I'm working on a function that takes two arguments: a match value and a list of tuples. The goal is to match the first value (a string) in each tuple against the match value (also a string) and add the second value (an int) in those matching tuples to a new list, which is returned in sorted order. I started out with:
let getElems strMatch tupList =
let rec loop acc = function
| [] -> acc
| hd :: tl ->
match hd with
| (strMatch, v) -> loop (v :: acc) tl
| _ -> loop (acc) tl
List.sort (loop [] tupList)
...but came to realize that strMatch is out of scope as a pattern match so the second rule would never get matched. So I started trying to pass strMatch to the inner code blocks like so:
let getElems strMatch tupList =
let rec loop strMatch acc tupList =
match tupList with
| [] -> acc
| hd :: tl ->
match hd with
| (strMatch, v) -> loop strMatch (v :: acc) tl
| _ -> loop strMatch (acc) tl
List.sort (loop strMatch [] tupList)
...but the value is still out of scope in the match blocks. I suppose it would be possible to pass strMatch into those blocks but this seems messy and I'm wondering if there is a more elegant way.
EDIT: So here are my results...
First, I get the warning "This rule will never be matched." When I run the function as-is:
getElems "A" [("A",5);("BB",6);("AA",9);("A",0)];;
> val it : int list = [0; 5; 6; 9]
But if I hard code strMatch as "A" in the function:
getElems "A" [("A",5);("BB",6);("AA",9);("A",0)];;
> val it : int list = [0; 5]
Which is what is desired. But I'm required to take any match as an argument.
Related
I am trying to create module/interface (i dont exactly know how its called, i am new to the language) for basic operations on BST in OCaml. My goal is to have an implementation that lets me doing something like this:
T.create();;
T.push(2);;
T.push(3);;
T.push(5);;
in order to get a bst tree consisting of 2,3,5.
But at the moment to achieve this i have to write something like this:
let teeBst = T.push(2)(T.push(3)(T.push(5)(T.create())));;
So when I am checking/using my code I have to do it like this:
let tee2 = T.push(2)(T.push(3)(T.push(5)(T.create())));;
T.postorder(tee2);;
The output is fine:
# val tee2 : T.bt = <abstr>
# - : int list = [2; 3; 5]
But, as I said before, I would like to achieve this doing as below:
T.push(2);;
T.push(3);;
T.push(5);;
T.postorder();;
(I realise this requires some changes to my postorder function but the one I am currently using is a temporary one so I can check the tree I have atm )
Below is my implementation. If you see the solution, please let me know ;)
module type Tree =
sig
type bt
val create: unit -> bt
val push: int -> bt -> bt
val find: int -> bt -> bool
val preorder: bt -> int list
val postorder: bt -> int list
val inorder: bt -> int list
end;;
module T : Tree =
struct
type bt = E | B of bt * int * bt
let create () = E
let rec push x = function
| E -> B(E, x, E)
| B (l, y, r) when x<y -> B(push x l, y, r)
| B (l, y, r) when x>y -> B(l, y, push x r)
| xs -> xs;;
let rec find x = function
| E -> false
| B(l, y,_) when x< y -> find x l
| B(_,y,r) when x>y -> find x r
| _ -> true;;
let rec preorder = function
| B(l,v,r) -> v::(preorder r) # (preorder l)
| E -> [];;
let rec inorder = function
| B(l,v,r) ->(inorder r) # v::(inorder l)
| E -> []
let rec postorder = function
| B(l,v,r) -> (postorder r) # (postorder l) # [v]
| E -> []
end;;
It seems like you want modules to be classes, but I'd advise you to consider more idiomatic solutions. Have you considered using the pipe operator?
T.create()
|> T.push(2)
|> T.push(3)
|> T.push(5)
|> T.postorder;;
Or with local open (which makes more sense if you have a module with a longer name than just T of course) you can even do
T.(
create()
|> push(2)
|> push(3)
|> push(5)
|> postorder
);
What you're asking for would require introducing global mutable state, which isn't just "some changes" but an entirely different paradigm. And one that is generally frowned upon because it makes your code unpredictable and hard to debug since it relies on state that might change at any moment from anywhere.
Another possibility is to actually use classes, since OCaml has those too. Then you'd still have mutable state, but it would at least be contained.
I've written this mergesort implementation, which works fine if I put the divide function outside of the mergesort function. But when I try to make divide an inner function of mergesort I encounter a syntax error.
I know, there must be some really simple explanation for this. I've looked all over the internet, yet found nothing.
Here is the code:
let mergesort list =
let rec sort lists acc = (
let rec merge sublist1 sublist2 merged_list =
match sublist1 with
|[] -> merged_list # sublist2
|hd1 :: tl1 ->
match sublist2 with
|[] -> merged_list # sublist1
|hd2 :: tl2 ->
if hd1 < hd2 then merge tl1 sublist2 (merged_list # hd1::[])
else merge sublist1 tl2 (merged_list # hd2::[])
in match lists with
|[] ->
(match acc with
|[] -> []
|hd :: [] -> hd
|_ -> sort acc [])
|hd :: tl -> sort (List.tl tl) ((merge (List.hd tl) hd [])::acc)
)
and rec divide list list_of_lists = (
match list with
[] -> list_of_lists
|hd :: tl -> divide tl ((hd :: []) :: list_of_lists)
)
in sort (divide list []) []
;;
and it results into:
Characters 567-570:
and rec divide list list_of_lists = (
^^^
Error: Syntax error
A local definition has the following syntax in OCaml:
let [rec] pattern1 = expr1 and … and patternN = exprN in expr
Thus an extra rec is not allowed after the and keyword, and is allowed only after the first let. The rec flag extends to all values defined in the local definition, thus you just need to remove this erroneous rec after and.
You need to simply remove the rec keyword from your definition there.
This is because when you use the and keyword, you’re effectively repeating the previous definition syntactically, which in this case is let rec.
So your current implementation is effectively the same as saying let rec rec
I want a find function for Streams of size-bounded types which is analogous to the find functions for Lists and Vects.
total
find : MaxBound a => (a -> Bool) -> Stream a -> Maybe a
The challenge is it to make it:
be total
consume no more than constant log_2 N space where N is the number of bits required to encode the largest a.
take no longer than a minute to check at compile time
impose no runtime cost
Generally a total find implementation for Streams sounds absurd. Streams are infinite and a predicate of const False would make the search go on forever. A nice way to handle this general case is the infinite fuel technique.
data Fuel = Dry | More (Lazy Fuel)
partial
forever : Fuel
forever = More forever
total
find : Fuel -> (a -> Bool) -> Stream a -> Maybe a
find Dry _ _ = Nothing
find (More fuel) f (value :: xs) = if f value
then Just value
else find fuel f xs
That works well for my use case, but I wonder if in certain specialized cases the totality checker could be convinced without using forever. Otherwise, somebody may suffer a boring life waiting for find forever ?predicateWhichHappensToAlwaysReturnFalse (iterate S Z) to finish.
Consider the special case where a is Bits32.
find32 : (Bits32 -> Bool) -> Stream Bits32 -> Maybe Bits32
find32 f (value :: xs) = if f value then Just value else find32 f xs
Two problems: it's not total and it can't possibly return Nothing even though there's a finite number of Bits32 inhabitants to try. Maybe I could use take (pow 2 32) to build a List and then use List's find...uh, wait...the list alone would take up GBs of space.
In principle it doesn't seem like this should be difficult. There's finitely many inhabitants to try, and a modern computer can iterate through all 32-bit permutations in seconds. Is there a way to have the totality checker verify the (Stream Bits32) $ iterate (+1) 0 eventually cycles back to 0 and once it does assert that all the elements have been tried since (+1) is pure?
Here's a start, although I'm unsure how to fill the holes and specialize find enough to make it total. Maybe an interface would help?
total
IsCyclic : (init : a) -> (succ : a -> a) -> Type
data FinStream : Type -> Type where
MkFinStream : (init : a) ->
(succ : a -> a) ->
{prf : IsCyclic init succ} ->
FinStream a
partial
find : Eq a => (a -> Bool) -> FinStream a -> Maybe a
find pred (MkFinStream {prf} init succ) = if pred init
then Just init
else find' (succ init)
where
partial
find' : a -> Maybe a
find' x = if x == init
then Nothing
else
if pred x
then Just x
else find' (succ x)
total
all32bits : FinStream Bits32
all32bits = MkFinStream 0 (+1) {prf=?prf}
Is there a way to tell the totality checker to use infinite fuel verifying a search over a particular stream is total?
Let's define what it means for a sequence to be cyclic:
%default total
iter : (n : Nat) -> (a -> a) -> (a -> a)
iter Z f = id
iter (S k) f = f . iter k f
isCyclic : (init : a) -> (next : a -> a) -> Type
isCyclic init next = DPair (Nat, Nat) $ \(m, n) => (m `LT` n, iter m next init = iter n next init)
The above means that we have a situation which can be depicted as follows:
-- x0 -> x1 -> ... -> xm -> ... -> x(n-1) --
-- ^ |
-- |---------------------
where m is strictly less than n (but m can be equal to zero). n is some number of steps after which we get an element of the sequence we previously encountered.
data FinStream : Type -> Type where
MkFinStream : (init : a) ->
(next : a -> a) ->
{prf : isCyclic init next} ->
FinStream a
Next, let's define a helper function, which uses an upper bound called fuel to break out from the loop:
findLimited : (p : a -> Bool) -> (next : a -> a) -> (init : a) -> (fuel : Nat) -> Maybe a
findLimited p next x Z = Nothing
findLimited p next x (S k) = if p x then Just x
else findLimited pred next (next x) k
Now find can be defined like so:
find : (a -> Bool) -> FinStream a -> Maybe a
find p (MkFinStream init next {prf = ((_,n) ** _)}) =
findLimited p next init n
Here are some tests:
-- I don't have patience to wait until all32bits typechecks
all8bits : FinStream Bits8
all8bits = MkFinStream 0 (+1) {prf=((0, 256) ** (LTESucc LTEZero, Refl))}
exampleNothing : Maybe Bits8
exampleNothing = find (const False) all8bits -- Nothing
exampleChosenByFairDiceRoll : Maybe Bits8
exampleChosenByFairDiceRoll = find ((==) 4) all8bits -- Just 4
exampleLast : Maybe Bits8
exampleLast = find ((==) 255) all8bits -- Just 255
I'm trying to create a functor that makes a polynomial ring out of a ring. My underlying type, Ring_elt, has the following signature:
module type Ring_elt = sig
type t
val add : t -> t -> t
val mul : t -> t -> t
val zer : t
val one : t
val neg : t -> t
end;;
My polynomial functor looks like:
module Make_Poly2(Underlying:Ring_elt) = struct
type t = Poly of Underlying.t list
let rec create lst =
match List.rev lst with
| Underlying.zer :: tl -> create List.rev tl
| _ -> Poly of lst
end;;
(so the 'create' function should take a list, remove the leading zeros, and then return the polynomial of the result). However, I get a syntax error and utop underlines the "zer" after "Underlying."
By comparison, the following code (for making integer polynomials) works:
module Make_int_poly = struct
type t = Poly of int list
let rec create lst =
match List.rev lst with
| 0 :: tl -> create (List.rev tl)
| _ -> Poly lst
end;;
Any idea what's going on?
An OCaml pattern is built from constants, data constructors, and new names bound by the pattern match. Underlying.zer isn't any of those things. But 0 is one of them.
Seems like you can just use an if to compare against Underlying.zer.
Jeffrey's answer is good but instead of correcting it with an if construction, what you should do is the following : use algebraic data types
Instead of writing
val zer : t
val one : t
You could write
module type Ring_elt = sig
type t = Zer | One | Num of t
val add : t -> t -> t
val mul : t -> t -> t
val neg : t -> t
end
module Make_int_poly = struct
type t = Poly of int list
let rec create lst =
match List.rev lst with
| Underlying.Zer :: tl -> create (List.rev tl)
| _ -> Poly lst
end
It's a much better way of doing it since you can easily pattern match on it and even add some constants to your type t without problems.
I need a function that produces primes in F#. I found this:
let primesSeq =
let rec nextPrime n p primes =
if primes |> Map.containsKey n then
nextPrime (n + p) p primes
else
primes.Add(n, p)
let rec prime n primes =
seq {
if primes |> Map.containsKey n then
let p = primes.Item n
yield! prime (n + 1) (nextPrime (n + p) p (primes.Remove n))
else
yield n
yield! prime (n + 1) (primes.Add(n * n, n))
}
prime 2 Map.empty
This works very well, but sometimes I need to work with int64/BigInts as well. Is there a more clever way of reusing this code than providing another sequences like these:
let primesSeq64 = Seq.map int64 primesSeq
let primesBigInts = Seq.map (fun (x : int) -> BigInteger(x)) primesSeq
I've heard about modifying a code using "inline" and "LanguagePrimitives", but all I've found was connected with function while my problem is related to a value.
Moreover - I'd like to have a function that works with integer types and computes a floor of a square root.
let inline sqRoot arg = double >> Math.Sqrt >> ... ?
but I can't see a way of returning the same type as "arg" is, as Math.Sqrt returns a double. Again - is there anything better than reimplementing the logic that computes a square root by myself ?
So the general way to do this requires a function and languageprimitives - in your case everywhere you have 1 you write LanguagePrimitives.GenericOne which will produce 1 or 1.0 etc depending on what is required.
To get this to work, you need to create a function value - you can avoid this by doing something like:
let inline primesSeq() = ...
let primesintSeq = primesSeq() //if you use this as an int seq later the compiler will figure it out, otherwise you use
let specified : int seq = primesSeq()
I am not so sure about the sqrt case though - it probably depends on how hacky you are willing to make the solution.
A naïve implementation of generic sqRoot may go along these lines:
let sqRoot arg =
let inline sqrtd a = (double >> sqrt) a
let result = match box(arg) with
| :? int64 as i -> (sqrtd i) |> int64 |> box
| :? int as i -> (sqrtd i) |> int |> box
// cases for other relevant integral types
| _ -> failwith "Unsupported type"
unbox result
and then, checking in FSI:
> let result: int = sqRoot 4;;
val result : int = 2
> let result: int64 = sqRoot 9L;;
val result : int64 = 3L