I'm pretty new to programming in F#, and I am working on a project at the moment, with a function that takes an integer and returns a string value.
My problem (se my code below) is that no matter what I do, I cant return the values of my str, calling my function.
let mulTable (n:int):string = string n
let mutable m = 1
let mutable str = ""
while m < 10 do
str <- "m\t" + str
m <- m + 1
printfn "%A" (mulTable str)
My idea here is that I want to store the value of m, in str, så that str in the end of my while loop contains the values of "1 2 3 4 5 6 7 8 9". But no matter what I try my printfn "%A" mulTable str, returns "this expressions was exspected to have type int, but here has type string". I have tried converting my str to a string in my mutable value like:
let mutable str = ""
let mutable str1 = str |> int
and then I try to call my str1 using function mulTable instead of calling str. But still it does not work.
What am I missing here? I've been trying every single possible solution I can think of, without being able to solve my problem.
A fix of your own algorithm could be:
let getSequenceAsString max =
let concat s x = sprintf "%s\t%i" s x
let mutable m = 1
let mutable str = ""
while m < max do
str <- concat str m
m <- m + 1
str
printfn "%A" (getSequenceAsString 10)
But as others have shown it's a lot of work that can be done more easily:
open System
let getSequenceAsString max =
String.Join("\t", [1..max-1])
If you want each number reverted as you ask for in a comment it could be done this way:
let getSequenceAsString min max =
let revert x =
let rec rev y acc =
match y with
| 0 -> acc
| _ -> rev (y / 10) (sprintf "%s%i" acc (y % 10))
rev x ""
String.Join("\t", ([min..max-1] |> List.map revert))
printfn "%A" (getSequenceAsString 95 105)
Gives:
"59 69 79 89 99 001 101 201 301 401"
You can easily join an array of strings into a string array, and then print it out if necessary.
open System
let xs = [1..9] |> List.map string
//you should avoid using mutable variables, and instead generate your list of numbers with an list comprehension or something similar.
String.Join("\t", xs)
//A little exploration of the List/Array/String classes will bring this method up: "concatenates the members of a collection using the separator string.
This gives me:
val it : string = "1 2 3 4 5 6 7 8 9"
I've adjusted the code to make it produce results similar to what you wanted:
let mulTable (n:int):string = string n
let mutable m = 1
let mutable str = ""
while m < 10 do
str <- mulTable m+ "\t" + str
m <- m + 1
printfn "%A" (str)
I've used your mulTable to convert m to string, but for printfn you don't need to use that, because str is already a string.
Still the result would be 9 8 7 6 5 4 3 2 1
There are more then one way to revert the string, one of them would be to split the string into an array of characthers and then revert the array. From resulting array we will build a new string again. It would look something like:
printf "%A" (new System.String(str.ToCharArray() |> Array.rev ))
Edit
To achieve the same result, I would suggest to use more functional style, using recursion and avoiding mutating variables.
let getNumbersString upperLimit =
let rec innerRecursion rem acc=
match rem with
| 0 -> acc
| _ -> innerRecursion (rem-1) (sprintf "%i "rem::acc)
innerRecursion upperLimit [] |> String.concat ""
getNumbersString 9
Will result in
val it : string = "1 2 3 4 5 6 7 8 9 "
I need iterating over a list while condition is true. I done that by function iterc below:
let data = [12; 3; 4; 56; 7]
let restriction = 146
let convert elem = pown elem 2 + 1
let rec iterc (cond : ('T -> bool)) (action : ('T -> unit)) (list : 'T list) =
match list with
| head::tail ->
match (cond head) with
| true ->
action head
iterc cond action tail
| false -> ()
| [] -> ()
iterc ((>) restriction << convert)
(printfn "%A" << convert)
data
> 145
10
17
I don't like that convert is used twice. The same expression is computed in cond and in action. How to solve this problem more properly? Thanks.
There are existing F# functions that seem to do what you want.
You can write most of what you have above like this:
let data = [12; 3; 4; 56; 7]
let restriction = 146
let convert elem = pown elem 2 + 1
for value in data |> Seq.map convert |> Seq.takeWhile ((>) restriction) do
printfn "%A" value
Is your attempted solution supposed to ignore the data point that is 7? I assumed otherwise. Squimmy's posted solution has a bug because it is using Seq.takeWhile instead of Seq.filter or Seq.where. What you probably want is the following:
let data = [12; 3; 4; 56; 7]
let restriction = 146
let convert elem = pown elem 2 + 1
data |> List.map (fun value -> convert value )
|> List.filter (fun value -> value < restriction)
|> List.iter(fun value -> printfn "%A" value)
returns
145
10
17
50
I am seeking help, mainly because I am very new to F# environment. I need to use F# stream to generate an infinite stream of Armstrong Numbers. Can any one help with this one. I have done some mambo jumbo but I have no clue where I'm going.
type 'a stream = | Cons of 'a * (unit -> 'a stream)
let rec take n (Cons(x, xsf)) =
if n = 0 then []
else x :: take (n-1) (xsf());;
//to test if two integers are equal
let test x y =
match (x,y) with
| (x,y) when x < y -> false
| (x,y) when x > y -> false
| _ -> true
//to check for armstrong number
let check n =
let mutable m = n
let mutable r = 0
let mutable s = 0
while m <> 0 do
r <- m%10
s <- s+r*r*r
m <- m/10
if (test n s) then true else false
let rec armstrong n =
Cons (n, fun () -> if check (n+1) then armstrong (n+1) else armstrong (n+2))
let pos = armstrong 0
take 5 pos
To be honest your code seems a bit like a mess.
The most basic version I could think of is this:
let isArmstrong (a,b,c) =
a*a*a + b*b*b + c*c*c = (a*100+b*10+c)
let armstrongs =
seq {
for a in [0..9] do
for b in [0..9] do
for c in [0..9] do
if isArmstrong (a,b,c) then yield (a*100+b*10+c)
}
of course assuming a armstrong number is a 3-digit number where the sum of the cubes of the digits is the number itself
this will yield you:
> Seq.toList armstrongs;;
val it : int list = [0; 1; 153; 370; 371; 407]
but it should be easy to add a wider range or remove the one-digit numbers (think about it).
general case
the problem seems so interesting that I choose to implement the general case (see here) too:
let numbers =
let rec create n =
if n = 0 then [(0,[])] else
[
for x in [0..9] do
for (_,xs) in create (n-1) do
yield (n, x::xs)
]
Seq.initInfinite create |> Seq.concat
let toNumber (ds : int list) =
ds |> List.fold (fun s d -> s*10I + bigint d) 0I
let armstrong (m : int, ds : int list) =
ds |> List.map (fun d -> bigint d ** m) |> List.sum
let leadingZero =
function
| 0::_ -> true
| _ -> false
let isArmstrong (m : int, ds : int list) =
if leadingZero ds then false else
let left = armstrong (m, ds)
let right = toNumber ds
left = right
let armstrongs =
numbers
|> Seq.filter isArmstrong
|> Seq.map (snd >> toNumber)
but the numbers get really sparse quickly and using this will soon get you out-of-memory but the
first 20 are:
> Seq.take 20 armstrongs |> Seq.map string |> Seq.toList;;
val it : string list =
["0"; "1"; "2"; "3"; "4"; "5"; "6"; "7"; "8"; "9"; "153"; "370"; "371";
"407"; "1634"; "8208"; "9474"; "54748"; "92727"; "93084"]
remark/disclaimer
this is the most basic version - you can get big speed/performance if you just enumerate all numbers and use basic math to get and exponentiate the digits ;) ... sure you can figure it out
Is it possible to combine memoization and tail-recursion somehow? I'm learning F# at the moment and understand both concepts but can't seem to combine them.
Suppose I have the following memoize function (from Real-World Functional Programming):
let memoize f = let cache = new Dictionary<_, _>()
(fun x -> match cache.TryGetValue(x) with
| true, y -> y
| _ -> let v = f(x)
cache.Add(x, v)
v)
and the following factorial function:
let rec factorial(x) = if (x = 0) then 1 else x * factorial(x - 1)
Memoizing factorial isn't too difficult and making it tail-recursive isn't either:
let rec memoizedFactorial =
memoize (fun x -> if (x = 0) then 1 else x * memoizedFactorial(x - 1))
let tailRecursiveFactorial(x) =
let rec factorialUtil(x, res) = if (x = 0)
then res
else let newRes = x * res
factorialUtil(x - 1, newRes)
factorialUtil(x, 1)
But can you combine memoization and tail-recursion? I made some attempts but can't seem to get it working. Or is this simply not possible?
As always, continuations yield an elegant tailcall solution:
open System.Collections.Generic
let cache = Dictionary<_,_>() // TODO move inside
let memoizedTRFactorial =
let rec fac n k = // must make tailcalls to k
match cache.TryGetValue(n) with
| true, r -> k r
| _ ->
if n=0 then
k 1
else
fac (n-1) (fun r1 ->
printfn "multiplying by %d" n //***
let r = r1 * n
cache.Add(n,r)
k r)
fun n -> fac n id
printfn "---"
let r = memoizedTRFactorial 4
printfn "%d" r
for KeyValue(k,v) in cache do
printfn "%d: %d" k v
printfn "---"
let r2 = memoizedTRFactorial 5
printfn "%d" r2
printfn "---"
// comment out *** line, then run this
//let r3 = memoizedTRFactorial 100000
//printfn "%d" r3
There are two kinds of tests. First, this demos that calling F(4) caches F(4), F(3), F(2), F(1) as you would like.
Then, comment out the *** printf and uncomment the final test (and compile in Release mode) to show that it does not StackOverflow (it uses tailcalls correctly).
Perhaps I'll generalize out 'memoize' and demonstrate it on 'fib' next...
EDIT
Ok, here's the next step, I think, decoupling memoization from factorial:
open System.Collections.Generic
let cache = Dictionary<_,_>() // TODO move inside
let memoize fGuts n =
let rec newFunc n k = // must make tailcalls to k
match cache.TryGetValue(n) with
| true, r -> k r
| _ ->
fGuts n (fun r ->
cache.Add(n,r)
k r) newFunc
newFunc n id
let TRFactorialGuts n k memoGuts =
if n=0 then
k 1
else
memoGuts (n-1) (fun r1 ->
printfn "multiplying by %d" n //***
let r = r1 * n
k r)
let memoizedTRFactorial = memoize TRFactorialGuts
printfn "---"
let r = memoizedTRFactorial 4
printfn "%d" r
for KeyValue(k,v) in cache do
printfn "%d: %d" k v
printfn "---"
let r2 = memoizedTRFactorial 5
printfn "%d" r2
printfn "---"
// comment out *** line, then run this
//let r3 = memoizedTRFactorial 100000
//printfn "%d" r3
EDIT
Ok, here's a fully generalized version that seems to work.
open System.Collections.Generic
let memoize fGuts =
let cache = Dictionary<_,_>()
let rec newFunc n k = // must make tailcalls to k
match cache.TryGetValue(n) with
| true, r -> k r
| _ ->
fGuts n (fun r ->
cache.Add(n,r)
k r) newFunc
cache, (fun n -> newFunc n id)
let TRFactorialGuts n k memoGuts =
if n=0 then
k 1
else
memoGuts (n-1) (fun r1 ->
printfn "multiplying by %d" n //***
let r = r1 * n
k r)
let facCache,memoizedTRFactorial = memoize TRFactorialGuts
printfn "---"
let r = memoizedTRFactorial 4
printfn "%d" r
for KeyValue(k,v) in facCache do
printfn "%d: %d" k v
printfn "---"
let r2 = memoizedTRFactorial 5
printfn "%d" r2
printfn "---"
// comment out *** line, then run this
//let r3 = memoizedTRFactorial 100000
//printfn "%d" r3
let TRFibGuts n k memoGuts =
if n=0 || n=1 then
k 1
else
memoGuts (n-1) (fun r1 ->
memoGuts (n-2) (fun r2 ->
printfn "adding %d+%d" r1 r2 //%%%
let r = r1+r2
k r))
let fibCache, memoizedTRFib = memoize TRFibGuts
printfn "---"
let r5 = memoizedTRFib 4
printfn "%d" r5
for KeyValue(k,v) in fibCache do
printfn "%d: %d" k v
printfn "---"
let r6 = memoizedTRFib 5
printfn "%d" r6
printfn "---"
// comment out %%% line, then run this
//let r7 = memoizedTRFib 100000
//printfn "%d" r7
The predicament of memoizing tail-recursive functions is, of course, that when tail-recursive function
let f x =
......
f x1
calls itself, it is not allowed to do anything with a result of the recursive call, including putting it into cache. Tricky; so what can we do?
The critical insight here is that since the recursive function is not allowed to do anything with a result of recursive call, the result for all arguments to recursive calls will be the same! Therefore if recursion call trace is this
f x0 -> f x1 -> f x2 -> f x3 -> ... -> f xN -> res
then for all x in x0,x1,...,xN the result of f x will be the same, namely res. So the last invocation of a recursive function, the non-recursive call, knows the results for all the previous values - it is in a position to cache them. The only thing you need to do is to pass a list of visited values to it. Here is what it might look for factorial:
let cache = Dictionary<_,_>()
let rec fact0 l ((n,res) as arg) =
let commitToCache r =
l |> List.iter (fun a -> cache.Add(a,r))
match cache.TryGetValue(arg) with
| true, cachedResult -> commitToCache cachedResult; cachedResult
| false, _ ->
if n = 1 then
commitToCache res
cache.Add(arg, res)
res
else
fact0 (arg::l) (n-1, n*res)
let fact n = fact0 [] (n,1)
But wait! Look - l parameter of fact0 contains all the arguments to recursive calls to fact0 - just like the stack would in a non-tail-recursive version! That is exactly right. Any non-tail recursive algorithm can be converted to a tail-recursive one by moving the "list of stack frames" from stack to heap and converting the "postprocessing" of recursive call result into a walk over that data structure.
Pragmatic note: The factorial example above illustrates a general technique. It is quite useless as is - for factorial function it is quite enough to cache the top-level fact n result, because calculation of fact n for a particular n only hits a unique series of (n,res) pairs of arguments to fact0 - if (n,1) is not cached yet, then none of the pairs fact0 is going to be called on are.
Note that in this example, when we went from non-tail-recursive factorial to a tail-recursive factorial, we exploited the fact that multiplication is associative and commutative - tail-recursive factorial execute a different set of multiplications than a non-tail-recursive one.
In fact, a general technique exists for going from non-tail-recursive to tail-recursive algorithm, which yields an algorithm equivalent to a tee. This technique is called "continuatuion-passing transformation". Going that route, you can take a non-tail-recursive memoizing factorial and get a tail-recursive memoizing factorial by pretty much a mechanical transformation. See Brian's answer for exposition of this method.
I'm not sure if there's a simpler way to do this, but one approach would be to create a memoizing y-combinator:
let memoY f =
let cache = Dictionary<_,_>()
let rec fn x =
match cache.TryGetValue(x) with
| true,y -> y
| _ -> let v = f fn x
cache.Add(x,v)
v
fn
Then, you can use this combinator in lieu of "let rec", with the first argument representing the function to call recursively:
let tailRecFact =
let factHelper fact (x, res) =
printfn "%i,%i" x res
if x = 0 then res
else fact (x-1, x*res)
let memoized = memoY factHelper
fun x -> memoized (x,1)
EDIT
As Mitya pointed out, memoY doesn't preserve the tail recursive properties of the memoee. Here's a revised combinator which uses exceptions and mutable state to memoize any recursive function without overflowing the stack (even if the original function is not itself tail recursive!):
let memoY f =
let cache = Dictionary<_,_>()
fun x ->
let l = ResizeArray([x])
while l.Count <> 0 do
let v = l.[l.Count - 1]
if cache.ContainsKey(v) then l.RemoveAt(l.Count - 1)
else
try
cache.[v] <- f (fun x ->
if cache.ContainsKey(x) then cache.[x]
else
l.Add(x)
failwith "Need to recurse") v
with _ -> ()
cache.[x]
Unfortunately, the machinery which is inserted into each recursive call is somewhat heavy, so performance on un-memoized inputs requiring deep recursion can be a bit slow. However, compared to some other solutions, this has the benefit that it requires fairly minimal changes to the natural expression of recursive functions:
let fib = memoY (fun fib n ->
printfn "%i" n;
if n <= 1 then n
else (fib (n-1)) + (fib (n-2)))
let _ = fib 5000
EDIT
I'll expand a bit on how this compares to other solutions. This technique takes advantage of the fact that exceptions provide a side channel: a function of type 'a -> 'b doesn't actually need to return a value of type 'b, but can instead exit via an exception. We wouldn't need to use exceptions if the return type explicitly contained an additional value indicating failure. Of course, we could use the 'b option as the return type of the function for this purpose. This would lead to the following memoizing combinator:
let memoO f =
let cache = Dictionary<_,_>()
fun x ->
let l = ResizeArray([x])
while l.Count <> 0 do
let v = l.[l.Count - 1]
if cache.ContainsKey v then l.RemoveAt(l.Count - 1)
else
match f(fun x -> if cache.ContainsKey x then Some(cache.[x]) else l.Add(x); None) v with
| Some(r) -> cache.[v] <- r;
| None -> ()
cache.[x]
Previously, our memoization process looked like:
fun fib n ->
printfn "%i" n;
if n <= 1 then n
else (fib (n-1)) + (fib (n-2))
|> memoY
Now, we need to incorporate the fact that fib should return an int option instead of an int. Given a suitable workflow for option types, this could be written as follows:
fun fib n -> option {
printfn "%i" n
if n <= 1 then return n
else
let! x = fib (n-1)
let! y = fib (n-2)
return x + y
} |> memoO
However, if we're willing to change the return type of the first parameter (from int to int option in this case), we may as well go all the way and just use continuations in the return type instead, as in Brian's solution. Here's a variation on his definitions:
let memoC f =
let cache = Dictionary<_,_>()
let rec fn n k =
match cache.TryGetValue(n) with
| true, r -> k r
| _ ->
f fn n (fun r ->
cache.Add(n,r)
k r)
fun n -> fn n id
And again, if we have a suitable computation expression for building CPS functions, we can define our recursive function like this:
fun fib n -> cps {
printfn "%i" n
if n <= 1 then return n
else
let! x = fib (n-1)
let! y = fib (n-2)
return x + y
} |> memoC
This is exactly the same as what Brian has done, but I find the syntax here is easier to follow. To make this work, all we need are the following two definitions:
type CpsBuilder() =
member this.Return x k = k x
member this.Bind(m,f) k = m (fun a -> f a k)
let cps = CpsBuilder()
I wrote a test to visualize the memoization. Each dot is a recursive call.
......720 // factorial 6
......720 // factorial 6
.....120 // factorial 5
......720 // memoizedFactorial 6
720 // memoizedFactorial 6
120 // memoizedFactorial 5
......720 // tailRecFact 6
720 // tailRecFact 6
.....120 // tailRecFact 5
......720 // tailRecursiveMemoizedFactorial 6
720 // tailRecursiveMemoizedFactorial 6
.....120 // tailRecursiveMemoizedFactorial 5
kvb's solution returns the same results are straight memoization like this function.
let tailRecursiveMemoizedFactorial =
memoize
(fun x ->
let rec factorialUtil x res =
if x = 0 then
res
else
printf "."
let newRes = x * res
factorialUtil (x - 1) newRes
factorialUtil x 1
)
Test source code.
open System.Collections.Generic
let memoize f =
let cache = new Dictionary<_, _>()
(fun x ->
match cache.TryGetValue(x) with
| true, y -> y
| _ ->
let v = f(x)
cache.Add(x, v)
v)
let rec factorial(x) =
if (x = 0) then
1
else
printf "."
x * factorial(x - 1)
let rec memoizedFactorial =
memoize (
fun x ->
if (x = 0) then
1
else
printf "."
x * memoizedFactorial(x - 1))
let memoY f =
let cache = Dictionary<_,_>()
let rec fn x =
match cache.TryGetValue(x) with
| true,y -> y
| _ -> let v = f fn x
cache.Add(x,v)
v
fn
let tailRecFact =
let factHelper fact (x, res) =
if x = 0 then
res
else
printf "."
fact (x-1, x*res)
let memoized = memoY factHelper
fun x -> memoized (x,1)
let tailRecursiveMemoizedFactorial =
memoize
(fun x ->
let rec factorialUtil x res =
if x = 0 then
res
else
printf "."
let newRes = x * res
factorialUtil (x - 1) newRes
factorialUtil x 1
)
factorial 6 |> printfn "%A"
factorial 6 |> printfn "%A"
factorial 5 |> printfn "%A\n"
memoizedFactorial 6 |> printfn "%A"
memoizedFactorial 6 |> printfn "%A"
memoizedFactorial 5 |> printfn "%A\n"
tailRecFact 6 |> printfn "%A"
tailRecFact 6 |> printfn "%A"
tailRecFact 5 |> printfn "%A\n"
tailRecursiveMemoizedFactorial 6 |> printfn "%A"
tailRecursiveMemoizedFactorial 6 |> printfn "%A"
tailRecursiveMemoizedFactorial 5 |> printfn "%A\n"
System.Console.ReadLine() |> ignore
That should work if mutual tail recursion through y are not creating stack frames:
let rec y f x = f (y f) x
let memoize (d:System.Collections.Generic.Dictionary<_,_>) f n =
if d.ContainsKey n then d.[n]
else d.Add(n, f n);d.[n]
let rec factorialucps factorial' n cont =
if n = 0I then cont(1I) else factorial' (n-1I) (fun k -> cont (n*k))
let factorialdpcps =
let d = System.Collections.Generic.Dictionary<_, _>()
fun n -> y (factorialucps >> fun f n -> memoize d f n ) n id
factorialdpcps 15I //1307674368000
Lets say I have a string "COLIN".
The numeric value of this string would is worth:
3 + 15 + 12 + 9 + 14 = 53.
So
A = 1, B = 2, C = 3, and so on.
I have no idea how to even start in F# for this.
let mutable nametotal = 0
let rec tcalculate name =
name.ToString().ToCharArray()
|> Seq.length
Here is what I have so far. The seq.length is just there for testing to see if the toCharArray actually worked.
What you have is decent; here's another version:
#light
let Value (c:char) =
(int c) - (int 'A') + 1
let CalcValue name =
name |> Seq.sum_by Value
printfn "COLIN = %d" (CalcValue "COLIN")
// may be of interest:
printfn "%A" ("COLIN" |> Seq.map Value |> Seq.to_list)
It assumes the original input is uppercase. "int" is a function that converts a char (or whatever) to an int; Seq.sum_by is perfect for this.
I also show an example of using map, not sure what you're interested in.
If the 'mapping' is more arbitrary, you could use a strategy like the code below, where you can specify a data structure of what value each letter maps to.
#light
let table = [
'C', 3
'O', 15
'L', 12
'I', 9
'N', 14
]
let dictionary = dict table
let Value c =
match dictionary.TryGetValue(c) with
| true, v -> v
| _ -> failwith (sprintf "letter '%c' was not in lookup table" c)
let CalcValue name =
name |> Seq.sum_by Value
printfn "COLIN = %d" (CalcValue "COLIN")
I've found a hackish way to do this using the ascii value of the character, and getting the number from there but i think there might be a better way.
let tcalculate name =
name.ToString().ToLower().ToCharArray()
|> Seq.map (fun char -> Convert.ToInt32 char - 96)
|> Seq.sum
work's beautifully and maybe even more efficient then "mapping" but I'd like to view the solution I asked for
thanks all.
all you need to do, is make the string lowercase, turn it into a char array like you have done, loop through each letter, take the value of each char and subtract the value of 'a' and add one. that will make each letter have the value of its position in the alphabet.
I realize this is very old but I am recently learning F# and playing with the ideas in this question. Maybe someone will find it useful:
let table =
Seq.zip ['A'..'Z'] (Seq.initInfinite((+) 1))
|> Map.ofSeq
let calc (input : string) =
let s = input.ToUpper()
match s with
| _ when Seq.forall System.Char.IsLetter s ->
Some (Seq.sumBy (fun c -> table.[c]) s)
| _ -> None
let sumOfChar name = // F# functional answer
name
|> List.ofSeq // to char array
|> List.map (fun c -> int (System.Char.ToUpper c) - int 'A' + 1) // to value
|> List.fold (+) 0 // sum
sumOfChar "Herb" // 33
// Or simply this version:
let sumOfCharBy name =
let value c = int (System.Char.ToUpper c) - int 'A' + 1
List.sumBy value (List.ofSeq name)
sumOfCharBy "HerbM" // 46
// or simply:
let sumOfCharBy name =
name |> Seq.sumBy (fun c -> int (System.Char.ToUpper c) - int 'A' + 1)
sumOfCharBy "HMartin" // 83