I have a fold which iterates through elements, dependently modifies them one by one and at the same time modifies their parent.
Currently I replace the elements in their parent one by one in the fold, they are just few and it is not a real performance issue, but I wonder if there is perhaps a nicer way to express this.
case class Behavior(x: Int) {
def simulate(s: Entity): Behavior = copy(x = x + (if (s.alternate) 2 else 1))
}
case class Entity(alternate: Boolean, behaviors: List[Behavior]) {
def replaceBehavior(o: Behavior, n: Behavior): Entity = {
copy(behaviors = behaviors.patch(behaviors.indexOf(o), Seq(n), 1))
}
def toggleAlternate: Entity = copy(alternate = !alternate)
def simulate: Entity = {
behaviors.foldLeft(this) { (e, b) =>
e.replaceBehavior(b, b.simulate(e)).toggleAlternate
}
}
}
val entity = Entity(false, List(Behavior(10), Behavior(20), Behavior(30)))
entity.simulate
Is there some operation or perhaps some clever use of scan or something like that which would allow me to perform foldLeft and map dependent of the foldLeft result in one step? (I would prefer vanilla standard Scala library, but using functional frameworks is possible too).
Folds (fold, foldLeft, foldRight, ...) usually turn some Collection[A] into B.
You could map over A before folding result to B - foldMap maps A => B and assumed existence of Monoid[B] (this is available in Cats in Foldable typeclass), so you would perform transformation Collection[A] --using f--> Collection[B] --using Monoid[B]--> B (code can optimize it to perform things in one step using e.g. foldLeft internally).
Reversing the order of operations - we fold and then we map - is in general impossible because there is nothing that can let us assume that after fold step we will end up with something that is a Functor.
Depending on your specific use case we might try using foldMap to achieve your goal.
Related
I have this two functions
def pattern(s: String): Option[Pattern] =
try {
Some(Pattern.compile(s))
} catch {
case e: PatternSyntaxException => None
}
and
def mkMatcher(pat: String): Option[String => Boolean] =
pattern(pat) map (p => (s: String) => p.matcher(s).matches)
Map is the higher-order function that applies a given function to each element of a list.
Now I am not getting that how map is working here as per above statement.
Map is the higher-order function that applies a given function to each element of a list.
This is an uncommonly restrictive definition of map.
At any rate, it works because it was defined by someone who did not hold to that.
For example, that someone wrote something akin to
sealed trait Option[+A] {
def map[B](f: A => B): Option[B] = this match {
case Some(value) => Some(f(value))
case None => None
}
}
as part of the standard library. This makes map applicable to Option[A]
It was defined because it makes sense to map many kinds of data structures not just lists.
Mapping is a transformation applied to the elements held by the data structure.
It applies a function to each element.
Option[A] can be thought of as a trivial sequence. It either has zero or one elements. To map it means to apply the function on its element if it has one.
Now it may not make much sense to use this facility all of the time, but there are cases where it is useful.
For example, it is one of a few distinct methods that, when present enable enable For Expressions to operate on a type. Option[A] can be used in for expressions which can be convenient.
For example
val option: Option[Int] = Some(2)
val squared: Option[Int] = for {
n <- option
if n % 2 == 0
} yield n * n
Interestingly, this implies that filter is also defined on Option[A].
If you just have a simple value it may well be clearer to use a less general construct.
Map is working the same way that it does with other collections types like List and Vector. It applies your function to the contents of the collection, potentially changing the type but keeping the collection type the same.
In many cases you can treat an Option just like a collection with either 0 or 1 elements. You can do a lot of the same operations on Option that you can on other collections.
You can modify the value
var opt = Option(1)
opt.map(_ + 3)
opt.map(_ * math.Pi)
opt.filter(_ == 1)
opt.collect({case i if i > 0 => i.toString })
opt.foreach(println)
and you can test the value
opt.contains(3)
opt.forall(_ > 0)
opt.exists(_ > 0)
opt.isEmpty
Using these methods you rarely need to use a match statement to unpick an Option.
I use sequenceU to turn inside type out while working with disjunctions in scalaz.
for e.g.
val res = List[\/[Errs,MyType]]
doing
res.sequenceU will give \/[Errs,List[MyType]]
Now if I have a val res2 = List[(\/[Errs,MyType], DefModel)] - List containing tuples of disjunctions; what's the right way to convert
res2 to \/[Errs,List[ (Mype,DefModel)]
As noted in the comments, the most straightforward way to write this is probably just with a traverse and map:
def sequence(xs: List[(\/[Errs, MyType], DefModel)]): \/[Errs, List[(MyType, DefModel)]] =
xs.traverseU { case (m, d) => m.map((_, d)) }
It's worth noting, though, that tuples are themselves traversable, so the following is equivalent:
def sequence(xs: List[(\/[Errs, MyType], DefModel)]): \/[Errs, List[(MyType, DefModel)]] =
xs.traverseU(_.swap.sequenceU.map(_.swap))
Note that this would be even simpler if the disjunction were on the right side of the tuple. If you're willing to make that change, you can also more conveniently take advantage of the fact that Traverse instances compose:
def sequence(xs: List[(DefModel, \/[Errs, MyType])]): \/[Errs, List[(DefModel, MyType)]] =
Traverse[List].compose[(DefModel, ?)].sequenceU(xs)
I'm using kind-projector here but you could also write out the type lambda.
Now I have some Scala code similar to the following:
def foo(x: Int, fn: (Int, Int) => Boolean): Boolean = {
for {
i <- 0 until x
j <- i + 1 until x
if fn(i, j)
} return true
false
}
But I get the feeling that return true is not so functional (or maybe it is?). Is there a way to rewrite this piece of code in a more elegant way?
In general, what is the more functional (if any) way to write the return-early-from-a-loop kind of code?
There are several methods can help, such as find, exists, etc. For your case, try this:
def foo2(x: Int, fn: (Int, Int) => Boolean): Boolean = {
(0 until x).exists(i =>
(i+1 until x).exists(j=>fn(i, j)))
}
Since all you are checking for is existence, you can just compose 2 uses of exists:
(0 until x).exists(i => (i + 1 until x).exists(fn(i, _)))
More generally, if you are concerned with more than just determining if a certain element exists, you can convert your comprehension to a series of Streams, Iterators, or views, you can use exists and it will evaluate lazily, avoiding unnecessary executions of the loop:
def foo(x: Int, fn: (Int, Int) => Boolean): Boolean = {
(for {
i <- (0 until x).iterator
j <- (i + 1 until x).iterator
} yield(i, j)).exists(fn.tupled)
}
You can also use map and flatMap instead of a for, and toStream or view instead of iterator:
(0 until x).view.flatMap(i => (i + 1 until x).toStream.map(j => i -> j)).exists(fn.tupled)
You can also use view on any collection to get a collection where all the transformers are performed lazily. This is possibly the most idiomatic way to short-circuit a collection traversal. From the docs on views:
Scala collections are by default strict in all their transformers, except for Stream, which implements all its transformer methods lazily. However, there is a systematic way to turn every collection into a lazy one and vice versa, which is based on collection views. A view is a special kind of collection that represents some base collection, but implements all transformers lazily.
As far as overhead is concerned, it really depends on the specifics! Different collections have different implementations of view, toStream, and iterator that may vary in amount of overhead. If fn is very expensive to compute, this overhead is probably worth it, and keeping a consistent, idiomatic, functional style to your code makes it more maintainable, debuggable, and readable. If you are in a situation that calls for extreme optimization, you may want to fall back to the lower-level constructs like return (which isn't without it's own overhead!).
I'm writing a programming language interpreter.
I have need of the right code idiom to both evaluate a sequence of expressions to get a sequence of their values, and propagate state from one evaluator to the next to the next as the evaluations take place. I'd like a functional programming idiom for this.
It's not a fold because the results come out like a map. It's not a map because of the state prop across.
What I have is this code which I'm using to try to figure this out. Bear with a few lines of test rig first:
// test rig
class MonadLearning extends JUnit3Suite {
val d = List("1", "2", "3") // some expressions to evaluate.
type ResType = Int
case class State(i : ResType) // trivial state for experiment purposes
val initialState = State(0)
// my stub/dummy "eval" function...obviously the real one will be...real.
def computeResultAndNewState(s : String, st : State) : (ResType, State) = {
val State(i) = st
val res = s.toInt + i
val newStateInt = i + 1
(res, State(newStateInt))
}
My current solution. Uses a var which is updated as the body of the map is evaluated:
def testTheVarWay() {
var state = initialState
val r = d.map {
s =>
{
val (result, newState) = computeResultAndNewState(s, state)
state = newState
result
}
}
println(r)
println(state)
}
I have what I consider unacceptable solutions using foldLeft which does what I call "bag it as you fold" idiom:
def testTheFoldWay() {
// This startFold thing, requires explicit type. That alone makes it muddy.
val startFold : (List[ResType], State) = (Nil, initialState)
val (r, state) = d.foldLeft(startFold) {
case ((tail, st), s) => {
val (r, ns) = computeResultAndNewState(s, st)
(tail :+ r, ns) // we want a constant-time append here, not O(N). Or could Cons on front and reverse later
}
}
println(r)
println(state)
}
I also have a couple of recursive variations (which are obvious, but also not clear or well motivated), one using streams which is almost tolerable:
def testTheStreamsWay() {
lazy val states = initialState #:: resultStates // there are states
lazy val args = d.toStream // there are arguments
lazy val argPairs = args zip states // put them together
lazy val resPairs : Stream[(ResType, State)] = argPairs.map{ case (d1, s1) => computeResultAndNewState(d1, s1) } // map across them
lazy val (results , resultStates) = myUnzip(resPairs)// Note .unzip causes infinite loop. Had to write my own.
lazy val r = results.toList
lazy val finalState = resultStates.last
println(r)
println(finalState)
}
But, I can't figure out anything as compact or clear as the original 'var' solution above, which I'm willing to live with, but I think somebody who eats/drinks/sleeps monad idioms is going to just say ... use this... (Hopefully!)
With the map-with-accumulator combinator (the easy way)
The higher-order function you want is mapAccumL. It's in Haskell's standard library, but for Scala you'll have to use something like Scalaz.
First the imports (note that I'm using Scalaz 7 here; for previous versions you'd import Scalaz._):
import scalaz._, syntax.std.list._
And then it's a one-liner:
scala> d.mapAccumLeft(initialState, computeResultAndNewState)
res1: (State, List[ResType]) = (State(3),List(1, 3, 5))
Note that I've had to reverse the order of your evaluator's arguments and the return value tuple to match the signatures expected by mapAccumLeft (state first in both cases).
With the state monad (the slightly less easy way)
As Petr Pudlák points out in another answer, you can also use the state monad to solve this problem. Scalaz actually provides a number of facilities that make working with the state monad much easier than the version in his answer suggests, and they won't fit in a comment, so I'm adding them here.
First of all, Scalaz does provide a mapM—it's just called traverse (which is a little more general, as Petr Pudlák notes in his comment). So assuming we've got the following (I'm using Scalaz 7 again here):
import scalaz._, Scalaz._
type ResType = Int
case class Container(i: ResType)
val initial = Container(0)
val d = List("1", "2", "3")
def compute(s: String): State[Container, ResType] = State {
case Container(i) => (Container(i + 1), s.toInt + i)
}
We can write this:
d.traverse[({type L[X] = State[Container, X]})#L, ResType](compute).run(initial)
If you don't like the ugly type lambda, you can get rid of it like this:
type ContainerState[X] = State[Container, X]
d.traverse[ContainerState, ResType](compute).run(initial)
But it gets even better! Scalaz 7 gives you a version of traverse that's specialized for the state monad:
scala> d.traverseS(compute).run(initial)
res2: (Container, List[ResType]) = (Container(3),List(1, 3, 5))
And as if that wasn't enough, there's even a version with the run built in:
scala> d.runTraverseS(initial)(compute)
res3: (Container, List[ResType]) = (Container(3),List(1, 3, 5))
Still not as nice as the mapAccumLeft version, in my opinion, but pretty clean.
What you're describing is a computation within the state monad. I believe that the answer to your question
It's not a fold because the results come out like a map. It's not a map because of the state prop across.
is that it's a monadic map using the state monad.
Values of the state monad are computations that read some internal state, possibly modify it, and return some value. It is often used in Haskell (see here or here).
For Scala, there is a trait in the ScalaZ library called State that models it (see also the source). There are utility methods in States for creating instances of State. Note that from the monadic point of view State is just a monadic value. This may seem confusing at first, because it's described by a function depending on a state. (A monadic function would be something of type A => State[B].)
Next you need is a monadic map function that computes values of your expressions, threading the state through the computations. In Haskell, there is a library method mapM that does just that, when specialized to the state monad.
In Scala, there is no such library function (if it is, please correct me). But it's possible to create one. To give a full example:
import scalaz._;
object StateExample
extends App
with States /* utility methods */
{
// The context that is threaded through the state.
// In our case, it just maps variables to integer values.
class Context(val map: Map[String,Int]);
// An example that returns the requested variable's value
// and increases it's value in the context.
def eval(expression: String): State[Context,Int] =
state((ctx: Context) => {
val v = ctx.map.get(expression).getOrElse(0);
(new Context(ctx.map + ((expression, v + 1)) ), v);
});
// Specialization of Haskell's mapM to our State monad.
def mapState[S,A,B](f: A => State[S,B])(xs: Seq[A]): State[S,Seq[B]] =
state((initState: S) => {
var s = initState;
// process the sequence, threading the state
// through the computation
val ys = for(x <- xs) yield { val r = f(x)(s); s = r._1; r._2 };
// return the final state and the output result
(s, ys);
});
// Example: Try to evaluate some variables, starting from an empty context.
val expressions = Seq("x", "y", "y", "x", "z", "x");
print( mapState(eval)(expressions) ! new Context(Map[String,Int]()) );
}
This way you can create simple functions that take some arguments and return State and then combine them into more complex ones by using State.map or State.flatMap (or perhaps better using for comprehensions), and then you can run the whole computation on a list of expressions by mapM.
See also http://blog.tmorris.net/posts/the-state-monad-for-scala-users/
Edit: See Travis Brown's answer, he described how to use the state monad in Scala much more nicely.
He also asks:
But why, when there's a standard combinator that does exactly what you need in this case?
(I ask this as someone who's been slapped for using the state monad when mapAccumL would do.)
It's because the original question asked:
It's not a fold because the results come out like a map. It's not a map because of the state prop across.
and I believe the proper answer is it is a monadic map using the state monad.
Using mapAccumL is surely faster, both less memory and CPU overhead. But the state monad captures the concept of what is going on, the essence of the problem. I believe in many (if not most) cases this is more important. Once we realize the essence of the problem, we can either use the high-level concepts to nicely describe the solution (perhaps sacrificing speed/memory a little) or optimize it to be fast (or perhaps even manage to do both).
On the other hand, mapAccumL solves this particular problem, but doesn't give us a broader answer. If we need to modify it a little, it might happen it won't work any more. Or, if the library starts to be complex, the code can start to be messy and we won't know how to improve it, how to make the original idea clear again.
For example, in the case of evaluating stateful expressions, the library can become complicated and complex. But if we use the state monad, we can build the library around small functions, each taking some arguments and returning something like State[Context,Result]. These atomic computations can be combined to more complex ones using flatMap method or for comprehensions, and finally we'll construct the desired task. The principle will stay the same across the whole library, and the final task will also be something that returns State[Context,Result].
To conclude: I'm not saying using the state monad is the best solution, and certainly it's not the fastest one. I just believe it is most didactic for a functional programmer - it describes the problem in a clean, abstract way.
You could do this recursively:
def testTheRecWay(xs: Seq[String]) = {
def innerTestTheRecWay(xs: Seq[String], priorState: State = initialState, result: Vector[ResType] = Vector()): Seq[ResType] = {
xs match {
case Nil => result
case x :: tail =>
val (res, newState) = computeResultAndNewState(x, priorState)
innerTestTheRecWay(tail, newState, result :+ res)
}
}
innerTestTheRecWay(xs)
}
Recursion is a common practice in functional programming and is most of the time easier to read, write and understand than loops. In fact scala does not have any loops other than while. fold, map, flatMap, for (which is just sugar for flatMap/map), etc. are all recursive.
This method is tail recursive and will be optimized by the compiler to not build a stack, so it is absolutely safe to use. You can add the #annotation.tailrec annotaion, to force the compiler to apply tail recursion elimination. If your method is not tailrec the compiler will then complain.
edit: renamed inner method to avoid ambiguity
It is quite possible that to know whether a function is defined at some point, a significant part of computing its value has to be done. In a PartialFunction, when implementing isDefined and apply, both methods will have to do that. What to do is this common job is costly?
There is the possibility of caching its result, hoping that apply will be called after isDefined. Definitely ugly.
I often wish that PartialFunction[A,B] would be Function[A, Option[B]], which is clearly isomorphic. Or maybe, there could be another method in PartialFunction, say applyOption(a: A): Option[B]. With some mixins, implementors would have a choice of implementing either isDefined and apply or applyOption. Or all of them to be on the safe side, performance wise. Clients which test isDefined just before calling apply would be encouraged to use applyOption instead.
However, this is not so. Some major methods in the library, among them collect in collections require a PartialFunction. Is there a clean (or not so clean) way to avoid paying for computations repeated between isDefined and apply?
Also, is the applyOption(a: A): Option[B] method reasonable? Does it sound feasible to add it in a future version? Would it be worth it?
Why is caching such a problem? In most cases, you have a local computation, so as long as you write a wrapper for the caching, you needn't worry about it. I have the following code in my utility library:
class DroppedFunction[-A,+B](f: A => Option[B]) extends PartialFunction[A,B] {
private[this] var tested = false
private[this] var arg: A = _
private[this] var ans: Option[B] = None
private[this] def cache(a: A) {
if (!tested || a != arg) {
tested = true
arg = a
ans = f(a)
}
}
def isDefinedAt(a: A) = {
cache(a)
ans.isDefined
}
def apply(a: A) = {
cache(a)
ans.get
}
}
class DroppableFunction[A,B](f: A => Option[B]) {
def drop = new DroppedFunction(f)
}
implicit def function_is_droppable[A,B](f: A => Option[B]) = new DroppableFunction(f)
and then if I have an expensive computation, I write a function method A => Option[B] and do something like (f _).drop to use it in collect or whatnot. (If you wanted to do it inline, you could create a method that takes A=>Option[B] and returns a partial function.)
(The opposite transformation--from PartialFunction to A => Option[B]--is called lifting, hence the "drop"; "unlift" is, I think, a more widely used term for the opposite operation.)
Have a look at this thread, Rethinking PartialFunction. You're not the only one wondering about this.
This is an interesting question, and I'll give my 2 cents.
First of resist the urge for premature optimization. Make sure the partial function is the problem. I was amazed at how fast they are on some cases.
Now assuming there is a problem, where would it come from?
Could be a large number of case clauses
Complex pattern matching
Some complex computation on the if causes
One option I'd try to find ways to fail fast. Break the pattern matching into layer, then chain partial functions. This way you can fail the match early. Also extract repeated sub matching. For example:
Lets assume OddEvenList is an extractor that break a list into a odd list and an even list:
var pf1: PartialFuntion[List[Int],R] = {
case OddEvenList(1::ors, 2::ers) =>
case OddEvenList(3::ors, 4::ors) =>
}
Break to two part, one that matches the split then one that tries to match re result (to avoid repeated computation. However this may require some re-engineering
var pf2: PartialFunction[(List[Int],List[Int],R) = {
case (1 :: ors, 2 :: ers) => R1
case (3 :: ors, 4 :: ors) => R2
}
var pf1: PartialFuntion[List[Int],R] = {
case OddEvenList(ors, ers) if(pf2.isDefinedAt(ors,ers) => pf2(ors,ers)
}
I have used this when progressively reading XML files that hard a rather inconstant format.
Another option is to compose partial functions using andThen. Although a quick test here seamed to indicate that only the first was is actually tests.
There is absolutely nothing wrong with caching mechanism inside the partial function, if:
the function returns always the same input, when passed the same argument
it has no side effects
it is completely hidden from the rest of the world
Such cached function is not distiguishable from a plain old pure partial function...