Further to my last question:
let safeInput:Map<'a,'b> option -> 'a -> 'b -> Map<'a,'b> option = fun x y z ->
match x with
| Some d -> Some(d.Add(y,z))
| None -> Some([y,z]|>Map.ofList)
I understand how simple higher-order functions are declared as a type... reading from right to left if '->' is used more than once to decipher what it returns.. i.e. a higher order function.
For the above example from a book... I understand this is adding to a map, I'm just a bit hazy on how the top line should be deciphered? And the use of the 'fun' keyword?
So the first line states that safeInput is a function which takes a Map option a key a value and then returns a map option. The fun keyword is just a way of creating the function.
An equivalent function is
let safeInput (x:Map<'a,'b> option) (y:'a) (z:'b) :Map<'a,'b> option =
match x with
| Some d -> Some(d.Add(y,z))
| None -> Some([y,z]|>Map.ofList)
Related
I am trying to implement BST in F#. Since I am starting my journey with F# I wanted to ask for help.
I have simple a test;
[<Fact>]
let ``Data is retained`` () =
let treeData = create [4]
treeData |> data |> should equal 4
treeData |> left |> should equal None
treeData |> right |> should equal None
Tree type which uses discriminated unions
type Tree<'T> =
| Leaf
| Node of value: 'T * left: Tree<'T> * right: Tree<'T>
a recursive function which inserts data nodes into the tree
let rec insert newValue (targetTree: Tree<'T>) =
match targetTree with
| Leaf -> Node(newValue, Leaf, Leaf)
| Node (value, left, right) when newValue < value ->
let left' = insert newValue left
Node(value, left', right)
| Node (value, left, right) when newValue > value ->
let right' = insert newValue right
Node(value, left, right')
| _ -> targetTree
now I have problems with create function. I have this:
let create items =
List.fold insert Leaf items
and resulting error:
FS0001 Type mismatch. Expecting a
''a -> Tree<'a> -> 'a' but given a
''a -> Tree<'a> -> Tree<'a>' The types ''a' and 'Tree<'a>' cannot be unified.
The List.fold documentation shows its type signature as:
List.fold : ('State -> 'T -> 'State) -> 'State -> 'T list -> 'State
Let's unpack that. The first argument is a function of type 'State -> 'T -> 'State. That means it takes a state and an argument of type T, and returns a new state. Here, the state is your Tree type: starting at a basic Leaf, you're building up the tree step by step. Second argument to List.fold is the initial state (a Leaf in this case), and third argument is the list of items of type T to fold over.
Your second and third arguments are correct, but your first argument doesn't line up with the signature that List.fold is expecting. List.fold wants something of type 'State -> 'T -> 'State, which in your case would be Tree<'a> -> 'a -> Tree<'a>. That is, a function that takes the tree as its first parameter and a single item as its second parameter. But your insert function takes the parameters the other way around (the item as the first parameter, and the tree as the second parameter).
I'll pause here to note that your insert function is correct according to the style rules of idiomatic F#, and you should not change the order of its parameters. When writing functions that deal with collections, you always want to take the collection as the last parameter so that you can write something like tree |> insert 5. So I strongly suggest you don't change the order of the arguments your insert function takes.
So if you shouldn't change the order of arguments of your insert function, yet they're in the wrong order to use with List.fold, what do you do? Simple: you create an anonymous function with the arguments flipped around, so that you can use insert with List.fold:
let create items =
List.fold (fun tree item -> insert item tree) Leaf items
Now we'll go one step further and generalize this. It's actually pretty common in F# programming to find that your two-parameter function has the parameters the right way around for most things, but the wrong way around for one particular use case. To solve that problem, sometimes it's useful to create a general-purpose function called flip:
let flip f = fun a b -> f b a
Then you could just write your create function like this:
let create items =
List.fold (flip insert) Leaf items
Sometimes the use of flip can make code more confusing rather than less confusing, so I don't recommend using it all the time. (This is also why there isn't a flip function in the F# standard library: because it's not always the best solution. And because it's trivial to write yourself, its lack in the standard library is not a big deal). But sometimes using flip makes code simpler, and I think this is one of those cases.
P.S. The flip function could also have been written like this:
let flip f a b = f b a
This definition is identical to the let flip f = fun a b -> f b a definition I used in the main example. Do you know why?
I have found a presentation by Don Syme which shows that Erlang's
fac(0) -> 1
fac(N) -> N * fac(N-1).
is equivalent to F#'s
let rec fac = function
| 0 -> 1
| n -> n * fac (n-1)
But it looks like there is no way to use pattern matching for a different arity without losing type safety. E.g. one could use a list pattern matching, but then a type must be a common base type (such as object):
let concat = function
| [x;y] -> x.ToString() + y.ToString()
| [x] -> x.ToString()
Given that F# functions in modules do not support overloads, it looks like the only way to rewrite Erlang code into F# with static typing is to use static classes with method overloading instead of modules. Is there a better way to rewrite Erlang functions with different arity in F#?
In general, is it correct to say that Erlang's argument matching is closer to .NET's (including C#) method overloading rather than to F#'s pattern matching? Or there is no direct replacement between the two, e.g. there could be a function in Erlang with different arities + a guard:
max(x) -> x.
max(x,y) when x > y -> x.
max(x,y) -> y.
max(comparer, x, y) -> if comparer(x,y) > 0 -> x; true -> y end.
In the last case the arguments are of different types. How would you rewrite it in F#?
You can achieve something close to overloading by rethinking the problem slightly. Instead of thinking about the function as the axis of variability, think of the input as the variable part. If you do that, you'll realise that you can achieve the same with a discriminated union.
Here's a more contrived example than the one in the linked article:
type MyArguments = One of int | Two of int * int
let foo = function
| One x -> string x
| Two (x, y) -> sprintf "%i%i" x y
Usage:
> foo (One 42);;
val it : string = "42"
> foo (Two (13, 37));;
val it : string = "1337"
Obviously, instead of defining such a 'stupid' type as the above MyArguments, you'd define a discriminated union that makes sense in the domain you're modelling.
I'm trying to write some function that handle errors by returning double options instead of doubles. Many of these functions call eachother, and so take double options as inputs to output other double options. The problem is, I can't do with double options what I can do with doubles--something simple like add them using '+'.
For example, a function that divides two doubles, and returns a double option with none for divide by zero error. Then another function calls the first function and adds another double option to it.
Please tell me if there is a way to do this, or if I have completely misunderstood the meaning of F# option types.
This is called lifting - you can write function to lift another function over two options:
let liftOpt f o1 o2 =
match (o1, o2) with
| (Some(v1), Some(v2)) -> Some(f v1 v2)
| _ -> None
then you can supply the function to apply e.g.:
let inline addOpt o1 o2 = liftOpt (+) o1 o2
liftA2 as mentioned above will provide a general way to 'lift' any function that works on the double arguments to a function that can work on the double option arguments.
However, in your case, you may have to write special functions yourself to handle the edge cases you mention
let (<+>) a b =
match (a, b) with
| (Some x, Some y) -> Some (x + y)
| (Some x, None) -> Some (x)
| (None, Some x) -> Some (x)
| (None, None) -> None
Note that liftA2 will not put the cases where you want to add None to Some(x) in automatically.
The liftA2 method for divide also needs some special handling, but its structure is generally what we would write ourselves
let (</>) a b =
match (a, b) with
| (Some x, Some y) when y <> 0.0d -> Some (x/y)
| _ -> None
You can use these functions like
Some(2.0) <+> Some(3.0) // will give Some(5.0)
Some(1.0) </> Some(0.0) // will give None
Also, strictly speaking, lift is defined as a "higher order function" - something that takes a function and returns another function.
So it would look something like this:
let liftOpt2 f =
(function a b ->
match (a, b) with
| (Some (a), Some (b)) -> f a b |> Some
| _ -> None)
In the end, I realized what I was really looking for was the Option.get function, which simply takes a 'a option and returns an 'a. That way, I can pattern match, and return the values I want.
In this case you might want to consider Nullables over Options, for two reasons:
Nullables are value types, while Options are reference types. If you have large collections of these doubles, using Nullables will keep the numbers on the stack instead of putting them on the heap, potentially improving your performance.
Microsoft provides a bunch of built-in Nullable Operators that do let you directly perform math on nullables, exactly as you're trying to do with options.
I have a problem when pattern matching with F#. I'm building an F# library and have this so far:
namespace parser
module parse =
let public y = function
| x when x.Contains("hi") -> "HELLO"
| x when x.Contains("hello") -> "HI"
| x -> x
but it gives me error: Error Lookup on object of indeterminate type based on information prior to this program point. A type annotation may be needed prior to this program point to constrain the type of the object. This may allow the lookup to be resolved.
Essentially, the compiler doesn't understand that you want the argument to your function to be of type string. Basically, you can NOT invoke instance methods on implicitly declared function arguments. You'll need to use something like the following.
let y (value:string) =
match value when
| x when x.Contains("hi") -> "HELLO"
| x when x.Contains("hello") -> "HI"
| x -> x
Interestingly, if you were not invoking an instance method, but instead using it in some other way (where the type was already known), you would be fine. In other words, suppose a StringUtils module contained a method Has, which took in two strings and performed the same check as Contains; if so, you could use the implicit argument, because the compiler already knows of which type the value must be.
module StringUtils =
let has (word:string) value = word.Contains(value)
module Parse =
let y = function
| x when x |> StringUtils.has "hi" -> "HELLO"
| x when x |> StringUtils.has "hello" -> "HI"
| x -> x
Obviously, in many cases, this sort of thing is unnecessarily verbose. But it demonstrates the larger point about F#'s type inference behavior.
The compiler wants to know the type of x is in your y function so you need to annotate it, like this:
let y (x: string) =
match x with
| x when x.Contains "hi" -> "HELLO"
| x when x.Contains "hello" -> "HI"
| x -> x
Sometimes I see code like
let (alt : recognizer -> recognizer -> recognizer) =
fun a b p -> union (a p) (b p)
Or like:
let hd = function
Cons(x,xf) -> x
| Nil -> raise Empty
What is the difference between fun and function?
The semantics for this is the same as in F# (probably because F# is based on OCaml):
function allows the use of pattern matching (i.e. |), but consequently it can be passed only one argument.
function p_1 -> exp_1 | … | p_n -> exp_n
is equivalent to
fun exp -> match exp with p_1 -> exp_1 | … | p_n -> exp_n
fun does not allow pattern matching, but can be passed multiple arguments, e.g.
fun x y -> x + y
When either of the two forms can be used, fun is generally preferred due to its compactness.
See also OCaml documentation on Functions.
The way I think about it
function patterns
is shorthand for
(fun x -> match x with patterns)
where 'patterns' is e.g.
| Some(x) -> yadda | None -> blah
(And
fun args -> expr
is how you define a lambda.)
Russ Cam is correct in his answer.
Here is a posting on the OCaml list talking about it
http://caml.inria.fr/pub/ml-archives/ocaml-beginners/2003/11/b8036b7a0c1d082111d7a83c8f6dbfbb.en.html
function only allows for one argument but allows for pattern matching, while fun is the more general and flexible way to define a function.
I generally use fun unless there is a good reason to use function.
You can see this in the code you posted where the fun declaration takes 3 arguments and the function declaration does pattern matching on it's input
fun x1 ... xn -> e
is an abbreviation for
function x1 -> ... -> function xn -> e