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A session type is an abstraction of a set of sequences of heterogeneous values sent and received over a communication channel. Session types can be used for specifying stream-based Internet protocols.

Abstract. We use a code generator—type-directed partial evaluation— to verify conversions between isomorphic types, or more precisely to verify that a composite function is the identity function at some complicated type. A typed functional language such as ML provides a natural support to express the functions and type-directed partial evaluation provides a convenient setting to obtain the normal form of their composition. However, off-the-shelf type-directed partial evaluation turns out to yield gigantic normal forms. We identify that this gigantism is due to redundancies, and that these redundancies originate in the handling of sums, which uses delimited continuations. We successfully eliminate these redundancies by extending type-directed partial evaluation with memoization capabilities. The result only works for pure functional programs, but it provides an unexpected use of code generation and it yields orders-of-magnitude improvements both in time and in space for type isomorphisms. 1

The notion of program transformation is ubiquitous in programming language studies on interpreters, compilers, partial evaluators, etc. In order to implement a program transformation, we need to choose a representation in the meta language, that is, the programming language in which we construct programs, for representing object programs, that is, the programs in the object language on which the program transformation is to be performed. In practice, most representations chosen for typed...

Contents Fun with phantom types 5 Fun with phantom types Haskell is renowned for its many extensions to the Hindley-Milner type system (type classes, polymorphic recursion, rank-n types, existential types, functional dependencies---just to name a few). In this chapter we look at yet another extension. I can hear you groaning but this is quite a mild extension and one that fits nicely within the Hindley-Milner framework. Of course, whenever you add a new feature to a language, you should throw out an existing one (especially if the language at hand is named after a logician). Now, for this chapter we abandon type classes---judge for yourself how well we get along without Haskell's most beloved feature. 1 Introducing phantom types Suppose you want to embed a programming language, say, a simple expression language in Haskell. Since you are a firm believer of static typing, you would like your embedded language to be statically typed, as well. This requirement rules out a simple Term dat

We give a Haskell implementation of Filinski’s normalisation by evaluation algorithm for the computational lambda-calculus with sums. Taking advantage of extensions to the GHC compiler, our implementation represents object language types as Haskell types and ensures that type errors are detected statically. Following Filinski, the implementation is parameterised over a residualising monad. The standard residualising monad for sums is a continuation monad. Defunctionalising the uses of the continuation monad we present the binding tree monad as an alternative. 1

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