theory ExPS8

imports "../NewParser"

begin

(* example 8 from Peter Sewell's bestiary *)

atom_decl name

ML {* val _ = cheat_fv_rsp := true *}

ML {* val _ = cheat_alpha_bn_rsp := true *}

nominal_datatype exp =

  EVar name

| EUnit

| EPair exp exp

| ELetRec l::lrbs e::exp bind_set "b_lrbs l" in l e

and fnclause =

  K x::name p::pat f::exp bind_set "b_pat p" in f

and fnclauses =

  S fnclause

| ORs fnclause fnclauses

and lrb =

  Clause fnclauses

and lrbs =

  Single lrb

| More lrb lrbs

and pat =

  PVar name

| PUnit

| PPair pat pat

binder

  b_lrbs :: "lrbs \<Rightarrow> atom set" and

  b_pat :: "pat \<Rightarrow> atom set" and

  b_fnclauses :: "fnclauses \<Rightarrow> atom set" and

  b_fnclause :: "fnclause \<Rightarrow> atom set" and

  b_lrb :: "lrb \<Rightarrow> atom set"

where

  "b_lrbs (Single l) = b_lrb l"

| "b_lrbs (More l ls) = b_lrb l \<union> b_lrbs 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_lrb (Clause fcs) = (b_fnclauses fcs)"

| "b_fnclause (K x pat exp) = {atom x}"

thm exp_fnclause_fnclauses_lrb_lrbs_pat.fv

thm exp_fnclause_fnclauses_lrb_lrbs_pat.eq_iff

declare permute_exp_raw_permute_fnclause_raw_permute_fnclauses_raw_permute_lrb_raw_permute_lrbs_raw_permute_pat_raw.simps[eqvt]

declare alpha_gen_eqvt[eqvt]

equivariance alpha_exp_raw

end