Fsharp: Passing N Parameters for a function - f#

I'm trying to create a function that takes in a variable amount of parameters but I can't seem to find any viable solution for F#.
let expression = (fun a b -> a || b)
let expressionTriple = (fun a b c -> (a || b) && c)
// This doesn't work because expression can either be a function that takes fixed arguments
let truthTable numPredicates expression =
if numPredicates = 2 then
expression true true
else
expression true true false
truthTable 2 expression
truthTable 3 expressionTriple
How can I pass in a variable amount of arguments into the expression function?

In F#, functions with different signatures (including a different number of parameters) are considered distinct types. And any time you want to have a function take a parameter that could be two distinct types (or even a dozen distinct types), you need to use discriminated unions. Here's how you could write your code in a way that will compile and do what you're trying to do:
type Expression<'a> =
| Double of ('a -> 'a -> 'a)
| Triple of ('a -> 'a -> 'a -> 'a)
let expression = fun a b -> a || b
let expressionTriple = fun a b c -> (a || b) && c
// This works because expression is a discriminated union
let truthTable expression =
match expression with
| Double f -> f true true
| Triple f -> f true true false
truthTable (Double expression)
truthTable (Triple expressionTriple)
If you wanted to add a four-parameter version, just add a Quad of ('a -> 'a -> 'a -> 'a -> 'a) case to that discriminated union, and so on.
If you have any questions about this, like why I wrote this with generic type 'a instead of bool, please feel free to ask follow-up questions.

let expression = (fun [a; b] -> a || b)
let expressionTriple = (fun [a; b; c] -> (a || b) && c)
let truthTable numPredicates expression =
if numPredicates = 2 then
expression [true; true]
else
expression [true; true; false]
truthTable 2 expression
truthTable 3 expressionTriple

Related

match by value in a discriminated union, in F#

with this union:
type T =
| A
| B
| C
and a T list
I would like to implement something like this pseudo code:
let countOfType (t: Type) (l: T list) =
l
|> List.filter (fun x -> x.GetType() = t)
|> List.length
when I would pass if I want to count the 'A', 'B', etc..
but A.GetType() and B.GetType() return the T type, so this doesn't work.
Is there a way where I could check the type by passing it as a parameter?
The practical case here is that I have a Map that gets updated every few seconds and its values are part of the same DU. I need to be able to see how many of each type, without having to update the code (like a match block) each time an entry gets added.
Addendum:
I simplified the original question too much and realized it after seeing Fyodor's answer.
So I would like to add the additional part:
how could this also be done for cases like these:
type T =
| A of int
| B of string
| C of SomeOtherType
For such enum type T as you specified, you can just use regular comparison:
let countOfType t (l: T list) =
l
|> List.filter (fun x -> x = t)
|> List.length
Usage:
> countOfType A [A; A; B; C; A]
3
> countOfType B [A; A; B; C; A]
1
Try List.choose: ('a -> 'b option) -> 'a list -> 'b list, it filters list based on 'a -> 'b option selector. If selectors evaluates to Some, then value will be included, if selector evaluates to None, then value will be skipped. If you worry about allocations caused by instantiation of Some, then you'll have to implement version that will use ValueOption
let onlyA lis =
lis |> List.choose (function
| (A _) as a -> Some a
| _ -> None)
let onlyB lis =
lis |> List.choose (function
| (B _) as b -> Some b
| _ -> None)
let lis = [
A 1
A 22
A 333
B ""
B "123"
]
lis |> onlyA |> List.length |> printfn "%d"
You can pattern match, and throw away the data, to create a function for the filter.
type T =
| A of int
| B of string
| C of float
[A 3;A 1;B "foo";B "bar";C 3.1; C 4.6]
|> List.filter (fun x ->
match x with
| A _ -> true
| B _ -> false
| C _ -> false
)
|> List.length
But in general i would asume, that you create a predicate function in your modul.
let isA x =
match x with
| A _ -> true
| _ -> false
if you have those functions you can just write
[A 3;A 1;B "foo";B "bar";C 3.1; C 4.6]
|> List.filter isA
|> List.length

How do sequence expressions and polymorphic recursion play together?

This project really is a source of questions for me.
I already learned about polymorphic recursion and I understand why it is a special case and therefore F# needs full type annotations.
For regular functions I might need some fiddeling but usually get it right. Now I'm trying to adapt a (working) basic toSeq to a more specialized finger tree, but can't.
My feeling is that the use of the computation expression has something to do with it. This is the condensed working version:
module ThisWorks =
module Node =
type Node<'a> =
| Node2 of 'a * 'a
| Node3 of 'a * 'a * 'a
let toList = function
| Node2(a, b) -> [a; b]
| Node3(a, b, c) -> [a; b; c]
module Digit =
type Digit<'a> =
| One of 'a
| Two of 'a * 'a
| Three of 'a * 'a * 'a
| Four of 'a * 'a * 'a * 'a
let toList = function
| One a -> [a]
| Two(a, b) -> [a; b]
| Three(a, b, c) -> [a; b; c]
| Four(a, b, c, d) -> [a; b; c; d]
module FingerTree =
open Node
open Digit
type FingerTree<'a> =
| Empty
| Single of 'a
| Deep of Digit<'a> * Lazy<FingerTree<Node<'a>>> * Digit<'a>
let rec toSeq<'a> (tree:FingerTree<'a>) : seq<'a> = seq {
match tree with
| Single single ->
yield single
| Deep(prefix, Lazy deeper, suffix) ->
yield! prefix |> Digit.toList
yield! deeper |> toSeq |> Seq.collect Node.toList
yield! suffix |> Digit.toList
| Empty -> ()
}
The one I don't manage to get to compile is this:
module ThisDoesnt =
module Monoids =
type IMonoid<'m> =
abstract Zero:'m
abstract Plus:'m -> 'm
type IMeasured<'m when 'm :> IMonoid<'m>> =
abstract Measure:'m
type Size(value) =
new() = Size 0
member __.Value = value
interface IMonoid<Size> with
member __.Zero = Size()
member __.Plus rhs = Size(value + rhs.Value)
type Value<'a> =
| Value of 'a
interface IMeasured<Size> with
member __.Measure = Size 1
open Monoids
module Node =
type Node<'m, 'a when 'm :> IMonoid<'m>> =
| Node2 of 'm * 'a * 'a
| Node3 of 'm * 'a * 'a * 'a
let toList = function
| Node2(_, a, b) -> [a; b]
| Node3(_, a, b, c) -> [a; b; c]
module Digit =
type Digit<'m, 'a when 'm :> IMonoid<'m>> =
| One of 'a
| Two of 'a * 'a
| Three of 'a * 'a * 'a
| Four of 'a * 'a * 'a * 'a
let toList = function
| One a -> [a]
| Two(a, b) -> [a; b]
| Three(a, b, c) -> [a; b; c]
| Four(a, b, c, d) -> [a; b; c; d]
module FingerTree =
open Node
open Digit
type FingerTree<'m, 'a when 'm :> IMonoid<'m>> =
| Empty
| Single of 'a
| Deep of 'm * Digit<'m, 'a> * Lazy<FingerTree<'m, Node<'m, 'a>>> * Digit<'m, 'a>
let unpack (Value v) = v
let rec toSeq<'a> (tree:FingerTree<Size, Value<'a>>) : seq<'a> = seq {
match tree with
| Single(Value single) ->
yield single
| Deep(_, prefix, Lazy deeper, suffix) ->
yield! prefix |> Digit.toList |> List.map unpack
#if ITERATE
for (Value deep) in toSeq deeper do
^^^^^
yield deep
#else
yield! deeper |> toSeq |> Seq.collect (Node.toList >> List.map unpack)
^^^^^
#endif
yield! suffix |> Digit.toList |> List.map unpack
| Empty -> ()
}
The error message I get says
Error Type mismatch. Expecting a
FingerTree<Size,Node<Size,Value<'a>>> -> 'b
but given a
FingerTree<Size,Value<'c>> -> seq<'c>
The type 'Node<Size,Value<'a>>' does not match the type 'Value<'b>'
and the squiggles underline the recursive call of toSeq.
I know that the “deeper” type is encapsulated in a Node and in the working code I just unpack it afterwards. But here the compiler trips already before I get the chance to unpack. Trying a for (Value deep) in toSeq deeper do yield deep has the same problem.
I already have a way out, namely to use the toSeq of the “base” Tree and Seq.map unpack afterwards. Not true, trying that yields a very similar error message.
I'm curious what makes this code break and how it could be fixed.
The compiler's error message seems clear to me: toSeq is applicable only to values of type FingerTree<Size, Value<'a>> for some 'a, but you're trying to call it on a value of type FingerTree<Size,Node<Size,Value<'a>>> instead, which is not compatible. There's nothing specific to polymorphic recursion or sequence expressions, these types just don't match.
Instead, it seems like it would be much simpler to make toSeq more generic by taking an input of type FingerTree<Size, 'a> (without any reference to Value), which would enable the recursive call you want. Then you can easily derive the more specific function you actually want by composing the more general toSeq with Seq.map unpack.

Pattern match on a list of tuples

If I want to add all the elements of a list of tuples, I get an error with the following
let rec addTupLst (xs: 'a * 'a list) =
match xs with
| (a, b) :: rst -> a + b + (addTupLst rst)
| _ -> 0
addTupLst [(1, 2)]
I get the warning
error FS0001: This expression was expected to have type
'a * 'a list
but here has type
'b list
Is it not possible to pattern match on a list of tuples this way, or is there another error?
You just forgot a pair of parens
let rec addTupLst (xs: ('a * 'a) list) =
match xs with
| (a, b) :: rst -> a + b + (addTupLst rst)
| _ -> 0
addTupLst [(1, 2)]
The problem is that you declare the function as taking a 'a * 'a list, but what you actually want to write is ('a * 'a) list.
This is one of the reasons why I don't really like the common but (IMO) inconsistent style of using prefix notation for type parameters for some built-in types and postfix notation for the rest. I prefer to write the type as list<'a * 'a>.

F# Create Factorial function without recursion, library functions or loops

In this video about functional programming at 35:14 Jim Weirich writes a function to compute factorial without using recursion, library functions or loops:
see image of Ruby code here
The code in Ruby
fx = ->(improver) {
improver.(improver)
}.(
->(improver) {
->(n) { n.zero ? 1 : n * improver.(improver).(n-1) }
}
)
I'm trying to express this approach F#
let fx =
(fun improver -> improver(improver))(
fun improver ->
fun n ->
if n = 0 then 1
else n * improver(improver(n - 1)))
I'm currently stuck at
Type mismatch. Expecting a 'a but given a 'a -> 'b
The resulting type would be infinite when unifying ''a' and ''a -> 'b'
I can't seem find the right type annotation or other way of expressing the function
Edit:
*without the rec keyword
Languages with ML-style type inference won't be able to infer a type for the term fun improver -> improver improver; they start by assuming the type 'a -> 'b for a lambda-definition (for some undetermined types 'a and 'b), so as the argument improver has type 'a, but then it's applied to itself to give the result (of type 'b), so improver must simultaneously have type 'a -> 'b. But in the F# type system there's no way to unify these types (and in the simply-typed lambda calculus there's no way to give this term a type at all). My answer to the question that you linked to in your comment covers some workarounds. #desco has given one of those already. Another is:
let fx = (fun (improver:obj->_) -> improver improver)
(fun improver n ->
if n = 0 then 1
else n * (improver :?> _) improver (n-1))
This is cheating, but you can use types
type Self<'T> = delegate of Self<'T> -> 'T
let fx1 = (fun (x: Self<_>) -> x.Invoke(x))(Self(fun x -> fun n -> if n = 0 then 1 else x.Invoke(x)(n - 1) * n))
type Rec<'T> = Rec of (Rec<'T> -> 'T)
let fx2 = (fun (Rec(f ) as r) -> f r)(Rec(fun ((Rec f) as r) -> fun n -> if n = 0 then 1 else f(r)(n - 1) * n))

Built in f# operator to compose functions with the same input but different outputs?

I understand the << compose operator takes two functions that both take in and return the same type. e.g. (lhs:'a -> 'a) -> (rhs:'a -> 'a) -> 'a
I often find myself wanting something like (lhs:'a -> 'b) -> (rhs:'c -> 'b) -> 'b in cases where I'm interested in side affects and not the return value 'b is probably the unit type. This is only when I have two lines in succession where I'm persisting something to a database.
Is there a built in function or idiomatic F# way of doing this without writing something like
let myCompose lhs rhs arg =
lhs arg
rhs arg
Backward composition operator (<<) is defined as:
( << ) : ('b -> 'c) -> ('a -> 'b) -> 'a -> 'c`
With two predicates applied, it is actually a function that takes initial value of 'a returning 'c, while the value of 'b is processed inside.
From the code sample you provided, let me assume that you need applying an argument to both predicates. There are several ways to do this:
Discarding the value returned by the (first) predicate, returning the original argument instead. Such operator exists in WebSharper:
let ( |>! ) x f = f x; x
// Usage:
let ret =
x
|>! f1
|>! f2
|> f3
I like this approach because:
it does not complicate things; each function application is atomic, and the code appears more readable;
it allows chaining throughout three or more predicates, like in the example above;
In this case, f must return unit, but you can easily work this around:
let ( |>!! ) x f = ignore(f x); x
Applying the argument to both predicates, returning a tuple of results, exactly as in your own example. There's such operator OCaml, easy to adapt to F#:
val (&&&) : ('a -> 'b) -> ('a -> 'c) -> 'a -> 'b * 'c
As #JackP noticed, &&& is already defined in F# for another purpose, so let's use another name:
/// Applying two functions to the same argument.
let (.&.) f g x = (f x, g x)
// Usage
let ret1, ret2 =
x
|> (f .&. g)
Note The samples above are for straight order of function application. If you need them applied in a reverse order, you need to modify the code accordingly.
The backward or reverse composition operator (<<) does not take two functions that both take in and return the same type; the only constraint is that the output type of the first function to be applied must be the same as the input type of the function it's being composed into. According to MSDN, the function signature is:
// Signature:
( << ) : ('T2 -> 'T3) -> ('T1 -> 'T2) -> 'T1 -> 'T3
// Usage:
func2 << func1
I don't know of a built-in composition operator that works like you want, but if this pattern is something you use frequently in your code and having such an operator would simplify your code, I think it's reasonable to define your own. For example:
> let (<<!) func2 func1 arg = func1 arg; func2 arg;;
val ( <<! ) : func2:('a -> 'b) -> func1:('a -> unit) -> arg:'a -> 'b
Or, if you know both functions are going to return unit, you can write it like this to constrain the output type to be unit:
> let (<<!) func2 func1 arg = func1 arg; func2 arg; ();;
val ( <<! ) : func2:('a -> unit) -> func1:('a -> unit) -> arg:'a -> unit
For composing of any number of functions of type f:'a->unit in any desired order you may simply fold their list:
("whatever",[ printfn "funX: %A"; printfn "funY: %A"; printfn "funZ: %A" ])
||> List.fold (fun arg f -> f arg; arg )
|> ignore
getting in FSI
funX: "whatever"
funY: "whatever"
funZ: "whatever"
val it : unit = ()

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