In Haskell, if I have a list of union typed values like this:
example :: [Either Int Char]
example = [Left 3, Right 'b', Left 6, Left 9, Right 'c']
I can use a little "trick" to extract all the results matching some specific pattern:
lefts :: [Int]
lefts = [l | Left l <- example]
However, if I try to translate this to F#, I get an error:
let lefts = [for Choice1Of2 l in example -> l]
~~~~~~~~~~~~
Incomplete pattern matches on this expression. (...)
This makes a lot of sense (it might even be better behavior than silently ignoring Right values like Haskell does!), but in F#, is there some convenient way to extract (and match on) all values matching a certain pattern in a list/sequence?
In F# if you don't match against all cases you will get a warn, in all scenarios.
So you can write the match with both cases inside the expression, but for your example rather than comprehensions I would use the function List.choose:
let example = [Choice2Of2 3; Choice1Of2 'b'; Choice2Of2 6; Choice2Of2 9; Choice1Of2 'c']
List.choose (function (Choice1Of2 x) -> Some x | _ -> None) example
// val it : char list = ['b'; 'c']
This function is handy for those cases.
I think the closest thing you can do using F# list expressions is something like this:
let lefts example =
[ for e in example do
match e with Choice1Of2 l -> yield l | _ -> () ]
If I understand the Haskell code correctly, the part after | is used not just as an extractor, but also as a filter - implicitly skipping over all things that do not match the pattern.
F# does not have the same kind of concept in list expressions, so you have to be more verbose. Here, we just iterate over all items using for and then we explicitly use yield to produce a new value for each Choice1Of2 in the source list (and we just skip over anything else).
Depending on what you're doing, using List.choose (as mentioned in Gustavo's answer) might be easier. But the above is probably closest you can get to the Haskell's comprehension syntax.
Related
I have a list/sequence as follows Result<DataEntry, exn> []. This list is populated by calling multiple API endpoints in parallel based on some user inputs.
I don't care if some of the calls fail as long as at least 1 succeeds. I then need to perform multiple operations on the success list.
My question is how to partition the Result list into exn [] and DataEntry [] lists. I tried the following:
// allData is Result<DataEntry, exn> []
let filterOutErrors (input: Result<DataEntry, exn>) =
match input with
| Ok v -> true
| _ -> false
let values, err = allData |> Array.partition filterOutErrors
This in principle meets the requirement since values contains all the success cases but understandably the compiler can't infer the types so both values and err contains Result<DataEntry, exn>.
Is there any way to split a list of result Result<Success, Err> such that you end up with separate lists of the inner type?
Is there any way to split a list of result Result<Success, Err> such that you end up with separate lists of the inner type?
Remember that Seq / List / Array are foldable, so you can use fold to convert a Seq / List / Array of 'Ts into any other type 'S. Here you want to go from []Result<DataEntry, exn> to, e.g., the tuple list<DataEntry> * list<exn>. We can define the following folder function, that takes an initial state s of type list<'a> * list<'b> and a Result Result<'a, 'b> and returns your tuple of lists list<'a> * list<'b>:
let listFolder s r =
match r with
| Ok data -> (data :: (fst s), snd s)
| Error err -> (fst s, err :: (snd s))
then you can fold over your array as follows:
let (values, err) = Seq.fold listFolder ([], []) allData
You can extract the good and the bad like this.
let values =
allData
|> Array.choose (fun r ->
match r with
| Result.Ok ok -> Some ok
| Result.Error _ -> None)
let err =
allData
|> Array.choose (fun r ->
match r with
| Result.Ok _ -> None
| Result.Error error -> Some error)
You seem confused about whether you have arrays or lists. The F# code you use, in the snippet and in your question text, all points to use of arrays, in spite of you several times mentioning lists.
It has recently been recommended that we use array instead of the [] symbol in types, since there are inconsistencies in the way F# uses the symbol [] to mean list in some places, and array in other places. There is also the symbol [||] for arrays, which may add more confusion.
So that would be recommending Result<DataEntry,exn> array in this case.
The answer from Víctor G. Adán is functional, but it's a downside that the API requires you to pass in two empty lists, exposing the internal implementation.
You could wrap this into a "starter" function, but then the code grows, requires nested functions or using modules and the intention is obscured.
The answer from Bent Tranberg, while more readable requires two passes of the data, and it seems inefficient to map into Option type just to be able to filter on it using .Choose.
I propose KISS'ing it with some good old mutation.
open System.Collections.Generic
let splitByOkAndErrors xs =
let oks = List<'T>()
let errors = List<'V>()
for x in xs do
match x with
| Ok v -> oks.Add v
| Error e -> errors.Add e
(oks |> seq, errors |> seq)
I know I know, mutation, yuck right? I believe you should not shy away from that even in F#, use the right tool for every situation: the mutation is kept local to the function, so it's still pure. The API is clean just taking in the list of Result to split, there is no concepts like folding, recursive calls, list cons pattern matching etc. to understand, and the function won't reverse the input list, you also have the option to return array or seq, that is, you are not confined to a linked list that can only be appended to in O(1) in the head - which in my experience seldom fits well into business case, win win win in my book.
I general, I hope to see F# grow into a more multi-paradigm programming language in the community's mind. It's nice to see these functional solutions, but I fear they scare some people away unnecessarily, as F# is already multi-paradigm!
I'm trying to do this exercise:
I'm not sure how to use Type in F#, in F# interactive, I wrote type term = Term of float *int, Then I tried to create a value of type term by let x: term = (3.5,8);;But it gives an error.
Then I tried let x: term = Term (3.5,8);; and it worked. So Why is that?
For the first function, I tried:
let multiplyPolyByTerm (x:term, p:poly)=
match p with
|[]->[]
But that gives an error on the line |[]->[] saying that the expression is expecting a type poly, but poly is a in fact a list right? So why is it wrong here? I fixed it by |Poly[]->Poly[]. Then I tried to finish the function by giving the recursive definition of multiplying each term of the polynomial by the given term: |Poly a::af-> This gives an error so I'm stuck on trying to break down the Poly list.
If anyone has suggestion on good readings about Type in F#, please share it.
I got all the methods now, However,I find myself unable to throw an exception when the polynomial is an empty list as the base case of my recursive function is an empty list. Also, I don't know how to group common term together, Please help, Here are my codes:
type poly=Poly of (float*int) list
type term = Term of float *int
exception EmptyList
(*
let rec mergeCommonTerm(p:poly)=
let rec iterator ((a: float,b: int ), k: (float*int) list)=
match k with
|[]->(a,b)
|ki::kf-> if b= snd ki then (a+ fst ki,b)
match p with
|Poly [] -> Poly []
|Poly (a::af)-> match af with
|[]-> Poly [a]
|b::bf -> if snd a =snd b then Poly (fst a +fst b,snd a)::bf
else
*)
let rec multiplyPolyByTerm (x:term, p:poly)=
match x with
| Term (coe,deg) -> match p with
|Poly[] -> Poly []
|Poly (a::af) -> match multiplyPolyByTerm (x,Poly af) with
|Poly recusivep-> Poly ((fst a *coe,snd a + deg)::recusivep)
let rec addTermToPoly (x:term, p:poly)=
match x with
|Term (coe, deg)-> match p with
|Poly[] -> Poly [(coe,deg)]
|Poly (a::af)-> if snd a=deg then Poly ((fst a+coe,deg)::af)
else match addTermToPoly (x,Poly af) with
|Poly recusivep-> Poly (a::recusivep)
let rec addPolys (x:poly, y: poly)=
match x with
|Poly []->y
|Poly (xh::xt)-> addPolys(Poly xt,addTermToPoly(Term xh, y))
let rec multPolys (x:poly,y:poly)=
match x with
|Poly []-> Poly[]
|Poly (xh::xt)->addPolys (multiplyPolyByTerm(Term xh,y),multPolys(Poly xt,y))
let evalTerm (values:float) (termmm : term) :float=
match termmm with
|Term (coe,deg)->coe*(values**float(deg))
let rec evalPoly (polyn : poly, v: float) :float=
match polyn with
|Poly []->0.0
|Poly (ph::pt)-> (evalTerm v (Term ph)) + evalPoly (Poly pt,v)
let rec diffPoly (p:poly) :poly=
match p with
|Poly []->Poly []
|Poly (ah::at)-> match diffPoly (Poly at) with
|Poly [] -> if snd ah = 0 then Poly []
else Poly [(float(snd ah)*fst ah,snd ah - 1)]
|Poly (bh::bt)->Poly ((float(snd ah)*fst ah,snd ah - 1)::bh::bt)
As I mentioned in a comment, reading https://fsharpforfunandprofit.com/posts/discriminated-unions/ will be very helpful for you. But let me give you some quick help to get you unstuck and starting to solve your immediate problems. You're on the right track, you're just struggling a little with the syntax (and operator precedence, which is part of the syntax).
First, load the MSDN operator precedence documentation in another tab while you read the rest of this answer. You'll want to look at it later on, but first I'll explain a subtlety of how F# treats discriminated unions that you probably haven't understood yet.
When you define a discriminated union type like poly, the name Poly acts like a constructor for the type. In F#, constructors are functions. So when you write Poly (something), the F# parser interprets this as "take the value (something) and pass it to the function named Poly". Here, the function Poly isn't one you had to define explicitly; it was implicitly defined as part of your type definition. To really make this clear, consider this example:
type Example =
| Number of int
| Text of string
5 // This has type int
Number 5 // This has type Example
Number // This has type (int -> Example), i.e. a function
"foo" // This has type string
Text "foo" // This has type Example
Text // This has type (string -> Example), i.e. a function
Now look at the operator precedence list that you loaded in another tab. Lowest precedence is at the top of the table, and highest precedence is at the bottom; in other words, the lower something is on the table, the more "tightly" it binds. As you can see, function application (f x, calling f with parameter x) binds very tightly, more tightly than the :: operator. So when you write f a::b, that is not read as f (a::b), but rather as (f a)::b. In other words, f a::b reads as "Item b is a list of some type which we'll call T, and the function call f a produces an item of type T that should go in front of list b". If you instead meant "take the list formed by putting item a at the head of list b, and then call f with the resulting list", then that needs parentheses: you have to write f (a::b) to get that meaning.
So when you write Poly a::af, that's interpreted as (Poly a)::af, which means "Here is a list. The first item is a Poly a, which means that a is a (float * int) list. The rest of the list will be called af". And since the value your passing into it is not a list, but rather a poly type, that is a type mismatch. (Note that items of type poly contain lists, but they are not themselves lists). What you needed to write was Poly (a::af), which would have meant "Here is an item of type poly that contains a list. That list should be split into the head, a, and the rest, af."
I hope that helped rather than muddle the waters further. If you didn't understand any part of this, let me know and I'll try to make it clearer.
P.S. Another point of syntax you might want to know: F# gives you many ways to signal an error condition (like an empty list in this assignment), but your professor has asked you to use exception EmptyList when invalid input is given. That means he expects your code to "throw" or "raise" an exception when you encounter an error. In C# the term is "throw", but in F# the term is "raise", and the syntax looks like this:
if someErrorCondition then
raise EmptyList
// Or ...
match listThatShouldNotBeEmpty with
| [] -> raise EmptyList
| head::rest -> // Do something with head, etc.
That should take care of the next question you would have needed to ask. :-)
Update 2: You've edited your question to clarify another issue you're having, where your recursive function boils down to an empty list as the base case — yet your professor asked you to consider an empty list as an invalid input. There are two ways to solve this. I'll discuss the more complicated one first, then I'll discuss the easier one.
The more complicated way to solve this is to have two separate functions, an "outer" one and an "inner" one, for each of the functions you have been asked to define. In each case, the "outer" one checks whether the input is an empty list and throws an exception if that's the case. If the input is not an empty list, then it passes the input to the "inner" function, which does the recursive algorithm (and does NOT consider an empty list to be an error). So the "outer" function is basically only doing error-checking, and the "inner" function is doing all the work. This is a VERY common approach in professional programming, where all your error-checking is done at the "edges" of your code, while the "inner" code never has to deal with errors. It's therefore a good approach to know about — but in your particular case, I think it's more complicated than you need.
The easier solution is to rewrite your functions to consider a single-item list as the base case, so that your recursive functions never go all the way to an empty list. Then you can always consider an empty list to be an error. Since this is homework I won't give you an example based on your actual code, but rather an example based on a simple "take the sum of a list of integers" exercise where an empty list would be considered an error:
let rec sumNonEmptyList (input : int list) : int =
match input with
| [] -> raise EmptyList
| [x] -> x
| x::rest -> x + sumNonEmptyList rest
The syntax [x] in a match expression means "This matches a list with exactly one item in it, and assigns the name x to the value of that item". In your case, you'd probably be matching against Poly [] to raise an exception, Poly [a] as the base case, and Poly (a::af) as the "more than one item" case. (That's as much of a clue as I think I should give you; you'll learn better if you work out the rest yourself).
I am watching a tutorial on parsers in haskell https://www.youtube.com/watch?v=9FGThag0Fqs. The lecture starts with defining some really basic parsers. These are to be used together to create more complicated parsers later. One of the basic parsers is item. This is used to extract a character from the string we are parsing.
All parsers have the following type:
type Parser a = String -> [(a, String)]
The parser item is defined like this:
item :: Parser Char
item = \inp -> case inp of
[] -> []
(x:xs) -> [(x,xs)]
I am not so used to this syntax, so it looks strange to me. I would have written it:
item' :: Parser Char
item' [] = []
item' (x:xs) = [(x,xs)]
Testing it in ghci indicates that they are equal:
*Main> item ""
[]
*Main> item "abc"
[('a',"bc")]
*Main> item' ""
[]
*Main> item' "abc"
[('a',"bc")]
The lecturer makes a short comment about thinking it looks clearer, but I disagree. So my questions are:
Are they indeed completely identical?
Why is the lambda version clearer?
I believe this comes from the common practice of writing
f :: Type1 -> ... -> Typen -> Result
f x1 ... xn = someResult
where we have exactly n function arrows in the type, and exactly n arguments in the left hand side of the equation. This makes it easy to relate types and formal parameters.
If Result is a type alias for a function, then we may write
f :: Type1 -> ... -> Typen -> Result
f x1 ... xn y = something
or
f :: Type1 -> ... -> Typen -> Result
f x1 ... xn = \y -> something
The latter follows the convention above: n arrows, n variables in the left hand side. Also, on the right hand side we have something of type Result, making it easier to spot. The former instead does not, and one might miss the extra argument when reading the code quickly.
Further, this style makes it easy to convert Result to a newtype instead of a type alias:
newtype Result = R (... -> ...)
f :: Type1 -> ... -> Typen -> Result
f x1 ... xn = R $ \y -> something
The posted item :: Parser Char code is an instance of this style when n=0.
Why you should avoid equational function definitions (by Roman Cheplyaka):
http://ro-che.info/articles/2014-05-09-clauses
Major Points from the above link:
DRY: Function and argument names are repeated --> harder to refactor
Clearer shows which arguments the function decides upon
Easy to add pragmas (e.g. for profiling)
Syntactically closer to lower level code
This doesn't explain the lambda though..
I think they are absolutely equal. The lambda-style definition puts a name item to an anonymous lambda function which does pattern matching inside. The pattern-matching-style definition defines it directly. But in the end both are functions that do pattern matching. I think it's a matter of personal taste.
Also, the lambda-style definition could be considered to be in pointfree style, i.e. a function defined without explicitly writing down its arguments actually it is not very much pointfree since the argument is still written (but in a different place), but in this case you don't get anything with this.
Here is another possible definion, somewhere in between of those two:
item :: Parser Char
item inp = case inp of
[] -> []
(x:xs) -> [(x, xs)]
It's essentially identical to the lambda-style, but not pointfree.
I was reading this post While or Tail Recursion in F#, what to use when? were several people say that the 'functional way' of doing things is by using maps/folds and higher order functions instead of recursing and looping.
I have this function that returns the item at position x in a list:
let rec getPos l c = if c = 0 then List.head l else getPos (List.tail l) (c - 1)
how can it be converted to be more functional?
This is a primitive list function (also known as List.nth).
It is okay to use recursion, especially when creating the basic building blocks. Although it would be nicer with pattern matching instead of if-else, like this:
let rec getPos l c =
match l with
| h::_ when c = 0 -> h
| _::t -> getPos t (c-1)
| [] -> failwith "list too short"
It is possible to express this function with List.fold, however the result is less clear than the recursive version.
I'm not sure what you mean by more functional.
Are you rolling this yourself as a learning exercise?
If not, you could just try this:
> let mylist = [1;2;3;4];;
> let n = 2;;
> mylist.[n];;
Your definition is already pretty functional since it uses a tail-recursive function instead of an imperative loop construct. However, it also looks like something a Scheme programmer might have written because you're using head and tail.
I suspect you're really asking how to write it in a more idiomatic ML style. The answer is to use pattern matching:
let rec getPos list n =
match list with
| hd::tl ->
if n = 0 then hd
else getPos tl (n - 1)
| [] -> failWith "Index out of range."
The recursion on the structure of the list is now revealed in the code. You also get a warning if the pattern matching is non-exhaustive so you're forced to deal with the index too big error.
You're right that functional programming also encourages the use of combinators like map or fold (so called points-free style). But too much of it just leads to unreadable code. I don't think it's warranted in this case.
Of course, Benjol is right, in practice you would just write mylist.[n].
If you'd like to use high-order functions for this, you could do:
let nth n = Seq.take (n+1) >> Seq.fold (fun _ x -> Some x) None
let nth n = Seq.take (n+1) >> Seq.reduce (fun _ x -> x)
But the idea is really to have basic constructions and combine them build whatever you want. Getting the nth element of a sequence is clearly a basic block that you should use. If you want the nth item, as Benjol mentioned, do myList.[n].
For building basic constructions, there's nothing wrong to use recursion or mutable loops (and often, you have to do it this way).
Not as a practical solution, but as an exercise, here is one of the ways to express nth via foldr or, in F# terms, List.foldBack:
let myNth n xs =
let step e f = function |0 -> e |n -> f (n-1)
let error _ = failwith "List is too short"
List.foldBack step xs error n
A real F# noob question, but what is |> called and what does it do?
It's called the forward pipe operator. It pipes the result of one function to another.
The Forward pipe operator is simply defined as:
let (|>) x f = f x
And has a type signature:
'a -> ('a -> 'b) -> 'b
Which resolves to: given a generic type 'a, and a function which takes an 'a and returns a 'b, then return the application of the function on the input.
You can read more detail about how it works in an article here.
I usually refer to |> as the pipelining operator, but I'm not sure whether the official name is pipe operator or pipelining operator (though it probably doesn't really matter as the names are similar enough to avoid confusion :-)).
#LBushkin already gave a great answer, so I'll just add a couple of observations that may be also interesting. Obviously, the pipelining operator got it's name because it can be used for creating a pipeline that processes some data in several steps. The typical use is when working with lists:
[0 .. 10]
|> List.filter (fun n -> n % 3 = 0) // Get numbers divisible by three
|> List.map (fun n -> n * n) // Calculate squared of such numbers
This gives the result [0; 9; 36; 81]. Also, the operator is left-associative which means that the expression input |> f |> g is interpreted as (input |> f) |> g, which makes it possible to sequence multiple operations using |>.
Finally, I find it quite interesting that pipelining operaor in many cases corresponds to method chaining from object-oriented langauges. For example, the previous list processing example would look like this in C#:
Enumerable.Range(0, 10)
.Where(n => n % 3 == 0) // Get numbers divisible by three
.Select(n => n * n) // Calculate squared of such numbers
This may give you some idea about when the operator can be used if you're comming fromt the object-oriented background (although it is used in many other situations in F#).
As far as F# itself is concerned, the name is op_PipeRight (although no human would call it that). I pronounce it "pipe", like the unix shell pipe.
The spec is useful for figuring out these kinds of things. Section 4.1 has the operator names.
http://research.microsoft.com/en-us/um/cambridge/projects/fsharp/manual/spec.html
Don't forget to check out the library reference docs:
http://msdn.microsoft.com/en-us/library/ee353754(v=VS.100).aspx
which list the operators.