I am writing a function in f# that could be done with several if/else blocks but reads much cleaner with a match/with clause. The issue is that in many cases, I do not care about the variable actually being matched; I am using "when" everywhere instead.
The question is, is there a way of doing a "match/with" using only "when" blocks and no actual match variable?
let primes (input:bigint) =
let rec factors acc (input':bigint, factor:bigint) =
match input' with
| _ when input' = 1I -> acc
| _ when input = factor -> factor::acc
| _ when input' = factor -> factor::acc
| _ when input' % factor = 0I -> factor::factors acc (input'/factor, factor)
| _ -> factors acc (input', factor+1I)
in factors [] (input, 2I)
primes 1I |> List.iter (printf "%A "); printfn "..";
primes 12I |> List.iter (printf "%A "); printfn "..";
primes 60I |> List.iter (printf "%A "); printfn "..";
primes 420I |> List.iter (printf "%A "); printfn "..";
primes 1260I |> List.iter (printf "%A "); printfn "..";
primes 13I |> List.iter (printf "%A "); printfn "..";
[Edit] It has been suggested that this is the same question as this and I suppose it is. But if not for this post, I would not have seen Carsten's answer, which is what I thought I was looking for. Now that I know it, I guess the two alternatives are as follows
let primes (input:bigint) =
let rec factors acc (input':bigint, factor:bigint) =
match () with
| () when input' = 1I -> acc
| () when input = factor -> factor::acc
| () when input' = factor -> factor::acc
| () when input' % factor = 0I -> factor::factors acc (input'/factor, factor)
| _ -> factors acc (input', factor+1I)
in factors [] (input, 2I)
let primes' (input:bigint) =
let rec factors acc (input':bigint, factor:bigint) =
if input' = 1I then acc
elif input = factor then factor::acc
elif input' = factor then factor::acc
elif input' % factor = 0I then factor::factors acc (input'/factor, factor)
else factors acc (input', factor+1I)
in factors [] (input, 2I)
Seeing them side by side like this leaves me with the opinion that I should use the elif's.
The conditions supplied here relate to different inputs, so there's not much to match on. These are the situation where if/else chains are more concise. You can, however, use the slightly short elif keyword:
let primes (input:bigint) =
let rec factors acc (input':bigint, factor:bigint) =
if input' = 1I then acc
elif input = factor then factor::acc
elif input' = factor then factor::acc
elif input' % factor = 0I then factor::factors acc (input'/factor, factor)
else factors acc (input', factor+1I)
in factors [] (input, 2I)
Pattern matching is valuable when you have a single input that can have various different flavours or shapes, but in this case, you rather have various different inputs, where the relationship between those determine the branching, in a hierarchical fashion.
Well you could use active-patterns, but I think it's too much overhead in this case here - if not you cannot really escape the where here (or at least I am not aware of any way).
There is a pattern that will make this a bit more obvious (that you don't care about the value matched only about the when clauses):
match () with
| () when ... -> ...
| () when ... -> ...
| _ -> ...
you might have seen.
Related
I have, in F#, 2 sequences, each containing distinct integers, strictly in ascending order: listMaxes and numbers.
If not Seq.isEmpty numbers, then it is guaranteed that not Seq.isEmpty listMaxes and Seq.last listMaxes >= Seq.last numbers.
I would like to implement in F# a function that returns a list of list of integers, whose List.length equals Seq.length listMaxes, containing the elements of numbers divided in lists, where the elements of listMaxes limit each group.
For example: called with the arguments
listMaxes = seq [ 25; 56; 65; 75; 88 ]
numbers = seq [ 10; 11; 13; 16; 20; 25; 31; 38; 46; 55; 65; 76; 88 ]
this function should return
[ [10; 11; 13; 16; 20; 25]; [31; 38; 46; 55]; [65]; List.empty; [76; 88] ]
I can implement this function, iterating over numbers only once:
let groupByListMaxes listMaxes numbers =
if Seq.isEmpty numbers then
List.replicate (Seq.length listMaxes) List.empty
else
List.ofSeq (seq {
use nbe = numbers.GetEnumerator ()
ignore (nbe.MoveNext ())
for lmax in listMaxes do
yield List.ofSeq (seq {
if nbe.Current <= lmax then
yield nbe.Current
while nbe.MoveNext () && nbe.Current <= lmax do
yield nbe.Current
})
})
But this code feels unclean, ugly, imperative, and very un-F#-y.
Is there any functional / F#-idiomatic way to achieve this?
Here's a version based on list interpretation, which is quite functional in style. You can use Seq.toList to convert between them, whenever you want to handle that. You could also use Seq.scan in conjunction with Seq.partition ((>=) max) if you want to use only library functions, but beware that it's very very easy to introduce a quadratic complexity in either computation or memory when doing that.
This is linear in both:
let splitAt value lst =
let rec loop l1 = function
| [] -> List.rev l1, []
| h :: t when h > value -> List.rev l1, (h :: t)
| h :: t -> loop (h :: l1) t
loop [] lst
let groupByListMaxes listMaxes numbers =
let rec loop acc lst = function
| [] -> List.rev acc
| h :: t ->
let out, lst' = splitAt h lst
loop (out :: acc) lst' t
loop [] numbers listMaxes
It can be done like this with pattern matching and tail recursion:
let groupByListMaxes listMaxes numbers =
let rec inner acc numbers =
function
| [] -> acc |> List.rev
| max::tail ->
let taken = numbers |> Seq.takeWhile ((>=) max) |> List.ofSeq
let n = taken |> List.length
inner (taken::acc) (numbers |> Seq.skip n) tail
inner [] numbers (listMaxes |> List.ofSeq)
Update: I also got inspired by fold and came up with the following solution that strictly refrains from converting the input sequences.
let groupByListMaxes maxes numbers =
let rec inner (acc, (cur, numbers)) max =
match numbers |> Seq.tryHead with
// Add n to the current list of n's less
// than the local max
| Some n when n <= max ->
let remaining = numbers |> Seq.tail
inner (acc, (n::cur, remaining)) max
// Complete the current list by adding it
// to the accumulated result and prepare
// the next list for fold.
| _ ->
(List.rev cur)::acc, ([], numbers)
maxes |> Seq.fold inner ([], ([], numbers)) |> fst |> List.rev
I have found a better implementation myself. Tips for improvements are still welcome.
Dealing with 2 sequences is really a pain. And I really do want to iterate over numbers only once without turning that sequence into a list. But then I realized that turning listMaxes (generally the shorter of the sequences) is less costly. That way only 1 sequence remains, and I can use Seq.fold over numbers.
What should be the state that we want to keep and change while iterating with Seq.fold over numbers? First, it should definitely include the remaining of the listMaxes, yet the previous maxes that we already have surpassed are no longer of interest. Second, the accumulated lists so far, although, like in the other answers, these can be kept in reverse order. More to the point: the state is a couple which has as second element a reversed list of reversed lists of the numbers so far.
let groupByListMaxes listMaxes numbers =
let rec folder state number =
match state with
| m :: maxes, _ when number > m ->
folder (maxes, List.empty :: snd state) number
| m :: maxes, [] ->
fst state, List.singleton (List.singleton number)
| m :: maxes, h :: t ->
fst state, (number :: h) :: t
| [], _ ->
failwith "Guaranteed not to happen"
let listMaxesList = List.ofSeq listMaxes
let initialState = listMaxesList, List.empty
let reversed = snd (Seq.fold folder initialState numbers)
let temp = List.rev (List.map List.rev reversed)
let extraLength = List.length listMaxesList - List.length temp
let extra = List.replicate extraLength List.empty
List.concat [temp; extra]
I know this is an old question but I had a very similar problem and I think this is a simple solution:
let groupByListMaxes cs xs =
List.scan (fun (_, xs) c -> List.partition (fun x -> x <= c) xs)
([], xs)
cs
|> List.skip 1
|> List.map fst
Is there already a way to do something like a chooseTill or a foldTill, where it will process until a None option is received? Really, any of the higher order functions with a "till" option. Granted, it makes no sense for stuff like map, but I find I need this kind of thing pretty often and I wanted to make sure I wasn't reinventing the wheel.
In general, it'd be pretty easy to write something like this, but I'm curious if there is already a way to do this, or if this exists in some known library?
let chooseTill predicate (sequence:seq<'a>) =
seq {
let finished = ref false
for elem in sequence do
if not !finished then
match predicate elem with
| Some(x) -> yield x
| None -> finished := true
}
let foldTill predicate seed list =
let rec foldTill' acc = function
| [] -> acc
| (h::t) -> match predicate acc h with
| Some(x) -> foldTill' x t
| None -> acc
foldTill' seed list
let (++) a b = a.ToString() + b.ToString()
let abcdef = foldTill (fun acc v ->
if Char.IsWhiteSpace v then None
else Some(acc ++ v)) "" ("abcdef ghi" |> Seq.toList)
// result is "abcdef"
I think you can get that easily by combining Seq.scan and Seq.takeWhile:
open System
"abcdef ghi"
|> Seq.scan (fun (_, state) c -> c, (string c) + state) ('x', "")
|> Seq.takeWhile (fst >> Char.IsWhiteSpace >> not)
|> Seq.last |> snd
The idea is that Seq.scan is doing something like Seq.fold, but instead of waiting for the final result, it yields the intermediate states as it goes. You can then keep taking the intermediate states until you reach the end. In the above example, the state is the current character and the concatenated string (so that we can check if the character was whitespace).
A more general version based on a function that returns option could look like this:
let foldWhile f initial input =
// Generate sequence of all intermediate states
input |> Seq.scan (fun stateOpt inp ->
// If the current state is not 'None', then calculate a new one
// if 'f' returns 'None' then the overall result will be 'None'
stateOpt |> Option.bind (fun state -> f state inp)) (Some initial)
// Take only 'Some' states and get the last one
|> Seq.takeWhile Option.isSome
|> Seq.last |> Option.get
I write some code to learning F#.
Here is a example:
let nextPrime list=
let rec loop n=
match n with
| _ when (list |> List.filter (fun x -> x <= ( n |> double |> sqrt |> int)) |> List.forall (fun x -> n % x <> 0)) -> n
| _ -> loop (n+1)
loop (List.max list + 1)
let rec findPrimes num=
match num with
| 1 -> [2]
| n ->
let temp = findPrimes <| n-1
(nextPrime temp ) :: temp
//find 10 primes
findPrimes 10 |> printfn "%A"
I'm very happy that it just works!
I'm totally beginner to recursion
Recursion is a wonderful thing.
I think findPrimes is not efficient.
Someone help me to refactor findPrimes to tail recursion if possible?
BTW, is there some more efficient way to find first n primes?
Regarding the first part of your question, if you want to write a recursive list building function tail-recursively you should pass the list of intermediate results as an extra parameter to the function. In your case this would be something like
let findPrimesTailRecursive num =
let rec aux acc num =
match num with
| 1 -> acc
| n -> aux ((nextPrime acc)::acc) (n-1)
aux [2] num
The recursive function aux gathers its results in an extra parameter conveniently called acc (as in acc-umulator). When you reach your ending condition, just spit out the accumulated result. I've wrapped the tail-recursive helper function in another function, so the function signature remains the same.
As you can see, the call to aux is the only, and therefore last, call to happen in the n <> 1 case. It's now tail-recursive and will compile into a while loop.
I've timed your version and mine, generating 2000 primes. My version is 16% faster, but still rather slow. For generating primes, I like to use an imperative array sieve. Not very functional, but very (very) fast.
An alternative is to use an extra continuation argument to make findPrimes tail recursive. This technique always works. It will avoid stack overflows, but probably won't make your code faster.
Also, I put your nextPrime function a little closer to the style I'd use.
let nextPrime list=
let rec loop n = if list |> List.filter (fun x -> x*x <= n)
|> List.forall (fun x -> n % x <> 0)
then n
else loop (n+1)
loop (1 + List.head list)
let rec findPrimesC num cont =
match num with
| 1 -> cont [2]
| n -> findPrimesC (n-1) (fun temp -> nextPrime temp :: temp |> cont)
let findPrimes num = findPrimesC num (fun res -> res)
findPrimes 10
As others have said, there's faster ways to generate primes.
Why not simply write:
let isPrime n =
if n<=1 then false
else
let m = int(sqrt (float(n)))
{2..m} |> Seq.forall (fun i->n%i<>0)
let findPrimes n =
{2..n} |> Seq.filter isPrime |> Seq.toList
or sieve (very fast):
let generatePrimes max=
let p = Array.create (max+1) true
let rec filter i step =
if i <= max then
p.[i] <- false
filter (i+step) step
{2..int (sqrt (float max))} |> Seq.iter (fun i->filter (i+i) i)
{2..max} |> Seq.filter (fun i->p.[i]) |> Seq.toArray
BTW, is there some more efficient way to find first n primes?
I described a fast arbitrary-size Sieve of Eratosthenes in F# here that accumulated its results into an ever-growing ResizeArray:
> let primes =
let a = ResizeArray[2]
let grow() =
let p0 = a.[a.Count-1]+1
let b = Array.create p0 true
for di in a do
let rec loop i =
if i<b.Length then
b.[i] <- false
loop(i+di)
let i0 = p0/di*di
loop(if i0<p0 then i0+di-p0 else i0-p0)
for i=0 to b.Length-1 do
if b.[i] then a.Add(p0+i)
fun n ->
while n >= a.Count do
grow()
a.[n];;
val primes : (int -> int)
I know that this is a bit late, and an answer was already accepted. However, I believe that a good step by step guide to making something tail recursive may be of interest to the OP or anyone else for that matter. Here are some tips that have certainly helped me out. I'm going to use a strait-forward example other than prime generation because, as others have stated, there are better ways to generate primes.
Consider a naive implementation of a count function that will create a list of integers counting down from some n. This version is not tail recursive so for long lists you will encounter a stack overflow exception:
let rec countDown = function
| 0 -> []
| n -> n :: countDown (n - 1)
(* ^
|... the cons operator is in the tail position
as such it is evaluated last. this drags
stack frames through subsequent recursive
calls *)
One way to fix this is to apply continuation passing style with a parameterized function:
let countDown' n =
let rec countDown n k =
match n with
| 0 -> k [] (* v--- this is continuation passing style *)
| n -> countDown (n - 1) (fun ns -> n :: k ns)
(* ^
|... the recursive call is now in tail position *)
countDown n (fun ns -> ns)
(* ^
|... and we initialize k with the identity function *)
Then, refactor this parameterized function into a specialized representation. Notice that the function countDown' is not actually counting down. This is an artifact of the way the continuation is built up when n > 0 and then evaluated when n = 0. If you have something like the first example and you can't figure out how to make it tail recursive, what I'm suggesting is that you write the second one and then try to optimize it to eliminate the function parameter k. That will certainly improve the readability. This is an optimization of the second example:
let countDown'' n =
let rec countDown n ns =
match n with
| 0 -> List.rev ns (* reverse so we are actually counting down again *)
| n -> countDown (n - 1) (n :: ns)
countDown n []
I am currently learning F# and have tried (an extremely) simple example of FizzBuzz.
This is my initial attempt:
for x in 1..100 do
if x % 3 = 0 && x % 5 = 0 then printfn "FizzBuzz"
elif x % 3 = 0 then printfn "Fizz"
elif x % 5 = 0 then printfn "Buzz"
else printfn "%d" x
What solutions could be more elegant/simple/better (explaining why) using F# to solve this problem?
Note: The FizzBuzz problem is going through the numbers 1 to 100 and every multiple of 3 prints Fizz, every multiple of 5 prints Buzz, every multiple of both 3 AND 5 prints FizzBuzz. Otherwise, simple the number is displayed.
Thanks :)
I think you already have the "best" solution.
If you want to show off more functional/F#-isms, you could do e.g.
[1..100]
|> Seq.map (function
| x when x%5=0 && x%3=0 -> "FizzBuzz"
| x when x%3=0 -> "Fizz"
| x when x%5=0 -> "Buzz"
| x -> string x)
|> Seq.iter (printfn "%s")
and use lists, sequences, map, iter, patterns, and partial application.
[1..100] // I am the list of numbers 1-100.
// F# has immutable singly-linked lists.
// List literals use square brackets.
|> // I am the pipeline operator.
// "x |> f" is just another way to write "f x".
// It is a common idiom to "pipe" data through
// a bunch of transformative functions.
Seq.map // "Seq" means "sequence", in F# such sequences
// are just another name for IEnumerable<T>.
// "map" is a function in the "Seq" module that
// applies a function to every element of a
// sequence, returning a new sequence of results.
(function // The function keyword is one way to
// write a lambda, it means the same
// thing as "fun z -> match z with".
// "fun" starts a lambda.
// "match expr with" starts a pattern
// match, that then has |cases.
| x when x%5=0 && x%3=0
// I'm a pattern. The pattern is "x", which is
// just an identifier pattern that matches any
// value and binds the name (x) to that value.
// The "when" clause is a guard - the pattern
// will only match if the guard predicate is true.
-> "FizzBuzz"
// After each pattern is "-> expr" which is
// the thing evaluated if the pattern matches.
// If this pattern matches, we return that
// string literal "FizzBuzz".
| x when x%3=0 -> "Fizz"
// Patterns are evaluated in order, just like
// if...elif...elif...else, which is why we did
// the 'divisble-by-both' check first.
| x when x%5=0 -> "Buzz"
| x -> string x)
// "string" is a function that converts its argument
// to a string. F# is statically-typed, so all the
// patterns have to evaluate to the same type, so the
// return value of the map call can be e.g. an
// IEnumerable<string> (aka seq<string>).
|> // Another pipeline; pipe the prior sequence into...
Seq.iter // iter applies a function to every element of a
// sequence, but the function should return "unit"
// (like "void"), and iter itself returns unit.
// Whereas sequences are lazy, "iter" will "force"
// the sequence since it needs to apply the function
// to each element only for its effects.
(printfn "%s")
// F# has type-safe printing; printfn "%s" expr
// requires expr to have type string. Usual kind of
// %d for integers, etc. Here we have partially
// applied printfn, it's a function still expecting
// the string, so this is a one-argument function
// that is appropriate to hand to iter. Hurrah!
My example is just a minor improvement over the code posted by 'ssp'. It uses parameterized active patterns (which take the divisor as an argument). Here is a more in-depth explanation:
The following defines an active pattern that we can later use in the match
expression to test if a value i is divisible by a value divisor. When we write:
match 9 with
| DivisibleBy 3 -> ...
...it means that the value '9' will be passed to the following function as i and the value 3 will be passed as divisor. The name (|DivisibleBy|_|) is a special syntax, whith means that we're declaring an active pattern (and the name can appear in the
match on the left side of ->. The |_| bit means that the pattern can fail (our example fails when value is not divisible by divisor)
let (|DivisibleBy|_|) divisor i =
// If the value is divisible, then we return 'Some()' which
// represents that the active pattern succeeds - the '()' notation
// means that we don't return any value from the pattern (if we
// returned for example 'Some(i/divisor)' the use would be:
// match 6 with
// | DivisibleBy 3 res -> .. (res would be asigned value 2)
// None means that pattern failed and that the next clause should
// be tried (by the match expression)
if i % divisor = 0 then Some () else None
Now we can iterate over all the numbers and match them against patterns (our active pattern) using match (or using Seq.iter or some other technique as shown in other answers):
for i in 1..100 do
match i with
// & allows us to run more than one pattern on the argument 'i'
// so this calls 'DivisibleBy 3 i' and 'DivisibleBy 5 i' and it
// succeeds (and runs the body) only if both of them return 'Some()'
| DivisibleBy 3 & DivisibleBy 5 -> printfn "FizzBuzz"
| DivisibleBy 3 -> printfn "Fizz"
| DivisibleBy 5 -> printfn "Buzz"
| _ -> printfn "%d" i
For more information on F# active patterns, here is an MSDN documentation link. I think that if you remove all the comments, the code will be slightly more readable than the original version. It shows some quite useful tricks :-), but in your case, the task is relatively easy...
Yet one solution in F# style (i.e. with Active Patterns usage):
let (|P3|_|) i = if i % 3 = 0 then Some i else None
let (|P5|_|) i = if i % 5 = 0 then Some i else None
let f = function
| P3 _ & P5 _ -> printfn "FizzBuzz"
| P3 _ -> printfn "Fizz"
| P5 _ -> printfn "Buzz"
| x -> printfn "%d" x
Seq.iter f {1..100}
//or
for i in 1..100 do f i
To add one more possible answer - here is another approach without pattern matching. It uses the fact that Fizz + Buzz = FizzBuzz, so you don't actually need to test for all three cases, you only need to see if it is divisible by 3 (then print "Fizz") and also see if it is divisible by 5 (then print "Buzz") and finally, print a new line:
for i in 1..100 do
for divisor, str in [ (3, "Fizz"); (5, "Buzz") ] do
if i % divisor = 0 then printf "%s" str
printfn ""
The nested for loop assignes 3 and "Fizz" to divisor and str in the first iteration and then the second pair of values in the second iteration. The beneift is, you could easily add printing of "Jezz" when the value is divisible by 7 :-) ...in case that extensibility of the solution is a concern!
Here's one more:
let fizzy num =
match num%3, num%5 with
| 0,0 -> "fizzbuzz"
| 0,_ -> "fizz"
| _,0 -> "buzz"
| _,_ -> num.ToString()
[1..100]
|> List.map fizzy
|> List.iter (fun (s:string) -> printfn "%s" s)
I find this to be a bit more readable answer edited was inspired a bit by the others
let FizzBuzz n =
match n%3,n%5 with
| 0,0 -> "FizzBuzz"
| 0,_ -> "Fizz"
| _,0 -> "Buzz"
| _,_ -> string n
[1..100]
|> Seq.map (fun n -> FizzBuzz n)
|> Seq.iter (printfn "%s")
Here is my version:
//initialize array a with values from 1 to 100
let a = Array.init 100 (fun x -> x + 1)
//iterate over array and match *indexes* x
Array.iter (fun x ->
match x with
| _ when x % 15 = 0 -> printfn "FizzBuzz"
| _ when x % 5 = 0 -> printfn "Buzz"
| _ when x % 3 = 0 -> printfn "Fizz"
| _ -> printfn "%d" x
) a
This is my first program in F#.
It's not perfect, but I think someone who starts learning F# (like me :)) can figure out what happens here quite fast.
However I am wondering what is the difference between matching to any _ or to x itself in pattern matching above?
I couldn't find a working solution that didn't include testing for i % 15 = 0. I've always felt that not testing for that is part of this "stupid" assignment. Be aware that this is probably not idiomatic F# since it's my first program in the language.
for n in 1..100 do
let s = seq {
if n % 3 = 0 then yield "Fizz"
if n % 5 = 0 then yield "Buzz" }
if Seq.isEmpty s then printf "%d"n
printfn "%s"(s |> String.concat "")
Here's a version emphasizing a generic tuple list of carbonations:
let carbonations = [(3, "Spizz") ; (5, "Fuzz"); (15, "SpizzFuzz");
(30, "DIZZZZZZZZ"); (18, "WHIIIIII")]
let revCarbonated = carbonations |> List.sort |> List.rev
let carbonRoute someCarbonations findMe =
match(List.tryFind (fun (x,_) -> findMe % x = 0) someCarbonations) with
| Some x -> printfn "%d - %s" findMe (snd x)
| None -> printfn "%d" findMe
let composeCarbonRoute = carbonRoute revCarbonated
[1..100] |> List.iter composeCarbonRoute
I don't like all these repeated strings, here's mine:
open System
let ar = [| "Fizz"; "Buzz"; |]
[1..100] |> List.map (fun i ->
match i % 3 = 0, i % 5 = 0 with
| true, false -> ar.[0]
| false, true -> ar.[1]
| true, true -> ar |> String.Concat
| _ -> string i
|> printf "%s\n"
)
|> ignore
Here is an attempt that factors out the modulo checks
let DivisibleBy x y = y % x = 0
[ 1 .. 100 ]
|> List.map (function
| x when DivisibleBy (3 * 5) x -> "fizzbuzz"
| x when DivisibleBy 3 x -> "fizz"
| x when DivisibleBy 5 x -> "buzz"
| x -> string x)
|> List.iter (fun x -> printfn "%s" x)
Here is how I refined it
I have two snippets of code that tries to convert a float list to a Vector3 or Vector2 list. The idea is to take 2/3 elements at a time from the list and combine them as a vector. The end result is a sequence of vectors.
let rec vec3Seq floatList =
seq {
match floatList with
| x::y::z::tail -> yield Vector3(x,y,z)
yield! vec3Seq tail
| [] -> ()
| _ -> failwith "float array not multiple of 3?"
}
let rec vec2Seq floatList =
seq {
match floatList with
| x::y::tail -> yield Vector2(x,y)
yield! vec2Seq tail
| [] -> ()
| _ -> failwith "float array not multiple of 2?"
}
The code looks very similiar and yet there seems to be no way to extract a common portion. Any ideas?
Here's one approach. I'm not sure how much simpler this really is, but it does abstract some of the repeated logic out.
let rec mkSeq (|P|_|) x =
seq {
match x with
| P(p,tail) ->
yield p
yield! mkSeq (|P|_|) tail
| [] -> ()
| _ -> failwith "List length mismatch" }
let vec3Seq =
mkSeq (function
| x::y::z::tail -> Some(Vector3(x,y,z), tail)
| _ -> None)
As Rex commented, if you want this only for two cases, then you probably won't have any problem if you leave the code as it is. However, if you want to extract a common pattern, then you can write a function that splits a list into sub-list of a specified length (2 or 3 or any other number). Once you do that, you'll only use map to turn each list of the specified length into Vector.
The function for splitting list isn't available in the F# library (as far as I can tell), so you'll have to implement it yourself. It can be done roughly like this:
let divideList n list =
// 'acc' - accumulates the resulting sub-lists (reversed order)
// 'tmp' - stores values of the current sub-list (reversed order)
// 'c' - the length of 'tmp' so far
// 'list' - the remaining elements to process
let rec divideListAux acc tmp c list =
match list with
| x::xs when c = n - 1 ->
// we're adding last element to 'tmp',
// so we reverse it and add it to accumulator
divideListAux ((List.rev (x::tmp))::acc) [] 0 xs
| x::xs ->
// add one more value to 'tmp'
divideListAux acc (x::tmp) (c+1) xs
| [] when c = 0 -> List.rev acc // no more elements and empty 'tmp'
| _ -> failwithf "not multiple of %d" n // non-empty 'tmp'
divideListAux [] [] 0 list
Now, you can use this function to implement your two conversions like this:
seq { for [x; y] in floatList |> divideList 2 -> Vector2(x,y) }
seq { for [x; y; z] in floatList |> divideList 3 -> Vector3(x,y,z) }
This will give a warning, because we're using an incomplete pattern that expects that the returned lists will be of length 2 or 3 respectively, but that's correct expectation, so the code will work fine. I'm also using a brief version of sequence expression the -> does the same thing as do yield, but it can be used only in simple cases like this one.
This is simular to kvb's solution but doesn't use a partial active pattern.
let rec listToSeq convert (list:list<_>) =
seq {
if not(List.isEmpty list) then
let list, vec = convert list
yield vec
yield! listToSeq convert list
}
let vec2Seq = listToSeq (function
| x::y::tail -> tail, Vector2(x,y)
| _ -> failwith "float array not multiple of 2?")
let vec3Seq = listToSeq (function
| x::y::z::tail -> tail, Vector3(x,y,z)
| _ -> failwith "float array not multiple of 3?")
Honestly, what you have is pretty much as good as it can get, although you might be able to make a little more compact using this:
// take 3 [1 .. 5] returns ([1; 2; 3], [4; 5])
let rec take count l =
match count, l with
| 0, xs -> [], xs
| n, x::xs -> let res, xs' = take (count - 1) xs in x::res, xs'
| n, [] -> failwith "Index out of range"
// split 3 [1 .. 6] returns [[1;2;3]; [4;5;6]]
let rec split count l =
seq { match take count l with
| xs, ys -> yield xs; if ys <> [] then yield! split count ys }
let vec3Seq l = split 3 l |> Seq.map (fun [x;y;z] -> Vector3(x, y, z))
let vec2Seq l = split 2 l |> Seq.map (fun [x;y] -> Vector2(x, y))
Now the process of breaking up your lists is moved into its own generic "take" and "split" functions, its much easier to map it to your desired type.