Type Inference and Principal Typings for Symmetric Record Concatenation and Mixin Modules

The obvious simple type system for a λ-calculus extended with recordconcatenation has a typability problem that was believed to be expensive,and which we prove NP-complete. Some previous approaches to this prob-lem employ subtyping polymorphism. We present Bowtie, a system of simpletypes for record concatenation which has principal typings, no subtyping, anda clean separation between unification-based type inference with type androw variables and constraint solving for safety of concatenation and fieldselection. Because Bowtie has no subtyping, we succeeded in straightfor-wardly generalizing it to a similar type system, Martini, for mixin modules.The type inference complexity for both systems is O(n), or O(n) given abounded number of field labels. We have implemented type inference forboth type systems. Because they have principal typings, extending eitherwith Milner’s let-polymorphism is straightforward.