Is my understanding of transducers correct?

Question

Let's start with a definition: A transducer is a function that takes a reducer function and returns a reducer function.

A reducer is a binary function that takes an accumulator and a value and returns an accumulator. A reducer can be executed with a reduce function (note: all function are curried but I've cat out this as well as definitions for pipe and compose for the sake of readability - you can see them in live demo):

const reduce = (reducer, init, data) => {
  let result = init;
  for (const item of data) {
    result = reducer(result, item);
  }
  return result;
}

With reduce we can implement map and filter functions:

const mapReducer = xf => (acc, item) => [...acc, xf(item)];
const map = (xf, arr) => reduce(mapReducer(xf), [], arr);

const filterReducer = predicate => (acc, item) => predicate(item) ?
  [...acc, item] :
  acc;
const filter = (predicate, arr) => reduce(filterReducer(predicate), [], arr);

As we can see there're a few similarities between map and filter and both of those functions work only with arrays. Another disadvantage is that when we compose those two functions, in each step a temporary array is created that gets passed to another function.

const even = n => n % 2 === 0;
const double = n => n * 2;

const doubleEven = pipe(filter(even), map(double));

doubleEven([1,2,3,4,5]);
// first we get [2, 4] from filter
// then final result: [4, 8]

Transducers help us solve that concerns: when we use a transducer there are no temporary arrays created and we can generalize our functions to work not only with arrays. Transducers need a transduce function to work Transducers are generally executed by passing to transduce function:

const transduce = (xform, iterator, init, data) =>
  reduce(xform(iterator), init, data);

const mapping = (xf, reducer) => (acc, item) => reducer(acc, xf(item));

const filtering = (predicate, reducer) => (acc, item) => predicate(item) ?
  reducer(acc, item) :
  acc;

const arrReducer = (acc, item) => [...acc, item];

const transformer = compose(filtering(even), mapping(double));

const performantDoubleEven = transduce(transformer, arrReducer, [])

performantDoubleEven([1, 2, 3, 4, 5]); // -> [4, 8] with no temporary arrays created

We can even define array map and filter using transducer because it's so composable:

const map = (xf, data) => transduce(mapping(xf), arrReducer, [], data);

const filter = (predicate, data) => transduce(filtering(predicate), arrReducer, [], data);

live version if you'd like to run the code -> https://runkit.com/marzelin/transducers

Does my reasoning makes sense?

Answer 1

Your understanding is correct but incomplete.

In addition to the concepts you've described, transducers can do the following:

• Support a early exit semantic
• Support a completion semantic
• Be stateful
• Support an init value for the step function.

So for instance, an implementation in JavaScript would need to do this:

// Ensure reduce preserves early termination
let called = 0;
let updatesCalled = map(a => { called += 1; return a; });
let hasTwo = reduce(compose(take(2), updatesCalled)(append), [1,2,3]).toString();
console.assert(hasTwo === '1,2', hasTwo);
console.assert(called === 2, called);

Here because of the call to take the reducing operation bails early.

It needs to be able to (optionally) call the step function with no arguments for an initial value:

// handles lack of initial value
let mapDouble = map(n => n * 2);
console.assert(reduce(mapDouble(sum), [1,2]) === 6);

Here a call to sum with no arguments returns the additive identity (zero) to seed the reduction.

In order to accomplish this, here's a helper function:

const addArities = (defaultValue, reducer) => (...args) => {
  switch (args.length) {
    case 0: return typeof defaultValue === 'function' ? defaultValue() : defaultValue;
    case 1: return args[0];
    default: return reducer(...args);
  }
};

This takes an initial value (or a function that can provide one) and a reducer to seed for:

const sum = addArities(0, (a, b) => a + b);

Now sum has the proper semantics, and it's also how append in the first example is defined. For a stateful transducer, look at take (including helper functions):

// Denotes early completion
class _Wrapped {
  constructor (val) { this[DONE] = val }
};

const isReduced = a => a instanceof _Wrapped;
// ensures reduced for bubbling
const reduced = a => a instanceof _Wrapped ? a : new _Wrapped(a);
const unWrap = a => isReduced(a) ? a[DONE] : a;

const enforceArgumentContract = f => (xform, reducer, accum, input, state) => {
  // initialization
  if (!exists(input)) return reducer();
  // Early termination, bubble
  if (isReduced(accum)) return accum;
  return f(xform, reducer, accum, input, state);
};

/*
 * factory
 *
 * Helper for creating transducers.
 *
 * Takes a step process, intial state and returns a function that takes a
 * transforming function which returns a transducer takes a reducing function,
 * optional collection, optional initial value. If collection is not passed
 * returns a modified reducing function, otherwise reduces the collection.
 */
const factory = (process, initState) => xform => (reducer, coll, initValue) => {
  let state = {};
  state.value = typeof initState === 'function' ? initState() : initState;
  let step = enforceArgumentContract(process);
  let trans = (accum, input) => step(xform, reducer, accum, input, state);
  if (coll === undefined) {
    return trans; // return transducer
  } else if (typeof coll[Symbol.iterator] === 'function') {
    return unWrap(reduce(...[trans, coll, initValue].filter(exists))); 
  } else {
    throw NON_ITER;
  }
};

const take = factory((n, reducer, accum, input, state) => {
  if (state.value >= n) {
    return reduced(accum);
  } else {
    state.value += 1;
  }
  return reducer(accum, input);
}, () => 0);

If you want to see all of this in action I made a little library a while back. Although I ignored the interop protocol from Cognitect (I just wanted to get the concepts) I did try to implement the semantics as accurately as possible based on Rich Hickey's talks from Strange Loop and Conj.