Hazel is a live functional programming environment featuring typed holes.

Quick Summary

Hazel is a live functional programming environment that is able to typecheck, manipulate, and even run incomplete programs, i.e. programs with holes. There are no meaningless editor states.


When programming, we spend a substantial amount of our time working with program text that is not yet a formally complete program, e.g. because there are blank spots, type errors or merge conflicts at various locations. Conventional programming language definitions assign no formal meaning to structures like these, so program editors and other tools have no choice but to resort to complex and ad hoc heuristics to provide various useful language services (like code completion, type inspection, code navigation, and live programming services) without gaps in service.

We are developing a more principled approach to working with incomplete programs, rooted in (contextual modal and gradual) type theory. We model incomplete programs as programs with holes, which (1) stand for parts of the program that are missing; and (2) serve as membranes around parts of the program that are erroneous or, in the collaborative setting, conflicted.

We are implementing these ideas into Hazel, a web-based programming environment for an Elm/ML-like functional programming language being designed from the ground up around typed hole-driven development.

Uniquely, every incomplete program that you can construct using Hazel's language of type-aware edit actions is both statically and dynamically well-defined, i.e. it has a (possibly incomplete) type, and you can run it to produce a (possibly incomplete) result. Consequently, Hazel serves as an elegant platform for research on the future of programming.

The following paper describes our research vision in more detail.

Hazelnut (POPL 2017)

To start, we developed a core calculus, Hazelnut, that contributes (1) a static semantics (i.e. type system) for expressions with holes in both expression and type position, and (2) a language of edit actions that insert holes automatically to ensure that every edit state has static meaning.

The following research paper details Hazelnut.

Hazelnut: A Bidirectionally Typed Structure Editor Calculus
C. Omar, I. Voysey, M. Hilton, J. Aldrich and M. Hammer
POPL 2017 [.bib] [slides]

We have mechanized the metatheory of Hazelnut using the Agda proof assistant.

Hazelnut Live (POPL 2019)

Next, we developed Hazelnut Live, which contributes a dynamic semantics for expressions with holes in both expression and type position.

Rather than stopping as soon as we encounter a hole at run-time, we continue evaluation as far as possible, producing a result containing hole closures. Hole closures allow us to continuously provide granular live feedback to the programmer, and to resume evaluation once a hole is filled.

The following research paper details how we achieve this by adapting machinery from gradual type theory and contextual modal type theory.

Live Functional Programming with Typed Holes
C. Omar, I. Voysey, R. Chugh and M. Hammer
POPL 2019 [.bib]

We have mechanized the metatheory of Hazelnut Live using the Agda proof assistant.

Hazel Assistant (ICFP 2020)

We are developing an intelligent programming assistant that synthesizes code satisfying specifications provided by human programmers in the form of types, tests, and sketches, and further guided by a learned understanding of idiomatic code.

To start with, we developed the Smyth synthesizer, which adds support for sketching to Myth, a type-and-example directed synthesizer, by combining the live programming mechanisms from Hazelnut Live with a novel form of unevaluation, which propagates constraints to where they are relevant. Our approach solves a long-standing problem: we no longer need a trace-complete set of examples.

Program Sketching with Live Bidirectional Evaluation
J. Lubin, N. Collins, C. Omar, and R. Chugh
ICFP 2020 [.bib, tutorial]

We are now working to scale up and integrate Smyth into the Hazel user interface, which requires considering the problems of interactivity, incrementality, and readability. Check out our first demo!

Incubating Ideas

We have a number of ideas incubating — if you're interested in any of these, definitely get in touch. We would also love to hear about other ideas you might have.

Linearly Editing Typed Trees

We are working on a keyboard-driven editing experience that builds on your intuitions from text editing and that supports complex code restructuring patterns. We are doing user studies.

Livelits: Filling Typed Holes with Live GUIs

We are working on allowing programmers to fill holes by direct manipulation of live GUIs with holes.

Collaborative Structure Editing with CRDTs

We are thinking about how to specify an edit action semantics that obeys the invariants necessary to make a Hazelnut program a convergent replicated data type (CRDT).

Hazel Tutor: Guiding Novices Through Type-Driven Development Strategies

We are planning to use Hazel to teach introductory functional programming. We are developing a number of mechanisms to support this, including a type-driven cursor inspector and strategy guide.

Other Applications

As Hazel evolves, we plan to use Hazel to support data analysis (think a next-generation Jupyter). One day, we hope that Hazel will be the foundation for a new kind of computational wiki.

Team Hazel

Hazel is an open source project led by the Future of Programming Lab (FP Lab) at the University of Michigan.

Hazel has benefited from the work of many contributors.

If you are interested in contributing to Hazel, or you'd like to join the Slack where we help folks learn the necessary type theory and discuss project directions, get in touch with Cyrus!


Aug 2020
ICFP 2020 published our Smyth paper.
Sep 2019
Cyrus started as an Assistant Professor at the University of Michigan.
Jan 2019
May 2018
NSF selected the research that Cyrus, Ravi and Matthew proposed for three years of funding.
May 2017
SNAPL 2017 published our vision paper.
Jan 2017
POPL 2017 published our Hazelnut paper.

Recent & Upcoming Talks

Dec 2, 2020
Hannah Potter presented progress on Hazel Tutor at HATRA 2020.
Aug 26, 2020
Justin Lubin presented our Smyth paper at ICFP 2020.
Aug 26, 2020
Zhiyi Pan won Third Place in the Undergraduate category of the ICFP Student Research Competition for her work on Type Hole Inference. Yongwei Yuan also presented his work on Pattern Matching with Typed Holes.
Sep 23, 2019
Cyrus and David presented progress on the Hazel editing experience and livelits at the Midwest PL Summit at Purdue.
Aug 18, 2019
David presented progress on the Hazel editing experience [extended abstract] and Cyrus presented livelits in Hazel [slides, extended abstract] at the TyDe workshop at ICFP 2019 in Berlin.
Jan 17, 2019
Cyrus presented our Hazelnut Live paper at POPL 2019 in Lisbon.
Nov 6, 2018
Cyrus presented Hazel at the LIVE workshop at SPLASH in Boston.
Oct 31, 2018
Cyrus gave a POP seminar at CMU.
Oct 2018
Cyrus presented Hazel at the Midwest PL Summit in Madison.
Sep 2018
Cyrus presented Hazel at Strange Loop in St. Louis.

(h/t Vincent Zeng)