Jason (jcreed) wrote,

Frank talked a bit about some work he's been doing with Luis on term assignment for sequent proofs in linear logic, with the terms being pi-calculus processes. I find it rather mysterious but quite interesting, for as I mentioned in an email to drl and wjl, I think I usually think of the pi calculus not as a functional programming language, but as a logic programming language --- I can't really account for the peculiar symmetric negotiation between reads and writes that the synchronous pi calculus does (if I remember right) but execution of process P in the asynchronous pi calculus seems to be utterly explainable-away as focusing proof search for a proof of P* |- 1, given the translation
(P + P)*  = (P* & P*)                                                           
0*        = 1                                                                   
(P | P)*  = P* tensor P*                                                        
(nu x.P)* = exists x . P*                                                       
(!P)*     = !(P*)                                                               
(c(x).P)* = all x . msg(c,x) -o P*                                              
(c<d>)* = msg(c,d)   

where the quantifiers range over some first-order domain of "channels", and msg is some positive atom that takes two channels.
Tags: logic, pi calculus

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