Sam Lindley, Conor McBride, Phil Trinder, Don Sannella's A List of Successes That Can Change the World: Essays PDF

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By Sam Lindley, Conor McBride, Phil Trinder, Don Sannella

ISBN-10: 3319309358

ISBN-13: 9783319309354

ISBN-10: 3319309366

ISBN-13: 9783319309361

This quantity is released in Honor of Philip Wadler at the celebration of his sixtieth birthday, and the gathering of papers shape a Festschrift for him. The contributions are made via many of the many that recognize Phil and feature been motivated by means of him. The examine papers integrated the following characterize a number of the components during 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. furthermore, we describe the private variety and exuberance that Phil has delivered to the subject.

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Figure 1 gives the typing rules of CP. The typing judgement is of the form P Γ , where P is a CP process term, and Γ is a channel typing environment. A for some type A. Note that CP’s typing rules implicitly rebind identifiers: for example, in the hypothesis of the rule for , x identifies a proof of B, while in the conclusion it identifies a proof of A B. CP includes two rules that are logically derivable: the axiom rule, which is interpreted as channel forwarding, and the cut rule, which is interpreted as process composition.

Abou-Saleh et al. create b) It suffices to construct a span sp = (l , r ) :: S1 and l ; r1 = r ; r2 . get s2 ) Notice that by construction l :: R S1 and r :: R S2 , that is, since we have used l0 and r0 to define l and r , we do not need to do any more work to check that the pairs produced by create and put remain in R. Notice also that l and r only use the lenses l1 and l2 , not r1 and r2 ; we will show nevertheless that they satisfy the required properties. First, to show that l ; l1 = r ; l2 , we proceed as follows for each operation.

This is complicated by the fact that the complement types of the composition idsl ; sl and of sl differ, so it is not even type-correct to ask whether idsl ; sl and sl are equal. To make it possible to relate the behaviour of symmetric lenses with different complement types, Hofmann et al. 1. Suppose R ⊆ C1 ×C2 . Then f ∼R g means that for all c1 , c2 , x , if (c1 , c2 ) ∈ R and (y, c1 ) = f (x , c1 ) and (y , c2 ) = g (y, c2 ), then y = y and ♦ (c1 , c2 ) ∈ R. 2 (Symmetric Lens Equivalence). Two symmetric lenses sl 1 :: C C 1 2 X ←→ Y and sl 2 :: X ←→ Y are considered equivalent (sl 1 ≡sl sl 2 ) if there is a relation R ⊆ C1 × C2 such that 1.

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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


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