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 few of the many that be aware of Phil and feature been inspired through him. The examine papers integrated the following characterize a number of the components 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 clinical achievements. furthermore, we describe the non-public 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
The key constructors of session types include input and output, characterising the exchange of data, and internal and external choice, characterising branching evaluation. Honda’s typing discipline assures session fidelity, meaning that at each synchronisation the communicating 34 R. Atkey et al. processes agree on the types of values exchanged. His system is extended to πcalculus-like processes by Takeuchi et al. (1994) and Honda et al. (1998). Session typing relies on a substructural type system to assure session ﬁdelity; however, Honda did not relate his types to the propositions of linear logic, and he relies on a self-dual type for closed channels.
Fiore (2007) shows that conﬂation of products and coproducts into biproducts is equivalent to the existence of a monoidal structure on morphisms; we will attempt a similar conﬂation (Sect. 3) Conﬂation Confers Concurrency 35 to give a logical interpretation of nondeterminism. Compact closed categories provide a model of classical linear logic in which ⊗ and are identiﬁed; we will consider a similar conﬂation as well (Sect. 2). However, we do not yet understand the exact relationship between compact closed categories, and our system with the multicut rule.
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. ♦ 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.