I want to create a simple Map from math operators to the relevant functions:
var ops = Map("+" -> +, "-" -> -)
How would I do this in Scala?
If you want the functions to be curried, the following is probably the most concise way to do it.
scala> val ops: Map[String, Int => Int => Int] = Map(
| "+" -> (x => y => x + y),
| "-" -> (x => y => x - y)
| )
ops: Map[String,Int => Int => Int] = Map(+ -> <function1>, - -> <function1>)
This map however is only limited to Ints. If you want generic operations, you will have to use Numeric context bound.
scala> def ops[N : Numeric]: Map[String, N => N => N] = {
| import Numeric.Implicits._
| Map(
| "+" -> (x => y => x + y),
| "-" -> (x => y => x - y)
| )
| }
ops: [N](implicit evidence$1: Numeric[N])Map[String,N => N => N]
A major caveat with this approach is that a map gets created every time you call ops.
val ops = Map("+" -> ((_: Int) + (_: Int)), "-" -> ((_: Int) - (_:Int)))
or
val ops = Map[String, (Int, Int) => Int]("+" -> (_+_), "-" -> (_-_))
or even, for actual currying,
val ops = Map("+" -> ((_: Int) + (_: Int)).curried, "-" -> ((_: Int) - (_:Int)).curried)
These functions are all bind to Int. Well, Scala is not a point-free programming language, it's an object oriented one, and one in which there's no superclass common to all numeric types. Anyway, if you object to that, then you have an entirely different problem, which was asked and answered many times here on Stack Overflow (in fact, it was my first Scala question, iirc).
Related
Having this code
def mergeWith[K, X, Y, Z](xs: mutable.LinkedHashMap[K, X], ys: mutable.LinkedHashMap[K, Y])(f: (X, Y) => Z): mutable.LinkedHashMap[K, Z] =
xs.flatMap {
case (k, x) => ys.get(k).map(k -> f(x, _))
}
it gives me this:
val map1 = LinkedHashMap(4 -> (4), 7 -> (4,7))
val map2 = LinkedHashMap(3 -> (3), 6 -> (3,6), 7 -> (3,7))
val merged = mergeWith(map1,map2){ (x, y) => (x, y) }
merged: scala.collection.mutable.LinkedHashMap[Int,(Any, Any)] = Map(7 -> ((4,7),(3,7)))
But what i want is this:
merged: scala.collection.mutable.LinkedHashMap[Int,(Any, Any)] = Map(3 -> (3), 4 -> (4), 6 -> (3,6), 7 -> ((4,7),(3,7)))
How to modify my code to obtain it?
It can't be done with the current mergeWith() signature. In particular, you're trying to create a LinkedHashMap[K,Z] but there is no Z input. The only way to get a Z is to invoke f() which requires both X and Y as passed parameters.
So if xs is type LinkedHashMap[Int,Char] and has element (2 -> 'w'), and ys is type LinkedHashMap[Int,Long] and has element (8 -> 4L), how are you going to invoke f(c:Char, l:Long) so that you have a [K,Z] entry for both keys 2 and 8? Not possible.
If the mergeWith() signature can be simplified you might do something like this.
def mergeWith[K,V](xs: collection.mutable.LinkedHashMap[K, V]
,ys: collection.mutable.LinkedHashMap[K, V]
)(f: (V, V) => V): collection.mutable.LinkedHashMap[K,V] = {
val ns = collection.mutable.LinkedHashMap[K,V]()
(xs.keySet ++ ys.keySet).foreach{ k =>
if (!xs.isDefinedAt(k)) ns.update(k, ys(k))
else if (!ys.isDefinedAt(k)) ns.update(k, xs(k))
else ns.update(k, f(xs(k), ys(k)))
}
ns
}
This produces the desired result for the example you've given, but it has a number of undesirable qualities, not the least of which is the mutable data structures.
BTW, there is no such thing as a Tuple1 so (4) is the same thing as 4. And whenever you see type Any, it's a pretty good sign that your design needs a re-think.
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I am new to scala, I have a use case where I want to define a partial function to add three numbers in which one number is constant and two
numbers can be passed as inputs and define another method which can take the partial
function as input and gives its cube as result.
Well... That depends on where is your constant coming from?
Choice 1 - Your function forms a closure with a constant present in scope.
val yourConstant = 10
val pf: PartialFunction[(Int, Int), Int] = {
case (x, y) => x + y + yourConstant
}
pf((5, 10))
Choice 2 - Your function has a local constant.
val pf: PartialFunction[(Int, Int), Int] = {
case (x, y) => x + y + 10
}
pf((5, 10))
Also, as many others pointed out - this does not look like a use case of partial function. Are you sure that you want a Partial Function and not a partially applied function ?
if you were looking for a partially applied function then,
// first you need a curried function
// Curries function are function which can take parameters in steps to build intermidatary functions.
def normalDef(c: Int)(x: Int, y: Int): Int = c + y + x
// normalDef: normalDef[](val c: Int)(val x: Int,val y: Int) => Int
// now you can "partially apply" this "curried" function to your partially applied function
val addTo10PartiallyApplied = normalDef(10) _
// addTo10PartiallyApplied: (Int, Int) => Int = $Lambda$1240/1924827254#46202553
val total = addTo10PartiallyApplied(1, 2)
// total: Int = 13
The following partial function adds 12345 to each number in the tuple passed to it
scala> val addConstantTo: PartialFunction[(Int, Int), Int] = {
| case (a, b) => a + b + 12345
| }
addConstantTo: PartialFunction[(Int, Int),Int] = <function1>
scala> addConstantTo((12, 34))
res4: Int = 12391
This expands on the concept, by programmatically defining a partial function which adds any number to the elements of a tuple:
scala> def addTo(c: Int): PartialFunction[(Int, Int), Int] = {
| case (a, b) => a + b + c
| }
addTo: (c: Int)PartialFunction[(Int, Int),Int]
scala> val pf = addTo(3)
pf: PartialFunction[(Int, Int),Int] = <function1>
scala> pf((1, 2))
res5: Int = 6
Let that sink in for a bit :)
OK, so I'm trying to implement the basics of lambda calculus. Here it goes.
My numbers:
def zero[Z](s: Z => Z)(z: Z): Z = z
def one[Z](s: Z => Z)(z: Z): Z = s(z)
def two[Z](s: Z => Z)(z: Z): Z = s(s(z))
Partially (actually, non) applied version of them is smth like that:
def z[Z]: (Z => Z) => (Z => Z) = zero _
Before I continue I define some types:
type FZ[Z] = Z => Z
type FFZ[Z] = FZ[Z] => FZ[Z]
Fine, succ function goes like (Application order should be exactly like that! I took the definition here):
def succ[Z](w: FFZ[Z])(y: FZ[Z])(x: Z): Z = y((w(y))(x))
And the unapplied version of it gets as scary as:
def s[Z]: FFFZ[Z] = successor _
Beg your pardon, here is the missing types:
type FFFZ[Z] = FFZ[Z] => FFZ[Z]
type FFFFZ[Z] = FFFZ[Z] => FFFZ[Z]
But I'm stuck at the add function. If conformed to types and definition (taken here as well) it goes like
def add[Z](a: FFFFZ[Z])(b: FFZ[Z]): FFZ[Z] =
(a(s))(b)
But I want a to be a common number of type FFZ[Z].
So -- how can I define addition?
It's totally possible to implement Church numerals in Scala. Here is one such rather straight-forward implementation:
object ChurchNumerals {
type Succ[Z] = Z => Z
type ChNum[Z] = Succ[Z] => Z => Z
def zero[Z]: ChNum[Z] =
(_: Succ[Z]) => (z: Z) => z
def succ[Z] (num: ChNum[Z]): ChNum[Z] =
(s: Succ[Z]) => (z: Z) => s( num(s)(z) )
// a couple of church constants
def one[Z] : ChNum[Z] = succ(zero)
def two[Z] : ChNum[Z] = succ(one)
// the addition function
def add[Z] (a: ChNum[Z]) (b: ChNum[Z]) =
(s: Succ[Z]) => (z: Z) => a(s)( b(s)(z) )
def four[Z] : ChNum[Z] = add(two)(two)
// test
def church_to_int (num: ChNum[Int]): Int =
num((x: Int) => x + 1)(0)
def fourInt: Int = church_to_int(four)
def main(args: Array[String]): Unit = {
println(s"2 + 2 = ${fourInt}")
}
}
Compiles and prints:
$ scala church-numerals.scala
2 + 2 = 4
If I were to explain Church numerals from scratch I'd add more commentaries. But taking the context into account, I'm not sure on what to comment in this case. Please feel free to ask and I'll add more explanations.
I have coded Numerals, Booleans and Pairs: https://github.com/pedrofurla/church/blob/master/src/main/scala/Church.scala following Church's style.
One thing I noticed is that using the curried function syntax was much easier than using multiple argument lists. Some of the interesting snippets
type NUM[A] = (A => A) => A => A
def succ [A]: NUM[A] => NUM[A] = m => n => x => n(m(n)(x))
def zero [A]: NUM[A] = f => x => x
def one [A]: NUM[A] = f => x => f(x)
def two [A]: NUM[A] = f => x => f(f(x))
def three [A]: NUM[A] = f => x => f(f(f(x)))
def plus [A]: (NUM[A]) => (NUM[A]) => NUM[A] = m => n => f => x => m(f)(n(f)(x))
Now for printing them out (very similar to Antov Trunov's solution):
def nvalues[A] = List(zero[A], one[A], two[A], three[A])
val inc: Int => Int = _ + 1
def num: (NUM[Int]) => Int = n => n(inc)(0)
def numStr: (NUM[String]) => String = n => n("f (" + _ + ") ")("z")
Some output:
scala> println(nvalues map num)
List(0, 1, 2, 3)
scala> println(nvalues map numStr) // Like this better :)
List(z, f (z) , f (f (z) ) , f (f (f (z) ) ) )
This seems not logical for me:
scala> val a = Map((1, "111"), (2, "222"))
a: scala.collection.immutable.Map[Int,String] = Map(1 -> 111, 2 -> 222)
scala> val b = a.map((key, value) => value)
<console>:8: error: wrong number of parameters; expected = 1
val b = a.map((key, value) => value)
^
scala> val c = a.map(x => x._2)
c: scala.collection.immutable.Iterable[String] = List(111, 222)
I know that I can say val d = a.map({ case(key, value) => value })
But why isn't it possible to say a.map((key, value) => value) ? There is only one argument there of type Tuple2[Int, String] or Pair of Int, String. What's the difference between a.map((key, value) => value) and a.map(x => x._2) ?
UPDATE:
val myTuple2 = (1, 2) -- this is one variable, correct?
for ( (k, v) <- a ) yield v -- (k, v) is also only one variable, correct?
map((key, value) => value) -- 2 variables. weird.
So how do I specify a variable of type Tuple2 (or any other type) in map without using case?
UPDATE2:
What's wrong with that?
Map((1, "111"), (2, "222")).map( ((x,y):Tuple2[Int, String]) => y) -- wrong
Map((1, "111"), (2, "222")).map( ((x):Tuple2[Int, String]) => x._2) -- ok
Okay, you still not convinced. In cases like this it is pretty reasonable to fallback to the source of the truth (well, kinda): The Holy Specification (aka, Scala Language Specification).
So, in anonymous function parameters are treated on individual basis, not as a whole tuple band (and it is pretty smart, otherwise, how would you call the anonymous function with 2, ... n parameters?).
At the same time
val x = (1, 2)
is a single item of type Tiple2[Int,Int] (if you're interested you may find corresponding section of spec as well).
for ( (k, v) <- a ) yield v
In this case you have one variable unpacked to two variables. It is similar to
val x = (1, 2) // one variable -- tuple
val (y,z) = x // two integer variables unpacked from one
Some call this destructuring assignment and this is a particular case of pattern matching. And you've already provided another example of pattern matching in action:
a.map({ case(key, value) => value })
Which we can read as map accepts a function produced by a partial function literal, which enables use of pattern matching.
You're basically asking this same questions:
Scala - can a lambda parameter match a tuple?
You've already listed most of the options they listed there, including the accepted answer of using a PartialFunction.
However, since you're using your lambda in a map function, you could use a for comprehension instead:
for ( (k, v) <- a ) yield v
Alternatively, you can use the Function2.tupled method to fix your lambda's type:
scala> val a = Map((1, "111"), (2, "222"))
a: scala.collection.immutable.Map[Int,String] = Map(1 -> 111, 2 -> 222)
scala> a.map( ((k:Int,v:String) => v).tupled )
res1: scala.collection.immutable.Iterable[String] = List(111, 222)
To answer your question in your thread with om-nom-nom above, look at this output:
scala> ( (x:Int,y:String) => y ).getClass.getSuperclass
res0: Class[?0] forSome { type ?0 >: ?0; type ?0 <: (Int, String) => String } = class scala.runtime.AbstractFunction2
Notice that the superclass of the anonymous function (x:Int,y:String) => y is Function2[Int, String, String], not Function1[(Int, String), String].
You can use pattern matching (or partial function, in this instance this is the same), notice angular brackets:
val b = a.map{ case (key, value) => value }
I'm guessing that there must be a better functional way of expressing the following:
def foo(i: Any) : Int
if (foo(a) < foo(b)) a else b
So in this example f == foo and p == _ < _. There's bound to be some masterful cleverness in scalaz for this! I can see that using BooleanW I can write:
p(f(a), f(b)).option(a).getOrElse(b)
But I was sure that I would be able to write some code which only referred to a and b once. If this exists it must be on some combination of Function1W and something else but scalaz is a bit of a mystery to me!
EDIT: I guess what I'm asking here is not "how do I write this?" but "What is the correct name and signature for such a function and does it have anything to do with FP stuff I do not yet understand like Kleisli, Comonad etc?"
Just in case it's not in Scalaz:
def x[T,R](f : T => R)(p : (R,R) => Boolean)(x : T*) =
x reduceLeft ((l, r) => if(p(f(l),f(r))) r else l)
scala> x(Math.pow(_ : Int,2))(_ < _)(-2, 0, 1)
res0: Int = -2
Alternative with some overhead but nicer syntax.
class MappedExpression[T,R](i : (T,T), m : (R,R)) {
def select(p : (R,R) => Boolean ) = if(p(m._1, m._2)) i._1 else i._2
}
class Expression[T](i : (T,T)){
def map[R](f: T => R) = new MappedExpression(i, (f(i._1), f(i._2)))
}
implicit def tupleTo[T](i : (T,T)) = new Expression(i)
scala> ("a", "bc") map (_.length) select (_ < _)
res0: java.lang.String = a
I don't think that Arrows or any other special type of computation can be useful here. Afterall, you're calculating with normal values and you can usually lift a pure computation that into the special type of computation (using arr for arrows or return for monads).
However, one very simple arrow is arr a b is simply a function a -> b. You could then use arrows to split your code into more primitive operations. However, there is probably no reason for doing that and it only makes your code more complicated.
You could for example lift the call to foo so that it is done separately from the comparison. Here is a simiple definition of arrows in F# - it declares *** and >>> arrow combinators and also arr for turning pure functions into arrows:
type Arr<'a, 'b> = Arr of ('a -> 'b)
let arr f = Arr f
let ( *** ) (Arr fa) (Arr fb) = Arr (fun (a, b) -> (fa a, fb b))
let ( >>> ) (Arr fa) (Arr fb) = Arr (fa >> fb)
Now you can write your code like this:
let calcFoo = arr <| fun a -> (a, foo a)
let compareVals = arr <| fun ((a, fa), (b, fb)) -> if fa < fb then a else b
(calcFoo *** calcFoo) >>> compareVals
The *** combinator takes two inputs and runs the first and second specified function on the first, respectively second argument. >>> then composes this arrow with the one that does comparison.
But as I said - there is probably no reason at all for writing this.
Here's the Arrow based solution, implemented with Scalaz. This requires trunk.
You don't get a huge win from using the arrow abstraction with plain old functions, but it is a good way to learn them before moving to Kleisli or Cokleisli arrows.
import scalaz._
import Scalaz._
def mod(n: Int)(x: Int) = x % n
def mod10 = mod(10) _
def first[A, B](pair: (A, B)): A = pair._1
def selectBy[A](p: (A, A))(f: (A, A) => Boolean): A = if (f.tupled(p)) p._1 else p._2
def selectByFirst[A, B](f: (A, A) => Boolean)(p: ((A, B), (A, B))): (A, B) =
selectBy(p)(f comap first) // comap adapts the input to f with function first.
val pair = (7, 16)
// Using the Function1 arrow to apply two functions to a single value, resulting in a Tuple2
((mod10 &&& identity) apply 16) assert_≟ (6, 16)
// Using the Function1 arrow to perform mod10 and identity respectively on the first and second element of a `Tuple2`.
val pairs = ((mod10 &&& identity) product) apply pair
pairs assert_≟ ((7, 7), (6, 16))
// Select the tuple with the smaller value in the first element.
selectByFirst[Int, Int](_ < _)(pairs)._2 assert_≟ 16
// Using the Function1 Arrow Category to compose the calculation of mod10 with the
// selection of desired element.
val calc = ((mod10 &&& identity) product) ⋙ selectByFirst[Int, Int](_ < _)
calc(pair)._2 assert_≟ 16
Well, I looked up Hoogle for a type signature like the one in Thomas Jung's answer, and there is on. This is what I searched for:
(a -> b) -> (b -> b -> Bool) -> a -> a -> a
Where (a -> b) is the equivalent of foo, (b -> b -> Bool) is the equivalent of <. Unfortunately, the signature for on returns something else:
(b -> b -> c) -> (a -> b) -> a -> a -> c
This is almost the same, if you replace c with Bool and a in the two places it appears, respectively.
So, right now, I suspect it doesn't exist. It occured to me that there's a more general type signature, so I tried it as well:
(a -> b) -> ([b] -> b) -> [a] -> a
This one yielded nothing.
EDIT:
Now I don't think I was that far at all. Consider, for instance, this:
Data.List.maximumBy (on compare length) ["abcd", "ab", "abc"]
The function maximumBy signature is (a -> a -> Ordering) -> [a] -> a, which, combined with on, is pretty close to what you originally specified, given that Ordering is has three values -- almost a boolean! :-)
So, say you wrote on in Scala:
def on[A, B, C](f: ((B, B) => C), g: A => B): (A, A) => C = (a: A, b: A) => f(g(a), g(b))
The you could write select like this:
def select[A](p: (A, A) => Boolean)(a: A, b: A) = if (p(a, b)) a else b
And use it like this:
select(on((_: Int) < (_: Int), (_: String).length))("a", "ab")
Which really works better with currying and dot-free notation. :-) But let's try it with implicits:
implicit def toFor[A, B](g: A => B) = new {
def For[C](f: (B, B) => C) = (a1: A, a2: A) => f(g(a1), g(a2))
}
implicit def toSelect[A](t: (A, A)) = new {
def select(p: (A, A) => Boolean) = t match {
case (a, b) => if (p(a, b)) a else b
}
}
Then you can write
("a", "ab") select (((_: String).length) For (_ < _))
Very close. I haven't figured any way to remove the type qualifier from there, though I suspect it is possible. I mean, without going the way of Thomas answer. But maybe that is the way. In fact, I think on (_.length) select (_ < _) reads better than map (_.length) select (_ < _).
This expression can be written very elegantly in Factor programming language - a language where function composition is the way of doing things, and most code is written in point-free manner. The stack semantics and row polymorphism facilitates this style of programming. This is what the solution to your problem will look like in Factor:
# We find the longer of two lists here. The expression returns { 4 5 6 7 8 }
{ 1 2 3 } { 4 5 6 7 8 } [ [ length ] bi# > ] 2keep ?
# We find the shroter of two lists here. The expression returns { 1 2 3 }.
{ 1 2 3 } { 4 5 6 7 8 } [ [ length ] bi# < ] 2keep ?
Of our interest here is the combinator 2keep. It is a "preserving dataflow-combinator", which means that it retains its inputs after the given function is performed on them.
Let's try to translate (sort of) this solution to Scala.
First of all, we define an arity-2 preserving combinator.
scala> def keep2[A, B, C](f: (A, B) => C)(a: A, b: B) = (f(a, b), a, b)
keep2: [A, B, C](f: (A, B) => C)(a: A, b: B)(C, A, B)
And an eagerIf combinator. if being a control structure cannot be used in function composition; hence this construct.
scala> def eagerIf[A](cond: Boolean, x: A, y: A) = if(cond) x else y
eagerIf: [A](cond: Boolean, x: A, y: A)A
Also, the on combinator. Since it clashes with a method with the same name from Scalaz, I'll name it upon instead.
scala> class RichFunction2[A, B, C](f: (A, B) => C) {
| def upon[D](g: D => A)(implicit eq: A =:= B) = (x: D, y: D) => f(g(x), g(y))
| }
defined class RichFunction2
scala> implicit def enrichFunction2[A, B, C](f: (A, B) => C) = new RichFunction2(f)
enrichFunction2: [A, B, C](f: (A, B) => C)RichFunction2[A,B,C]
And now put this machinery to use!
scala> def length: List[Int] => Int = _.length
length: List[Int] => Int
scala> def smaller: (Int, Int) => Boolean = _ < _
smaller: (Int, Int) => Boolean
scala> keep2(smaller upon length)(List(1, 2), List(3, 4, 5)) |> Function.tupled(eagerIf)
res139: List[Int] = List(1, 2)
scala> def greater: (Int, Int) => Boolean = _ > _
greater: (Int, Int) => Boolean
scala> keep2(greater upon length)(List(1, 2), List(3, 4, 5)) |> Function.tupled(eagerIf)
res140: List[Int] = List(3, 4, 5)
This approach does not look particularly elegant in Scala, but at least it shows you one more way of doing things.
There's a nice-ish way of doing this with on and Monad, but Scala is unfortunately very bad at point-free programming. Your question is basically: "can I reduce the number of points in this program?"
Imagine if on and if were differently curried and tupled:
def on2[A,B,C](f: A => B)(g: (B, B) => C): ((A, A)) => C = {
case (a, b) => f.on(g, a, b)
}
def if2[A](b: Boolean): ((A, A)) => A = {
case (p, q) => if (b) p else q
}
Then you could use the reader monad:
on2(f)(_ < _) >>= if2
The Haskell equivalent would be:
on' (<) f >>= if'
where on' f g = uncurry $ on f g
if' x (y,z) = if x then y else z
Or...
flip =<< flip =<< (if' .) . on (<) f
where if' x y z = if x then y else z