Stefan Holdermans

Generic programming with fixed points for mutually recursive datatypes

Many datatype-generic functions need access to the recursive positions in the structure of the datatype, and therefore adopt a fixed point view on datatypes. Examples include variants of fold that traverse the data following the recursive structure, or the Zipper data structure that enables navigation along the recursive positions. However, Hindley-Milner-inspired type systems with algebraic datatypes make it difficult to express fixed points for anything but regular datatypes. Many real-life examples such as abstract syntax trees are in fact systems of mutually recursive datatypes and therefore excluded. Using Haskells GADTs and type families, we describe a technique that allows a fixed-point view for systems of mutually recursive datatypes. We demonstrate that our approach is widely applicable by giving several examples of generic functions for this view, most prominently the Zipper.

Optimizing generics is easy

Datatype-generic programming increases program reliability by reducing code duplication and enhancing reusability and modularity. Several generic programming libraries for Haskell have been developed in the past few years. These libraries have been compared in detail with respect to expressiveness, extensibility, typing issues, etc., but performance comparisons have been brief, limited, and preliminary. It is widely believed that generic programs run slower than hand-written code. In this paper we present an extensive benchmark suite for generic functions and analyze the potential for automatic code optimization at compilation time. Our benchmark confirms that generic programs, when compiled with the standard optimization flags of the Glasgow Haskell Compiler (GHC), are substantially slower than their hand-written counterparts. However, we also find that more advanced optimization capabilities of GHC can be used to further optimize generic functions, sometimes achieving the same efficiency as hand-written code.

A generic usage analysis with subeffect qualifiers

Sharing analysis and uniqueness typing are static analyses that aim at determining which of a programs objects are to be used at most once. There are many commonalities between these two forms of usage analysis. We make their connection precise by developing an expressive generic analysis that can be instantiated to both sharing analysis and uniqueness typing. The resulting system, which combines parametric polymorphism with effect subsumption, is specified within the general framework of qualified types, so that readily available tools and techniques can be used for the development of implementations and metatheory.

Making "stricterness" more relevant

Adapting a strictness analyser to have it take into account explicit strictness annotations can be a tricky business. Straightforward extensions of analyses based on relevance typing are likely to either be unsafe or fail to pick the fruits of increases in strictness that are introduced through annotations. We propose a more involved adaptation of relevance typing, that can be used to derive strictness analyses that are both safe and effective in the presence of explicit strictness annotations. The resulting type system provides a firm foundation for implementations of type-based strictness analysers in compilers for lazy programming languages such as Haskell and Clean.

Dependently typed grammars

Parser combinators are a popular tool for designing parsers in functional programming languages. If such combinators generate an abstract representation of the grammar as an intermediate step, it becomes easier to perform analyses and transformations that can improve the behaviour of the resulting parser. Grammar transformations must satisfy a number of invariants. In particular, they have to preserve the semantics associated with the grammar. Using conventional type systems, these constraints cannot be expressed satisfactorily, but as we show in this article, dependent types are a natural fit. We present a framework for grammars and grammar transformations using Agda. We implement the left-corner transformation for left-recursion removal and prove a language-inclusion property as use cases.

A lightweight approach to datatype-generic rewriting

Term-rewriting systems can be expressed as generic programs parameterised over the shape of the terms being rewritten. Previous implementations of generic rewriting libraries require users to either adapt the datatypes that are used to describe these terms or to specify rewrite rules as functions. These are fundamental limitations: the former implies a lot of work for the user, while the latter makes it hard if not impossible to document, test, and analyze rewrite rules. In this article, we demonstrate how to overcome these limitations by making essential use of type-indexed datatypes. Our approach is lightweight in that it is entirely expressible in Haskell with GADTs and type families and can be readily packaged for use with contemporary Haskell distributions.

Polyvariant flow analysis with higher-ranked polymorphic types and higher-order effect operators

We present a type and effect system for flow analysis that makes essential use of higher-ranked polymorphism. We show that, for higher-order functions, the expressiveness of higher-ranked types enables us to improve on the precision of conventional let-polymorphic analyses. Modularity and decidability of the analysis are guaranteed by making the analysis of each program parametric in the analyses of its inputs; in particular, we have that higher-order functions give rise to higher-order operations on effects. As flow typing is archetypical to a whole class of type and effect systems, our approach can be used to boost the precision of a wide range of type-based program analyses for higher-order languages.

Heap recycling for lazy languages

Pure functional programming languages preclude destructive updates of heap-allocated data. In such languages, all newly computed algebraic values claim freshly allocated heap space, which typically causes idiomatic programs to be notoriously inefficient when compared to their imperative and impure counterparts. We partly overcome this shortcoming by considering a syntactically light language construct for enabling user-controlled in-place updates of algebraic values. The resulting calculus, that is based on a combination of type-based uniqueness and constructor analysis, is guaranteed to maintain referential transparency and is fully compatible with existing run-time systems for nonstrict, pure functional languages.

Security type error diagnosis for higher-order, polymorphic languages

We combine the type error slicing and heuristics based approaches to type error diagnostic improvement within the context of type based security analysis on a let-polymorphic call by value lambda calculus extended with lists, pairs and the security specific constructs declassify and protect. We define and motivate four classes of heuristics that help diagnose inconsistencies among the constraints, and show their effect on a selection of security incorrect programs. Combines type error slicing with type error diagnosis heuristics.Source language is higher-order and parametrically polymorphic.Features tailored heuristics to deal with parametricity.Features tailored heuristics for dealing with dependency based analyses.A working implementation in Haskell is available.

On the rôle of minimal typing derivations in type-driven program transformation

Standard inference algorithms for type systems involving ML-style polymorphism aim at reconstructing most general types for all let-bound identifiers. Using such algorithms to implement modular program optimisations by means of type-driven transformation techniques generally yields suboptimal results. We demonstrate how this defect can be made up for by using algorithms that target at obtaining so-called minimal typing derivations instead. The resulting approach retains modularity and is applicable to a large class of polyvariant program transformations.