Polymorphic algebraic data type reconstruction

Abstract

One of the disadvantages of statically typed languages is the programming overhead caused by writing all the necessary type information: Both type declarations and type definitions are typically required. Traditional type inference aims at relieving the programmer from the former.We present a rule-based constraint rewriting algorithm that reconstructs both type declarations and type definitions, allowing the programmer to effectively program type-less in a strictly typed language. This effectively combines strong points of dynamically typed languages (rapid prototyping) and statically typed ones (documentation, optimized compilation). Moreover it allows to quickly port code from a statically untyped to a statically typed setting.Our constraint-based algorithm reconstructs uniform polymorphic definitions of algebraic data types and simultaneously infers the types of all expressions and functions (supporting polymorphic recursion) in the program. The declarative nature of the algorithm allows us to easily show that it has a number of highly desirable properties such as soundness, completeness and various optimality properties. Moreover, we show how to easily extend and adapt it to suit a number of different language constructs and type system features.

As time goes by: Constraint Handling Rules

“…Coquery and Fages (2003; presented TCLP, a CHR-based type checker for Prolog and CHR(Prolog) that deals with parametric polymorphism, subtyping and overloading. Schrijvers and Bruynooghe (2006) reconstruct type definitions for untyped functional and logic programs.…”

From Monomorphic to Polymorphic Well-Typings and Beyond

“…The type signature of non-recursive predicate calls is an instance of the predicate signature, rather than being identical to it. In [5] a type inference is described that allows this also for recursive calls. It is straightforward to adapt that approach to the current setting where recursive calls have the same signature as the predicate (only the constraint derivation phase needs to be altered).…”

“…The motivation of the restriction is that it can be computationally very demanding when a recursive call is allowed to have a type that is a true instance of the definition's type. Indeed, [2] showed that type checking in a similar setting is undecidable, and [5] gave strong indications that this undecidability also holds for type inference in the above setting. Applied on Example 1, polymorphic type inference [5] gives: :-app(list1(T),list2(T),list2(T)).…”

“…Indeed, [2] showed that type checking in a similar setting is undecidable, and [5] gave strong indications that this undecidability also holds for type inference in the above setting. Applied on Example 1, polymorphic type inference [5] gives: :-app(list1(T),list2(T),list2(T)). :-p(list2(list2(elem))).…”

“…However, the rules presented there are incomplete. We refer to [5] for a comprehensive set. In this paper, we revisit the problem of inferring a polymorphic typing.…”