Autogeneration of functor and monad instances for Scala types

Mercator makes it possible to abstract over monads and functors, automatically constructing contextual instances for types with the requisite methods.

This allows generic implementations of sequence and traverse to be provided for all types which define map and flatMap, provided an appropriate implementation of Point (providing the monadic "unit" operation) can be found.

• provides an abstraction over functor-like and monad-like types
• generates Monad, Functor and Point typeclasses for type constructors
• constructs a monad typeclass instance for any type with flatMap, map and a "unit" constructor
• implements sequence and traverse extension methods for instances of monadic types

It is not possible to write code such as,

def increment[MonadicType[_]](xs: MonadicType[Int]) =
  for(x <- xs) yield x + 1

because the compiler is not able to express the constraint that the type constructor F[_] provides the methods map and flatMap (with the correct signatures), which are necessary for the for-comprehension to compile.

With Mercator, it is possible to demand a contextual instance of Monad[MonadicType] to enforce this constraint. Mercator will automatically instantiate such an instance at the use-site for any type which has the required methods, like so,

import mercator._
def increment[F[_]: Monad](xs: F[Int]) = for(x <- xs) yield x + 1

The methods flatMap and map will be provided to the instance of F[_] as extension methods, which are then used by the for-comprehension.

An instance of Monad[F] will generate an implementation of point (sometimes called "unit", though not to be confused with Unit) which constructs a new instance of the type from a single value. For example, point(x) for Option is Some(x), or for Either it is Right(x). This implementation assumes the existence of a unique apply method on the type's companion object, and that applying the value to it will produce a result of the correct type.

A Point[MonadicType] instance can always be provided to explicitly specify the point instance for the given type constructor.

Mercator also provides a Functor typeclass, which provides implementations of just point and map. If map is required for a particular operation, but flatMap is not, then only the Functor typeclass should be summoned.

Mercator is classified as embryotic. For reference, Soundness projects are categorized into one of the following five stability levels:

• embryonic: for experimental or demonstrative purposes only, without any guarantees of longevity
• fledgling: of proven utility, seeking contributions, but liable to significant redesigns
• maturescent: major design decisions broady settled, seeking probatory adoption and refinement
• dependable: production-ready, subject to controlled ongoing maintenance and enhancement; tagged as version 1.0.0 or later
• adamantine: proven, reliable and production-ready, with no further breaking changes ever anticipated

Projects at any stability level, even embryonic projects, can still be used, as long as caution is taken to avoid a mismatch between the project's stability level and the required stability and maintainability of your own project.

Mercator is designed to be small. Its entire source code currently consists of 211 lines of code.

Mercator will ultimately be built by Fury, when it is published. In the meantime, two possibilities are offered, however they are acknowledged to be fragile, inadequately tested, and unsuitable for anything more than experimentation. They are provided only for the necessity of providing some answer to the question, "how can I try Mercator?".

1. Copy the sources into your own project

   Read the fury file in the repository root to understand Mercator's build structure, dependencies and source location; the file format should be short and quite intuitive. Copy the sources into a source directory in your own project, then repeat (recursively) for each of the dependencies.

   The sources are compiled against the latest nightly release of Scala 3. There should be no problem to compile the project together with all of its dependencies in a single compilation.

2. Build with Wrath

   Wrath is a bootstrapping script for building Mercator and other projects in the absence of a fully-featured build tool. It is designed to read the fury file in the project directory, and produce a collection of JAR files which can be added to a classpath, by compiling the project and all of its dependencies, including the Scala compiler itself.

   Download the latest version of wrath, make it executable, and add it to your path, for example by copying it to /usr/local/bin/.

   Clone this repository inside an empty directory, so that the build can safely make clones of repositories it depends on as peers of mercator. Run wrath -F in the repository root. This will download and compile the latest version of Scala, as well as all of Mercator's dependencies.

   If the build was successful, the compiled JAR files can be found in the .wrath/dist directory.

Contributors to Mercator are welcome and encouraged. New contributors may like to look for issues marked beginner.

We suggest that all contributors read the Contributing Guide to make the process of contributing to Mercator easier.

Please do not contact project maintainers privately with questions unless there is a good reason to keep them private. While it can be tempting to repsond to such questions, private answers cannot be shared with a wider audience, and it can result in duplication of effort.

Mercator was designed and developed by Jon Pretty, and commercial support and training on all aspects of Scala 3 is available from Propensive OÜ.

Gerardus Mercator was a cartographer who developed a general method of projecting a map of the surface of a sphere onto a flat surface, while preserving straight lines. Similarly, Mercator provides map and flatMap methods to objects which support them.

In general, Soundness project names are always chosen with some rationale, however it is usually frivolous. Each name is chosen for more for its uniqueness and intrigue than its concision or catchiness, and there is no bias towards names with positive or "nice" meanings—since many of the libraries perform some quite unpleasant tasks.

Names should be English words, though many are obscure or archaic, and it should be noted how willingly English adopts foreign words. Names are generally of Greek or Latin origin, and have often arrived in English via a romance language.

The logo shows the lines of latitude of an Oblique Mercator Projection.

Mercator is copyright © 2024 Jon Pretty & Propensive OÜ, and is made available under the Apache 2.0 License.