(* Title: Codatatype_Examples/Misc_Data.thy
Author: Dmitriy Traytel, TU Muenchen
Author: Andrei Popescu, TU Muenchen
Copyright 2012
Miscellaneous codatatype declarations.
*)
header {* Miscellaneous Codatatype Declarations *}
theory Misc_Codata
imports "../Codatatype"
begin
codata simple = X1 | X2 | X3 | X4
codata simple' = X1' unit | X2' unit | X3' unit | X4' unit
codata 'a stream = Stream 'a "'a stream"
codata 'a mylist = MyNil | MyCons 'a "'a mylist"
codata ('b, 'c, 'd, 'e) some_passive =
SP1 "('b, 'c, 'd, 'e) some_passive" | SP2 'b | SP3 'c | SP4 'd | SP5 'e
codata lambda =
Var string |
App lambda lambda |
Abs string lambda |
Let "(string \<times> lambda) fset" lambda
codata 'a par_lambda =
PVar 'a |
PApp "'a par_lambda" "'a par_lambda" |
PAbs 'a "'a par_lambda" |
PLet "('a \<times> 'a par_lambda) fset" "'a par_lambda"
(*
('a, 'b1, 'b2) F1 = 'a * 'b1 + 'a * 'b2
('a, 'b1, 'b2) F2 = unit + 'b1 * 'b2
*)
codata 'a J1 = J11 'a "'a J1" | J12 'a "'a J2"
and 'a J2 = J21 | J22 "'a J1" "'a J2"
codata 'a tree = TEmpty | TNode 'a "'a forest"
and 'a forest = FNil | FCons "'a tree" "'a forest"
codata 'a tree' = TEmpty' | TNode' "'a branch" "'a branch"
and 'a branch = Branch 'a "'a tree'"
codata ('a, 'b) exp = Term "('a, 'b) trm" | Sum "('a, 'b) trm" "('a, 'b) exp"
and ('a, 'b) trm = Factor "('a, 'b) factor" | Prod "('a, 'b) factor" "('a, 'b) trm"
and ('a, 'b) factor = C 'a | V 'b | Paren "('a, 'b) exp"
codata ('a, 'b, 'c) some_killing =
SK "'a \<Rightarrow> 'b \<Rightarrow> ('a, 'b, 'c) some_killing + ('a, 'b, 'c) in_here"
and ('a, 'b, 'c) in_here =
IH1 'b 'a | IH2 'c
codata_raw some_killing': 'a = "'b \<Rightarrow> 'd \<Rightarrow> ('a + 'c)"
and in_here': 'c = "'d + 'e"
codata_raw some_killing'': 'a = "'b \<Rightarrow> 'c"
and in_here'': 'c = "'d \<times> 'b + 'e"
codata ('b, 'c) less_killing = LK "'b \<Rightarrow> 'c"
codata 'b cps = CPS1 'b | CPS2 "'b \<Rightarrow> 'b cps"
codata ('b1, 'b2, 'b3, 'b4, 'b5, 'b6, 'b7, 'b8, 'b9) fun_rhs =
FR "'b1 \<Rightarrow> 'b2 \<Rightarrow> 'b3 \<Rightarrow> 'b4 \<Rightarrow> 'b5 \<Rightarrow> 'b6 \<Rightarrow> 'b7 \<Rightarrow> 'b8 \<Rightarrow> 'b9 \<Rightarrow>
('b1, 'b2, 'b3, 'b4, 'b5, 'b6, 'b7, 'b8, 'b9) fun_rhs"
codata ('b1, 'b2, 'b3, 'b4, 'b5, 'b6, 'b7, 'b8, 'b9, 'b10, 'b11, 'b12, 'b13, 'b14, 'b15, 'b16, 'b17,
'b18, 'b19, 'b20) fun_rhs' =
FR' "'b1 \<Rightarrow> 'b2 \<Rightarrow> 'b3 \<Rightarrow> 'b4 \<Rightarrow> 'b5 \<Rightarrow> 'b6 \<Rightarrow> 'b7 \<Rightarrow> 'b8 \<Rightarrow> 'b9 \<Rightarrow> 'b10 \<Rightarrow> 'b11 \<Rightarrow> 'b12 \<Rightarrow> 'b13 \<Rightarrow> 'b14 \<Rightarrow>
'b15 \<Rightarrow> 'b16 \<Rightarrow> 'b17 \<Rightarrow> 'b18 \<Rightarrow> 'b19 \<Rightarrow> 'b20 \<Rightarrow>
('b1, 'b2, 'b3, 'b4, 'b5, 'b6, 'b7, 'b8, 'b9, 'b10, 'b11, 'b12, 'b13, 'b14, 'b15, 'b16, 'b17,
'b18, 'b19, 'b20) fun_rhs'"
codata ('a, 'b, 'c) wit3_F1 = W1 'a "('a, 'b, 'c) wit3_F1" "('a, 'b, 'c) wit3_F2"
and ('a, 'b, 'c) wit3_F2 = W2 'b "('a, 'b, 'c) wit3_F2"
and ('a, 'b, 'c) wit3_F3 = W31 'a 'b "('a, 'b, 'c) wit3_F1" | W32 'c 'a 'b "('a, 'b, 'c) wit3_F1"
codata ('c, 'e, 'g) coind_wit1 =
CW1 'c "('c, 'e, 'g) coind_wit1" "('c, 'e, 'g) ind_wit" "('c, 'e, 'g) coind_wit2"
and ('c, 'e, 'g) coind_wit2 =
CW21 "('c, 'e, 'g) coind_wit2" 'e | CW22 'c 'g
and ('c, 'e, 'g) ind_wit =
IW1 | IW2 'c
codata ('b, 'a) bar = BAR "'a \<Rightarrow> 'b"
codata ('a, 'b, 'c, 'd) foo = FOO "'d + 'b \<Rightarrow> 'c + 'a"
codata 'a dead_foo = A
codata ('a, 'b) use_dead_foo = Y "'a" "'b dead_foo"
(* SLOW, MEMORY-HUNGRY
codata ('a, 'c) D1 = A1 "('a, 'c) D2" | B1 "'a list"
and ('a, 'c) D2 = A2 "('a, 'c) D3" | B2 "'c list"
and ('a, 'c) D3 = A3 "('a, 'c) D3" | B3 "('a, 'c) D4" | C3 "('a, 'c) D4" "('a, 'c) D5"
and ('a, 'c) D4 = A4 "('a, 'c) D5" | B4 "'a list list list"
and ('a, 'c) D5 = A5 "('a, 'c) D6"
and ('a, 'c) D6 = A6 "('a, 'c) D7"
and ('a, 'c) D7 = A7 "('a, 'c) D8"
and ('a, 'c) D8 = A8 "('a, 'c) D1 list"
*)
end