Colored local type inference

Abstract

We present a type system for a language based on F ≤ , which allows certain type annotations to be elided in actual programs. Local type inference determines types by a combination of type propagation and local constraint solving, rather than by global constraint solving. We refine the previously existing local type inference system of Pierce and Turner[PT98] by allowing partial type information to be propagated. This is expressed by coloring types to indicate propagation directions. Propagating partial type information allows us to omit type annotations for the visitor pattern, the analogue of pattern matching in languages without sum types.

Scalable component abstractions

“…Scala defines a sophisticated type inference system which permits to omit actual type arguments. Type arguments of a method or constructor are inferred from the expected result type and the argument types by local type inference [39,36]. Hence, the body of function main in Listing 3 can also be written without any type arguments: val x = new GenCell(1); val y = new GenCell(2); swap(x, y)…”

A Core Calculus for Scala Type Checking

“…Most of the additional syntactic constructs in full Scala do not cause particular problems for type-checking. However, unlike Featherweight Scala, full Scala has local type inference [30,26]. Local type inference needs to construct least upper bounds and greatest lower bounds (wrt the subtype ordering) of sets of types.…”

Simple, partial type-inference for System F based on type-containment

“…However, VWP also improves over PVWS in at least two significant ways. First, checking and inference modes are carried on types rather than on typing judgments, much as for colored local type inference [OZZ01]. This provides with a more precise control of these modes.…”

“…The first approach is known as local type inference [PT00,OZZ01]. By definition, these solutions cover all of System F. However, they are not yet conservative over ML, that is, there remain ML programs that fail to type without annotations.…”