Lexicographic sorting in F#

Question

I am playing with a toy problem (Convex hull identification) and needed lexicographic sorting twice already. One of the cases was given a list of type Point = { X: float; Y: float }, I would like to sort by X coordinate, and in case of equality, by Y coordinate.
I ended up writing the following:

let rec lexiCompare comparers a b =
   match comparers with
   [ ] -> 0
   | head :: tail -> 
      if not (head a b = 0) then head a b else
      lexiCompare tail a b 

let xComparer p1 p2 = 
   if p1.X > p2.X then 1 else
   if p1.X < p2.X then -1 else
   0

let yComparer p1 p2 = 
   if p1.Y > p2.Y then 1 else
   if p1.Y < p2.Y then -1 else
   0

let coordCompare =
   lexiCompare [ yComparer; xComparer ]

Which allows me to do

let lowest (points: Point list) =
   List.sortWith coordCompare points 
   |> List.head

So far, so good. However, this feels a bit heavy-handed. I have to create specific comparers returning -1, 0 or 1, and so far I can't see a straightforward way to use this in cases like List.minBy. Ideally, I would like to do something along the lines of providing a list of functions that can be compared (like [(fun p -> p.X); (fun p -> p.Y)]) and do something like lexicographic min of a list of items supporting that list of functions.

Is there a way to achieve this in F#? Or am I thinking about this incorrectly?

Answer 1

Is there a way to achieve this in F#? Or am I thinking about this incorrectly?

F# does this for you automatically when you define a record type like yours:

> type Point = { X: float; Y: float };;
type Point =
  {X: float;
   Y: float;}

You can immediately start comparing values. For example, defining a 3-element list of points and sorting it into lexicographic order using the built-in List.sort:

> [ { X = 2.0; Y = 3.0 }
    { X = 2.0; Y = 2.0 }
    { X = 1.0; Y = 3.0 } ]
  |> List.sort;;
val it : Point list = [{X = 1.0;
                        Y = 3.0;}; {X = 2.0;
                                    Y = 2.0;}; {X = 2.0;
                                                Y = 3.0;}]

Note that the results were sorted first by X and then by Y.

You can compare two values of any comparable type using the built-in compare function.

If you want to use a custom ordering then you have two options. If you want to do all of your operations using your custom total order then it belongs in the type definition as an implementation of IComparable and friends. If you want to use a custom ordering for a few operations then you can use higher-order functions like List.sortBy and List.sortWith. For example, List.sortBy (fun p -> p.Y, p.X) will sort by Y and then X because F# generates the lexicographic comparison over 2-tuples for you (!).

This is one of the big advantages of F#.