src/HOL/Datatype_Examples/Misc_Primrec.thy
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 blanchet@58309 ` 1` ```(* Title: HOL/Datatype_Examples/Misc_Primrec.thy ``` blanchet@53303 ` 2` ``` Author: Jasmin Blanchette, TU Muenchen ``` blanchet@53303 ` 3` ``` Copyright 2013 ``` blanchet@53303 ` 4` blanchet@53303 ` 5` ```Miscellaneous primitive recursive function definitions. ``` blanchet@53303 ` 6` ```*) ``` blanchet@53303 ` 7` wenzelm@58889 ` 8` ```section {* Miscellaneous Primitive Recursive Function Definitions *} ``` blanchet@53303 ` 9` blanchet@53303 ` 10` ```theory Misc_Primrec ``` blanchet@53304 ` 11` ```imports Misc_Datatype ``` blanchet@53303 ` 12` ```begin ``` blanchet@53303 ` 13` blanchet@55530 ` 14` ```primrec nat_of_simple :: "simple \ nat" where ``` blanchet@53303 ` 15` ``` "nat_of_simple X1 = 1" | ``` blanchet@53303 ` 16` ``` "nat_of_simple X2 = 2" | ``` blanchet@54193 ` 17` ``` "nat_of_simple X3 = 3" | ``` blanchet@53303 ` 18` ``` "nat_of_simple X4 = 4" ``` blanchet@53303 ` 19` blanchet@55530 ` 20` ```primrec simple_of_simple' :: "simple' \ simple" where ``` blanchet@53303 ` 21` ``` "simple_of_simple' (X1' _) = X1" | ``` blanchet@53303 ` 22` ``` "simple_of_simple' (X2' _) = X2" | ``` blanchet@53303 ` 23` ``` "simple_of_simple' (X3' _) = X3" | ``` blanchet@53303 ` 24` ``` "simple_of_simple' (X4' _) = X4" ``` blanchet@53303 ` 25` blanchet@55530 ` 26` ```primrec inc_simple'' :: "nat \ simple'' \ simple''" where ``` blanchet@53303 ` 27` ``` "inc_simple'' k (X1'' n i) = X1'' (n + k) (i + int k)" | ``` blanchet@53303 ` 28` ``` "inc_simple'' _ X2'' = X2''" ``` blanchet@53303 ` 29` blanchet@55530 ` 30` ```primrec myapp :: "'a mylist \ 'a mylist \ 'a mylist" where ``` blanchet@53303 ` 31` ``` "myapp MyNil ys = ys" | ``` blanchet@53303 ` 32` ``` "myapp (MyCons x xs) ys = MyCons x (myapp xs ys)" ``` blanchet@53303 ` 33` blanchet@55530 ` 34` ```primrec myrev :: "'a mylist \ 'a mylist" where ``` blanchet@53303 ` 35` ``` "myrev MyNil = MyNil" | ``` blanchet@53303 ` 36` ``` "myrev (MyCons x xs) = myapp (myrev xs) (MyCons x MyNil)" ``` blanchet@53303 ` 37` blanchet@58231 ` 38` ```primrec shuffle_sp :: "('a \ ord, 'b \ ord, 'c, 'd) some_passive \ ('d, 'a, 'b, 'c) some_passive" where ``` blanchet@53303 ` 39` ``` "shuffle_sp (SP1 sp) = SP1 (shuffle_sp sp)" | ``` blanchet@53303 ` 40` ``` "shuffle_sp (SP2 a) = SP3 a" | ``` blanchet@53303 ` 41` ``` "shuffle_sp (SP3 b) = SP4 b" | ``` blanchet@53303 ` 42` ``` "shuffle_sp (SP4 c) = SP5 c" | ``` blanchet@53303 ` 43` ``` "shuffle_sp (SP5 d) = SP2 d" ``` blanchet@53303 ` 44` blanchet@55530 ` 45` ```primrec ``` blanchet@53303 ` 46` ``` hf_size :: "hfset \ nat" ``` blanchet@53303 ` 47` ```where ``` blanchet@54019 ` 48` ``` "hf_size (HFset X) = 1 + setsum id (fset (fimage hf_size X))" ``` blanchet@53303 ` 49` blanchet@55530 ` 50` ```primrec rename_lam :: "(string \ string) \ lambda \ lambda" where ``` blanchet@53303 ` 51` ``` "rename_lam f (Var s) = Var (f s)" | ``` blanchet@53303 ` 52` ``` "rename_lam f (App l l') = App (rename_lam f l) (rename_lam f l')" | ``` blanchet@53303 ` 53` ``` "rename_lam f (Abs s l) = Abs (f s) (rename_lam f l)" | ``` blanchet@55932 ` 54` ``` "rename_lam f (Let SL l) = Let (fimage (map_prod f (rename_lam f)) SL) (rename_lam f l)" ``` blanchet@53303 ` 55` blanchet@55530 ` 56` ```primrec ``` blanchet@53303 ` 57` ``` sum_i1 :: "('a\{zero,plus}) I1 \ 'a" and ``` blanchet@53303 ` 58` ``` sum_i2 :: "'a I2 \ 'a" ``` blanchet@53303 ` 59` ```where ``` blanchet@53303 ` 60` ``` "sum_i1 (I11 n i) = n + sum_i1 i" | ``` blanchet@53303 ` 61` ``` "sum_i1 (I12 n i) = n + sum_i2 i" | ``` blanchet@53303 ` 62` ``` "sum_i2 I21 = 0" | ``` blanchet@53303 ` 63` ``` "sum_i2 (I22 i j) = sum_i1 i + sum_i2 j" ``` blanchet@53303 ` 64` blanchet@55530 ` 65` ```primrec forest_of_mylist :: "'a tree mylist \ 'a forest" where ``` blanchet@53303 ` 66` ``` "forest_of_mylist MyNil = FNil" | ``` blanchet@53303 ` 67` ``` "forest_of_mylist (MyCons t ts) = FCons t (forest_of_mylist ts)" ``` blanchet@53303 ` 68` blanchet@55530 ` 69` ```primrec mylist_of_forest :: "'a forest \ 'a tree mylist" where ``` blanchet@53303 ` 70` ``` "mylist_of_forest FNil = MyNil" | ``` blanchet@53303 ` 71` ``` "mylist_of_forest (FCons t ts) = MyCons t (mylist_of_forest ts)" ``` blanchet@53303 ` 72` blanchet@53303 ` 73` ```definition frev :: "'a forest \ 'a forest" where ``` blanchet@53622 ` 74` ``` "frev = forest_of_mylist \ myrev \ mylist_of_forest" ``` blanchet@53303 ` 75` blanchet@55530 ` 76` ```primrec ``` blanchet@53303 ` 77` ``` mirror_tree :: "'a tree \ 'a tree" and ``` blanchet@53303 ` 78` ``` mirror_forest :: "'a forest \ 'a forest" ``` blanchet@53303 ` 79` ```where ``` blanchet@53303 ` 80` ``` "mirror_tree TEmpty = TEmpty" | ``` blanchet@53303 ` 81` ``` "mirror_tree (TNode x ts) = TNode x (mirror_forest ts)" | ``` blanchet@53303 ` 82` ``` "mirror_forest FNil = FNil" | ``` blanchet@53303 ` 83` ``` "mirror_forest (FCons t ts) = frev (FCons (mirror_tree t) (mirror_forest ts))" ``` blanchet@53303 ` 84` blanchet@55530 ` 85` ```primrec ``` blanchet@53303 ` 86` ``` mylist_of_tree' :: "'a tree' \ 'a mylist" and ``` blanchet@53303 ` 87` ``` mylist_of_branch :: "'a branch \ 'a mylist" ``` blanchet@53303 ` 88` ```where ``` blanchet@53303 ` 89` ``` "mylist_of_tree' TEmpty' = MyNil" | ``` blanchet@53303 ` 90` ``` "mylist_of_tree' (TNode' b b') = myapp (mylist_of_branch b) (mylist_of_branch b')" | ``` blanchet@53303 ` 91` ``` "mylist_of_branch (Branch x t) = MyCons x (mylist_of_tree' t)" ``` blanchet@53303 ` 92` blanchet@55530 ` 93` ```primrec ``` blanchet@55484 ` 94` ``` id_tree :: "'a bin_rose_tree \ 'a bin_rose_tree" and ``` blanchet@55484 ` 95` ``` id_trees1 :: "'a bin_rose_tree mylist \ 'a bin_rose_tree mylist" and ``` blanchet@55484 ` 96` ``` id_trees2 :: "'a bin_rose_tree mylist \ 'a bin_rose_tree mylist" ``` blanchet@55484 ` 97` ```where ``` blanchet@55484 ` 98` ``` "id_tree (BRTree a ts ts') = BRTree a (id_trees1 ts) (id_trees2 ts')" | ``` blanchet@55484 ` 99` ``` "id_trees1 MyNil = MyNil" | ``` blanchet@55484 ` 100` ``` "id_trees1 (MyCons t ts) = MyCons (id_tree t) (id_trees1 ts)" | ``` blanchet@55484 ` 101` ``` "id_trees2 MyNil = MyNil" | ``` blanchet@55484 ` 102` ``` "id_trees2 (MyCons t ts) = MyCons (id_tree t) (id_trees2 ts)" ``` blanchet@55484 ` 103` blanchet@55530 ` 104` ```primrec ``` blanchet@55774 ` 105` ``` trunc_tree :: "'a bin_rose_tree \ 'a bin_rose_tree" and ``` blanchet@55774 ` 106` ``` trunc_trees1 :: "'a bin_rose_tree mylist \ 'a bin_rose_tree mylist" and ``` blanchet@55774 ` 107` ``` trunc_trees2 :: "'a bin_rose_tree mylist \ 'a bin_rose_tree mylist" ``` blanchet@55774 ` 108` ```where ``` blanchet@55774 ` 109` ``` "trunc_tree (BRTree a ts ts') = BRTree a (trunc_trees1 ts) (trunc_trees2 ts')" | ``` blanchet@55774 ` 110` ``` "trunc_trees1 MyNil = MyNil" | ``` blanchet@55774 ` 111` ``` "trunc_trees1 (MyCons t ts) = MyCons (id_tree t) MyNil" | ``` blanchet@55774 ` 112` ``` "trunc_trees2 MyNil = MyNil" | ``` blanchet@55774 ` 113` ``` "trunc_trees2 (MyCons t ts) = MyCons (id_tree t) MyNil" ``` blanchet@55774 ` 114` blanchet@55774 ` 115` ```primrec ``` blanchet@53303 ` 116` ``` is_ground_exp :: "('a, 'b) exp \ bool" and ``` blanchet@53303 ` 117` ``` is_ground_trm :: "('a, 'b) trm \ bool" and ``` blanchet@53303 ` 118` ``` is_ground_factor :: "('a, 'b) factor \ bool" ``` blanchet@53303 ` 119` ```where ``` blanchet@53303 ` 120` ``` "is_ground_exp (Term t) \ is_ground_trm t" | ``` blanchet@53303 ` 121` ``` "is_ground_exp (Sum t e) \ is_ground_trm t \ is_ground_exp e" | ``` blanchet@53303 ` 122` ``` "is_ground_trm (Factor f) \ is_ground_factor f" | ``` blanchet@53303 ` 123` ``` "is_ground_trm (Prod f t) \ is_ground_factor f \ is_ground_trm t" | ``` blanchet@53303 ` 124` ``` "is_ground_factor (C _) \ True" | ``` blanchet@53303 ` 125` ``` "is_ground_factor (V _) \ False" | ``` blanchet@53303 ` 126` ``` "is_ground_factor (Paren e) \ is_ground_exp e" ``` blanchet@53303 ` 127` blanchet@55530 ` 128` ```primrec map_ftreeA :: "('a \ 'a) \ 'a ftree \ 'a ftree" where ``` blanchet@53303 ` 129` ``` "map_ftreeA f (FTLeaf x) = FTLeaf (f x)" | ``` blanchet@53622 ` 130` ``` "map_ftreeA f (FTNode g) = FTNode (map_ftreeA f \ g)" ``` blanchet@53303 ` 131` blanchet@55530 ` 132` ```primrec map_ftreeB :: "('a \ 'b) \ 'a ftree \ 'b ftree" where ``` blanchet@53303 ` 133` ``` "map_ftreeB f (FTLeaf x) = FTLeaf (f x)" | ``` blanchet@53622 ` 134` ``` "map_ftreeB f (FTNode g) = FTNode (map_ftreeB f \ g \ the_inv f)" ``` blanchet@53303 ` 135` blanchet@53303 ` 136` ```end ```