--- a/src/HOL/BNF_Examples/Misc_Primrec.thy Thu Sep 11 19:20:23 2014 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,136 +0,0 @@
-(* Title: HOL/BNF_Examples/Misc_Primrec.thy
- Author: Jasmin Blanchette, TU Muenchen
- Copyright 2013
-
-Miscellaneous primitive recursive function definitions.
-*)
-
-header {* Miscellaneous Primitive Recursive Function Definitions *}
-
-theory Misc_Primrec
-imports Misc_Datatype
-begin
-
-primrec nat_of_simple :: "simple \<Rightarrow> nat" where
- "nat_of_simple X1 = 1" |
- "nat_of_simple X2 = 2" |
- "nat_of_simple X3 = 3" |
- "nat_of_simple X4 = 4"
-
-primrec simple_of_simple' :: "simple' \<Rightarrow> simple" where
- "simple_of_simple' (X1' _) = X1" |
- "simple_of_simple' (X2' _) = X2" |
- "simple_of_simple' (X3' _) = X3" |
- "simple_of_simple' (X4' _) = X4"
-
-primrec inc_simple'' :: "nat \<Rightarrow> simple'' \<Rightarrow> simple''" where
- "inc_simple'' k (X1'' n i) = X1'' (n + k) (i + int k)" |
- "inc_simple'' _ X2'' = X2''"
-
-primrec myapp :: "'a mylist \<Rightarrow> 'a mylist \<Rightarrow> 'a mylist" where
- "myapp MyNil ys = ys" |
- "myapp (MyCons x xs) ys = MyCons x (myapp xs ys)"
-
-primrec myrev :: "'a mylist \<Rightarrow> 'a mylist" where
- "myrev MyNil = MyNil" |
- "myrev (MyCons x xs) = myapp (myrev xs) (MyCons x MyNil)"
-
-primrec shuffle_sp :: "('a \<Colon> ord, 'b \<Colon> ord, 'c, 'd) some_passive \<Rightarrow> ('d, 'a, 'b, 'c) some_passive" where
- "shuffle_sp (SP1 sp) = SP1 (shuffle_sp sp)" |
- "shuffle_sp (SP2 a) = SP3 a" |
- "shuffle_sp (SP3 b) = SP4 b" |
- "shuffle_sp (SP4 c) = SP5 c" |
- "shuffle_sp (SP5 d) = SP2 d"
-
-primrec
- hf_size :: "hfset \<Rightarrow> nat"
-where
- "hf_size (HFset X) = 1 + setsum id (fset (fimage hf_size X))"
-
-primrec rename_lam :: "(string \<Rightarrow> string) \<Rightarrow> lambda \<Rightarrow> lambda" where
- "rename_lam f (Var s) = Var (f s)" |
- "rename_lam f (App l l') = App (rename_lam f l) (rename_lam f l')" |
- "rename_lam f (Abs s l) = Abs (f s) (rename_lam f l)" |
- "rename_lam f (Let SL l) = Let (fimage (map_prod f (rename_lam f)) SL) (rename_lam f l)"
-
-primrec
- sum_i1 :: "('a\<Colon>{zero,plus}) I1 \<Rightarrow> 'a" and
- sum_i2 :: "'a I2 \<Rightarrow> 'a"
-where
- "sum_i1 (I11 n i) = n + sum_i1 i" |
- "sum_i1 (I12 n i) = n + sum_i2 i" |
- "sum_i2 I21 = 0" |
- "sum_i2 (I22 i j) = sum_i1 i + sum_i2 j"
-
-primrec forest_of_mylist :: "'a tree mylist \<Rightarrow> 'a forest" where
- "forest_of_mylist MyNil = FNil" |
- "forest_of_mylist (MyCons t ts) = FCons t (forest_of_mylist ts)"
-
-primrec mylist_of_forest :: "'a forest \<Rightarrow> 'a tree mylist" where
- "mylist_of_forest FNil = MyNil" |
- "mylist_of_forest (FCons t ts) = MyCons t (mylist_of_forest ts)"
-
-definition frev :: "'a forest \<Rightarrow> 'a forest" where
- "frev = forest_of_mylist \<circ> myrev \<circ> mylist_of_forest"
-
-primrec
- mirror_tree :: "'a tree \<Rightarrow> 'a tree" and
- mirror_forest :: "'a forest \<Rightarrow> 'a forest"
-where
- "mirror_tree TEmpty = TEmpty" |
- "mirror_tree (TNode x ts) = TNode x (mirror_forest ts)" |
- "mirror_forest FNil = FNil" |
- "mirror_forest (FCons t ts) = frev (FCons (mirror_tree t) (mirror_forest ts))"
-
-primrec
- mylist_of_tree' :: "'a tree' \<Rightarrow> 'a mylist" and
- mylist_of_branch :: "'a branch \<Rightarrow> 'a mylist"
-where
- "mylist_of_tree' TEmpty' = MyNil" |
- "mylist_of_tree' (TNode' b b') = myapp (mylist_of_branch b) (mylist_of_branch b')" |
- "mylist_of_branch (Branch x t) = MyCons x (mylist_of_tree' t)"
-
-primrec
- id_tree :: "'a bin_rose_tree \<Rightarrow> 'a bin_rose_tree" and
- id_trees1 :: "'a bin_rose_tree mylist \<Rightarrow> 'a bin_rose_tree mylist" and
- id_trees2 :: "'a bin_rose_tree mylist \<Rightarrow> 'a bin_rose_tree mylist"
-where
- "id_tree (BRTree a ts ts') = BRTree a (id_trees1 ts) (id_trees2 ts')" |
- "id_trees1 MyNil = MyNil" |
- "id_trees1 (MyCons t ts) = MyCons (id_tree t) (id_trees1 ts)" |
- "id_trees2 MyNil = MyNil" |
- "id_trees2 (MyCons t ts) = MyCons (id_tree t) (id_trees2 ts)"
-
-primrec
- trunc_tree :: "'a bin_rose_tree \<Rightarrow> 'a bin_rose_tree" and
- trunc_trees1 :: "'a bin_rose_tree mylist \<Rightarrow> 'a bin_rose_tree mylist" and
- trunc_trees2 :: "'a bin_rose_tree mylist \<Rightarrow> 'a bin_rose_tree mylist"
-where
- "trunc_tree (BRTree a ts ts') = BRTree a (trunc_trees1 ts) (trunc_trees2 ts')" |
- "trunc_trees1 MyNil = MyNil" |
- "trunc_trees1 (MyCons t ts) = MyCons (id_tree t) MyNil" |
- "trunc_trees2 MyNil = MyNil" |
- "trunc_trees2 (MyCons t ts) = MyCons (id_tree t) MyNil"
-
-primrec
- is_ground_exp :: "('a, 'b) exp \<Rightarrow> bool" and
- is_ground_trm :: "('a, 'b) trm \<Rightarrow> bool" and
- is_ground_factor :: "('a, 'b) factor \<Rightarrow> bool"
-where
- "is_ground_exp (Term t) \<longleftrightarrow> is_ground_trm t" |
- "is_ground_exp (Sum t e) \<longleftrightarrow> is_ground_trm t \<and> is_ground_exp e" |
- "is_ground_trm (Factor f) \<longleftrightarrow> is_ground_factor f" |
- "is_ground_trm (Prod f t) \<longleftrightarrow> is_ground_factor f \<and> is_ground_trm t" |
- "is_ground_factor (C _) \<longleftrightarrow> True" |
- "is_ground_factor (V _) \<longleftrightarrow> False" |
- "is_ground_factor (Paren e) \<longleftrightarrow> is_ground_exp e"
-
-primrec map_ftreeA :: "('a \<Rightarrow> 'a) \<Rightarrow> 'a ftree \<Rightarrow> 'a ftree" where
- "map_ftreeA f (FTLeaf x) = FTLeaf (f x)" |
- "map_ftreeA f (FTNode g) = FTNode (map_ftreeA f \<circ> g)"
-
-primrec map_ftreeB :: "('a \<Rightarrow> 'b) \<Rightarrow> 'a ftree \<Rightarrow> 'b ftree" where
- "map_ftreeB f (FTLeaf x) = FTLeaf (f x)" |
- "map_ftreeB f (FTNode g) = FTNode (map_ftreeB f \<circ> g \<circ> the_inv f)"
-
-end