src/HOL/Codatatype/Examples/Misc_Data.thy

respect order of/additional type variables supplied by the user in fixed point constructions;

(*  Title:      Codatatype_Examples/Misc_Data.thy
    Author:     Dmitriy Traytel, TU Muenchen
    Author:     Andrei Popescu, TU Muenchen
    Copyright   2012

Miscellaneous datatype declarations.
*)

header {* Miscellaneous Datatype Declarations *}

theory Misc_Data
imports "../Codatatype"
begin

data simple = X1 | X2 | X3 | X4

data simple' = X1' unit | X2' unit | X3' unit | X4' unit

data 'a mylist = MyNil | MyCons 'a "'a mylist"

data ('b, 'c, 'd, 'e) some_passive =
  SP1 "('b, 'c, 'd, 'e) some_passive" | SP2 'b | SP3 'c | SP4 'd | SP5 'e

data lambda =
  Var string |
  App lambda lambda |
  Abs string lambda |
  Let "(string \<times> lambda) fset" lambda

data '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
*)

data 'a I1 = I11 'a "'a I1" | I12 'a "'a I2"
 and 'a I2 = I21 | I22 "'a I1" "'a I2"

data 'a tree = TEmpty | TNode 'a "'a forest"
 and 'a forest = FNil | FCons "'a tree" "'a forest"

data 'a tree' = TEmpty' | TNode' "'a branch" "'a branch"
 and 'a branch = Branch 'a "'a tree'"

data ('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"

data ('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

data 'b nofail1 = NF11 "'b nofail1 \<times> 'b" | NF12 'b
data 'b nofail2 = NF2 "('b nofail2 \<times> 'b \<times> 'b nofail2 \<times> 'b) list"
data 'b nofail3 = NF3 "'b \<times> ('b nofail3 \<times> 'b \<times> 'b nofail3 \<times> 'b) fset"
data 'b nofail4 = NF4 "('b nofail3 \<times> ('b nofail3 \<times> 'b \<times> 'b nofail3 \<times> 'b) fset) list"

(*
data 'b fail = F "'b fail \<times> 'b \<times> 'b fail \<times> 'b list"
data 'b fail = F "'b fail \<times> 'b \<times> 'b fail \<times> 'b"
data 'b fail = F "'b fail \<times> 'b + 'b fail"
data 'b fail = F "'b fail \<times> 'b"
*)

data l1 = L1 "l2 list"
 and l2 = L21 "l1 fset" | L22 l2

data kk1 = KK1 kk2
 and kk2 = KK2 kk3
 and kk3 = KK3 "kk1 list"

data t1 = T11 t3 | T12 t2
 and t2 = T2 t1
 and t3 = T3

data t1' = T11' t2' | T12' t3'
 and t2' = T2' t1'
 and t3' = T3'

(*
data fail1 = F1 fail2
 and fail2 = F2 fail3
 and fail3 = F3 fail1

data fail1 = F1 "fail2 list" fail2
 and fail2 = F2 "fail2 fset" fail3
 and fail3 = F3 fail1

data fail1 = F1 "fail2 list" fail2
 and fail2 = F2 "fail1 fset" fail1
*)

(* SLOW
data ('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"

(*time comparison*)
datatype ('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"
*)

(* fail:
data tt1 = TT11 tt2 tt3 | TT12 tt2 tt4
 and tt2 = TT2
 and tt3 = TT3 tt4
 and tt4 = TT4 tt1
*)

data k1 = K11 k2 k3 | K12 k2 k4
 and k2 = K2
 and k3 = K3 k4
 and k4 = K4

data tt1 = TT11 tt3 tt2 | TT12 tt2 tt4
 and tt2 = TT2
 and tt3 = TT3 tt1
 and tt4 = TT4

(* SLOW
data s1 = S11 s2 s3 s4 | S12 s3 | S13 s2 s6 | S14 s4 s2 | S15 s2 s2
 and s2 = S21 s7 s5 | S22 s5 s4 s6
 and s3 = S31 s1 s7 s2 | S32 s3 s3 | S33 s4 s5
 and s4 = S4 s5
 and s5 = S5
 and s6 = S61 s6 | S62 s1 s2 | S63 s6
 and s7 = S71 s8 | S72 s5
 and s8 = S8 nat
*)

data ('a, 'b) bar = BAR "'b \<Rightarrow> 'a"
data ('a, 'b, 'c, 'd) foo = FOO "'d + 'b \<Rightarrow> 'c + 'a"

data 'a dead_foo = A
(* FIXME: handle unknown type constructors using DEADID?
data ('a, 'b) use_dead_foo = Y "'a" "'b dead_foo"
*)
end