Applicative Computation Expressions - 2

In the last post we used BindReturnand MergeSources to implement the applicative. The advantage of implementing them is that it will work for any number of and!.

When using let! with a single and!, it makes one call to MergeSources to pair arguments and one call to BindReturn to pass values to the function.

When using let! with two and!, it makes two calls to MergeSources to tuple arguments and one call to BindReturn to pass values to the function.

This can be expensive, so you can provide specific implementations for given numbers of paramters to reduce the number of calls.

For two arguments, you can implement Bind2Return:

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type AsyncBuilder with
    member this.Bind2Return(x: 'a Async,y: 'b Async,f: 'a * 'b -> 'c) : 'c Async =
        this.Bind(Async.StartChild x, fun xa ->
            this.Bind(Async.StartChild y, fun ya ->
                this.Bind(xa, fun xv ->
                    this.Bind(ya, fun yv -> this.Return (f(xv, yv)))
                    )
                )
            
            )

its signature is:

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M<'a> * M<'b> * ('a * 'b -> 'c) -> M<'c>

Notice that it is similar to map2 signature.

We can check that it's working as expected:

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async {
    let! parisCoords = 
        async {
            let! paris = ZipCode.AsyncLoad "http://api.zippopotam.us/fr/75020"
            return coord paris }
    and! londonCoords = 
        async { 
            let! london = ZipCode.AsyncLoad "http://api.zippopotam.us/GB/EC1"
            return coord london}
                
    return dist parisCoords londonCoords

}
|> Async.RunSynchronously

To handle a let! and! and! case you have to provide a Bind3Return member that takes 3 values and a function. You can also provide a Bind4Return, Bind5Return... and from my tests there is no limit in the number of arguments you can test. F# would happily call a Bind265Return if it had to.

Those additional functions are occasions to optimise the implementation by reducing the number of intermediate allocations and function calls.

Obviously, it's advised to provide only a few special cases and fall back to BindReturn and MergeSources for the rest.

Other options for implementation is to provide MergeSources3, MergeSources4 to reduce the number of intermediate tuples. The signature will be for MergeSources3:

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M<'a> * M<'b> * M<'c> -> M<'a * 'b * 'c>

It's also possible to define Bind2, Bind3 with the following signatures:

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M<'a> * M<'b> * ('a * 'b -> M<'c>) -> M<'c>

This looks like the Bind2Return except that the function already returns a wrapped value.

You can find the complete documentation in the RFC