F# Finding paths in an n-ary tree - f#

Given this tree type:
type T<'a> = N of 'a * T<'a> list
which could be declared as:
let ta = N("b", [N("c", [])])
How would I get all the possible paths in this tree? I've tried by applying the method mentioned in this post, but it just returns an empty list. This is how I've implemented it:
let rec isPath is t =
match t with
| N(x, t) -> List.collect (isPath (x::is)) t
isPath [] ta |> (printf "isPath: %A")
but it only returns isPath: []. What am I doing wrong? My secondary goal would then be to make a second function where I can pass a list of ints to check if there are any paths that correspond to this list.

You need another match condition that catches empty lists and doesn't iterate through them. Right now your List.collect, when t is empty, is iterating through an empty list and is therefore returning an empty list to the "previous" level of your recursive function. Which is then appending all those empty lists together to get... an empty list, and so on.
Add the following match case and you should get what you need:
| N(x, []) -> is
Note that this should come before your other match case in order to work: since F# processes match cases from top to bottom, N(x, t) will match anything, and N(x, []) won't ever be checked if it's second.
So you want your function to look like:
let rec isPath is t =
match t with
| N(x, []) -> is
| N(x, t) -> List.collect (isPath (x::is)) t
Again, if you don't see why this works, let me know and I'll explain further.

Related

Concatenating lists with recursion f#

I have an exercise that asks me to make a recursive function that uses # to create a list of [1;2;3..n]. Unfortunately I cannot get this method to work.
let lstInt: int list = []
let rec oneToN (n:int) : int list =
let addList = [n]
match n with
0 ->
lstInt
|_ ->
lstInt#addList
oneToN (n-1)
I have tried making my list mutable, but that doesn't seem to actually matter nor make much sense as you can still add and remove elements from lists in f# even though it is not mutable.
I have also tried removing space between # but that shouldn't matter either.
Edit: I should clarify, the issue is the lstInt#addList, which gives me the error:
"The result of this expression has type 'int list' and is implicitly ignored. Consider using 'ignore' to discard this value explicitly, e.g. 'expr |> ignore', or 'let' to bind the result to a name, e.g. 'let result = expr"
That warning is not the issue, but it points you to the issue: you're creating a new list which is a concatenation of an empty list and [n], but then you're doing nothing with that new list. It's just dropped on the floor.
After that, you proceed to call oneToN (n-1) recursively and return its result. At the end of recursion, the very last call to oneToN will ultimately return an empty list, and that will be the return value of every previous iteration, since every iteration (except the last one) returns whatever the next iteration returns.
What you need to do is call oneToN (n-1), which will give you a list of numbers from 1 to n-1, and then append [n] to that list. And the result of that appending would be your return value: after all, if you take a list of numbers from 1 to n-1 and attach n to the end of it, you'll get a list of numbers from 1 to n.
let rec oneToN (n:int) : int list =
let addList = [n]
match n with
0 ->
lstInt
|_ ->
(oneToN (n-1)) # addList

How to split F# result type list into lists of inner type

I have a list/sequence as follows Result<DataEntry, exn> []. This list is populated by calling multiple API endpoints in parallel based on some user inputs.
I don't care if some of the calls fail as long as at least 1 succeeds. I then need to perform multiple operations on the success list.
My question is how to partition the Result list into exn [] and DataEntry [] lists. I tried the following:
// allData is Result<DataEntry, exn> []
let filterOutErrors (input: Result<DataEntry, exn>) =
match input with
| Ok v -> true
| _ -> false
let values, err = allData |> Array.partition filterOutErrors
This in principle meets the requirement since values contains all the success cases but understandably the compiler can't infer the types so both values and err contains Result<DataEntry, exn>.
Is there any way to split a list of result Result<Success, Err> such that you end up with separate lists of the inner type?
Is there any way to split a list of result Result<Success, Err> such that you end up with separate lists of the inner type?
Remember that Seq / List / Array are foldable, so you can use fold to convert a Seq / List / Array of 'Ts into any other type 'S. Here you want to go from []Result<DataEntry, exn> to, e.g., the tuple list<DataEntry> * list<exn>. We can define the following folder function, that takes an initial state s of type list<'a> * list<'b> and a Result Result<'a, 'b> and returns your tuple of lists list<'a> * list<'b>:
let listFolder s r =
match r with
| Ok data -> (data :: (fst s), snd s)
| Error err -> (fst s, err :: (snd s))
then you can fold over your array as follows:
let (values, err) = Seq.fold listFolder ([], []) allData
You can extract the good and the bad like this.
let values =
allData
|> Array.choose (fun r ->
match r with
| Result.Ok ok -> Some ok
| Result.Error _ -> None)
let err =
allData
|> Array.choose (fun r ->
match r with
| Result.Ok _ -> None
| Result.Error error -> Some error)
You seem confused about whether you have arrays or lists. The F# code you use, in the snippet and in your question text, all points to use of arrays, in spite of you several times mentioning lists.
It has recently been recommended that we use array instead of the [] symbol in types, since there are inconsistencies in the way F# uses the symbol [] to mean list in some places, and array in other places. There is also the symbol [||] for arrays, which may add more confusion.
So that would be recommending Result<DataEntry,exn> array in this case.
The answer from Víctor G. Adán is functional, but it's a downside that the API requires you to pass in two empty lists, exposing the internal implementation.
You could wrap this into a "starter" function, but then the code grows, requires nested functions or using modules and the intention is obscured.
The answer from Bent Tranberg, while more readable requires two passes of the data, and it seems inefficient to map into Option type just to be able to filter on it using .Choose.
I propose KISS'ing it with some good old mutation.
open System.Collections.Generic
let splitByOkAndErrors xs =
let oks = List<'T>()
let errors = List<'V>()
for x in xs do
match x with
| Ok v -> oks.Add v
| Error e -> errors.Add e
(oks |> seq, errors |> seq)
I know I know, mutation, yuck right? I believe you should not shy away from that even in F#, use the right tool for every situation: the mutation is kept local to the function, so it's still pure. The API is clean just taking in the list of Result to split, there is no concepts like folding, recursive calls, list cons pattern matching etc. to understand, and the function won't reverse the input list, you also have the option to return array or seq, that is, you are not confined to a linked list that can only be appended to in O(1) in the head - which in my experience seldom fits well into business case, win win win in my book.
I general, I hope to see F# grow into a more multi-paradigm programming language in the community's mind. It's nice to see these functional solutions, but I fear they scare some people away unnecessarily, as F# is already multi-paradigm!

F# pattern matching with optional list of tuples

I'm trying to use pattern matching for an optional list of tuples but I could not write an exhaustive matching expression despite trying everything I can think of.
I'm struggling to understand why the F# compiler is insisting that my patterns in the following examples are not exhaustive.
module Mapper.PatternMatchingOddity
type A = A of string
type B = B of string
type ProblemType = ProblemType of (A * B) list option
//Incomplete pattern matches on this expression. Some ([_;_]) may indicate a case...
let matchProblem = function
|Some [(x:A,y:B)] -> []
|Some ([_,_]) -> [] //rider says this rule will never be matched
|None -> []
//same as before
let matchProblem1 = function
|Some [_,_] -> []
|Some [] -> []
//|Some _ -> []//this removes the warning but what is the case not covered by the previous two?
|None -> []
let matchProblem2 (input:ProblemType) =
match input with //same as before
|ProblemType (Some [(x:A,y:B)]) -> []
|ProblemType None -> []
How do I write the exhaustive matching and what am I missing above? Can you give an example for an input that would be accepted as a valid parameter to these functions and slip through the patterns?
Great question! I think many people that start out with F# grapple with how lists, options and tuples interact. Let me start by saying: the compiler is correct. The short answer is: you are only matching over singleton lists. Let me try to explain that a little deeper.
Your type is ('a * 'b) list option, essentially. In your case, 'a and 'b are themselves a single-case discriminated using of a string. Let's simplify this a bit and see what happens if we look at each part of your type in isolation (you may already know this, but it may help to put it in context):
First of all, your type is option. This has two values, None or Some 'a. To match over an option you can just do something like
match o with
| Some value -> value
| None -> failwith "nothing"`
Next, your type is a list. The items in a list are divided by semicolons ;. An empty list is [], a singleton list (one with a single item) is [x] and multiple items [x;y...]. To add something to the start of a list use ::. Lists are a special type of discriminated union and the syntax to match over them mimics the syntax of lists construction:
match myList with
| [] -> "empty"
| [x] -> printfn "one item: %A" x
| [x; y] -> printfn "two items: %A, %A" x y
| x::rest -> printfn "more items, first one: %A" x
Third, your list type is itself a tuple type. To deconstruct or match over a tuple type, you can use the comma ,, as with match (x, y) with 1, 2 -> "it's 1 and 2!" ....
Combine all this, we must match over an option (outer) then list (middle) then tuple. Something like Some [] for an empty list and None for the absence of a list and Some [a, b] for a singleton list and Some (a,b)::rest for a list with one or more items.
Now that we have the theory out of the way, let's see if we can tackle your code. First let's have a look at the warning messages:
Incomplete pattern matches on this expression. Some ([_;_]) may indicate a case...
This is correct, the item in your code is separated by , denoting the tuple, and the message says Some [something; something] (underscore means "anything"), which is a list of two items. But it wouldn't help you much to add it, because the list can still be longer than 2.
rider says this rule will never be matched
Rider is correct (which calls the FSC compiler services underneath). The rule above that line is Some [(x:A,y:B)] (the :A and :B are not needed here), which matches any Some singleton array with a tuple. Some [_,_] does the same, except that it doesn't catch the values in a variable.
this removes the warning but what is the case not covered by the previous two?
It removes the warning because Some _ means Some with anything, as _ means just that: it is a placeholder for anything. In this case, it matches the empty list, the 2-item list, the 3-item list the n-item list (the only one your match is the 1-item list in that example).
Can you give an example for an input that would be accepted as a valid parameter
Yes. Valid input that you were not matching is Some [] (empty list), Some [A "a", B "x"; A "2", B "2"] (list of two items) etc.
Let's take your first example. You had this:
let matchProblem = function
|Some [(x:A,y:B)] -> [] // matching a singleton list
|Some ([_,_]) -> [] // matches a singleton list (will never match, see before)
|None -> [] // matches None
Here's what you (probably) need:
let notAProblemAnymore = function
// first match all the 'Some' matches:
| Some [] -> "empty" // an empty list
| Some [x,y] -> "singleton" // a list with one item that is a tuple
| Some [_,a;_,b] -> "2-item list" // a list with two tuples, ignoring the first half of each tuple
| Some ((x,y)::rest) -> "multi-item list"
// a list with at least one item, and 'rest' as the
// remaining list, which can be empty (but won't,
// here it has at least three items because of the previous matches)
| None -> "Not a list at all" // matching 'None' for absence of a list
To sum it up: you were matching over a list that had only one item and the compiler complained that you missed lists of other lengths (empty lists and lists that have more than one item).
Usually it is not necessary to use option with a list, because the empty list already means the absence of data. So whenever you find yourself writing the type option list consider whether just list would suffice. It will make the matching easier.
You are struggling because your example is too “example”.
Let’s convert your example to a more meaningful one: check the input, so that
If it is none then print “nothing”, otherwise:
If it has zero element then print “empty”
If it has only one element then print “ony one element: ...”
If it has two elements then print “we have two elements: ...”
If it has three elements then print “there are three elements: ...”
If it has more than three elements then print “oh man, the first element is ..., the second element is ..., the third element is ..., and N elements more”
Now you can see that your code only covers the first 3 cases. So the F# compiler was correct.
To rewrite the code:
let matchProblem (ProblemType input) =
match input with
| None -> printfn "nothing"
| Some [] -> ...
| Some [(x, y)] -> ...
| Some [(x1, y1); (x2, y2)] -> ...
| Some [(x1, y1); (x2, y2); (x3, y3)] -> ...
| Some (x1, y1) :: (x2, y2) :: (x3, y3) :: rest -> // access rest.Length to print the number of more elements
Notice that I’m using pattern matching on the parameter ProblemType input so that I can extract the input in a convenient way. This makes the later patterns simpler.
Personally, when I learned F#, I didn’t understand many features/syntax until I used them in production code.

Pattern matching on a list of tuples

I am attempting to create a function to pattern match a structure which is a tuple containing a value and a list of tuples of the form
'a * ('b * 'c) list -> 'b list
for example given the following:
let clubDetails = ("MyClub", [("Secretary", "Jill");("Captain", "Bob");("Email", "Bob#MyClub.com")])
I need a function to return the list ["Secretary";"Captain";"Email"]
So I thought I could do something like this :
let getClubAttributes ca =
match ca with
| (a, [(b,c)]) -> [b]
| _ -> []
but here
getClubAttributes clubDetails
Returns the empty list. I feel like I am missing something pretty obvious.
Thanks,
Russell.
The pattern match form that you have written will only match if the list in your tuple has exactly one element.
I note that you have written a default _ case in your pattern match which returns the empty list and this is the case you are hitting. I suspect you've added this case to remove the compiler warning but the compiler warning is, in fact, warning you of this exact problem.
You do not actually need a pattern match because your data structure can be handled with only one case.
let clubDetails = ("MyClub", [("Secretary", "Jill");("Captain", "Bob");("Email", "Bob#MyClub.com")])
let getClubAttributes (ca, attribList) =
List.map fst attribList
The new getClubAttributes function simply creates a new list from the original by taking the first element of each item in the list.

How does the implementation of list in F# work?

I'm curious as to how the list module/type works in F#, specifically does it optimise this?
let xs = ["1"; "2"; "3"]
let ys = "0"::xs
let zs = ["hello"; "world"]#xs
I've looked over some of the source https://github.com/fsharp/fsharp/blob/68e37d03dfc15f8105aeb0ac70b846f82b364901/src/fsharp/FSharp.Core/prim-types.fs#L3493 seems to be the relevant area.
I would like to know if xs is copied when making ys.
I would have thought it's easy to just point to the existing list if you just cons element.
If you are concatenating I imagine it might be impossible as it would require mutating the last element of the list to point to the next one?
If someone could annotate/paste snippets of code from FSharp.Core that would be ideal.
So the implementation of List is a little odd. It is actually implemented as a discriminated union. From the spec:
type 'T list =
| ([])
| (::) of 'T * 'T list
So you can think of :: as a function that takes two arguments and creates a tuple (which is fast as it is independent of the list size).
# is much more complicated. Here is the implementation:
let (#) l1 l2 =
match l1 with
| [] -> l2
| (h::t) ->
match l2 with
| [] -> l1
| _ ->
let res = [h]
let lastCons = PrivateListHelpers.appendToFreshConsTail res t
PrivateListHelpers.setFreshConsTail lastCons l2;
res
The two weird functions basically mutate the list in place. appendToFreshConsTail copies the list and returns the last element. setFreshConsTail then changes the last element so that its next element is set to l2 rather than [] joining the lists.

Resources