(*<*)
theory Test
imports "Parser"
begin

(* This file contains only the examples that are not supposed to work yet. *)


atom_decl name

ML {* val _ = recursive := false  *}

(* example 7 from Peter Sewell's bestiary *)
(* dest_Const raised
nominal_datatype exp7 =
  EVar' name
| EUnit'
| EPair' exp7 exp7
| ELetRec' l::lrbs e::exp7 bind "b7s l" in e, bind "b7s l" in l
and lrb =
  Assign' name exp7
and lrbs =
  Single' lrb
| More' lrb lrbs
binder
  b7 :: "lrb \<Rightarrow> atom set" and
  b7s :: "lrbs \<Rightarrow> atom set"
where
  "b7 (Assign x e) = {atom x}"
| "b7s (Single a) = b7 a"
| "b7s (More a as) = (b7 a) \<union> (b7s as)"
thm alpha_exp7_raw_alpha_lrb_raw_alpha_lrbs_raw.intros
*)

(* example 8 from Peter Sewell's bestiary *)
(*
*** fv_bn: recursive argument, but wrong datatype.
*** At command "nominal_datatype".
nominal_datatype exp8 =
  EVar' name
| EUnit'
| EPair' exp8 exp8
| ELetRec' l::lrbs8 e::exp8 bind "b_lrbs8 l" in e, bind "b_lrbs8 l" in l
and fnclause =
  K' x::name p::pat8 e::exp8 bind "b_pat p" in e
and fnclauses =
  S' fnclause
| ORs' fnclause fnclauses
and lrb8 =
  Clause' fnclauses
and lrbs8 =
  Single' lrb8
| More' lrb8 lrbs8
and pat8 =
  PVar'' name
| PUnit''
| PPair'' pat8 pat8
binder
  b_lrbs8 :: "lrbs8 \<Rightarrow> atom set" and
  b_pat :: "pat8 \<Rightarrow> atom set" and
  b_fnclauses :: "fnclauses \<Rightarrow> atom set" and
  b_fnclause :: "fnclause \<Rightarrow> atom set" and
  b_lrb8 :: "lrb8 \<Rightarrow> atom set"
where
  "b_lrbs8 (Single' l) = b_lrb8 l"
| "b_lrbs8 (More' l ls) = b_lrb8 l \<union> b_lrbs8 ls"
| "b_pat (PVar'' x) = {atom x}"
| "b_pat (PUnit'') = {}"
| "b_pat (PPair'' p1 p2) = b_pat p1 \<union> b_pat p2"
| "b_fnclauses (S' fc) = (b_fnclause fc)"
| "b_fnclauses (ORs' fc fcs) = (b_fnclause fc) \<union> (b_fnclauses fcs)"
| "b_lrb8 (Clause' fcs) = (b_fnclauses fcs)"
| "b_fnclause (K' x pat exp8) = {atom x}"
thm alpha_exp8_raw_alpha_fnclause_raw_alpha_fnclauses_raw_alpha_lrb8_raw_alpha_lrbs8_raw_alpha_pat8_raw.intros
*)
(* example 4 from Terms.thy *)
(* fv_eqvt does not work, we need to repaire defined permute functions
   defined fv and defined alpha... *)
(* lists-datastructure does not work yet
nominal_datatype trm4 =
  Vr4 "name"
| Ap4 "trm4" "trm4 list"
| Lm4 x::"name" t::"trm4"  bind x in t

thm alpha_trm4_raw_alpha_trm4_raw_list.intros[no_vars]
thm fv_trm4_raw_fv_trm4_raw_list.simps[no_vars]
*)

(* example 8 from Terms.thy *)

(* Binding in a term under a bn, needs to fail *)
(*
nominal_datatype foo8 =
  Foo0 "name"
| Foo1 b::"bar8" f::"foo8" bind "bv8 b" in f --"check fo error if this is called foo"
and bar8 =
  Bar0 "name"
| Bar1 "name" s::"name" b::"bar8" bind s in b
binder
  bv8
where
  "bv8 (Bar0 x) = {}"
| "bv8 (Bar1 v x b) = {atom v}"
*)

(* example 9 from Peter Sewell's bestiary *)
(* run out of steam at the moment *)

end
(*>*)