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https://github.com/benrbray/type-safari

An interactive tour of type inference algorithms, powered by `ghc-wasm-meta`.
https://github.com/benrbray/type-safari

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An interactive tour of type inference algorithms, powered by `ghc-wasm-meta`.

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# `type-safari`



With this project, I aim to collect reference implementations of type inference algorithms, with particular emphasis on those features which are necessary for practical implementations, such as error reporting and incrementality.  



## Inspiration



* The original code is based off of Stephen Diehl's ["Write You a Haskell"](https://web.archive.org/web/20181017074008/http://dev.stephendiehl.com/fun/006_hindley_milner.html) series (and [corrections](https://github.com/JKTKops/Write-You-a-Haskell-2/blob/master/7/7.5_additions_to_poly.md)), but the implementation has diverged substantially.

* The name (and project) is inspired by Andrej Bauer and Matija Pretnar's ["Programming Language Zoo"](http://plzoo.andrej.com/) and Andras Kovacs' ["Elaboration Zoo"](https://github.com/AndrasKovacs/elaboration-zoo).  I briefly considered *Type Petting Zoo* for the name, but thought it might be a bit too silly :)

* Stephen Dolan's ["Counterexamples in Type Systems"](https://counterexamples.org/title.html)



## Goals



* implement a wide range of type inference algorithms in a consistent style to facilitate comparison

* maintain a clear correspondence between typing judgements on paper and Haskell code

* develop a generic web interface (not necessarily a language server, but something similar) for debugging and for comparing the behavior of different type systems.

  * should show detailed typing information about the typing context at each source position

  * if possible, allow the user to interactively step through the inference procedure



## Road Map / References



Hindley-Milner & Extensions



* [ ] Algorithm W

* [ ] Algorithm M

* [ ] Constraint Generation & First-Order Unification

* [ ] Type Annotations

* [ ] Typed Holes

* [ ] Recursive Definitions

* [ ] Mutual Recursion

* [ ] Pattern Matching

* [ ] Local vs. Top-Level

* [ ] Higher Rank Polymorphism

* [ ] Row Polymorphism

* [ ] Units of Measure, Commutative Group Unification a la [Gundry 2013](https://adam.gundry.co.uk/pub/thesis/thesis-2013-12-03.pdf)



Normalization by Evaluation



Type Inference for Dependent Types



* [ ] Calculus of Constructions

* [ ] Calculus of Inductive Constructions

* [ ] Bidirectional Type Inference

* [ ] Higher-Order Unification, Pattern Unification



## Uncategorized



Here are some topics I hope to cover, but I'm not quite sure how/where they fit in:



* interacttions between Hindley-Milner and subtyping

  * subsumption, and Haskell's "simplified subsumption"

  * Stephen Dolan's [Algebraic Subtyping](https://api.repository.cam.ac.uk/server/api/core/bitstreams/d50b4d1a-a688-46eb-bb4f-9f4e204d0f60/content)

* ML's value restriction, and OCaml's relaxation of the value restriction



## Resources



Hindley-Milner



* Ben Lynn, ["Hindley-Milner Type Inference (Outcoding Unix Geniuses)"](https://crypto.stanford.edu/~blynn/lambda/hm.html)

* Okmij, ["How OCaml Type Checker Works -- or What Polymorphism and Garbage Collection Have in Common"](https://okmij.org/ftp/ML/generalization.html)

  * explains Rémy's "efficient level-based generalization" [Rémy 1992, "Extension of ML Type System with a Sorted Equational Theory on Types"](http://gallium.inria.fr/~remy/ftp/eq-theory-on-types.pdf)

* StackOverflow, ["What part of Hindley-Milner do you not understand?"](https://stackoverflow.com/questions/12532552/what-part-of-hindley-milner-do-you-not-understand/42034379#42034379)

* Jones 2000, ["Typing Haskell in Haskell"](https://web.cecs.pdx.edu/~mpj/thih/thih.pdf)

* Brian McKenna 2013, ["Bottom-Up Type Annotation with the Cofree Comonad"](https://brianmckenna.org/blog/type_annotation_cofree)

  * a partial implementation (missing let-generalization) of Heeren2002's constraint-based Hindley-Milner using `Cofree` to represent annotated AST

* Kaminski 2010, ["Who ordered skolem constants?"](https://genericlanguage.wordpress.com/2010/08/23/who-ordered-skolem-constants/) (and [discussion](https://www.reddit.com/r/haskell/comments/d4v83/who_ordered_skolem_constants/))

* Vytiniotis 2010, ["Let should not be Generalized"](https://web.archive.org/web/20170530210526/https://www.microsoft.com/en-us/research/wp-content/uploads/2016/02/tldi10-vytiniotis.pdf)



System F



* Ben Lynn, ["System F"](https://crypto.stanford.edu/~blynn/lambda/systemf.html)



Bidirectional Type Inference



* Pfenning 2004, ["Lecture Notes on Bidirectional Type-Checking"](https://www.cs.cmu.edu/~fp/courses/15312-f04/handouts/15-bidirectional.pdf)

* Pierce & turner 2000, ["Local Type Inference"](https://www.cis.upenn.edu/~bcpierce/papers/lti-toplas.pdf)

  * Type inference algorithms have not caught up with the development of type _systems_, because it is hard to guarantee completeness.  Instead, this paper presents a bidirectional _local type inference_ algorithm for _partial type inference_.

* Dunfield & Krishnaswami 2013, ["Complete and Easy Bidirectional Typechecking for Higher-Rank Polymorphism"](https://www.cl.cam.ac.uk/~nk480/bidir.pdf)



Optimizations



* Gamari 2019, ["Writing Efficient Free Variable Traversals"](https://www.haskell.org/ghc/blog/20190728-free-variable-traversals.html)



Miscellaneous



* Scott 2019, ["The Surprising Rigidness of Higher-Rank Kinds"](https://ryanglscott.github.io/2019/07/10/the-surprising-rigidness-of-higher-rank-kinds/)