This paper presents a library for programming with polymorphic dynamic types in the dependently typed programming language Agda. The resulting library allows dynamically typed values with a polymorphic type to be instantiated to a less general (possibly monomorphic) type without compromising type soundness.

This paper presents a semantics of self-adjusting computation and proves that the semantics is correct and consistent. The semantics introduces memoizing change propagation, which enhances change propagation with the classic idea of memoization to enable reuse of computations even when memory is mutated via side effects. During evaluation, computation reuse via memoization triggers a change-propagation algorithm that adapts the reused computation to the memory mutations (side effects) that took place since the creation of the computation. Since the semantics includes both memoization and change propagation, it involves both non-determinism (due to memoization) and mutation (due to change propagation). Our consistency theorem states that the non-determinism is not harmful: any two evaluations of the same program starting at the same state yield the same result. Our correctness theorem states that mutation is not harmful: Self-adjusting programs are compatible with purely functional programming. We formalize the semantics and its meta-theory in the LF logical framework and machine check our proofs using Twelf.

Refactoring is the process of changing the design of a program without changing what it does. Typical refactorings, such as function extraction and generalisation, are intended to make a program more amenable to extension, more comprehensible and so on. Refactorings differ from other sorts of program transformation in being applied to source code, rather than to a ‘core’ language within a compiler, and also in having an effect across a code base, rather than to a single function definition, say. Because of this, there is a need to give automated support to the process. This paper reflects on our experience of building tools to refactor functional programs written in Haskell (HaRe) and Erlang (Wrangler). We begin by discussing what refactoring means for functional programming languages, first in theory, and then in the context of a larger example. Next, we address system design and details of system implementation as well as contrasting the style of refactoring and tooling for Haskell and Erlang. Building both tools led to reflections about what particular refactorings mean, as well as requiring analyses of various kinds, and we discuss both of these. We also discuss various extensions to the core tools, including integrating the tools with test frameworks; facilities for detecting and eliminating code clones; and facilities to make the systems extensible by users. We then reflect on our work by drawing some general conclusions, some of which apply particularly to functional languages, while many others are of general value.