theory Test

imports "Parser"

begin

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