How to encode corecursion/codata in a strictly evaluated setting?

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广开言路
广开言路 2021-01-16 09:11

Corecursion means calling oneself on data at each iteration that is greater than or equal to what one had before. Corecursion works on codata, which are recursively defined

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  •  说谎
    说谎 (楼主)
    2021-01-16 10:06

    I would encode the thunk within the data constructor itself. For example, consider.

    // whnf :: Object -> Object
    const whnf = obj => {
        for (const [key, val] of Object.entries(obj)) {
            if (typeof val === "function" && val.length === 0) {
                Object.defineProperty(obj, key, {
                    get: () => Object.defineProperty(obj, key, {
                        value: val()
                    })[key]
                });
            }
        }
    
        return obj;
    };
    
    // empty :: List a
    const empty = null;
    
    // cons :: (a, List a) -> List a
    const cons = (head, tail) => whnf({ head, tail });
    
    // fibs :: List Int
    const fibs = cons(0, cons(1, () => next(fibs, fibs.tail)));
    
    // next :: (List Int, List Int) -> List Int
    const next = (xs, ys) => cons(xs.head + ys.head, () => next(xs.tail, ys.tail));
    
    // take :: (Int, List a) -> List a
    const take = (n, xs) => n === 0 ? empty : cons(xs.head, () => take(n - 1, xs.tail));
    
    // toArray :: List a -> [a]
    const toArray = xs => xs === empty ? [] : [ xs.head, ...toArray(xs.tail) ];
    
    // [0,1,1,2,3,5,8,13,21,34]
    console.log(toArray(take(10, fibs)));

    This way, we can encode laziness in weak head normal form. The advantage is that the consumer has no idea whether a particular field of the given data structure is lazy or strict, and it doesn't need to care.

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