By Sam Lindley, Conor McBride, Phil Trinder, Don Sannella
This quantity is released in Honor of Philip Wadler at the social gathering of his sixtieth birthday, and the gathering of papers shape a Festschrift for him. The contributions are made via a number of the many that recognize Phil and feature been prompted via him. The learn papers integrated the following symbolize a few of the parts within which Phil has been energetic, and the editors thank their colleagues for agreeing to give a contribution to this Festschrift. we try to summarize Phil Wadler's medical achievements. moreover, we describe the private variety and exuberance that Phil has delivered to the subject.
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Extra resources for A List of Successes That Can Change the World: Essays Dedicated to Philip Wadler on the Occasion of His 60th Birthday
A bisimulation of M -lens spans sp 1 :: [A S1 B ]M and sp 2 :: [A S2 B ]M is a M -lens span B ]M where R ⊆ S1 × S2 and fst is a base map from sp to sp 1 sp :: [A R and snd is a base map from sp to sp 2 . We write sp 1 ≡b sp 2 when there is a ♦ bisimulation of spans sp 1 and sp 2 . Figure 2 illustrates the three equivalences diagrammatically. 7. Each of the relations ≡i , ≡s and ≡b are equivalence relations on compatible spans of M -lenses and satisfy (Identity), (Assoc) and (Cong). 8. sp1 ≡i sp2 implies sp1 ≡s sp2 , but not the converse.
One important consideration emphasised by Johnson and Rosebrugh is the need to avoid making all compatible spans equivalent to the “trivial” span B ]M . get · c = id . We chose instead to require h to be a full lens. get · c = id , that is, the (CreateGet) law. We have deﬁned span equivalence as the reﬂexive, symmetric, transitive closure of . Interestingly, even though span equivalence allows for an arbitrary sequence of (pure) lenses between the respective state spaces, it suﬃces to consider only spans of lenses.
Session types are interpreted via the connectives of linear logic— for example, the tensor product A⊗B characterises processes that output values of type A, and then proceed as B. Caires and Pfenning (2010) interpret the proof rules for intuitionistic linear logic as a type system for the π-calculus; they then show that the reduction steps for well-typed π-calculus terms correspond to the cut elimination rules for intuitionistic linear logic. Wadler (2014) adapts their approach to classical linear logic, emphasising the role of duality in typing; in his system, the semantics of terms is given directly by the cut elimination rules.
A List of Successes That Can Change the World: Essays Dedicated to Philip Wadler on the Occasion of His 60th Birthday by Sam Lindley, Conor McBride, Phil Trinder, Don Sannella