A Simple Take on Typed Abstract Syntax in Haskell-like Languages

We present a simple way to program typed abstract syntax in a language following a Hindley-Milner typing discipline, such as Haskell and ML, and we apply it to automate two proofs about normalization functions as embodied in type-directed partial evaluation for the simply typed lambda calculus: normalization functions (1) preserve types and (2) yield long beta-eta normal forms.Keywords: Type-directed partial evaluation, normalization functions, simply-typed lambda-calculus, higher-order abstract syntax, Haskell

Dynamically typed languages

Dynamically typed languages such as Python and Ruby have experienced a rapid grown in popularity in recent times. However, there is much confusion as to what makes these languages interesting relative to statically typed languages, and little knowledge of their rich history. In this chapter I explore the general topic of dynamically typed languages, how they differ from statically typed languages, their history, and their defining features

A Modular Toolkit for Distributed Interactions

We discuss the design, architecture, and implementation of a toolkit which supports some theories for distributed interactions. The main design principles of our architecture are flexibility and modularity. Our main goal is to provide an easily extensible workbench to encompass current algorithms and incorporate future developments of the theories. With the help of some examples, we illustrate the main features of our toolkit.Comment: In Proceedings PLACES 2010, arXiv:1110.385

Initial Algebra Semantics for Cyclic Sharing Tree Structures

Terms are a concise representation of tree structures. Since they can be naturally defined by an inductive type, they offer data structures in functional programming and mechanised reasoning with useful principles such as structural induction and structural recursion. However, for graphs or "tree-like" structures - trees involving cycles and sharing - it remains unclear what kind of inductive structures exists and how we can faithfully assign a term representation of them. In this paper we propose a simple term syntax for cyclic sharing structures that admits structural induction and recursion principles. We show that the obtained syntax is directly usable in the functional language Haskell and the proof assistant Agda, as well as ordinary data structures such as lists and trees. To achieve this goal, we use a categorical approach to initial algebra semantics in a presheaf category. That approach follows the line of Fiore, Plotkin and Turi's models of abstract syntax with variable binding

Linear Haskell: practical linearity in a higher-order polymorphic language

Linear type systems have a long and storied history, but not a clear path forward to integrate with existing languages such as OCaml or Haskell. In this paper, we study a linear type system designed with two crucial properties in mind: backwards-compatibility and code reuse across linear and non-linear users of a library. Only then can the benefits of linear types permeate conventional functional programming. Rather than bifurcate types into linear and non-linear counterparts, we instead attach linearity to function arrows. Linear functions can receive inputs from linearly-bound values, but can also operate over unrestricted, regular values. To demonstrate the efficacy of our linear type system - both how easy it can be integrated in an existing language implementation and how streamlined it makes it to write programs with linear types - we implemented our type system in GHC, the leading Haskell compiler, and demonstrate two kinds of applications of linear types: mutable data with pure interfaces; and enforcing protocols in I/O-performing functions