(* 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, 'b, '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_pair 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> is_J21 (j2_sum n)" |
"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
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