(* protocol *)
sortdef protocol = type
(* binary role *)
sortdef role = {n:int|n==0||n==1}
(* atomics *)
stacst msg: (int, vt@ype) -> protocol
stacst nil: int -> protocol
stacst seq: (protocol, protocol) -> protocol
#define :: seq
(* connectives *)
stacst addi: (int, protocol, protocol) -> protocol // additives: oplus, amp
stacst mult: (int, protocol, protocol) -> protocol // multiplicatives: tensor, parr
(* type constructor *)
absvtype chan (int, protocol)
(* axiom *)
fun create {r1,r2:role|r1 != r2} {p:protocol} (chan(r1,p) -<lincloptr1> void): chan(r2,p)
(* atomics *)
fun send {r:role} {p:protocol} {v:vt@ype} (!chan(r,msg(r,v)::p) >> chan(r,p), v): void
fun recv {r:role} {p:protocol} {v:vt@ype} (!chan(r,msg(1-r,v)::p) >> chan(r,p)): v
fun wait {r:role} (chan(r,nil(1-r))): void
fun close {r:role} (chan(r,nil r)): void
(* additive connectives *)
datavtype choice (protocol, p:protocol, q:protocol) =
| Left (p,p,q)
| Right (q,p,q)
(* In a cut, there is one oplus (choose) with many amp (offer)
As a user, they are holding one amp and many oplus.
Then users themselves are one oplus and many amp.
*)
fun amp {r,r0:role|r0 != r} {p,q:protocol} (!chan(r,addi(r0,p,q)) >> chan(r,s)): #[s:protocol] choice (s,p,q)
fun oplus {r,r0:role|r0==r} {p,q,s:protocol} (!chan(r,addi(r0,p,q)) >> chan(r,s), choice (s,p,q)): void
(* multiplicative connectives *)
(* In a cut, there is one parr with many tensor
As a user, they are holding one tensor and many parr
Then users themselves are one parr and many tensor
*)
fun tensor {r,r0:role|r0 != r} {p,q:protocol} (chan(r,mult(r0,p,q)), chan(r,p) -<lincloptr1> void, chan(r,q) -<lincloptr1> void): void
fun parr {r,r0:role|r0==r} {p,q:protocol} (chan(r,mult(r0,p,q))): @(chan(r,p), chan(r,q))
(* cut *)
fun cut {r1,r2:role|r1 != r2} {p:protocol} (chan(r1,p), chan(r2,p)): void
staload "session.sats"
staload UN = "prelude/SATS/unsafe.sats"
implement parr {r,r0} {p,q} (chan) = let
val chan = $UN.castvwtp0 {chan(r,msg(1-r,chan(r,p))::msg(1-r,chan(r,q))::nil(r))} {chan(r,mult(r0,p,q))} chan
val p = recv {r} {msg(1-r,chan(r,q))::nil(r)} {chan(r,p)} chan
val q = recv {r} {nil(r)} {chan(r,q)} chan
val _ = close chan
in
@(p, q)
end
implement tensor {r,r0} {p,q} (chan, fp, fq) = let
val pclient = create {r,1-r} (fp)
val qclient = create {r,1-r} (fq)
val chan = $UN.castvwtp0 {chan(r,msg(r,chan(1-r,p))::msg(r,chan(1-r,q))::nil(1-r))} {chan(r,mult(r0,p,q))} chan
val _ = send {r} {msg(r,chan(1-r,q))::nil(1-r)} {chan(1-r,p)} (chan, pclient)
val _ = send {r} {nil(1-r)} {chan(1-r,q)}(chan, qclient)
val _ = wait chan
in
end
