Using `should equal` with sequences in F# and FsUnit - .net-core

I am using FsUnit.Xunit. I am getting a failure for the following test case:
[<Fact>]
let ``Initialization of DFF`` () =
dff Seq.empty Seq.empty |> should equal (seq {Zero})
The test failure is:
Message: 
FsUnit.Xunit+MatchException : Exception of type 'FsUnit.Xunit+MatchException' was thrown.
Expected: Equals seq [Zero]
Actual: seq [Zero]
Stack Trace: 
That.Static[a](a actual, IMatcher`1 matcher)
Signal.Initialization of DFF() line 11
I get the same error if the test is:
[<Fact>]
let ``Initialization of DFF`` () =
dff Seq.empty Seq.empty |> should equal (Seq.singleton Zero)
I have never tested equality of sequences using FsUnit.Xunit, so I am confused what's going on. I'm not even for sure what the failure message is telling me, as it seems to be saying that the expected and actual are the same. I can get this to work fine by converting the sequences to lists, but it would be nice to not have to do that.
Could someone explain what's going on here? It seems I'm not understanding the error message and thus probably something about Equals and comparing sequence values (literals?). Thanks.
Source code to be able to reproduce (I think this is everything):
type Bit =
| Zero
| One
type Signal = seq<Bit>
let Nand a b =
match a, b with
| Zero, Zero -> One
| Zero, One -> One
| One, Zero -> One
| One, One -> Zero
let Not input =
Nand input input
let And a b =
Not (Nand a b)
let Or a b =
Nand (Not a) (Not b)
let private liftToSignal1 op (signal: Signal) : Signal =
Seq.map op signal
let private liftToSignal2 op (signalA: Signal) (signalB: Signal) : Signal =
Seq.map2 op signalA signalB
let Not' = liftToSignal1 Not
let And' = liftToSignal2 And
let Or' = liftToSignal2 Or
let rec dff data clock : Signal =
seq {
yield Zero
yield! Or' (And' data clock)
(And' (dff data clock) (Not' clock))
}

This is an issue with structural vs. referential equality.
In F# seq { 'a' } = seq { 'a' } // false but [ 'a' ] = [ 'a' ] // true due to seq being IEnumerable and not supporting structural equality (or comparison).
Lists (and other F# container-like types) are much more 'intelligent', i.e. they support structural equality / comparison if the contained objects support it:
[ {| foo = StringComparison.Ordinal; bar = Some(1.23) |} ] =
[ {| foo = StringComparison.Ordinal; bar = Some(1.23) |} ] // true
but don't, if they contain anything that doesn't:
[ box(fun() -> 3) ] = [ box(fun() -> 3) ] // false
So, to make the test work, add a List.ofSeq:
dff Seq.empty Seq.empty |> List.ofSeq |> should equal [ Zero ]

Related

how can I repeat monadic instructions inside kind's monads?

I know that I can run monadic instructions sequentially inside monads in Kind language, like this:
Test: _
IO {
IO.print(Nat.show(2))
IO.print(Nat.show(3))
IO.print(Nat.show(4))
}
output:
2
3
4
But is it possible to run monadic instructions repeatedly, like this below?
Test: _
a = [2,1,3,4,5]
IO {
for num in a:
IO.print(Nat.show(num))
}
If it is possible how can I do it correctly?
Monads are usually represented by only two operators :
return :: a -> m(a) // that encapulapse the value inside a effectful monad
>>= :: m a -> (a -> m b) -> m b
// the monadic laws are omitted
Notice, the bind operator is naturally recursive, once it can compose two monads or even discard the value of one and the return can be thought of as a "base case".
m >>= (\a -> ... >>= (\b -> ~ i have a and b, compose or discard? ~) >>= fixpoint)
You just have to produce that sequence, which is pretty straightforward. For example, in Kind we represent monads as a pair which takes a type-for-type value and encapluse a polymorphic type.
type Monad <M: Type -> Type> {
new(
bind: <A: Type, B: Type> M<A> -> (A -> M<B>) -> M<B>
pure: <A: Type> A -> M<A>
)
}
In your example, we just have to trigger the effect and discard the value, a recursive definition is enough :
action (x : List<String>): IO(Unit)
case x {
nil : IO.end!(Unit.new) // base case but we are not worried about values here, just the effects
cons : IO {
IO.print(x.head) // print and discard the value
action(x.tail) // fixpoint
}
}
test : IO(Unit)
IO {
let ls = ["2", "1", "3", "4", "5"]
action(ls)
}
The IO as you know it will be desugared by a sequence of binds!
Normally in case of list it can be generalized like the mapM function of haskell library :
Monadic.forM(A : Type -> Type, B : Type,
C : Type, m : Monad<A>, b : A(C), f : B -> A(C), x : List<A(B)>): A(C)
case x {
nil : b
cons :
open m
let k = App.Kaelin.App.mapM!!!(m, b, f, x.tail)
let ac = m.bind!!(x.head, f)
m.bind!!(ac, (c) k) // the >> operator
}
It naturally discard the value and finally we can do it :
action2 (ls : List<String>): IO(Unit)
let ls = [IO.end!(2), IO.end!(1), IO.end!(3), IO.end!(4), IO.end!(5)]
Monadic.forM!!!(IO.monad, IO.end!(Unit.new), (b) IO.print(Nat.show(b)), ls)
So, action2 do the same thing of action, but in one line!.
When you need compose the values you can represent as monadic fold :
Monadic.foldM(A : Type -> Type, B : Type,
C : Type, m : Monad<A>, b : A(C), f : B -> C -> A(C), x : List<A(B)>): A(C)
case x {
nil : b
cons :
open m
let k = Monadic.foldM!!!(m, b, f, x.tail)
m.bind!!(x.head, (b) m.bind!!(k, (c) f(b, c)))
}
For example, suppose that you want to sum a sequence of numbers that you ask for the user in a loop, you just have to call foldM and compose with a simple function :
Monad.action3 : IO(Nat)
let ls = [IO.get_line, IO.get_line, IO.get_line]
Monadic.foldM!!!(IO.monad, IO.end!(0),
(b, c) IO {
IO.end!(Nat.add(Nat.read(b), c))
},
ls)
test : IO(Unit)
IO {
get total = action3
IO.print(Nat.show(total))
}
For now, Kind do not support typeclass so it make the things a little more verbose, but i think a new support to forM loops syntax can be thought in the future. We hope so :)

A function that compare a two lists of string

I am a new at F# and i try to do this task:
Make a function compare : string list -> string list -> int that takes two string lists and returns: -1, 0 or 1
Please help. I spend a lot of time, and i can not understand how to implement this task.
Given the task I assume what your professor wants to teach you with this exercise. I'll try to give you a starting point without
Confusing you
Presenting a 'done-deal' solution
I assume the goal of this task is to work with recursive functions and pattern matching to element-wise compare their elements. It could looks somewhat like this here
open System
let aList = [ "Apple"; "Banana"; "Coconut" ]
let bList = [ "Apple"; "Banana"; "Coconut" ]
let cList = [ "Apple"; "Zebra" ]
let rec doSomething f (a : string list) (b : string list) =
match (a, b) with
| ([], []) ->
printfn "Both are empty"
| (x::xs, []) ->
printfn "A has elements (we can unpack the first element as x and the rest as xs) and B is empty"
| ([], x::xs) ->
printfn "A is empty and B has elements (we can unpack the first element as x and the rest as xs)"
| (x::xs, y::ys) ->
f x y
printfn "Both A and B have elements. We can unpack them as the first elements x and y and their respective tails xs and ys"
doSomething f xs ys
let isItTheSame (a : string) (b : string) =
if String.Equals(a, b) then
printfn "%s is equals to %s" a b
else
printfn "%s is not equals to %s" a b
doSomething isItTheSame aList bList
doSomething isItTheSame aList cList
The example has three different lists, two of them being equal and one of them being different. The doSomething function takes a function (string -> string -> unit) and two lists of strings.
Within the function you see a pattern match as well as a recursive call of doSomething in the last match block. The signatures aren't exactly what you need and you might want to think about how to change the parametrization for cases where you don't want to stop the recursion (the last match block - if the strings are equal you want to keep on comparing, right?).
Just take the code and try it out in FSI. I'm confident, that you'll find the solution 🙂
In F# many collections are comparable if their element type is:
let s1 = [ "a"; "b" ]
let s2 = [ "foo"; "bar" ]
compare s1 s2 // -5
let f1 = [ (fun () -> 1); fun () -> 2 ]
let f2 = [ (fun () -> 3); fun () -> 42 ]
// compare f1 f2 (* error FS0001: The type '(unit -> int)' does not support the 'comparison' constraint. *)
so
let slcomp (s1 : string list) s2 = compare s1 s2 |> sign
Posting for reference as the original question is answered already.

Automatic detection of domain for dependent type function in Idris

Idris language tutorial has simple and understandable example of the idea of Dependent Types:
http://docs.idris-lang.org/en/latest/tutorial/typesfuns.html#first-class-types
Here is the code:
isSingleton : Bool -> Type
isSingleton True = Int
isSingleton False = List Int
mkSingle : (x : Bool) -> isSingleton x
mkSingle True = 0
mkSingle False = []
sum : (single : Bool) -> isSingleton single -> Int
sum True x = x
sum False [] = 0
sum False (x :: xs) = x + sum False xs
I decided to spend more time on this example. What bothers me in sum function is that I need to explicitly pass single : Bool value to function. I don't want to do this and I want compiler to guess what this boolean value should be. Hence I pass only Int or List Int to sum function there should be 1-to-1 correspondence between boolean value and type of argument (if I pass some other type this just mustn't type check).
Of course, I understand, this is not possible in general case. Such compiler tricks require my function isSingleton (or any other similar function) be injective. But for this case it should be possible as it seems to me...
So I started with next implementation: I just made single argument implicit.
sum : {single : Bool} -> isSingleton single -> Int
sum {single = True} x = x
sum {single = False} [] = 0
sum {single = False} (x :: xs) = x + sum' {single = False} xs
Well, it doesn't really solve my problem because I still need to call this function in the next way:
sum {single=True} 1
But I read in tutorial about auto keyword. Though I don't quite understand what auto does (because I didn't find description of it) I decided to patch my function just a little bit more:
sum' : {auto single : Bool} -> isSingleton single -> Int
sum' {single = True} x = x
sum' {single = False} [] = 0
sum' {single = False} (x :: xs) = x + sum' {single = False} xs
And it works for lists!
*DepFun> :t sum'
sum' : {auto single : Bool} -> isSingleton single -> Int
*DepFun> sum' [1,2,3]
6 : Int
But doesn't work for single value :(
*DepFun> sum' 3
When checking an application of function Main.sum':
List Int is not a numeric type
Can someone explain is it actually possible to achieve my goal in such injective function usages currently? I watched this short video about proving something is injective:
https://www.youtube.com/watch?v=7Ml8u7DFgAk
But I don't understand how I can use such proofs in my example.
If this is not possible what is the best way to write such functions?
The auto keyword basically tells Idris, "Find me any value of this type". So you're liable to get the wrong answer unless that type only contains one value. Idris sees {auto x : Bool} and fills it in with any old Bool, namely False. It doesn't use its knowledge of later arguments to help it choose - information doesn't flow from right to left.
One fix would be to make the information flow in the other direction. Rather using a universe-style construction as you have above, write a function accepting an arbitrary type and use a predicate to refine it to the two options you want. This way Idris can look at the type of the preceding argument and pick the only value of IsListOrInt whose type matches.
data IsListOrInt a where
IsInt : IsListOrInt Int
IsList : IsListOrInt (List Int)
sum : a -> {auto isListOrInt : IsListOrInt a} -> Int
sum x {IsInt} = x
sum [] {IsList} = 0
sum (x :: xs) {IsList} = x + sum xs
Now, in this case the search space is small enough (two values - True and False) that Idris could feasibly explore every option in a brute-force fashion and pick the first one that results in a program which passes the type checker, but that algorithm doesn't scale well when the types are much bigger than two, or when trying to infer multiple values.
Compare the left-to-right nature of the information flow in the above example with the behaviour of regular non-auto braces, which instruct Idris to find the result in a bidirectional fashion using unification. As you note, this could only succeed when the type functions in question are injective. You could structure your input as a separate, indexed datatype, and allow Idris to look at the constructor to find b using unification.
data OneOrMany isOne where
One : Int -> OneOrMany True
Many : List Int -> OneOrMany False
sum : {b : Bool} -> OneOrMany b -> Int
sum (One x) = x
sum (Many []) = 0
sum (Many (x :: xs)) = x + sum (Many xs)
test = sum (One 3) + sum (Many [29, 43])
Predicting when the machine will or won't be able to guess what you mean is an important skill in dependently-typed programming; you'll find yourself getting better at it with more experience.
Of course, in this case it's all moot because lists already have one-or-many semantics. Write your function over plain old lists; then if you need to apply it to a single value you can just wrap it in a singleton list.

Unique array of random numbers using functional programming

I'm trying to write some code in a functional paradigm for practice. There is one case I'm having some problems wrapping my head around. I am trying to create an array of 5 unique integers from 1, 100. I have been able to solve this without using functional programming:
let uniqueArray = [];
while (uniqueArray.length< 5) {
const newNumber = getRandom1to100();
if (uniqueArray.indexOf(newNumber) < 0) {
uniqueArray.push(newNumber)
}
}
I have access to lodash so I can use that. I was thinking along the lines of:
const uniqueArray = [
getRandom1to100(),
getRandom1to100(),
getRandom1to100(),
getRandom1to100(),
getRandom1to100()
].map((currentVal, index, array) => {
return array.indexOf(currentVal) > -1 ? getRandom1to100 : currentVal;
});
But this obviously wouldn't work because it will always return true because the index is going to be in the array (with more work I could remove that defect) but more importantly it doesn't check for a second time that all values are unique. However, I'm not quite sure how to functionaly mimic a while loop.
Here's an example in OCaml, the key point is that you use accumulators and recursion.
let make () =
Random.self_init ();
let rec make_list prev current max accum =
let number = Random.int 100 in
if current = max then accum
else begin
if number <> prev
then (number + prev) :: make_list number (current + 1) max accum
else accum
end
in
make_list 0 0 5 [] |> Array.of_list
This won't guarantee that the array will be unique, since its only checking by the previous. You could fix that by hiding a hashtable in the closure between make and make_list and doing a constant time lookup.
Here is a stream-based Python approach.
Python's version of a lazy stream is a generator. They can be produced in various ways, including by something which looks like a function definition but uses the key word yield rather than return. For example:
import random
def randNums(a,b):
while True:
yield random.randint(a,b)
Normally generators are used in for-loops but this last generator has an infinite loop hence would hang if you try to iterate over it. Instead, you can use the built-in function next() to get the next item in the string. It is convenient to write a function which works something like Haskell's take:
def take(n,stream):
items = []
for i in range(n):
try:
items.append(next(stream))
except StopIteration:
return items
return items
In Python StopIteration is raised when a generator is exhausted. If this happens before n items, this code just returns however much has been generated, so perhaps I should call it takeAtMost. If you ditch the error-handling then it will crash if there are not enough items -- which maybe you want. In any event, this is used like:
>>> s = randNums(1,10)
>>> take(5,s)
[6, 6, 8, 7, 2]
of course, this allows for repeats.
To make things unique (and to do so in a functional way) we can write a function which takes a stream as input and returns a stream consisting of unique items as output:
def unique(stream):
def f(s):
items = set()
while True:
try:
x = next(s)
if not x in items:
items.add(x)
yield x
except StopIteration:
raise StopIteration
return f(stream)
this creates an stream in a closure that contains a set which can keep track of items that have been seen, only yielding items which are unique. Here I am passing on any StopIteration exception. If the underlying generator has no more elements then there are no more unique elements. I am not 100% sure if I need to explicitly pass on the exception -- (it might happen automatically) but it seems clean to do so.
Used like this:
>>> take(5,unique(randNums(1,10)))
[7, 2, 5, 1, 6]
take(10,unique(randNums(1,10))) will yield a random permutation of 1-10. take(11,unique(randNums(1,10))) will never terminate.
This is a very good question. It's actually quite common. It's even sometimes asked as an interview question.
Here's my solution to generating 5 integers from 0 to 100.
let rec take lst n =
if n = 0 then []
else
match lst with
| [] -> []
| x :: xs -> x :: take xs (n-1)
let shuffle d =
let nd = List.map (fun c -> (Random.bits (), c)) d in
let sond = List.sort compare nd in
List.map snd sond
let rec range a b =
if a >= b then []
else a :: range (a+1) b;;
let _ =
print_endline
(String.concat "\t" ("5 random integers:" :: List.map string_of_int (take (shuffle (range 0 101)) 5)))
How's this:
const addUnique = (ar) => {
const el = getRandom1to100();
return ar.includes(el) ? ar : ar.concat([el])
}
const uniqueArray = (numberOfElements, baseArray) => {
if (numberOfElements < baseArray.length) throw 'invalid input'
return baseArray.length === numberOfElements ? baseArray : uniqueArray(numberOfElements, addUnique(baseArray))
}
const myArray = uniqueArray(5, [])

F# stop Seq.map when a predicate evaluates true

I'm currently generating a sequence in a similar way to:
migrators
|> Seq.map (fun m -> m())
The migrator function is ultimately returning a discriminated union like:
type MigratorResult =
| Success of string * TimeSpan
| Error of string * Exception
I want to stop the map once I encounter my first Error but I need to include the Error in the final sequence.
I have something like the following to display a final message to the user
match results |> List.rev with
| [] -> "No results equals no migrators"
| head :: _ ->
match head with
| Success (dt, t) -> "All migrators succeeded"
| Error (dt, ex) -> "Migration halted owing to error"
So I need:
A way to stop the mapping when one of the map steps produces an Error
A way to have that error be the final element added to the sequence
I appreciate there may be a different sequence method other than map that will do this, I'm new to F# and searching online hasn't yielded anything as yet!
I guess there are multiple approaches here, but one way would be to use unfold:
migrators
|> Seq.unfold (fun ms ->
match ms with
| m :: tl ->
match m () with
| Success res -> Some (Success res, tl)
| Error res -> Some (Error res, [])
| [] -> None)
|> List.ofSeq
Note the List.ofSeq at the end, that's just there for realizing the sequence. A different way to go would be to use sequence comprehensions, some might say it results in a clearer code.
The ugly things Tomaš alludes to are 1) mutable state, and 2) manipulation of the underlying enumerator. A higher-order function which returns up to and including when the predicate holds would then look like this:
module Seq =
let takeUntil pred (xs : _ seq) = seq{
use en = xs.GetEnumerator()
let flag = ref true
while !flag && en.MoveNext() do
flag := not <| pred en.Current
yield en.Current }
seq{1..10} |> Seq.takeUntil (fun x -> x % 5 = 0)
|> Seq.toList
// val it : int list = [1; 2; 3; 4; 5]
For your specific application, you'd map the cases of the DU to a boolean.
(migrators : seq<MigratorResult>)
|> Seq.takeUntil (function Success _ -> false | Error _ -> true)
I think the answer from #scrwtp is probably the nicest way to do this if your input is reasonably small (and you can turn it into an F# list to use pattern matching). I'll add one more version, which works when your input is just a sequence and you do not want to turn it into a list.
Essentially, you want to do something that's almost like Seq.takeWhile, but it gives you one additional item at the end (the one, for which the predicate fails).
To use a simpler example, the following returns all numbers from a sequence until one that is divisible by 5:
let nums = [ 2 .. 10 ]
nums
|> Seq.map (fun m -> m % 5)
|> Seq.takeWhile (fun n -> n <> 0)
So, you basically just need to look one element ahead - to do this, you could use Seq.pairwise which gives you the current and the next element in the sequence"
nums
|> Seq.map (fun m -> m % 5)
|> Seq.pairwise // Get sequence of pairs with the next value
|> Seq.takeWhile (fun (p, n) -> p <> 0) // Look at the next value for test
|> Seq.mapi (fun i (p, n) -> // For the first item, we return both
if i = 0 then [p;n] else [n]) // for all other, we return the second
|> Seq.concat
The only ugly thing here is that you then need to flatten the sequence again using mapi and concat.
This is not very nice, so a good thing to do would be to define your own higher-order function like Seq.takeUntilAfter that encapsulates the behavior you need (and hides all the ugly things). Then your code could just use the function and look nice & readable (and you can experiment with other ways of implementing this).

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