Hazelnut: A Bidirectionally Typed Structure Editor Calculus

TL;DR

Hazelnut introduces a formal, bidirectionally typed structure editor calculus that handles incomplete programs with holes, enabling flexible, type-safe program editing and providing a foundation for future tool development.

Contribution

It presents a formal lambda calculus for typed structure editing with holes, extending prior work by handling incomplete terms safely and guiding implementation strategies.

Findings

Hazelnut's semantics support safe editing of incomplete programs.

The calculus connects with gradual typing and modal type theory.

Mechanized in Agda, it informs implementation as a functional reactive system.

Abstract

Structure editors allow programmers to edit the tree structure of a program directly. This can have cognitive benefits, particularly for novice and end-user programmers. It also simplifies matters for tool designers, because they do not need to contend with malformed program text. This paper defines Hazelnut, a structure editor based on a small bidirectionally typed lambda calculus extended with holes and a cursor. Hazelnut goes one step beyond syntactic well-formedness: its edit actions operate over statically meaningful incomplete terms. Naively, this would force the programmer to construct terms in a rigid "outside-in" manner. To avoid this problem, the action semantics automatically places terms assigned a type that is inconsistent with the expected type inside a hole. This safely defers the type consistency check until the term inside the hole is finished. Hazelnut is a foundational type-theoretic account of typed structure editing, rather than an end-user tool itself. To that end, we describe how Hazelnut's rich metatheory, which we have mechanized in Agda, guides the definition of an extension to the calculus. We also discuss various plausible evaluation strategies for terms with holes, and in so doing reveal connections with gradual typing and contextual modal type theory, the Curry-Howard interpretation of contextual modal logic. Finally, we discuss how Hazelnut's semantics lends itself to implementation as a functional reactive program. Our reference implementation is written using js_of_ocaml.