A small Haskell implementation of Complete and Easy Bidirectional Typechecking for Higher-Rank Polymorphism
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A small Haskell implementation of Complete and Easy Bidirectional Typechecking for Higher-Rank Polymorphism. This is a sister project to the Racket implementation, which is adapted from this one.

This implementation is designed to be both simple and relatively complete. Where the two conflict, it prefers simplicity. This means that there is no source location reporting for type errors, for example, which would considerably complicate the implementation, but it does attempt to provide good error messages with the information it has.

The executable built by this project implements a simple REPL. You can run it from the command line with stack:

$ stack build
$ stack exec higher-rank
> ()
() : ()
> (\x -> x)
(\x -> x) : (a1' -> a1')
> ((\x -> x) ())
() : ()

The implementation is divided among the following modules:

  • Language.HigherRank.Types — Holds type definitions used by other modules. This module mostly only exists to break module loading cycles between the printer and interpreter/typechecker.

  • Language.HigherRank.Typecheck — The core implementation of the typechecker, which contains all of the code that implements the actual paper. If you are only interested in the typechecking algorithm and aren’t interested in the interpreter or REPL, you can focus exclusively on this module and Language.HigherRank.Types.

  • Language.HigherRank.Interpret — Contains the implementation of a very simple interpreter, which evaluates expressions without doing any typechecking.

  • Language.HigherRank.Parse — Contains monadic parsers for parsing both types and expressions, the results of which may be fed to the typechecker or interpreter.

  • Language.HigherRank.Print — Implements pretty-printers for types, expressions, and reduced expressions, which are the results of the interpreter. This is used to print results in the REPL as well as format types and expressions in error messages.

  • Language.HigherRank.Main — This implements the actual REPL by combining all of the above pieces together.