MONADJS

Some typescript code related to monads to help me learn what monads, functors and applicatives are.

So far this implements a type-safe infinite list of Fibonacci numbers with the help of a Maybe monad, a Lazy monad and a LinkedList implemented with both.

Maybe

Maybe is a monad that encapsulates a value either being of type T or undefined. Maybe makes it possible to create chains of transformations on a value that might not complete. For example, a file system read might not return a value and encapsulating this in maybe forces the programmer (through the type system) to handle it.

example:

const userID = maybeID(); // 50% chance of returning a number
const userIDNumber = fmap(parseInt, userID); // apply parseint to the possible userid
const userIDTimesTwo = fmap((x) => x * 2, userIDNumber); // multiply the possible parsed userid by 2
if (userIDTimesTwo.type === "nothing") {
  console.log("couldn't get userid");
} else {
  console.log(`userid is ${userIDTimesTwo}`);
}

Lazy

Lazy is a monad that encapsulates delayed execution of code. Instead of immediately calculating the result of a function it will chain promises together until the value is used. By doing this we will only calculate the result of functions we actualy use in our code. For example, we might make a list of HTTP calls where we end up only using the first 2 calls. If we use Lazy we can construct the list completely without having to do each HTTP call

example:

// first initialize a lazy value
const lazyString = lazy("2");
// transform the string into a number
// at this point `parseInt` won't be called
const a = bind(aString, (x) => lazy(parseInt(x)));

// multiple the value by two
// at this point both parseInt and *2 won't have been called yet
const double = fmap((x) => x * 2, a);

// create a new lazy value and add it to the doubled value
const b = lazy(4);
const add = applicative(
  fmap((x) => (y: number) => x + y, b),
  double,
);

// at this point neither parseInt, *2 and double+b will have been called yet
// after lifing the value `add` we will be calculating the actual functions
// and return the result of the chain of promises
const result = lift(add);

LinkedList

LinkedList is a linked list implemented as a lazy value. This means each next value will only be calculated at execution time. This allows us to use the LinkedList to define values with infinite ranges (like an infinite list of Fibonacci numbers). As an experiment, we implement a LinkedList node being either a Node or the end of the list with the Maybe monad. Combing both the laziness and the optional value we get a definition of Lazy<Maybe<Node<T>>>. This means that a LinkedList is a promise to return a value that is either a empty list, maybe.nothing, or a node with a next item.

example:

Deno.test("Test example in Readme", () => {
  const cc = new CallCounter(); // this will keep track of actual excecution
  // create a list of 3 numbers
  const list = linkedList(1, linkedList(2, linkedList(3)));
  // multiply each item in the list times 2
  const multiplied = map(list, (x) => cc.call(() => x * 2));

  // at this point multiplied is still a promise to multiple each value
  // to demonstrate this we create a infinite list starting at 1 incremented with 1
  const inf = infinite(0, 1);
  // we do the same multiplication
  const infMultiplied = map(inf, (x) => cc.call(() => x * 2));

  // now we combine both list together by appending the infinite list to the right of the firs
  // note that the other way is possible but will never reach the end of the left infinite list :p
  const combined = concat(multiplied, infMultiplied);

  // to demonstrate the combined list we sum the first 5 entries, of which 2 are in the infinite list,
  // with take and fold
  const sumOfFirst5 = lFold(
    (acc, x) => cc.call(() => acc + x),
    0,
    take(combined, 5),
  );

  // at this point sumOfFirst5 will be of type Lazy<number>
  // and none of the multiplication will have actually been excecute
  // only after we lift the value of sumOfFirst5 the concatation and multuplication will be done
  asserts.assertEquals(cc.count, 0); // verify no multiplications where made
  const result = lift(sumOfFirst5);
  asserts.assertEquals(cc.count, 10); // 3 multiplications in the first list, 2 in the second and 5 sums
  asserts.assertEquals(
    result,
    14,
  ); // sum of [1*2,2*2,3*2, 0*2,1*2] = 14

  // The same code without comments and the call counter adding syntax complexity
  const _l = map(arrayToLinkedList([1, 2, 3]), (x) => x * 2);
  const _inf = map(infinite(0, 1), (x) => x * 2);
  const _sum = lFold((acc, x) => acc + x, 0, take(concat(_l, _inf), 5));
  asserts.assertEquals(lift(_sum), 14);
});

Setup

setup nix (https://nixos.org/download.html) and run

nix-shell -p env.nix

This will also configure the .vscode/settings.json to enable use the nix installed version of deno and setup formatting on save

or install deno (https://deno.land/manual/tools/formatter) yourself

Run

to run the main.ts examples run:

deno run main.ts

Testing

The test code also contains examples on how to use the monads

deno test

linting / formating

deno lint
deno fmt