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A small utility for working with sum datatypes
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README.md

brief-cases

Install

$ npm i brief-cases

A small utility for working with sum datatypes

Many datatypes, particularly those having inductive definitions, are conveniently represented as "sum types", also known as "discriminated unions" or "variant records". Such datatypes describe values that might be of one or the other of several alternative types. While it is not difficult to represent values of such types (using object literals with string tags, for instance), they are often cumbersome to use.

The purpose of this utility is to make using sum datatypes simple and elegant. It is extremely easy to use, and not much harder to understand in full.

Usage

This utility is exposed as a single function. For instance, one could require it as createSumType:

const createSumType = require('brief-cases');

It is quite easy to use. Suppose one wishes to define the classic Maybe datatype. This is a simple matter of calling createSumType with the names of the desired variant constructors:

const Maybe = createSumType('Nothing', 'Just');

The value Maybe has two "static methods" named Nothing and Just that can be used to construct values as follows:

const justAThree = Maybe.Just('3');
const nothingAtAll = Maybe.Nothing();
const justAnObject = Maybe.Just({ test: 'value' });

To use these values, one can employ the cases method to call a function based on the name of the variant to which the value belongs:

Maybe.Just(3).cases({
  Just   : value => `Just a ${value.toString()}`,
  Nothing: ()    => 'Nothing at all'
}); // => 'Just a 3'

More likely, one would use cases within a function, say, for "mapping" over values of type Maybe, or transforming such values to Strings:

const mapMaybe = (mVal, fn) => mVal.cases({
  Just: value => Maybe.Just(fn(value)),
  _   : ()    => Maybe.Nothing()
});

const showMaybe = mVal => mVal.cases({
  Just   : value => `Just (${value.toString()})`,
  Nothing: ()    => 'Nothing'
});

showMaybe(mapMaybe(Maybe.Just('test'), v => v.toUpperCase())); // => 'Just (TEST)'

Here we have also introduced a "catch-all" handler, associated with _.

In many cases, one would prefer to define functions like mapMaybe and showMaybe as methods, so that the above expression could be rendered more readably as:

Maybe.Just('test').map(v => v.toUpperCase()).show(); // => 'Just (TEST)'

As it turns out, the variant constructors Maybe.Nothing and Maybe.Just have the same prototype as Maybe itself. Thus, values assigned to Maybe's prototype are available to values created by Maybe.Nothing and Maybe.Just. Here is how one might create a more usable version of the Maybe datatype:

const Maybe = createSumType('Nothing', 'Just');

// of : a -> Maybe a
Maybe.of = Maybe.Just;

// map : Maybe a ~> (a -> b) -> Maybe b
Maybe.prototype.map = function(f) {
  return this.cases({
    Just: v  => Maybe.of(f(v)),
    _   : () => this
  });
};

// chain : Maybe a ~> (a -> Maybe b) -> Maybe b
Maybe.prototype.chain = function(f) {
  return this.cases({
    Just: f,           // a point-free/eta equivalent of: v => f(v)
    _   : () => this
  });
};

// toString : Maybe a ~> String
Maybe.prototype.toString = function() {
  return this.cases({
    Just   : v  => `Just (${v.toString()})`,
    Nothing: () => 'Nothing'
  });
};

These methods are then available on values created by the variant constructors Maybe.Nothing and Maybe.Just:

const div = d => n => d === 0 ? Maybe.Nothing() : Maybe.of(n / d);

const square = n => n * n;

Maybe.of(12)
     .chain(div(3))
     .map(square)
     .toString(); // => 'Just (16)'

Maybe.of(7)
     .chain(div(0))
     .map(square)
     .toString(); // => 'Nothing'

Another Example

As another example, consider how one might represent expressions in the lambda calculus. The possible expressions are Names, consisting of a String, Abstractions, consisting of an identifier of type String along with a "body" that is itself a lambda calculus expression, and Applications, consisting of two lambda calculus expressions.

We can construct the Expression type as follows:

const Expr = createSumType('Name', 'Abs', 'App');

Individual expressions are now a cinch to create:

const { Name, Abs, App } = Expr;

// id = \x . x
const id = Abs('x', Name('x'));

// konst = \x . \y . x
const konst = Abs('x', Abs('y', Name('x')));

// subst = \x . \y . \z . ((x z) (y z))
const subst =
Abs('x',
  Abs('y',
    Abs('z',
      App(App(Name('x'), Name('z')), App(Name('y'), Name('z')))
    )
  )
);

Additionally, as above, we can define methods that are available on all values created by any of the variant constructors:

Expr.prototype.toString = function() {
  return this.cases({
    Name: name          => name,
    Abs : (id, body)    => `(lambda (${id}) ${body.toString()})`,
    App : (rator, rand) => `(${rator.toString()} ${rand.toString()})`
  });
};

id.toString();
// => '(lambda (x) x)'

konst.toString();
// => '(lambda (x) (lambda (y) x))'

subst.toString();
// => '(lambda (x) (lambda (y) (lambda (z) ((x z) (y z)))))'

Details

In general, to create a sum datatype having variants named <v1>, <v2>, ..., <vn> (where the <vi>'s are Strings), one should evaluate createSumType(<v1>, <v2>, ..., <vn>). This produces an object with "static methods" named <v1>, <v2>, ..., <vn>. These are the "variant constructors" and are used to create values belonging to a certain variant. Each of these static methods takes any number of arguments (that is, it is the caller's responsibility to ensure that these methods are called with the proper arguments). Any value produced by these variant constructors has a cases method.

This cases method should be called with an object having a function associated with each variant name, and/or a function associated with the catch-all method _. The function associated with the name of the variant to which the value belongs will be called with the original arguments used to construct the value. If no function has been provided for the variant in question and no "catch-all" function has been provided, then an error will be thrown indicating a non-exhaustive use of the cases method.

Lastly, any properties added to the object created by calling createSumType(<v1>, <v2>, ..., <vn>) (including its prototype) will be available to values created by the variant constructors themselves. This makes it very convenient to define methods shared by all variants of a particular type.

For more information, see the documentation of the source code.

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