Tom Schrijvers

Swi-prolog

SWI-Prolog is neither a commercial Prolog system nor a purely academic enterprise, but increasingly a community project. The core system has been shaped to its current form while being used as a tool for building research prototypes, primarily for knowledge-intensive and interactive systems. Community contributions have added several interfaces and the constraint (CLP) libraries. Commercial involvement has created the initial garbage collector, added several interfaces and two development tools: PlDoc (a literate programming documentation system) and PlUnit (a unit testing environment). In this article, we present SWI-Prolog as an integrating tool, supporting a wide range of ideas developed in the Prolog community and acting as glue between foreign resources. This article itself is the glue between technical articles on SWI-Prolog, providing context and experience in applying them over a longer period.

Functional and Logic Programming

proceedings of the 11th International symposium on Functional and Logic Programming (FLOPS 2012), held in Kobe, Japan, May 23-25, 2012

Type checking with open type functions

We report on an extension of Haskell with open type-level functions and equality constraints that unifies earlier work on GADTs, functional dependencies, and associated types. The contribution of the paper is that we identify and characterise the key technical challenge of entailment checking; and we give a novel, decidable, sound, and complete algorithm to solve it, together with some practically-important variants. Our system is implemented in GHC, and is already in active use.

Complete and decidable type inference for GADTs

GADTs have proven to be an invaluable language extension, for ensuring data invariants and program correctness among others. Unfortunately, they pose a tough problem for type inference: we lose the principal-type property, which is necessary for modular type inference. We present a novel and simplified type inference approach for local type assumptions from GADT pattern matches. Our approach is complete and decidable, while more liberal than previous such approaches.

Outsidein(x) modular type inference with local assumptions

Advanced type system features, such as GADTs, type classes and type families, have proven to be invaluable language extensions for ensuring data invariants and program correctness. Unfortunately, they pose a tough problem for type inference when they are used as local type assumptions. Local type assumptions often result in the lack of principal types and cast the generalisation of local let-bindings prohibitively difficult to implement and specify. User-declared axioms only make this situation worse. In this paper, we explain the problems and-perhaps controversially-argue for abandoning local let-binding generalisation. We give empirical results that local let generalisation is only sporadically used by Haskell programmers. Moving on, we present a novel constraint-based type inference approach for local type assumptions. Our system, called OutsideIn(X), is parameterised over the particular underlying constraint domain X, in the same way as HM(X). This stratification allows us to use a common metatheory and inference algorithm. OutsideIn(X) extends the constraints of X by introducing implication constraints on top. We describe the strategy for solving these implication constraints, which, in turn, relies on a constraint solver for X. We characterise the properties of the constraint solver for X so that the resulting algorithm only accepts programs with principal types, even when the type system specification accepts programs that do not enjoy principal types. Going beyond the general framework, we give a particular constraint solver for X = type classes + GADTs + type families, a non-trivial challenge in its own right. This constraint solver has been implemented and distributed as part of GHC 7.

Analyses, optimizations and extensions of constraint handling rules: ph.d. summary

This is a summary of the Ph.D. thesis of Tom Schrijvers [4]. Constraint Handling Rules (CHR) [3] is a rule-based language commonly embedded in a host language. It combines elements of Constraint Logic Programming and term rewriting. Several implementations of CHR exist: in Prolog, Haskell, Java and HAL. Typical applications of CHR are in the area of constraint solving, but currently CHR is also used in a wider range of applications, such as type checking, natural language processing and multi-agent systems. In this work we contribute program analyses, program optimizations and extensions of the CHR language. For the optimized compilation of CHR we present several new optimizations: code specialization for ground constraints, anti-monotonic delay avoidance, hashtable constraint stores and a new late storage optimization. These and other optimizations have been implemented in a new state-of-the-art CHR system: the K.U.Leuven CHR system [5] which is currently available in SWI-Prolog [10], XSB [9] and hProlog [2]. Abstract interpretation is a general technique for program analysis [1]. We propose a framework of abstract interpretation for the CHR language [7], in particular for the formulation of analyses that drive program optimization. This frameworks allows for the uniform formulation of program analyses as well as easier improvements and combinations of existing analyses. We also evaluate analyses for theoretical properties, confluence and time complexity, on a practical case study to investigate their relevance. We contribute two extensions to the expressivity of CHR. The first extension comprises the integration of CHR with tabled execution [8]. Tabled execution avoids many forms of non-termination and is useful for automatic program optimization through the dynamic reuse of previous computations. The second extension automatically provides implication checking functionality to constraint solvers written in CHR [6]. Implication checking is an essential building block for formulating complex constraints in terms of basic constraints and for composing constraint solvers.

The computational power and complexity of constraint handling rules

Constraint Handling Rules (CHR) is a high-level rule-based programming language which is increasingly used for general-purpose programming. We introduce the CHR machine, a model of computation based on the operational semantics of CHR. Its computational power and time complexity properties are compared to those of the well-understood Turing machine and Random Access Memory machine. This allows us to prove the interesting result that every algorithm can be implemented in CHR with the best known time and space complexity. We also investigate the practical relevance of this result and the constant factors involved. Finally we expand the scope of the discussion to other (declarative) programming languages.

Optimal union-find in Constraint Handling Rules

Constraint Handling Rules (CHR) is a committed-choice rule-based language that was originally intended for writing constraint solvers. In this paper we show that it is also possible to write the classic union-find algorithm and variants in CHR. The programs neither compromise in declarativeness nor efficiency. We study the time complexity of our programs: they match the almost-linear complexity of the best known imperative implementations. This fact is illustrated with experimental results.

User-definable rule priorities for CHR

This paper introduces CHRrp: Constraint Handling Rules with user-definable rule priorities. CHRrp offers flexible execution control which is lacking in CHR. A formal operational semantics for the extended language is given and is shown to be an instance of the theoretical operational semantics of CHR. It is discussed how the CHR rp semantics influences confluence results. A translation scheme for CHRrp programs with static rule priorities into (regular) CHR is presented. The translation is proven correct and bench-mark results are given. CHRrp is related to priority systems in other constraint programming and rule based languages.

Abstract interpretation for constraint handling rules

Program analysis is essential for the optimized compilation of Constraint Handling Rules (CHRs) as well as the inference of behavioral properties such as confluence and termination. Up to now all program analyses for CHRs have been developed in an ad hoc fashion.In this work we bring the general program analysis methodology of abstract interpretation to CHRs: we formulate an abstract interpretation framework over the call-based operational semantics of CHRs. The abstract interpretation framework is non-obvious since it needs to handle the highly non-deterministic execution of CHRs. The use of the framework is illustrated with two instantiations: the CHR-specific late storage analysis and the more generally known groundness analysis. In addition, we discuss optimizations based on these analyses and present experimental results.