By Sam Lindley, Conor McBride, Phil Trinder, Don Sannella
This quantity is released in Honor of Philip Wadler at the get together of his sixtieth birthday, and the gathering of papers shape a Festschrift for him. The contributions are made through a number of the many that understand Phil and feature been stimulated by way of him. The study papers incorporated the following characterize many of the components within which Phil has been lively, and the editors thank their colleagues for agreeing to give a contribution to this Festschrift. we try to summarize Phil Wadler's clinical achievements. moreover, we describe the private sort and exuberance that Phil has dropped at the subject.
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Extra info for A List of Successes That Can Change the World: Essays Dedicated to Philip Wadler on the Occasion of His 60th Birthday
The inner part of the type is an internal choice (⊕), indicating that the implementation of this type must make a choice between the two services. The two choices then describe the same pattern as the server, but from the point of view of the client. The left-hand choice ⊥ can be read as “the client must output two booleans, Bool ⊗ Bool ⊗ Bool⊥ input a boolean, and then signal the end of the session”. The right-hand choice is similar, but only speciﬁes the output of a single boolean. 2 Terms and Typing The terms of CP are given by the following grammar.
Sp1 ≡i sp2 implies sp1 ≡s sp2 , but not the converse. ♦ 16 F. Abou-Saleh et al. S1 S1 S1 fst A B A S B A R ⊆ S1 ×S2 B snd S2 S2 S2 (a) (b) (c) Fig. 2. (a) Isomorphism equivalence (≡i ), (b) span equivalence (≡s ), and (c) bisimulation (≡b ) equivalence. In (c), the dotted arrows are base maps; all other arrows are (monadic) lenses. Proof. get cannot be the identity function. 9. Given sp 1 :: [A sp 2 then sp 1 ≡b sp 2 . S1 B ]M , sp 2 :: [A S2 B ]M , if sp 1 ≡s ♦ Proof. get s1 = s2 }, and constructing an appropriate span sp : A R B .
Dardha and P´erez (2015) compare Kobayashi’s approach with the linear-logic based approaches of Caires, Pfenning, and Wadler. They observe that the linear logic-based approaches coincide with that of Kobayashi when restricted to one shared channel between processes. They also give a rewriting procedure from Kobayashi-typable processes with multiple shared channels to processes with one shared channel, and show an operational correspondence between the original and rewritten processes. Some of our results above are reminiscent of results obtained in categorytheoretic settings closely related to linear logic.