src/HOL/BNF_Examples/Misc_Primcorec.thy

-(*  Title:      HOL/BNF_Examples/Misc_Primcorec.thy
-    Author:     Jasmin Blanchette, TU Muenchen
-    Copyright   2013
-
-Miscellaneous primitive corecursive function definitions.
-*)
-
-header {* Miscellaneous Primitive Corecursive Function Definitions *}
-
-theory Misc_Primcorec
-imports Misc_Codatatype
-begin
-
-primcorec simple_of_bools :: "bool \<Rightarrow> bool \<Rightarrow> simple" where
-  "simple_of_bools b b' = (if b then if b' then X1 else X2 else if b' then X3 else X4)"
-
-primcorec simple'_of_bools :: "bool \<Rightarrow> bool \<Rightarrow> simple'" where
-  "simple'_of_bools b b' =
-     (if b then if b' then X1' () else X2' () else if b' then X3' () else X4' ())"
-
-primcorec inc_simple'' :: "nat \<Rightarrow> simple'' \<Rightarrow> simple''" where
-  "inc_simple'' k s = (case s of X1'' n i \<Rightarrow> X1'' (n + k) (i + int k) | X2'' \<Rightarrow> X2'')"
-
-primcorec sinterleave :: "'a stream \<Rightarrow> 'a stream \<Rightarrow> 'a stream" where
-  "sinterleave s s' = Stream (shd s) (sinterleave s' (stl s))"
-
-primcorec myapp :: "'a mylist \<Rightarrow> 'a mylist \<Rightarrow> 'a mylist" where
-  "myapp xs ys =
-     (if xs = MyNil then ys
-      else if ys = MyNil then xs
-      else MyCons (myhd xs) (myapp (mytl xs) ys))"
-
-primcorec shuffle_sp :: "('a \<Colon> ord, 'b \<Colon> ord, 'c, 'd) some_passive \<Rightarrow> ('d, 'a, 'b, 'c) some_passive" where
-  "shuffle_sp sp =
-     (case sp of
-       SP1 sp' \<Rightarrow> SP1 (shuffle_sp sp')
-     | SP2 a \<Rightarrow> SP3 a
-     | SP3 b \<Rightarrow> SP4 b
-     | SP4 c \<Rightarrow> SP5 c
-     | SP5 d \<Rightarrow> SP2 d)"
-
-primcorec rename_lam :: "(string \<Rightarrow> string) \<Rightarrow> lambda \<Rightarrow> lambda" where
-  "rename_lam f l =
-     (case l of
-       Var s \<Rightarrow> Var (f s)
-     | App l l' \<Rightarrow> App (rename_lam f l) (rename_lam f l')
-     | Abs s l \<Rightarrow> Abs (f s) (rename_lam f l)
-     | Let SL l \<Rightarrow> Let (fimage (map_prod f (rename_lam f)) SL) (rename_lam f l))"
-
-primcorec
-  j1_sum :: "('a\<Colon>{zero,one,plus}) \<Rightarrow> 'a J1" and
-  j2_sum :: "'a \<Rightarrow> 'a J2"
-where
-  "n = 0 \<Longrightarrow> is_J11 (j1_sum n)" |
-  "un_J111 (j1_sum _) = 0" |
-  "un_J112 (j1_sum _) = j1_sum 0" |
-  "un_J121 (j1_sum n) = n + 1" |
-  "un_J122 (j1_sum n) = j2_sum (n + 1)" |
-  "n = 0 \<Longrightarrow> j2_sum n = J21" |
-  "un_J221 (j2_sum n) = j1_sum (n + 1)" |
-  "un_J222 (j2_sum n) = j2_sum (n + 1)"
-
-primcorec forest_of_mylist :: "'a tree mylist \<Rightarrow> 'a forest" where
-  "forest_of_mylist ts =
-     (case ts of
-       MyNil \<Rightarrow> FNil
-     | MyCons t ts \<Rightarrow> FCons t (forest_of_mylist ts))"
-
-primcorec mylist_of_forest :: "'a forest \<Rightarrow> 'a tree mylist" where
-  "mylist_of_forest f =
-     (case f of
-       FNil \<Rightarrow> MyNil
-     | FCons t ts \<Rightarrow> MyCons t (mylist_of_forest ts))"
-
-primcorec semi_stream :: "'a stream \<Rightarrow> 'a stream" where
-  "semi_stream s = Stream (shd s) (semi_stream (stl (stl s)))"
-
-primcorec
-  tree'_of_stream :: "'a stream \<Rightarrow> 'a tree'" and
-  branch_of_stream :: "'a stream \<Rightarrow> 'a branch"
-where
-  "tree'_of_stream s =
-     TNode' (branch_of_stream (semi_stream s)) (branch_of_stream (semi_stream (stl s)))" |
-  "branch_of_stream s = (case s of Stream h t \<Rightarrow> Branch h (tree'_of_stream t))"
-
-primcorec
-  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 t = (case t of BRTree a ts ts' \<Rightarrow> BRTree a (id_trees1 ts) (id_trees2 ts'))" |
-  "id_trees1 ts = (case ts of
-       MyNil \<Rightarrow> MyNil
-     | MyCons t ts \<Rightarrow> MyCons (id_tree t) (id_trees1 ts))" |
-  "id_trees2 ts = (case ts of
-       MyNil \<Rightarrow> MyNil
-     | MyCons t ts \<Rightarrow> MyCons (id_tree t) (id_trees2 ts))"
-
-primcorec
-  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 t = (case t of BRTree a ts ts' \<Rightarrow> BRTree a (trunc_trees1 ts) (trunc_trees2 ts'))" |
-  "trunc_trees1 ts = (case ts of
-       MyNil \<Rightarrow> MyNil
-     | MyCons t _ \<Rightarrow> MyCons (trunc_tree t) MyNil)" |
-  "trunc_trees2 ts = (case ts of
-       MyNil \<Rightarrow> MyNil
-     | MyCons t ts \<Rightarrow> MyCons (trunc_tree t) MyNil)"
-
-primcorec
-  freeze_exp :: "('b \<Rightarrow> 'a) \<Rightarrow> ('a, 'b) exp \<Rightarrow> ('a, 'b) exp" and
-  freeze_trm :: "('b \<Rightarrow> 'a) \<Rightarrow> ('a, 'b) trm \<Rightarrow> ('a, 'b) trm" and
-  freeze_factor :: "('b \<Rightarrow> 'a) \<Rightarrow> ('a, 'b) factor \<Rightarrow> ('a, 'b) factor"
-where
-  "freeze_exp g e =
-     (case e of
-       Term t \<Rightarrow> Term (freeze_trm g t)
-     | Sum t e \<Rightarrow> Sum (freeze_trm g t) (freeze_exp g e))" |
-  "freeze_trm g t =
-     (case t of
-       Factor f \<Rightarrow> Factor (freeze_factor g f)
-     | Prod f t \<Rightarrow> Prod (freeze_factor g f) (freeze_trm g t))" |
-  "freeze_factor g f =
-     (case f of
-       C a \<Rightarrow> C a
-     | V b \<Rightarrow> C (g b)
-     | Paren e \<Rightarrow> Paren (freeze_exp g e))"
-
-primcorec poly_unity :: "'a poly_unit" where
-  "poly_unity = U (\<lambda>_. poly_unity)"
-
-primcorec build_cps :: "('a \<Rightarrow> 'a) \<Rightarrow> ('a \<Rightarrow> bool stream) \<Rightarrow> 'a \<Rightarrow> bool stream \<Rightarrow> 'a cps" where
-  "shd b \<Longrightarrow> build_cps f g a b = CPS1 a" |
-  "_ \<Longrightarrow> build_cps f g a b = CPS2 (\<lambda>a. build_cps f g (f a) (g a))"
-
-end