Dependent Session Types

IBM PL Day 2017

Transcript

1. Dependent Session Types Hanwen Wu and Hongwei Xi Boston University IBM PL Day 2017 & NE/NJ PLS 2017
2. Sending an Array Server send(sock, len) loop(sock, arr, 0, len) wait(sock) Client len = recv(sock) arr = malloc(len) loop(sock, arr, 0, len) close(sock)
3. Sending an Array, Untyped Server send(sock, len) loop(sock, arr, 0, len) wait(sock) Client len = recv(sock) arr = malloc(len) loop(sock, arr, 0, len) close(sock) The socket is untyped. What could go wrong?
4. Sending an Array, Simple Server send(len) loop(len) wait Client recv malloc loop(len) close The socket is typed using simple session types. Linear types guarantee correct order and no leak. What else could go wrong? msg(S,int)::repeat(n, msg(S,int))::end(C) repeat(n, msg(S,int))::end(C) send(socket, payload) recv(socket)
5. Sending an Array, Dependent Server send(len) loop(len) wait Client recv malloc loop(len) close quan(S,n:int.msg(S,int(n))::repeat(n,... ∀n:int.msg(S,int(n))::repeat(n,… forall(socket) ∃n:int.msg(S,int(n))::repeat(n,… exists(socket) The socket is typed using dependent session types. Nothing could go wrong.
6. Sending an Array, Dependent Server forall(sock) loop(sock, arr, 0, len) wait(sock) Client len = recv(sock) arr = malloc(len) loop(sock, arr, 0, len) close(sock) send(sock, len) exists(sock) unroll(sock) unroll(sock)
7. Show Me the Code rpt(n,s) := fix(n,f:int→stype.n:int.ite(n>0,s::f(n-1),end(1))) proto := quan(S,n:int.msg(S,int(n))::rpt(n,msg(S,int))) server ∀n.int (ch:sock(S,proto), arr:int[n], len:int(n)) = let loop ∀m.int,m≤n (ch:sock(S,rpt(m,msg(S,int))), x:int(m)) = if x = 0 then unroll(ch); ite_false(ch); close(ch) else unroll(ch); ite_true(ch); send(ch,arr[len-x]) loop(ch,x-1) in forall(ch); send(ch,len); loop(ch,len) end
8. Takeaway untyped sockets • runtime errors • hard to debug • deadlock • resource leak simple session types • type errors • correct use of sockets • deadlock-free • no leak dependent session types • more expressive • quantifiers • recursions • polymorphic sessions
9. Even More Implementations Erlang, C, Javascript Logic Foundation Multirole Logic, Cut-Free Multiparty Sessions Formulatation Lambda Calculus + Some Bi-directional Forwarding Multi-directional Forwarding Used in Classrooms Proof of Deadlock-Freeness Higher-order Sessions
10. learn more at multirolelogic.org Thank you! Hanwen Wu and Hongwei Xi Dec 2017, IBM Programming Language Day