I have a lit of functions
val f1 = (x: Int) => x + 1
val f2 = (x: Int) => x + 2
val f3 = (x: Int) => x + 3
I have a single value:
val data = 5
I want to apply all the functions to the value and return single value. So
f3(f2(f1(data)))
And must return 11.
Now, if I have a seq of functions:
val funcs = Seq(f1, f2, f3)
How can I get 11 from applying all the functions to the data variable ? What is the scala-way to do that ?
yet another way to doing it using chain method in the Function helper object
Function.chain(funcs)(data)
What you are looking for is foldLeft. Indeed, for each function, you apply it to the previous result:
funcs.foldLeft(data){ (previousres, f) => f(previousres) }
you can use foldLeft:
val result = funcs.foldLeft(5)((acc,curr) => curr(acc) )
Basically, you are trying to achieve Function Composition here. So, you could use compose and andThen methods here as:
val data = 5
val funcs = Seq(f1, f2, f3)
//using compose
val result1 = funcs.reduce((a,b) => a.compose(b))(data)
//using andThen
val result2 = funcs.reduce((a,b) => a.andThen(b))(data)
Both result1 and result2 will be 11 in your example.
Please note that the way andThen and compose operate are different. You could see Functional Composition for more information.
Related
Functional programming style of coding guideline says we should not use null or var in Scala for better functional programming code.
I want to perform some operation like below
var a = 2
if(condition==true){
a = a * 3 /*someOperation*/
}
if(condition2==true){
a = a * 6 /*someOperation*/
}
if(condition3==true){
a = a * 8 /*someOperation*/
}
val b = a * 2/*someOperation*/
So now how to avoid var in this condition and replace it with val?
The simplest way to avoid var with multiple conditions is to use temporary values
val a1 = 2
val a2 = if (condition) a1*3 else a1
val a3 = if (condition2) a2*6 else a2
val a = if (condition3) a3*8 else a3
val b = a * 2/*someOperation*/
In the real code you would give a1, a2, and a3 meaningful names to describe the result of each stage of processing.
If you are bothered about having these extra values in scope, put it in a block:
val a = {
val a1 = 2
val a2 = if (condition) a1*3 else a1
val a3 = if (condition2) a2*6 else a2
if (condition3) a3*8 else a3
}
Update
If you want a more functional approach, collect the conditions and modifications together and apply them in turn, like this:
val mods: List[(Boolean, Int=>Int)] = List(
(condition, _*3),
(condition2, _*6),
(condition3, _*8)
)
val a = mods.foldLeft(2){ case (a,(cond, mod)) => if (cond) mod(a) else a }
This is really only appropriate when either the conditions or the modifications are more complex, and keeping them together makes the code clearer.
val a = 2 * (if (condition) 3 else 1)
val b = 2 * a
Or, perhaps...
val a = 2
val b = 2 * (if (condition) a*3 else a)
It depends on if/how a is used after these operations.
I think you might have oversimplified your example, because we know the value of a when writing the code so you could just write it out like this:
val a = if (condition) 2 else 6
val b = a * 2
Assuming your real operation is more complex and can't be precalculated like that, then you might find a pattern match like this is a nicer way to do it:
val a = (condition, 2) match {
case (true, z) =>
z * 3
case (false, z) =>
z
}
val b = a * 2
You can try the following approach:
type Modification = Int => Int
type ModificationNo = Int
type Conditions = Map[ModificationNo, Boolean]
val modifications: List[(Modification, ModificationNo)] =
List[Modification](
a => a * 3,
a => a * 6,
a => a * 8
).zipWithIndex
def applyModifications(initial: Int, conditions: Conditions): Int =
modifications.foldLeft[Int](initial) {
case (currentA, (modificationFunc, modificationNo)) =>
if (conditions(modificationNo)) modificationFunc(currentA)
else currentA
}
val a: Int = applyModifications(initial = 2,
conditions = Map(0 -> true, 1 -> false, 2 -> true))
It may look complicated but this approach allows additional flexibility if number of conditions is big enough.
Now when you have to add more conditions, you don't need to write new if-statements and further reassignments to var. Just add a modification function to an existing list of
there is no 1 perfect solution.
sometimes it is ok to use var if it simplifies the code and limited in scope of a single function.
that being said, this is how I would do it in functional way:
val op1: Int => Int =
if (condition1) x => x * 3
else identity
val op2: Int => Int =
if (condition2) x => x * 6
else identity
val op3: Int => Int =
if (condition3) x => x * 8
else identity
val op = op1 andThen op2 andThen op3
// can also be written as
// val op = Seq(op1, op2, op3).reduceLeft(_ andThen _)
val a = 2
val b = op(a) * 2
The easiest way it to wrap your variable into a monad, so that you .map over it. The simplest monad is an Option, so you could write:
val result = Option(a).map {
case a if condition => a*2
case a => a
}.map {
case a if condition2 => a*6
case a => a
}.fold(a) {
case a if condition3 => a*8
case a => a
}
(The last operation is fold instead of map so that you end up with the "raw" value for the result, rather than an option. Equivalently, you could write it as a .map, and then add .getOrElse(a) at the end).
When you have many conditional operations like this, or many use cases where you have to repeat the pattern, it might help to put them into a list, and then traverse that list instead:
def applyConditionals[T](toApply: (() => Boolean, T => T)*) = toApply
.foldLeft(a) {
case (a, (cond, oper)) if cond() => oper(a)
case (a, _) => a
}
val result = applyConditionals[Int] (
(() => condition, _ * 2),
(() => condition2, _ * 6),
(() => condition3, _ * 8)
)
The important point is that FP is a whole new paradigm of programming. Its so fundamentally different that sometimes you can not take an excerpt of imperative code and try to convert it to functional code.
The difference applies not just to code but to the way of thinking towards solving a problem. Functional programming requires you to think in terms of chained mathematical computation which are more or less independent of each other (which means that each of these mathematical computation should not be changing anything outside of its own environment).
Functional programming totally avoids mutation of state. So, if your solution has a requirement to have a variable x which has a value 10 at one point and other value 100 at some other point... then your solution is not functional. And you can not write function code for a solution which is not functional.
Now, if you look at your case (assuming you do not actually need a to be 2 and then change to 6 after sometime) and try to convert it into chain of independent mathematical computation, then the simplest one is following,
val a = if (condition) 2 else 6
val b = a * 2
Whilst I understand what a partially applied/curried function is, I still don't fully understand why I would use such a function vs simply overloading a function. I.e. given:
def add(a: Int, b: Int): Int = a + b
val addV = (a: Int, b: Int) => a + b
What is the practical difference between
def addOne(b: Int): Int = add(1, b)
and
def addOnePA = add(1, _:Int)
// or currying
val addOneC = addV.curried(1)
Please note I am NOT asking about currying vs partially applied functions as this has been asked before and I have read the answers. I am asking about currying/partially applied functions VS overloaded functions
The difference in your example is that overloaded function will have hardcoded value 1 for the first argument to add, i.e. set at compile time, while partially applied or curried functions are meant to capture their arguments dynamically, i.e. at run time. Otherwise, in your particular example, because you are hardcoding 1 in both cases it's pretty much the same thing.
You would use partially applied/curried function when you pass it through different contexts, and it captures/fills-in arguments dynamically until it's completely ready to be evaluated. In FP this is important because many times you don't pass values, but rather pass functions around. It allows for higher composability and code reusability.
There's a couple reasons why you might prefer partially applied functions. The most obvious and perhaps superficial one is that you don't have to write out intermediate functions such as addOnePA.
List(1, 2, 3, 4) map (_ + 3) // List(4, 5, 6, 7)
is nicer than
def add3(x: Int): Int = x + 3
List(1, 2, 3, 4) map add3
Even the anonymous function approach (that the underscore ends up expanding out to by the compiler) feels a tiny bit clunky in comparison.
List(1, 2, 3, 4) map (x => x + 3)
Less superficially, partial application comes in handy when you're truly passing around functions as first-class values.
val fs = List[(Int, Int) => Int](_ + _, _ * _, _ / _)
val on3 = fs map (f => f(_, 3)) // partial application
val allTogether = on3.foldLeft{identity[Int] _}{_ compose _}
allTogether(6) // (6 / 3) * 3 + 3 = 9
Imagine if I hadn't told you what the functions in fs were. The trick of coming up with named function equivalents instead of partial application becomes harder to use.
As for currying, currying functions often lets you naturally express transformations of functions that produce other functions (rather than a higher order function that simply produces a non-function value at the end) which might otherwise be less clear.
For example,
def integrate(f: Double => Double, delta: Double = 0.01)(x: Double): Double = {
val domain = Range.Double(0.0, x, delta)
domain.foldLeft(0.0){case (acc, a) => delta * f(a) + acc
}
can be thought of and used in the way that you actually learned integration in calculus, namely as a transformation of a function that produces another function.
def square(x: Double): Double = x * x
// Ignoring issues of numerical stability for the moment...
// The underscore is really just a wart that Scala requires to bind it to a val
val cubic = integrate(square) _
val quartic = integrate(cubic) _
val quintic = integrate(quartic) _
// Not *utterly* horrible for a two line numerical integration function
cubic(1) // 0.32835000000000014
quartic(1) // 0.0800415
quintic(1) // 0.015449626499999999
Currying also alleviates a few of the problems around fixed function arity.
implicit class LiftedApply[A, B](fOpt: Option[A => B]){
def ap(xOpt: Option[A]): Option[B] = for {
f <- fOpt
x <- xOpt
} yield f(x)
}
def not(x: Boolean): Boolean = !x
def and(x: Boolean)(y: Boolean): Boolean = x && y
def and3(x: Boolean)(y: Boolean)(z: Boolean): Boolean = x && y && z
Some(not _) ap Some(false) // true
Some(and _) ap Some(true) ap Some(true) // true
Some(and3 _) ap Some(true) ap Some(true) ap Some(true) // true
By having curried functions, we've been able to "lift" a function to work on Option for as many arguments as we need. If our logic functions had not been curried, then we would have had to have separate functions to lift A => B to Option[A] => Option[B], (A, B) => C to (Option[A], Option[B]) => Option[C], (A, B, C) => D to (Option[A], Option[B], Option[C]) => Option[D] and so on for all the arities we cared about.
Currying also has some other miscellaneous benefits when it comes to type inference and is required if you have both implicit and non-implicit arguments for a method.
Finally, the answers to this question list out some more times you might want currying.
I am taking the Functional Programming in Scala course on Coursera and I am having a hard time understanding this code snippet -
def sqrtStream(x: Double): Stream[Double] = {
def improve(guess: Double): Double = (guess+ x/ guess) / 2
lazy val guesses: Stream[Double] = 1 #:: (guesses map improve)
guesses
}
This method would find 10 approximate square root of 4 in increasing order of accuracy when I would do sqrtSteam(4).take(10).toList.
Can someone explain the evaluation strategy of guesses here? My doubt is what value of guesses in substituted when the second value of guesses is picked up?
Let's start from simplified example:
scala> lazy val a: Int = a + 5
a: Int = <lazy>
scala> a
stack overflow here, because of infinite recursion
So a is recalculating til it gets some stable value, like here:
scala> def f(f:() => Any) = 0 //takes function with captured a - returns constant 0
f: (f: () => Any)Int
scala> lazy val a: Int = f(() => a) + 5
a: Int = <lazy>
scala> a
res4: Int = 5 // 0 + 5
You may replace def f(f:() => Any) = 0 with def f(f: => Any) = 0, so a definition will look like it's really passed to the f: lazy val a: Int = f(a) + 5.
Streams use same mechanism - guesses map improve will be passed as parameter called by name (and lambda linked to the lazy a will be saved inside Stream, but not calculated until tail is requested), so it's like lazy val guesses = #::(1, () => guesses map improve). When you call guessess.head - tail will not be evaluated; guesses.tail will lazily return Stream (improve(1), ?), guesses.tail.tail will be Stream(improve(improve(1)), ?) and so on.
The value of guesses is not substituted. A stream is like a list, but its elements are evaluated only when they are needed and then they stored, so next time you access them the evaluation will not be necessary. The reference to the stream itself does not change.
On top of the example Αλεχει wrote, there is a nice explanation in Scala API:
http://www.scala-lang.org/api/current/index.html#scala.collection.immutable.Stream
You can easily find out what's going on by modifying the map function, as described in the scaladoc example:
scala> def sqrtStream(x: Double): Stream[Double] = {
| def improve(guess: Double): Double = (guess + x / guess) / 2
| lazy val guesses: Stream[Double] = 1 #:: (guesses map {n =>
| println(n, improve(n))
| improve(n)
| })
| guesses
| }
sqrtStream: (x: Double)Stream[Double]
The output is:
scala> sqrtStream(4).take(10).toList
(1.0,2.5)
(2.5,2.05)
(2.05,2.000609756097561)
(2.000609756097561,2.0000000929222947)
(2.0000000929222947,2.000000000000002)
(2.000000000000002,2.0)
(2.0,2.0)
(2.0,2.0)
(2.0,2.0)
res0: List[Double] = List(1.0, 2.5, 2.05, 2.000609756097561, 2.0000000929222947, 2.000000000000002, 2.0, 2.0, 2.0, 2.0)
Is there a pre-existing / Scala-idiomatic / better way of accomplishing this?
def sum(x: Int, y: Int) = x + y
var x = 10
x = applyOrBypass(target=x, optValueToApply=Some(22), sum)
x = applyOrBypass(target=x, optValueToApply=None, sum)
println(x) // will be 32
My applyOrBypass could be defined like this:
def applyOrBypass[A, B](target: A, optValueToApply: Option[B], func: (A, B) => A) = {
optValueToApply map { valueToApply =>
func(target, valueToApply)
} getOrElse {
target
}
}
Basically I want to apply operations depending on wether certain Option values are defined or not. If they are not, I should get the pre-existing value. Ideally I would like to chain these operations and not having to use a var.
My intuition tells me that folding or reducing would be involved, but I am not sure how it would work. Or maybe there is another approach with monadic-fors...
Any suggestions / hints appreciated!
Scala has a way to do this with for comprehensions (The syntax is similar to haskell's do notation if you are familiar with it):
(for( v <- optValueToApply )
yield func(target, v)).getOrElse(target)
Of course, this is more useful if you have several variables that you want to check the existence of:
(for( v1 <- optV1
; v2 <- optV2
; v3 <- optV3
) yield func(target, v1, v2, v3)).getOrElse(target)
If you are trying to accumulate a value over a list of options, then I would recommend a fold, so your optional sum would look like this:
val vs = List(Some(1), None, None, Some(2), Some(3))
(target /: vs) ( (x, v) => x + v.getOrElse(0) )
// => 6 + target
You can generalise this, under the condition that your operation func has some identity value, identity:
(target /: vs) ( (x, v) => func(x, v.getOrElse(identity)) )
Mathematically speaking this condition is that (func, identity) forms a Monoid. But that's by-the-by. The actual effect is that whenever a None is reached, applying func to it and x will always produce x, (None's are ignored, and Some values are unwrapped and applied as normal), which is what you want.
What I would do in a case like this is use partially applied functions and identity:
def applyOrBypass[A, B](optValueToApply: Option[B], func: B => A => A): A => A =
optValueToApply.map(func).getOrElse(identity)
You would apply it like this:
def sum(x: Int)(y: Int) = x + y
var x = 10
x = applyOrBypass(optValueToApply=Some(22), sum)(x)
x = applyOrBypass(optValueToApply=None, sum)(x)
println(x)
Yes, you can use fold. If you have multiple optional operands, there are some useful abstractions in the Scalaz library I believe.
var x = 10
x = Some(22).fold(x)(sum(_, x))
x = None .fold(x)(sum(_, x))
If you have multiple functions, it can be done with Scalaz.
There are several ways to do it, but here is one of the most concise.
First, add your imports:
import scalaz._, Scalaz._
Then, create your functions (this way isn't worth it if your functions are always the same, but if they are different, it makes sense)
val s = List(Some(22).map((i: Int) => (j: Int) => sum(i,j)),
None .map((i: Int) => (j: Int) => multiply(i,j)))
Finally, apply them all:
(s.flatten.foldMap(Endo(_)))(x)
In Scala, I could generate a curried function like so:
def multiply(m: Int)(n: Int): Int = (m + 1) * (n + 2)
If I wanted, I could generate a new function, by filling that first parameter, like so:
val timesTwo = multiply(1) _
But what is the syntax for replacing the second argument, instead of the first?
val timesThree = multiply _ (1) // Incorrect Syntax
More importantly, why is there not a direct parallel to multiply(1) _?
val timesThree = multiply(_: Int)(1)
or
val timesThree = (x: Int) => multiply(x)(1)