Type inference with constrained types

Abstract

We present a general framework HM(X) for type systems with constraints. The framework stays in the tradition of the Hindley/Milner type system. Its type system instances are sound under a standard untyped compositional semantics. We can give a generic type inference algorithm for HM(X) so that, under sufficient conditions on X, type inference will always compute the principal type of a term. We discuss instances of the framework that deal with polymorphic records, equational theories, and subtypes. © 1999 John Wiley & Sons, Inc.

Skalpel: A constraint-based type error slicer for Standard ML

“…For example, constraint-based type inference algorithms [43,47,48] separate constraint generation and constraint solving. Many approaches use this idea to improve error reporting.…”

“…Pottier and Rémy define a constraint system [48] that reduces "type inference problems for HM(X) to constraint solving problems". Their HM(X) is similar to Odersky, Sulzmann, and Wehr's HM(X) constraint system [43]. This system is a "general framework for Hindley/Milner style type systems with constraints".…”

OutsideIn(X)Modular type inference with local assumptions

“…To formally describe the problem and our solution in the rest of the paper, we introduce notation and review constraint-based type inference (Pottier & Rémy, 2005;Odersky et al, 1999;Jones, 1992). In constraint-based type inference, constraints appear as part of the type system specification, and the implementation works by generating and solving those constraints.…”

Relaxing the Value Restriction

“…A good choice is Pottier's B(T ) [18], as its typing rules closely match ours. B(T ) was originally developed as an intermediate step in the proof of type soundness for HM(X), a constraint-based polymorphic type system [19]. B(T ) is particular by its extensional approach to polymorphism: polytypes are not expressed syntactically, but as (possibly infinite) sets of ground monotypes.…”