Getting Last Type of Curried Function - scala

Given a val that consists of the following (what I believe is a) type constructor with a curried function argument, F[A => B => C]...
val x: F[A => B => C] = foo() // foo does not matter
Is it possible for me to get F[C] from x?
val y: F[C] = x...
EDIT
For context, I'm trying to implement the map3 function from Functional Programming in Scala.

The only way to get F[C] from F[A => B => C] is if you can apply an A and a B to it. That is, you'll need to evaluate the contained function. Use the apply twice, once to get an B => C and then once again to get C.
def eval(myApp: F[A => B => C])(value: F[A]): F[B => C]
def evalAgain(myApp: F[B => C])(value: F[B]): F[C]
but if you just want to be able to get F[C] directly from the function itself without evaluation, you're SOL.
Edit:
I believe it would look like this.
def eval(myApp: F[A => B => C])(value: F[A], next: F[B])(implicit ap: Applicative[F[_]]) = ap(ap(myApp, value), next)

Related

scala generic function reference

I have several generic functions with the same signature:
def f1[A, B](v: A, f: (A, B) => B): B = ...
def f2[A, B](v: A, f: (A, B) => B): B = ...
And I need to define a function g that can accept any of these functions (f1 f2):
def g(f: ????) = ...
g internally uses multiple argument types, so I can not parameterize it like that:
def g[A, B](f: (A, (A, B) => B) => B) = ...
There isn't really a much better way to do it in Scala 2. Although your solution is a bit strange because FunctionHolder's apply method will return a function object and doesn't accept any arguments itself – that's a bit more complicated than it needs to be. So you can do this instead:
trait FunctionHolder {
def apply[A, B](v: A, f: (A, B) => B): B
}
def g(f: FunctionHolder) = …
But this isn't really all that much better.
In Scala 3, there are polymorphic function types to do this in a cleaner way:
def g(f: [A, B] => (A, (A, B) => B) => B) = …
That said, I'm not convinced that that type signature is really what you want. Remember, when you define a function with type parameters, it needs to work for all possible type parameters that the user might supply. This can't be done for this signature…
def f1[A, B](v: A, f: (A, B) => B): B
… because when I have a function like that, I can easily write an expression of type Nothing:
f1[Unit, Nothing]((), (a: Unit, b: Nothing) => b)
and it's not possible to write an expression of type Nothing unless you cheat (e. g. throw an exception or enter an infinite loop or something like that). So the type signature tells me you're cheating 😉
If you want to know more about this kind of reasoning, search for “Theorems for free!”
After wandering a bit, come up with following:
g(new FunctionHolder {
def apply[A, B](): (A, (A, B) => B) => B = f1
})
def g(f: FunctionHolder) = f()(..., (a, b) => ...)
abstract class FunctionHolder {
def apply[A, B](): (A, (A, B) => B) => B
}
But that just does not look right.
Hope there are more concise ways to do that

Making a partial function complete

Is there a standard way to complete a partial function PartialFunction[A, B]? Something like this:
completePartialFunction(pf: PartialFunction[A, B], z: B): A => B
or
completePartialFunction2(pf: PartialFunction[A, B], f: A => B): A => B
Yes, it's actually very simple:
def complete[A, B](pf: PartialFunction[A, B])(f: A => B): A => B =
pf.applyOrElse(_, f)
You can use lift method on PartialFunction, that returns Option[B]. So when the function is not defined for the input, None is returned. You can find more in the scaladocs.
Other solution that comes to my mind is when you're using cats or scalaz. You can then check whether the function is defined for the argument and when not, return empty from the Monoid[B] that you should pass (probably implicitly) to completePartialFunction.
If I understand the question, you want to use f() to supplement pf() so that all possible values of type A are covered.
def completePartialFunction2[A,B](pf : PartialFunction[A,B]
,f : A => B): A => B =
(a:A) => if (pf.isDefinedAt(a)) pf(a) else f(a)
Another simple version:
def completePartialFunction[A, B](pf: PartialFunction[A, B], f: A => B): A => B
= pf orElse { case a: A => f(a) }

Understanding curried function passed in to fold

I am having problems understanding this code from the Book FP in Scala. Here is the code:
trait Monoid[A] {
def op(a1: A, a2: A): A
def zero: A
}
def endoMonoid[A]: Monoid[A => A] = new Monoid[A => A] {
def op(f: A => A, g: A => A) = f compose g
val zero = (a: A) => a
}
def foldMap[A, B](as: List[A], m: Monoid[B])(f: A => B): B =
as.foldLeft(m.zero)((b, a) => m.op(b, f(a)))
// The function type `(A, B) => B`, when curried, is `A => (B => B)`.
// And of course, `B => B` is a monoid for any `B` (via function composition).
def foldRight[A, B](as: List[A])(z: B)(f: (A, B) => B): B =
foldMap(as, endoMonoid[B])(f.curried)(z)
foldMap is expecting a function f: A => B.
In foldRight, when f is curried you have A => (B => B), so I suppose f.curried is working because it is the same as (A => B => B), so foldRight is passing in to foldMap what it expect (a function with type A => B), then, what happends next is that foldMap is called and its returning a function B => B, and that's when z comes into play in (f.curried)(z) you call the function B => B with the argument z to get the final B.
Am I right? it is a litle complicated to reason about this code for me.
NOTE: Here is a scalafiddle if you want to play with it.
Well, you seem to be mostly comprehensive to me. Nevertheless, I would clarify some points:
I'd rather say "so I suppose f.curried is working because A => (B => B) is the same as (A => B => B)" (it is ambiguous here and you're talking about f.curried result type basically, not with z)
I'd rather put a point instead of a comma here: "foldMap is expecting a function f: A => B . In foldRight, ... " and pretty much every where else. Shorter phrases, clearer explanation.
what could be an error, (and what is confusing to you?) is that (f.curried)(z) doesn't work on its own and is not called after foldMap(as, endoMonoid[B]). It's first foldMap(as, endoMonoid[B])(f.curried) which is called and then (z). The first returns B => B and called with the second returns B.

Using scalaz kleisli without explicit wrapping the function before

Let's say I have two functions val f: A => M[B] and val g: B => M[C] where M is monadic. Thus I want to combine them by using kleisli.
What I currently do is this: kleisliU(f) andThenK g
But I have not found a way to execute this combination without manually wrapping into kleisli first.
How can write something like f <???> g so that f is wrapped into kleisli automatically and then combined with g? I hope something in scalaz already exists for that and that I don't need to write my own implicit class / conversion.
Just for sake of completeness, that should also work with more functions e.g. f <???> g <???> h.
Once I wanted the same thing and I did not find it in scalaz, so I just wrote it myself:
implicit def toKleisliK[M[_], A, B]: (A => M[B]) => Kleisli[M, A, B] = f => {
kleisli[M, A, B](a => f(a))
}
// then for example you can write such:
val f: Int => Option[String] = ???
val g: String => Option[Double] = ???
val result = f andThenK g // inferred type is ReaderT[Option, Int, Double]

Unpack the meaning of this lift function

I am not sure how the following function works:
def lift[A, B](f: A => B): Option[A] => Option[B] = _ map f
I know it transforms a function which takes a value of type A and returns a value of type B into a function which takes a value of type Option[A] and returns an Option[B]. But I am stuck on what the underscore is doing and how the map works. Can someone expand the function definition?
def lift[A, B](f: A => B): Option[A] => Option[B] = _ map f
it exapnds to
def lift[A, B](f: A => B): Option[A] => Option[B] = x => x map f
(this is how underscore works in this context)
The return type is annotated to be Option[A] => Option[B]. Thanks to this compiler will know that x is of type Option[A]. We can say it explicitly, expanding it further
def lift[A, B](f: A => B): Option[A] => Option[B] = (x: Option[A]) => x map f
So, the returned function takes an Option[A] and maps it using f. Option.map takes parameter that is a function A => B so everything is correct.
Note that since I annotated the type that function takes as a parameter you can now omit the type of lift method like this
def lift[A, B](f: A => B) = (x: Option[A]) => x map f
All the snippets I wrote in this post are equivalent.
_ map f in this case returns a function that takes an Option[A] and returns an Option[B].
The _ in this case is a shortcut to build and return a function by specifying its argument position.
So here, the position of the Option[A] argument.
Whenever this returned function will be further called, it would execute:
thePassedOptionA map f