//Return a tuple from a text file:
let ExtractFromLine (line:string) =
let strings = line.Split('\t') //data members are spaced by tab
let strlist = Array.toList(strings) //each data member is now a list of str
let year = System.Int32.Parse(strlist.Head) //year is first in file, so Head
let values = List.map System.Double.Parse strlist.Tail //tail are all values
let average = List.average values //not part of text file
let min = List.min values //not part of text file
let max = List.max values //not part of text file
(year, values, average, min, max) //return tuple with all info
//----------
let rec createList fileline =
if fileline = [] then
[]
else
let (year, values, average, min, max) = ExtractFromLine fileline.Head
let l = (year, values, average, min, max) :: createList fileline.Tail
l
//------------
let main argv =
let file = ReadFile "data.txt"
let biglist = createList file //recursive function to make a list of tuples
printfn"%A" biglist //This prints the year, all values, average, min, and max for each tuple created
I now have a giant list of tuples with all of the information that I need.
Have I retained the possibility of accessing all elements inside and performing calculations on them? I program in C++, and the solution is doable in that language, but F# is so much more powerful in my opinion. I'm sure its possible, I'm just missing the basics.
For example, how do I print the average of all the values for all years?
I'm thinking of a for loop, but I'm not sure how to iterate.
for(all tuples in biglist)
printfn"%A:%A" tuple.year tuple.average
It's wrong obviously, but I think you guys understand what I'm trying to do.
The above question involves pulling data from one tuple at a time across the list. What if I wanted to print the largest average?This would involve accessing each tuple's average data member and comparing them to return the largest one. Do I have to create another list containing these averages?
I learned about fst and snd but I had a hard time applying it to this example.
You don't have to answer all questions if it is too much, but any help is greatly appreciated as I start out in this language, thank you
You can loop in F# but it's a construct from imperative programming world. More idiomatic approach is to access items of the list recursively.
Below some sample code that creates tuples, constructs a list, and then access items and checks which one is bigger. Looking at your code the average was third item in the tuple. That's why I've added a trd function. It takes a 5-item tuple and returns a third item.
The prcsLst function takes 2 arguments: a list and a starting max value. The idea is that when processing the list we take the head (first item on the list), compare it's average with current max. Whichever is bigger is passed to the next recursive round together with list's tail (the list without the first item).In this case as the initial max I passed in the average of the first item.
You can run the example in F# Interactive to see the results.
// create sample tuples
let t1 = (2014, 35, 18, 5, 45)
let t2 = (2014, 32, 28, 8, 75)
let t3 = (2014, 25, 11, 9, 55)
let t4 = (2015, 16, 13, 2, 15)
let t5 = (2015, 29, 15, 1, 35)
// create sample list
let lst = [t1;t2;t3;t4;t5]
// a function to return third item in a tuple
let trd (_,_,t,_,_) = t
// process list recursively
let rec prcsLst l max =
match l with
| [] -> max
| hd::tl ->
if (trd hd) > max then
prcsLst tl (trd hd)
else
prcsLst tl max
// invoke the method on the sample list
// as a starting point use the first item in the list
prcsLst lst (trd t1);;
On a mobile so forgive me for not doing any code examples :)
I suspect that the missing piece of your puzzle is called pattern matching. In F# you address elements of a tuple like so:
let (y, v, Av, mn, mx) = mytuple
Note that you can also use this in function declarations, and when doing a 'match'.
(there is an exception for 'twoples' where you can use the functions 'fst' and 'snd')
Another thing you should play with is the |> operator.
Related
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.
I have a list of tuples like so:
let scorecard = [ for i in 0 .. 39 -> i,0 ]
I want to identify the nth tuple in it. I was thinking about it in this way:
let foundTuple = scorecard |> Seq.find(fun (x,y) -> x = 10)
I then want to create a new tuple based on the found one:
let newTuple = (fst foundTuple, snd foundTuple + 1)
And have a new list with that updated value
Does anyone have some code that matches this pattern? I think I have to split the list into 2 sublists: 1 list has 1 element (the tuple I want to replace) and the other list has the remaining elements. I then create a new list with the replacing tuple and the list of unchanged tuples...
You can use List.mapi which creates a new list using a specified projection function - but it also calls the projection function with the current index and so you can decide what to do based on this index.
For example, to increment second element of a list of integers, you can do:
let oldList = [0;0;0;0]
let newList = oldList |> List.mapi (fun index v -> if index = 1 then v + 1 else v)
Depending on the problem, it might make sense to use the Map type instead of list - map represents a mapping from keys to values and does not need to copy the entire contents when you change just a single value. So, for example:
// Map keys from 0 to 3 to values 0
let m = Map.ofList [0,0;1,0;2,0;3,0]
// Set the value at index 1 to 10 and get a new map
Map.add 1 10 m
I went back and thought about the problem and decided to use an array, which is mutable.
let scorecard = [| for i in 0 .. 39 -> i,0 |]
Since tuples are not mutable, I need to create a new tuple based on the existing one and overwrite it in the array:
let targetTuple = scorecard.[3]
let newTuple = (fst targetTuple, snd targetTuple + 1)
scorecard.[3] <- newTuple
I am using the "<-" which is a code smell in F#. I wonder if there a comparable purely functional equivalent?
I am just getting started with F# and am trying Problem Euler problem #3. To find primes I came up with the following code to compute all primes up to a maximum number:
let rec allPrimes foundPrimes, current, max =
// make sure the current number isn't too high
// or the current number isn't divisible by any known primes
if current >= max then
foundPrimes
else
let nextValue = current + 1
if not List.exists (fun x -> current % x = 0L) foundPrimes then
allPrimes foundPrimes nextValue max
else
allPrimes (foundPrimes :: current) nextValue max
Unfortunately, this gives the error:
Only simple variable patterns can be bound in 'let rec' constructs
Why am I getting this error?
You don't want to put the commas in the declaration - change
let rec allPrimes foundPrimes, current, max =
to
let rec allPrimes foundPrimes current max =
The correct version of your original would be
let rec allPrimes (foundPrimes, current, max) =
note the brackets around the tuple. However, this would require modifying the recursive calls to also use tuple form. In the original version the compiler thinks you are trying to do something like
let a,b,c=1,2,3
which won't work for recursive functions.
I'm attempting to learn myself up on F#, and I fear I'm not understanding something as well as I should.
I'm trying to recreate the functionality of a book I rather like (Creative Cursing from Royal and Panarese).
In a nutshell, you have two separate wordlists from which two random words can be chosen, resulting in an odd phrase. Simple enough?
Here's what I have:
#light
open System
open System.IO
let getWordList file =
File.ReadAllLines( file )
let getRandArrElement (arr : string[]) =
let rnd = Random( 0 )
arr |> Seq.nth (rnd.Next arr.Length)
let wordList1 = getWordList "words1.txt"
let wordList2 = getWordList "words2.txt"
let word1 = getRandArrElement wordList1
let word2 = getRandArrElement wordList2
printf "%s %s" word1 word2
It works, too. With the exception that it returns the same phrase every time it's run.
I have a feeling that what it's doing is calculating one random value per call to "getRandArrElement" at compile time, then using that value as THE value (which I think is weird, but what do I know?).
Whats wrong with my logic, and how do I fix it?
Your problem is here:
let getRandArrElement (arr : string[]) =
let rnd = Random( 0 )
arr |> Seq.nth (rnd.Next arr.Length
Random numbers aren't really truly random. They take a seed value, compute a random number between 0.0 and 1.0; that new value is used as the next seed. In other words, Random i spurely deterministic, so seeding with the same value over and over yields the same output sequence.
And since you're always constructor a new Random with the same seed, you're getting the same random number as output everytime.
I suggest a few improvements:
use let rnd = Random(). The default constructor uses the system clock as a seed, so that you'll get a different sequence. (Its still possible to get the same sequence. The system clock has a resolution of about 10 ms, so construction two Randoms in that interval will result, with high probability, of being seeded with the same value.
If you use let rnd = Random(0), even if rnd is outside your function, you'll get the same sentences in the exact same order everytime your run your program.
You can move the declaration of rnd outside your function so you're not constructing it over and over. As an alternative, you can write this:
let getRandArrElement =
let rnd = Random()
fun (arr : string[]) -> ...
F# executes all parameterless values when you open a module, so rnd will be assigned right away, and getRandArrElement is assigned the value of fun (arr : string[]) -> ....
Use arr.[index] instead of arr |> Seq.nth (rnd.Next arr.Length). Its not only more concise, but its also O(1). Seq.nth treats it like a sequence, it walks one element at a time until it gets to the element matching the given index, making the operation O(n).
The final result should be something like:
let getRandArrElement =
let rnd = Random()
fun (arr : string[]) -> arr.[rnd.Next(arr.Length)]
You are using a new Random with the same seed every time, this is expected behavior - if the same seed is used repeatedly, the same series of numbers is generated. I would suggest you move the declaration of rnd out of the function, that will solve your problem:
let rnd = Random();
let getRandArrElement (arr : string[]) =
arr |> Seq.nth (rnd.Next arr.Length)
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.