# HG changeset patch
# User haftmann
# Date 1229512238 -3600
# Node ID 3dac98ebae243687efe472ecb1fb06cd3139a292
# Parent  fd8bb7527f7bee017a79357614f582fe0e666e51
restructured; circumvent sort problem

diff -r fd8bb7527f7b -r 3dac98ebae24 src/HOL/ex/Quickcheck.thy
--- 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 *}