A Bowtie for a Beast: Overloading, Eta Expansion, and Extensible Data Types in F⋈

We present a novel approach to generic programming over extensible data types. Row types capture the structure of records and variants, and can be used to express record and variant subtyping, record extension, and modular composition of case branches. We extend row typing to capture generic programming over rows themselves, capturing patterns including lifting operations to records and variations from their component types, and the duality between cases blocks over variants and records of labeled functions, without placing specific requirements on the fields or constructors present in the records and variants. We formalize our approach in System R𝜔, an extension of F𝜔 with row types, and give a denotational semantics for (stratified) R𝜔 in Agda.

Generic Programming with Extensible Data Types: Or, Making Ad Hoc Extensible Data Types Less Ad Hoc

Hubers,

Morris

2023

Polymorphic Type Inference for Dynamic Languages

Castagna,

Laurent,

Nguyễn

2024

We present a type system that combines, in a controlled way, first-order polymorphism with intersection types, union types, and subtyping, and prove its safety. We then define a type reconstruction algorithm that is sound and terminating. This yields a system in which unannotated functions are given polymorphic types (thanks to Hindley-Milner) that can express the overloaded behavior of the functions they type (thanks to the intersection introduction rule) and that are deduced by applying advanced techniques of type narrowing (thanks to the union elimination rule). This makes the system a prime candidate to type dynamic languages.

Contextual Typing

Xue,

Oliveira

2024

Bidirectional typing is a simple, lightweight approach to type inference that propagates known type information during typing, and can scale up to many different type systems and features. It typically only requires a reasonable amount of annotations and eliminates the need for many obvious annotations. Nonetheless the power of inference is still limited, and complications arise in the presence of more complex features. In this paper we present a generalization of bidirectional typing called contextual typing . In contextual typing not only known type information is propagated during typing, but also other known information about the surrounding context of a term. This information can be of various forms, such as other terms or record labels. Due to this richer notion of contextual information, less annotations are needed, while the approach remains lightweight and scalable. For type systems with subtyping, contextual typing subsumption is also more expressive than subsumption with bidirectional typing, since partially known contextual information can be exploited. To aid specifying type systems with contextual typing, we introduce Q uantitative T ype A ssignment S ystem s (QTASs). A QTAS quantifies the amount of type information that a term needs in order to type check using counters. Thus, a counter in a QTAS generalizes modes in traditional bidirectional typing, which can only model an all (checking mode) or nothing (inference mode) approach. QTASs enable precise guidelines for annotatability of contextual type systems formalized as a theorem. We illustrate contextual typing first on a simply typed lambda calculus, and then on a richer calculus with subtyping, intersection types, records and overloading. All the metatheory is formalized in the Agda theorem prover.