Solving Functional Constraints by Variable Substitution

Functional constraints and bi-functional constraints are an important constraint class in Constraint Programming (CP) systems, in particular for Constraint Logic Programming (CLP) systems. CP systems with finite domain constraints usually employ CSP-based solvers which use local consistency, for example, arc consistency. We introduce a new approach which is based instead on variable substitution. We obtain efficient algorithms for reducing systems involving functional and bi-functional constraints together with other non-functional constraints. It also solves globally any CSP where there exists a variable such that any other variable is reachable from it through a sequence of functional constraints. Our experiments on random problems show that variable elimination can significantly improve the efficiency of solving problems with functional constraints

Refinement Type Inference via Horn Constraint Optimization

We propose a novel method for inferring refinement types of higher-order functional programs. The main advantage of the proposed method is that it can infer maximally preferred (i.e., Pareto optimal) refinement types with respect to a user-specified preference order. The flexible optimization of refinement types enabled by the proposed method paves the way for interesting applications, such as inferring most-general characterization of inputs for which a given program satisfies (or violates) a given safety (or termination) property. Our method reduces such a type optimization problem to a Horn constraint optimization problem by using a new refinement type system that can flexibly reason about non-determinism in programs. Our method then solves the constraint optimization problem by repeatedly improving a current solution until convergence via template-based invariant generation. We have implemented a prototype inference system based on our method, and obtained promising results in preliminary experiments.Comment: 19 page

Liquid Intersection Types

We present a new type system combining refinement types and the expressiveness of intersection type discipline. The use of such features makes it possible to derive more precise types than in the original refinement system. We have been able to prove several interesting properties for our system (including subject reduction) and developed an inference algorithm, which we proved to be sound.Comment: In Proceedings ITRS 2014, arXiv:1503.0437

Constraint Handling Rules with Binders, Patterns and Generic Quantification

Constraint Handling Rules provide descriptions for constraint solvers. However, they fall short when those constraints specify some binding structure, like higher-rank types in a constraint-based type inference algorithm. In this paper, the term syntax of constraints is replaced by $\lambda$-tree syntax, in which binding is explicit; and a new $\nabla$ generic quantifier is introduced, which is used to create new fresh constants.Comment: Paper presented at the 33nd International Conference on Logic Programming (ICLP 2017), Melbourne, Australia, August 28 to September 1, 2017 16 pages, LaTeX, no PDF figure