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

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 by means of many of the many that comprehend Phil and feature been motivated by means of him. The study papers incorporated right here symbolize the various parts 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 clinical achievements. moreover, 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

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Mget s , Just s ); 22 F. Abou-Saleh et al. 12. If sl :: SMLens Id C A B is well-behaved, then smlens2span sl is also well-behaved, with state space S consisting of the consistent triples of sl . ♦ Proof. First we show that, given a symmetric lens sl , the operations of sp = smlens2span sl preserve consistency of the state. Assume (a, b, c) is consistent. mput R (a , c). mput R (a , c ) = return (b , c ) is symmetric. mput R (a , c ) = [[ above, and (PutLRM) ]] return (b , c ) as required. mput (a, b, c) b is consistent is dual.

E. those for which do {a ← x ; b ← y; return (a, b)} = do {b ← y; a ← x ; return (a, b)} but this rules out many interesting monads, such as State and IO. 2 Entangled State Monads The types of the mput R and mput L operations of symmetric lenses can be seen (modulo mild reordering) as stateful operations in the state monad State γ α = γ → (α, γ), where the state γ = C . This observation was also anticipated by Hofmann et al. In a sequence of papers, we considered generalising these operations and their laws to an arbitrary monad (Cheney et al.

The only actual data that may be transmitted between processes are single bits, which take the form of a choice between a pair of sessions. Transmission of a single bit is represented by internal choice between two empty outputs. Bool = 1 ⊕ 1 Dually, receiving a single bit is represented by an external choice between two empty inputs. Bool⊥ = ⊥ & ⊥ The other propositional connectives of CLL can now be used to build more complex specifications. For example, we can write down the type of a server that offers a choice of a binary operation on booleans (single bits) and a unary operation on booleans, arbitrarily many times.

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