I'm trying to wrap my head around functional programming using F#. I'm working my way through the Project Euler problems, and I feel like I am just writing procedural code in F#. For instance, this is my solution to #3.
let Calc() =
let mutable limit = 600851475143L
let mutable factor = 2L // Start with the lowest prime
while factor < limit do
if limit % factor = 0L then
begin
limit <- limit / factor
end
else factor <- factor + 1L
limit
This works just fine, but all I've really done is taken how I would solve this problem in c# and converted it to F# syntax. Looking back over several of my solutions, this is becoming a pattern. I think that I should be able to solve this problem without using mutable, but I'm having trouble not thinking about the problem procedurally.
Why not with recursion?
let Calc() =
let rec calcinner factor limit =
if factor < limit then
if limit % factor = 0L then
calcinner factor (limit/factor)
else
calcinner (factor + 1L) limit
else limit
let limit = 600851475143L
let factor = 2L // Start with the lowest prime
calcinner factor limit
For algorithmic problems (like project Euler), you'll probably want to write most iterations using recursion (as John suggests). However, even mutable imperative code sometimes makes sense if you are using e.g. hashtables or arrays and care about performance.
One area where F# works really well which is (sadly) not really covered by the project Euler exercises is designing data types - so if you're interested in learning F# from another perspective, have a look at Designing with types at F# for Fun and Profit.
In this case, you could also use Seq.unfold to implement the solution (in general, you can often compose solutions to sequence processing problems using Seq functions - though it does not look as elegant here).
let Calc() =
// Start with initial state (600851475143L, 2L) and generate a sequence
// of "limits" by generating new states & returning limit in each step
(600851475143L, 2L)
|> Seq.unfold (fun (limit, factor) ->
// End the sequence when factor is greater than limit
if factor >= limit then None
// Update limit when divisible by factor
elif limit % factor = 0L then
let limit = limit / factor
Some(limit, (limit, factor))
// Update factor
else
Some(limit, (limit, factor + 1L)) )
// Take the last generated limit value
|> Seq.last
In functional programming when I think mutable I think heap and when trying to write code that is more functional, you should use the stack instead of the heap.
So how do you get values on to the stack for use with a function?
Place the value in the function's parameters.
let result01 = List.filter (fun x -> x % 2 = 0) [0;1;2;3;4;5]
here both a function an a list of values are hard coded into the List.filter parameter's.
Bind the value to a name and then reference the name.
let divisibleBy2 = fun x -> x % 2 = 0
let values = [0;1;2;3;4;5]
let result02 = List.filter divisibleBy2 values
here the function parameter for list.filter is bound to divisibleBy2 and the list parameter for list.filter is bound to values.
Create a nameless data structure and pipe it into the function.
let result03 =
[0;1;2;3;4;5]
|> List.filter divisibleBy2
here the list parameter for list.filter is forward piped into the list.filter function.
Pass the result of a function into the function
let result04 =
[ for i in 1 .. 5 -> i]
|> List.filter divisibleBy2
Now that we have all of the data on the stack, how do we process the data using only the stack?
One of the patterns often used with functional programming is to put data into a structure and then process the items one at a time using a recursive function. The structure can be a list, tree, graph, etc. and is usually defined using a discriminated union. Data structures that have one or more self references are typically used with recursive functions.
So here is an example where we take a list and multiply all the values by 2 and put the result back onto the stack as we progress. The variable on the stack holding the new values is accumulator.
let mult2 values =
let rec mult2withAccumulator values accumulator =
match values with
| headValue::tailValues ->
let newValue = headValue * 2
let accumulator = newValue :: accumulator
mult2withAccumulator tailValues accumulator
| [] ->
List.rev accumulator
mult2withAccumulator values []
We use an accumulator for this which being a parameter to a function and not defined mutable is stored on the stack. Also this method is using pattern matching and the list discriminated union. The accumulator holds the new values as we process the items in the input list and then when there are not more items in the list ([]) we just reverse the list to get the new list in the correct order because the new items are concatenated to the head of the accumulator.
To understand the data structure (discriminated union) for a list you need to see it, so here it is
type list =
| Item of 'a * List
| Empty
Notice how the end of the definition of an item is List referring back to itself, and that a list can ben an empty list, which is when used with pattern match is [].
A quick example of how list are built is
empty list - []
list with one int value - 1::[]
list with two int values - 1::2::[]
list with three int values - 1::2::3::[]
Here is the same function with all of the types defined.
let mult2 (values : int list) =
let rec mult2withAccumulator (values : int list) (accumulator : int list) =
match (values : int list) with
| (headValue : int)::(tailValues : int list) ->
let (newValue : int) = headValue * 2
let (accumulator : int list) =
(((newValue : int) :: (accumulator : int list)) : int list)
mult2withAccumulator tailValues accumulator
| [] ->
((List.rev accumulator) : int list)
mult2withAccumulator values []
So putting values onto the stack and using self referencing discriminated unions with pattern matching will help to solve a lot of problems with functional programming.
Related
Anyone have a decent example, preferably practical/useful, they could post demonstrating the concept?
I came across this term somewhere that I’m unable to find, probably it has to do something with a function returning a function while enclosing on some mutable variable. So there’s no visible mutation.
Probably Haskell community has originated the idea where mutation happens in another area not visible to the scope. I maybe vague here so seeking help to understand more.
It's a good idea to hide mutation, so the consumers of the API won't inadvartently change something unexpectedly. This just means that you have to encapsulate your mutable data/state. This can be done via objects (yes, objects), but what you are referring to in your question can be done with a closure, the canonical example is a counter:
let countUp =
let mutable count = 0
(fun () -> count <- count + 1
count)
countUp() // 1
countUp() // 2
countUp() // 3
You cannot access the mutable count variable directly.
Another example would be using mutable state within a function so that you cannot observe it, and the function is, for all intents and purposes, referentially transparent. Take for example the following function that reverses a string not character-wise, but rather by taking individual text elements (which, depending on language, can be more than one character):
let reverseStringU s =
if Core.string.IsNullOrEmpty s then s else
let rec iter acc (ee : System.Globalization.TextElementEnumerator) =
if not <| ee.MoveNext () then acc else
let e = ee.GetTextElement ()
iter (e :: acc) ee
let inline append x s = (^s : (member Append : ^x -> ^s) (s, x))
let sb = System.Text.StringBuilder s.Length
System.Globalization.StringInfo.GetTextElementEnumerator s
|> iter []
|> List.fold (fun a e -> append e a) sb
|> string
It uses a StringBuilder internally but you cannot observe this externally.
The Stats.expandingXXXX functions are pretty fast. However there is no public api to do a expandingWindow apply. The following solution i created is really slow when it comes to large dataset like 100k. Any suggestion is appreciated?
let ExpWindowApply f minSize data =
let keys = dataSeries.Keys
let startKey = dataSeries.FirstKey()
let values = keys
|> Seq.map(fun k ->
let ds = data.Between(startKey,k)
match ds with
|_ when ds.ValueCount >= minSize -> f ds.Values
|_ -> Double.NaN
)
let result = Series(keys, values)
result
I understand the Stats.expandingXXX function are actually special cases where the function being applied can be iterately calculated based on previous loop's state. And not all function can take advantage of states from previous calculation. Is there anything better way than Series.Between in terms of creating a window of data?
Update
For those who are also interested in the similar issue. The answer provides alternative implementation and insight into rarely documented series vector and index operation. But it doesn't improve performance.
The expanding functions in Deedle are fast because they are using an efficient online algorithm that makes it possible to calculate the statistics on the fly with just one pass - rather than actually building the intermediate series for the sub-ranges.
There is a built-in function aggregate that lets you do something this - though it works in the reversed way. For example, if you want to sum all elements starting from the current one to the end, you can write:
let s = series [ for i in 1 .. 10 -> i, float i ]
s |> Series.aggregateInto
(Aggregation.WindowWhile(fun _ _ -> true))
(fun seg -> seg.Data.FirstKey())
(fun seg -> OptionalValue(Stats.sum seg.Data))
If you want to do the same thing using the underlying representation, you can directly use the addressing scheme that Deedle uses to link the keys (in the index) with values (in the data vector). This is an ugly mutable sample, but you can encapsulate it into something nicer:
[ let firstAddr = s.Index.Locate(s.FirstKey())
for k in s.Index.KeySequence ->
let lastAddr = s.Index.Locate(k)
seq {
let a = ref firstAddr
while !a <> lastAddr do
yield s.Vector.GetValue(!a).Value
a := s.Index.AddressOperations.AdjustBy(!a, +1L) } |> Seq.sum ]
I'm looking for a clean set of ways to manage Test Specific Equality in F# unit tests. 90% of the time, the standard Structural Equality fits the bill and I can leverage it with unquote to express the relation between my result and my expected.
TL;DR "I can't find a clean way to having a custom Equality function for one or two properties in a value which 90% of is well served by Structural Equality, does F# have a way to match an arbitrary record with custom Equality for just one or two of its fields?"
Example of a general technique that works for me
When verifying a function that performs a 1:1 mapping of a datatype to another, I'll often extract matching tuples from both sides of in some cases and compare the input and output sets. For example, I have an operator:-
let (====) x y = (x |> Set.ofSeq) = (y |> Set.ofSeq)
So I can do:
let inputs = ["KeyA",DateTime.Today; "KeyB",DateTime.Today.AddDays(1); "KeyC",DateTime.Today.AddDays(2)]
let trivialFun (a:string,b) = a.ToLower(),b
let expected = inputs |> Seq.map trivialFun
let result = inputs |> MyMagicMapper
test <# expected ==== actual #>
This enables me to Assert that each of my inputs has been mapped to an output, without any superfluous outputs.
The problem
The problem is when I want to have a custom comparison for one or two of the fields.
For example, if my DateTime is being passed through a slightly lossy serialization layer by the SUT, I need a test-specific tolerant DateTime comparison. Or maybe I want to do a case-insensitive verification for a string field
Normally, I'd use Mark Seemann's SemanticComparison library's Likeness<Source,Destination> to define a Test Specific equality, but I've run into some roadblocks:
tuples: F# hides .ItemX on Tuple so I can't define the property via a .With strongly typed field name Expression<T>
record types: TTBOMK these are sealed by F# with no opt-out so SemanticComparison can't proxy them to override Object.Equals
My ideas
All I can think of is to create a generic Resemblance proxy type that I can include in a tuple or record.
Or maybe using pattern matching (Is there a way I can use that to generate an IEqualityComparer and then do a set comparison using that?)
Alternate failing test
I'm also open to using some other function to verify the full mapping (i.e. not abusing F# Set or involving too much third party code. i.e. something to make this pass:
let sut (a:string,b:DateTime) = a.ToLower(),b + TimeSpan.FromTicks(1L)
let inputs = ["KeyA",DateTime.Today; "KeyB",DateTime.Today.AddDays(1.0); "KeyC",DateTime.Today.AddDays(2.0)]
let toResemblance (a,b) = TODO generate Resemblance which will case insensitively compare fst and tolerantly compare snd
let expected = inputs |> List.map toResemblance
let result = inputs |> List.map sut
test <# expected = result #>
Firstly, thanks to all for the inputs. I was largely unaware of SemanticComparer<'T> and it definitely provides a good set of building blocks for building generalized facilities in this space. Nikos' post gives excellent food for thought in the area too. I shouldn't have been surprised Fil exists too - #ptrelford really does have a lib for everything (the FSharpValue point is also v valuable)!
We've thankfully arrived at a conclusion to this. Unfortunately it's not a single all-encompassing tool or technique, but even better, a set of techniques that can be used as necessary in a given context.
Firstly, the issue of ensuring a mapping is complete is really an orthogonal concern. The question refers to an ==== operator:-
let (====) x y = (x |> Set.ofSeq) = (y |> Set.ofSeq)
This is definitely the best default approach - lean on Structural Equality. One thing to note is that, being reliant on F# persistent sets, it requires your type to support : comparison (as opposed to just : equality).
When doing set comparisons off the proven Structural Equality path, a useful technique is to use HashSet<T> with a custom IEqualityComparer:-
[<AutoOpen>]
module UnorderedSeqComparisons =
let seqSetEquals ec x y =
HashSet<_>( x, ec).SetEquals( y)
let (==|==) x y equals =
let funEqualityComparer = {
new IEqualityComparer<_> with
member this.GetHashCode(obj) = 0
member this.Equals(x,y) =
equals x y }
seqSetEquals funEqualityComparer x y
the equals parameter of ==|== is 'a -> 'a -> bool which allows one to use pattern matching to destructure args for the purposes of comparison. This works well if either the input or the result side are naturally already tuples. Example:
sut.Store( inputs)
let results = sut.Read()
let expecteds = seq { for x in inputs -> x.Name,x.ValidUntil }
test <# expecteds ==|== results
<| fun (xN,xD) (yN,yD) ->
xF=yF
&& xD |> equalsWithinASecond <| yD #>
While SemanticComparer<'T> can do a job, it's simply not worth bothering for tuples with when you have the power of pattern matching. e.g. Using SemanticComparer<'T>, the above test can be expressed as:
test <# expecteds ==~== results
<| [ funNamedMemberComparer "Item2" equalsWithinASecond ] #>
using the helper:
[<AutoOpen>]
module MemberComparerHelpers =
let funNamedMemberComparer<'T> name equals = {
new IMemberComparer with
member this.IsSatisfiedBy(request: PropertyInfo) =
request.PropertyType = typedefof<'T>
&& request.Name = name
member this.IsSatisfiedBy(request: FieldInfo) =
request.FieldType = typedefof<'T>
&& request.Name = name
member this.GetHashCode(obj) = 0
member this.Equals(x, y) =
equals (x :?> 'T) (y :?> 'T) }
let valueObjectMemberComparer() = {
new IMemberComparer with
member this.IsSatisfiedBy(request: PropertyInfo) = true
member this.IsSatisfiedBy(request: FieldInfo) = true
member this.GetHashCode(obj) = hash obj
member this.Equals(x, y) =
x.Equals( y) }
let (==~==) x y mcs =
let ec = SemanticComparer<'T>( seq {
yield valueObjectMemberComparer()
yield! mcs } )
seqSetEquals ec x y
All of the above is best understood by reading Nikos Baxevanis' post NOW!
For types or records, the ==|== technique can work (except critically you lose Likeness<'T>s verifying coverage of fields). However the succinctness can make it a valuable tool for certain sorts of tests :-
sut.Save( inputs)
let expected = inputs |> Seq.map (fun x -> Mapped( base + x.ttl, x.Name))
let likeExpected x = expected ==|== x <| (fun x y -> x.Name = y.Name && x.ValidUntil = y.ValidUntil)
verify <# repo.Store( is( likeExpected)) #> once
Is it just me, or does F# not cater for cyclic lists?
I looked at the FSharpList<T> class via reflector, and noticed, that neither the 'structural equals' or the length methods check for cycles. I can only guess if 2 such primitive functions does not check, that most list functions would not do this either.
If cyclic lists are not supported, why is that?
Thanks
PS: Am I even looking at the right list class?
There are many different lists/collection types in F#.
F# list type. As Chris said, you cannot initialize a recursive value of this type, because the type is not lazy and not mutable (Immutability means that you have to create it at once and the fact that it's not lazy means that you can't use F# recursive values using let rec). As ssp said, you could use Reflection to hack it, but that's probably a case that we don't want to discuss.
Another type is seq (which is actually IEnumerable) or the LazyList type from PowerPack. These are lazy, so you can use let rec to create a cyclic value. However, (as far as I know) none of the functions working with them take cyclic lists into account - if you create a cyclic list, it simply means that you're creating an infinite list, so the result of (e.g.) map will be a potentially infinite list.
Here is an example for LazyList type:
#r "FSharp.PowerPack.dll"
// Valid use of value recursion
let rec ones = LazyList.consDelayed 1 (fun () -> ones)
Seq.take 5 l // Gives [1; 1; 1; 1; 1]
The question is what data types can you define yourself. Chris shows a mutable list and if you write operations that modify it, they will affect the entire list (if you interpret it as an infinite data structure).
You can also define a lazy (potentionally cyclic) data type and implement operations that handle cycles, so when you create a cyclic list and project it into another list, it will create cyclic list as a result (and not a potentionally infinite data structure).
The type declaration may look like this (I'm using object type, so that we can use reference equality when checking for cycles):
type CyclicListValue<'a> =
Nil | Cons of 'a * Lazy<CyclicList<'a>>
and CyclicList<'a>(value:CyclicListValue<'a>) =
member x.Value = value
The following map function handles cycles - if you give it a cyclic list, it will return a newly created list with the same cyclic structure:
let map f (cl:CyclicList<_>) =
// 'start' is the first element of the list (used for cycle checking)
// 'l' is the list we're processing
// 'lazyRes' is a function that returns the first cell of the resulting list
// (which is not available on the first call, but can be accessed
// later, because the list is constructed lazily)
let rec mapAux start (l:CyclicList<_>) lazyRes =
match l.Value with
| Nil -> new CyclicList<_>(Nil)
| Cons(v, rest) when rest.Value = start -> lazyRes()
| Cons(v, rest) ->
let value = Cons(f v, lazy mapAux start rest.Value lazyRes)
new CyclicList<_>(value)
let rec res = mapAux cl cl (fun () -> res)
res
The F# list type is essentially a linked list, where each node has a 'next'. This in theory would allow you to create cycles. However, F# lists are immutable. So you could never 'make' this cycle by mutation, you would have to do it at construction time. (Since you couldn't update the last node to loop around to the front.)
You could write this to do it, however the compiler specifically prevents it:
let rec x = 1 :: 2 :: 3 :: x;;
let rec x = 1 :: 2 :: 3 :: x;;
------------------------^^
stdin(1,25): error FS0260: Recursive values cannot appear directly as a construction of the type 'List`1' within a recursive binding. This feature has been removed from the F# language. Consider using a record instead.
If you do want to create a cycle, you could do the following:
> type CustomListNode = { Value : int; mutable Next : CustomListNode option };;
type CustomListNode =
{Value: int;
mutable Next: CustomListNode option;}
> let head = { Value = 1; Next = None };;
val head : CustomListNode = {Value = 1;
Next = null;}
> let head2 = { Value = 2; Next = Some(head) } ;;
val head2 : CustomListNode = {Value = 2;
Next = Some {Value = 1;
Next = null;};}
> head.Next <- Some(head2);;
val it : unit = ()
> head;;
val it : CustomListNode = {Value = 1;
Next = Some {Value = 2;
Next = Some ...;};}
The answer is same for all languages with tail-call optimization support and first-class functions (function types) support: it's so easy to emulate cyclic structures.
let rec x = seq { yield 1; yield! x};;
It's simplest way to emulate that structure by using laziness of seq.
Of course you can hack list representation as described here.
As was said before, your problem here is that the list type is immutable, and for a list to be cyclic you'd have to have it stick itself into its last element, so that doesn't work. You can use sequences, of course.
If you have an existing list and want to create an infinite sequence on top of it that cycles through the list's elements, here's how you could do it:
let round_robin lst =
let rec inner_rr l =
seq {
match l with
| [] ->
yield! inner_rr lst
| h::t ->
yield h
yield! inner_rr t
}
if lst.IsEmpty then Seq.empty else inner_rr []
let listcycler_sequence = round_robin [1;2;3;4;5;6]
Anyone have a decent example, preferably practical/useful, they could post demonstrating the concept?
(Edit: a small Ocaml FP Koan to start things off)
The Koan of Currying (A koan about food, that is not about food)
A student came to Jacques Garrigue and said, "I do not understand what currying is good for." Jacques replied, "Tell me your favorite meal and your favorite dessert". The puzzled student replied that he liked okonomiyaki and kanten, but while his favorite restaurant served great okonomiyaki, their kanten always gave him a stomach ache the following morning. So Jacques took the student to eat at a restaurant that served okonomiyaki every bit as good as the student's favorite, then took him across town to a shop that made excellent kanten where the student happily applied the remainder of his appetite. The student was sated, but he was not enlightened ... until the next morning when he woke up and his stomach felt fine.
My examples will cover using it for the reuse and encapsulation of code. This is fairly obvious once you look at these and should give you a concrete, simple example that you can think of applying in numerous situations.
We want to do a map over a tree. This function could be curried and applied to each node if it needs more then one argument -- since we'd be applying the one at the node as it's final argument. It doesn't have to be curried, but writing another function (assuming this function is being used in other instances with other variables) would be a waste.
type 'a tree = E of 'a | N of 'a * 'a tree * 'a tree
let rec tree_map f tree = match tree with
| N(x,left,right) -> N(f x, tree_map f left, tree_map f right)
| E(x) -> E(f x)
let sample_tree = N(1,E(3),E(4)
let multiply x y = x * y
let sample_tree2 = tree_map (multiply 3) sample_tree
but this is the same as:
let sample_tree2 = tree_map (fun x -> x * 3) sample_tree
So this simple case isn't convincing. It really is though, and powerful once you use the language more and naturally come across these situations. The other example with some code reuse as currying. A recurrence relation to create prime numbers. Awful lot of similarity in there:
let rec f_recurrence f a seed n =
match n with
| a -> seed
| _ -> let prev = f_recurrence f a seed (n-1) in
prev + (f n prev)
let rowland = f_recurrence gcd 1 7
let cloitre = f_recurrence lcm 1 1
let rowland_prime n = (rowland (n+1)) - (rowland n)
let cloitre_prime n = ((cloitre (n+1))/(cloitre n)) - 1
Ok, now rowland and cloitre are curried functions, since they have free variables, and we can get any index of it's sequence without knowing or worrying about f_recurrence.
While the previous examples answered the question, here are two simpler examples of how Currying can be beneficial for F# programming.
open System.IO
let appendFile (fileName : string) (text : string) =
let file = new StreamWriter(fileName, true)
file.WriteLine(text)
file.Close()
// Call it normally
appendFile #"D:\Log.txt" "Processing Event X..."
// If you curry the function, you don't need to keep specifying the
// log file name.
let curriedAppendFile = appendFile #"D:\Log.txt"
// Adds data to "Log.txt"
curriedAppendFile "Processing Event Y..."
And don't forget you can curry the Printf family of function! In the curried version, notice the distinct lack of a lambda.
// Non curried, Prints 1 2 3
List.iter (fun i -> printf "%d " i) [1 .. 3];;
// Curried, Prints 1 2 3
List.iter (printfn "%d ") [1 .. 3];;
Currying describes the process of transforming a function with multiple arguments into a chain of single-argument functions. Example in C#, for a three-argument function:
Func<T1, Func<T2, Func<T3, T4>>> Curry<T1, T2, T3, T4>(Func<T1, T2, T3, T4> f)
{
return a => b => c => f(a, b, c);
}
void UseACurriedFunction()
{
var curryCompare = Curry<string, string, bool, int>(String.Compare);
var a = "SomeString";
var b = "SOMESTRING";
Console.WriteLine(String.Compare(a, b, true));
Console.WriteLine(curryCompare(a)(b)(true));
//partial application
var compareAWithB = curryCompare(a)(b);
Console.WriteLine(compareAWithB(true));
Console.WriteLine(compareAWithB(false));
}
Now, the boolean argument is probably not the argument you'd most likely want to leave open with a partial application. This is one reason why the order of arguments in F# functions can seem a little odd at first. Let's define a different C# curry function:
Func<T3, Func<T2, Func<T1, T4>>> BackwardsCurry<T1, T2, T3, T4>(Func<T1, T2, T3, T4> f)
{
return a => b => c => f(c, b, a);
}
Now, we can do something a little more useful:
void UseADifferentlyCurriedFunction()
{
var curryCompare = BackwardsCurry<string, string, bool, int>(String.Compare);
var caseSensitiveCompare = curryCompare(false);
var caseInsensitiveCompare = curryCompare(true);
var format = Curry<string, string, string, string>(String.Format)("Results of comparing {0} with {1}:");
var strings = new[] {"Hello", "HELLO", "Greetings", "GREETINGS"};
foreach (var s in strings)
{
var caseSensitiveCompareWithS = caseSensitiveCompare(s);
var caseInsensitiveCompareWithS = caseInsensitiveCompare(s);
var formatWithS = format(s);
foreach (var t in strings)
{
Console.WriteLine(formatWithS(t));
Console.WriteLine(caseSensitiveCompareWithS(t));
Console.WriteLine(caseInsensitiveCompareWithS(t));
}
}
}
Why are these examples in C#? Because in F#, function declarations are curried by default. You don't usually need to curry functions; they're already curried. The major exception to this is framework methods and other overloaded functions, which take a tuple containing their multiple arguments. You therefore might want to curry such functions, and, in fact, I came upon this question when I was looking for a library function that would do this. I suppose it is missing (if indeed it is) because it's pretty trivial to implement:
let curry f a b c = f(a, b, c)
//overload resolution failure: there are two overloads with three arguments.
//let curryCompare = curry String.Compare
//This one might be more useful; it works because there's only one 3-argument overload
let backCurry f a b c = f(c, b, a)
let intParse = backCurry Int32.Parse
let intParseCurrentCultureAnyStyle = intParse CultureInfo.CurrentCulture NumberStyles.Any
let myInt = intParseCurrentCultureAnyStyle "23"
let myOtherInt = intParseCurrentCultureAnyStyle "42"
To get around the failure with String.Compare, since as far as I can tell there's no way to specify which 3-argument overload to pick, you can use a non-general solution:
let curryCompare s1 s2 (b:bool) = String.Compare(s1, s2, b)
let backwardsCurryCompare (b:bool) s1 s2 = String.Compare(s1, s2, b)
I won't go into detail about the uses of partial function application in F# because the other answers have covered that already.
It's a fairly simple process. Take a function, bind one of its arguments and return a new function. For example:
let concatStrings left right = left + right
let makeCommandPrompt= appendString "c:\> "
Now by currying the simple concatStrings function, you can easily add a DOS style command prompt to the front of any string! Really useful!
Okay, not really. A more useful case I find is when I want to have a make a function that returns me data in a stream like manner.
let readDWORD array i = array[i] | array[i + 1] << 8 | array[i + 2] << 16 |
array[i + 3] << 24 //I've actually used this function in Python.
The convenient part about it is that rather than creating an entire class for this sort of thing, calling the constructor, calling obj.readDWORD(), you just have a function that can't be mutated out from under you.
You know you can map a function over a list? For example, mapping a function to add one to each element of a list:
> List.map ((+) 1) [1; 2; 3];;
val it : int list = [2; 3; 4]
This is actually already using currying because the (+) operator was used to create a function to add one to its argument but you can squeeze a little more out of this example by altering it to map the same function of a list of lists:
> List.map (List.map ((+) 1)) [[1; 2]; [3]];;
val it : int list = [[2; 3]; [4]]
Without currying you could not partially apply these functions and would have to write something like this instead:
> List.map((fun xs -> List.map((fun n -> n + 1), xs)), [[1; 2]; [3]]);;
val it : int list = [[2; 3]; [4]]
I gave a good example of simulating currying in C# on my blog. The gist is that you can create a function that is closed over a parameter (in my example create a function for calculating the sales tax closed over the value of a given municipality)out of an existing multi-parameter function.
What is appealing here is instead of having to make a separate function specifically for calculating sales tax in Cook County, you can create (and reuse) the function dynamically at runtime.