src/HOL/Datatype_Examples/Misc_Primcorec.thy
author haftmann
Fri Oct 10 19:55:32 2014 +0200 (2014-10-10)
changeset 58646 cd63a4b12a33
parent 58309 a09ec6daaa19
child 58889 5b7a9633cfa8
permissions -rw-r--r--
specialized specification: avoid trivial instances
     1 (*  Title:      HOL/Datatype_Examples/Misc_Primcorec.thy
     2     Author:     Jasmin Blanchette, TU Muenchen
     3     Copyright   2013
     4 
     5 Miscellaneous primitive corecursive function definitions.
     6 *)
     7 
     8 header {* Miscellaneous Primitive Corecursive Function Definitions *}
     9 
    10 theory Misc_Primcorec
    11 imports Misc_Codatatype
    12 begin
    13 
    14 primcorec simple_of_bools :: "bool \<Rightarrow> bool \<Rightarrow> simple" where
    15   "simple_of_bools b b' = (if b then if b' then X1 else X2 else if b' then X3 else X4)"
    16 
    17 primcorec simple'_of_bools :: "bool \<Rightarrow> bool \<Rightarrow> simple'" where
    18   "simple'_of_bools b b' =
    19      (if b then if b' then X1' () else X2' () else if b' then X3' () else X4' ())"
    20 
    21 primcorec inc_simple'' :: "nat \<Rightarrow> simple'' \<Rightarrow> simple''" where
    22   "inc_simple'' k s = (case s of X1'' n i \<Rightarrow> X1'' (n + k) (i + int k) | X2'' \<Rightarrow> X2'')"
    23 
    24 primcorec sinterleave :: "'a stream \<Rightarrow> 'a stream \<Rightarrow> 'a stream" where
    25   "sinterleave s s' = Stream (shd s) (sinterleave s' (stl s))"
    26 
    27 primcorec myapp :: "'a mylist \<Rightarrow> 'a mylist \<Rightarrow> 'a mylist" where
    28   "myapp xs ys =
    29      (if xs = MyNil then ys
    30       else if ys = MyNil then xs
    31       else MyCons (myhd xs) (myapp (mytl xs) ys))"
    32 
    33 primcorec shuffle_sp :: "('a \<Colon> ord, 'b \<Colon> ord, 'c, 'd) some_passive \<Rightarrow> ('d, 'a, 'b, 'c) some_passive" where
    34   "shuffle_sp sp =
    35      (case sp of
    36        SP1 sp' \<Rightarrow> SP1 (shuffle_sp sp')
    37      | SP2 a \<Rightarrow> SP3 a
    38      | SP3 b \<Rightarrow> SP4 b
    39      | SP4 c \<Rightarrow> SP5 c
    40      | SP5 d \<Rightarrow> SP2 d)"
    41 
    42 primcorec rename_lam :: "(string \<Rightarrow> string) \<Rightarrow> lambda \<Rightarrow> lambda" where
    43   "rename_lam f l =
    44      (case l of
    45        Var s \<Rightarrow> Var (f s)
    46      | App l l' \<Rightarrow> App (rename_lam f l) (rename_lam f l')
    47      | Abs s l \<Rightarrow> Abs (f s) (rename_lam f l)
    48      | Let SL l \<Rightarrow> Let (fimage (map_prod f (rename_lam f)) SL) (rename_lam f l))"
    49 
    50 primcorec
    51   j1_sum :: "('a\<Colon>{zero,one,plus}) \<Rightarrow> 'a J1" and
    52   j2_sum :: "'a \<Rightarrow> 'a J2"
    53 where
    54   "n = 0 \<Longrightarrow> is_J11 (j1_sum n)" |
    55   "un_J111 (j1_sum _) = 0" |
    56   "un_J112 (j1_sum _) = j1_sum 0" |
    57   "un_J121 (j1_sum n) = n + 1" |
    58   "un_J122 (j1_sum n) = j2_sum (n + 1)" |
    59   "n = 0 \<Longrightarrow> j2_sum n = J21" |
    60   "un_J221 (j2_sum n) = j1_sum (n + 1)" |
    61   "un_J222 (j2_sum n) = j2_sum (n + 1)"
    62 
    63 primcorec forest_of_mylist :: "'a tree mylist \<Rightarrow> 'a forest" where
    64   "forest_of_mylist ts =
    65      (case ts of
    66        MyNil \<Rightarrow> FNil
    67      | MyCons t ts \<Rightarrow> FCons t (forest_of_mylist ts))"
    68 
    69 primcorec mylist_of_forest :: "'a forest \<Rightarrow> 'a tree mylist" where
    70   "mylist_of_forest f =
    71      (case f of
    72        FNil \<Rightarrow> MyNil
    73      | FCons t ts \<Rightarrow> MyCons t (mylist_of_forest ts))"
    74 
    75 primcorec semi_stream :: "'a stream \<Rightarrow> 'a stream" where
    76   "semi_stream s = Stream (shd s) (semi_stream (stl (stl s)))"
    77 
    78 primcorec
    79   tree'_of_stream :: "'a stream \<Rightarrow> 'a tree'" and
    80   branch_of_stream :: "'a stream \<Rightarrow> 'a branch"
    81 where
    82   "tree'_of_stream s =
    83      TNode' (branch_of_stream (semi_stream s)) (branch_of_stream (semi_stream (stl s)))" |
    84   "branch_of_stream s = (case s of Stream h t \<Rightarrow> Branch h (tree'_of_stream t))"
    85 
    86 primcorec
    87   id_tree :: "'a bin_rose_tree \<Rightarrow> 'a bin_rose_tree" and
    88   id_trees1 :: "'a bin_rose_tree mylist \<Rightarrow> 'a bin_rose_tree mylist" and
    89   id_trees2 :: "'a bin_rose_tree mylist \<Rightarrow> 'a bin_rose_tree mylist"
    90 where
    91   "id_tree t = (case t of BRTree a ts ts' \<Rightarrow> BRTree a (id_trees1 ts) (id_trees2 ts'))" |
    92   "id_trees1 ts = (case ts of
    93        MyNil \<Rightarrow> MyNil
    94      | MyCons t ts \<Rightarrow> MyCons (id_tree t) (id_trees1 ts))" |
    95   "id_trees2 ts = (case ts of
    96        MyNil \<Rightarrow> MyNil
    97      | MyCons t ts \<Rightarrow> MyCons (id_tree t) (id_trees2 ts))"
    98 
    99 primcorec
   100   trunc_tree :: "'a bin_rose_tree \<Rightarrow> 'a bin_rose_tree" and
   101   trunc_trees1 :: "'a bin_rose_tree mylist \<Rightarrow> 'a bin_rose_tree mylist" and
   102   trunc_trees2 :: "'a bin_rose_tree mylist \<Rightarrow> 'a bin_rose_tree mylist"
   103 where
   104   "trunc_tree t = (case t of BRTree a ts ts' \<Rightarrow> BRTree a (trunc_trees1 ts) (trunc_trees2 ts'))" |
   105   "trunc_trees1 ts = (case ts of
   106        MyNil \<Rightarrow> MyNil
   107      | MyCons t _ \<Rightarrow> MyCons (trunc_tree t) MyNil)" |
   108   "trunc_trees2 ts = (case ts of
   109        MyNil \<Rightarrow> MyNil
   110      | MyCons t ts \<Rightarrow> MyCons (trunc_tree t) MyNil)"
   111 
   112 primcorec
   113   freeze_exp :: "('b \<Rightarrow> 'a) \<Rightarrow> ('a, 'b) exp \<Rightarrow> ('a, 'b) exp" and
   114   freeze_trm :: "('b \<Rightarrow> 'a) \<Rightarrow> ('a, 'b) trm \<Rightarrow> ('a, 'b) trm" and
   115   freeze_factor :: "('b \<Rightarrow> 'a) \<Rightarrow> ('a, 'b) factor \<Rightarrow> ('a, 'b) factor"
   116 where
   117   "freeze_exp g e =
   118      (case e of
   119        Term t \<Rightarrow> Term (freeze_trm g t)
   120      | Sum t e \<Rightarrow> Sum (freeze_trm g t) (freeze_exp g e))" |
   121   "freeze_trm g t =
   122      (case t of
   123        Factor f \<Rightarrow> Factor (freeze_factor g f)
   124      | Prod f t \<Rightarrow> Prod (freeze_factor g f) (freeze_trm g t))" |
   125   "freeze_factor g f =
   126      (case f of
   127        C a \<Rightarrow> C a
   128      | V b \<Rightarrow> C (g b)
   129      | Paren e \<Rightarrow> Paren (freeze_exp g e))"
   130 
   131 primcorec poly_unity :: "'a poly_unit" where
   132   "poly_unity = U (\<lambda>_. poly_unity)"
   133 
   134 primcorec build_cps :: "('a \<Rightarrow> 'a) \<Rightarrow> ('a \<Rightarrow> bool stream) \<Rightarrow> 'a \<Rightarrow> bool stream \<Rightarrow> 'a cps" where
   135   "shd b \<Longrightarrow> build_cps f g a b = CPS1 a" |
   136   "_ \<Longrightarrow> build_cps f g a b = CPS2 (\<lambda>a. build_cps f g (f a) (g a))"
   137 
   138 end