rightarrow> 'a tree" where
- "mirror (Twig) = Twig "
- | "mirror (Leaf a) = Leaf a "
- | "mirror (Branch l r) = Branch (mirror r) (mirror l)"
-
-theorem "plant (rev (leaves xt)) = mirror xt"
- quickcheck [generator = code]
- --{* Wrong! *}
- oops
-
-theorem "plant (leaves xt @ leaves yt) = Branch xt yt"
- quickcheck [generator = code]
- --{* Wrong! *}
- oops
-
-datatype 'a ntree = Tip "'a" | Node "'a" "'a ntree" "'a ntree"
-
-primrec inOrder :: "'a ntree \<Rightarrow> 'a list" where
- "inOrder (Tip a)= [a]"
- | "inOrder (Node f x y) = (inOrder x)@[f]@(inOrder y)"
-
-primrec root :: "'a ntree \<Rightarrow> 'a" where
- "root (Tip a) = a"
- | "root (Node f x y) = f"
-
-theorem "hd (inOrder xt) = root xt"
- quickcheck [generator = code]
- --{* Wrong! *}
- oops
-
-lemma "int (f k) = k"
- quickcheck [generator = code]
- oops
-
-lemma "int (nat k) = k"
- quickcheck [generator = code]
- oops
-
-end