strategies
A simple implementation of session-based streams
A winning player strategy (WPS) is a sequence of well-bracketed winning opponent strategies. A winning opponent strategy (WOS) is a sequence of well-bracketed winning player strategies.
In symbols
WPS ::= ( WBOS )*
WOS ::= ( WBPS )*
WBOS ::= "(" WOS ")"
WBPS ::= "[" WPS "]"
We interpret these as denoting successful sessions. For example, to interpret HTTP we think of Player as the client and Opponent as the server; thus, "(" is taken as an outgoing HTTP GET request (i.e. the request as seen from the client code), and ")" as an incoming HTTP GET server response (i.e. the response as seen from the client code ). Then, the trace of a non-crashing HTTP client is ()()() ... (), and this trace clearly inhabits WPS.
Similarly, if we take "[" as the incoming HTTP GET request (i.e. the request as seen from the server code) and "]" as the outgoing HTTP GET response (i.e. the response as seen from the server code), then the trace of a non-crashing HTTP server is [][][] ... [], and this trace clearly inhabits WOS.
Note, however, that in HTTP the server cannot initiate a call back to a client in response to a request. This is tantamount to a mechanism for session state, and HTTP is noted for its lack of ability to properly handle session state -- a short-coming in protocol hygene that has left cookie crumbs all over the Internet.
In the view of protocols taken here we do get sessions, without sacrificing much of what makes HTTP attractive. Obviously, the protocol structure is simple. It takes a maximum of four lines to specify all legal traces. Yet, it's rich enough to model basic HTTP. Beyond that it provides an explicit representation of session state, while making client and server roles completely symmetric. Of equal importance, this model maps directly to models of Linear Logic. As a result, all of the tools of nearly 30 years of investigation into the computational interpretation of that logic are available to allow us to reason about protocols structured in this way.