Looking for idiomatic way to represent very similar but different data types

[making-a-racket]

Hello. I have a project where I am needing to represent vectors (in the mathematical sense), points, and colors. Both the vectors and points will be 3D. I'm having trouble knowing what's an idiomatic way to represent and interact with data types that are similar but different.

In general, I could simply all represent them with a list or vector (in the Racket sense). So I could have:

(define (vector i j k) #(i j k))

(define (point x y z) #(x y z))

Then I could readily use the existing vector functions, such as vector-map without having to define my own. But I don't super like this because I have to define my own accessor functions like vector-i and point-y and also don't get predicates like vector? for free.

Another way is that I could use structs, but then I'm stuck implementing things myself and across the structs. To avoid the latter point, I could use pattern matching. So something like:

(struct vector (i j k))

(struct point (x y z))

(define (tuple-map proc tuple)

  (match tuple

    [(struct vector (i j k)) (vector (proc (vector-i tuple))

                                     (proc (vector-j tuple))

                                     (proc (vector-k tuple)))]

    [(struct point (x y z)) (point (proc (point-x tuple))

                                   (proc (point-y tuple))

                                   (proc (point-z tuple)))]

    [(struct color (r g b)) (color (proc (color-r tuple))

                                   (proc (color-g tuple))

                                   (proc (color-b tuple)))]))

But of course, this map doesn't take multiple tuples. And this feels awkward, because I'll need to implement other things, like fold. Map and fold would be used in defining new operators on vectors and points, like addition, normalization (for vectors only), etc.

The ideal thing would be that I could define a struct for these types, that had the accessor functions like vector-i and predicates likes vector? but was actually represented by a vector (in the Racket sense) underneath the hood. Does something like this exist in Racket (not classes please).

In F#, I did this same thing using F#'s records for the vector, point, and color data types, and they inherited an ITuple interface (F#'s immutable, functional data types can implement interfaces). Can Racket's stucts inherit from interfaces? Is there something I can do with generics?

Thanks for any help on this design.

[jackh...@gmail.com]

I'd suggest just going with the structs and making them transparent. It's only three structs and only with a handful of fields, abstracting over them with map and fold doesn't seem worth the added complexity IMO. But if you'd really like to map and fold over structs, I highly recommend using macros, `syntax-parse` and the struct-id syntax class to do so:

(require (for-syntax syntax/parse/class/struct-id)
         syntax/parse/define)

(define-simple-macro (struct-map type:struct-id instance-expr:expr map-function-expr:expr)
  (let ([map-function map-function-expr]
        [instance instance-expr])
    (type.constructor-id (map-function (type.accessor-id instance)) ...)))

(struct point (x y z) #:transparent)

;; Outputs (point 2 3 4)
(struct-map point (point 1 2 3) add1)

[making-a-racket]

Thanks for the suggestion and for the macro implementation. I'll have to pour over that a bit.

I wanted to do map because I wanted to make it easy to idiomatically implement addition and other such operators on my data types such that they accept arbitrary amounts of arguments and provide the map for other uses.

So that's why the vector (in the Racket sense) is the most simple option in that respect, since I can trivially do:

(define (sum-vector v)
    (apply + (vector->list v)))

(define (vector+ . vs)
    (apply vector-map + vs)) 

(define (vector-i v)

    (vector-ref v 0))

;; and so on

The only think I don't get there are my wanted datatypes and associated predicates, since vectors, points, and colors would all be Racket vectors.

I could almost do structs with a fourth optional argument that holds a Racket vector that never gets used explicitly by the "user" and build helper functions to properly update it, which is then used to build all the operator and other such functions.

If I just do structs as I originally notated, how do you suggest I implement things like vector+ to take in arbitrary amounts of arguments?

[making-a-racket]

Apologies. By fourth optional argument, I meant a fourth field with the #auto field option. I'm experimenting with this now.

[making-a-racket]

Turns out that I don't see a way to calculate the #:auto-value using the constructor fields, so I don't see how to make something like

(struct test (x y z [data #:auto])

  #:auto-value #(x y z))

work.

So I've decided to go with something like this:

(struct color (r g b) #:transparent)

(struct vector (i j k) #:transparent)

(struct point (x y z) #:transparent)

(define/contract (tuple-map-elementwise proc tuple)

  (-> (-> real? real?) (or/c vector? point? color?) (or/c vector? point? color?))

  (match tuple

    [(struct vector (i j k)) (vector (proc (vector-i tuple))

                                     (proc (vector-j tuple))

                                     (proc (vector-k tuple)))]

    [(struct point (x y z)) (point (proc (point-x tuple))

                                   (proc (point-y tuple))

                                   (proc (point-z tuple)))]

    [(struct color (r g b)) (color (proc (color-r tuple))

                                   (proc (color-g tuple))

                                   (proc (color-b tuple)))]))

(define/contract (tuple-map-pairwise proc tuple1 tuple2)

  (-> (-> real? real? real?) (or/c vector? point? color?) (or/c vector? point? color?) (or/c vector? point? color?))

  (match (list tuple1 tuple2)

    [(list (struct vector (i1 j1 k1)) (struct vector (i2 j2 k2)))

     (vector (proc (vector-i tuple1) (vector-i tuple2))

             (proc (vector-j tuple1) (vector-j tuple2))

             (proc (vector-k tuple1) (vector-k tuple2)))]

    [(list (struct point (x1 y1 z1)) (struct point (x2 y2 z2)))

     (point (proc (point-x tuple1) (point-x tuple2))

            (proc (point-y tuple1) (point-y tuple2))

            (proc (point-z tuple1) (point-z tuple2)))]

    [(list (struct color (r1 g1 b1)) (struct color (r2 g2 b2)))

     (color (proc (color-r tuple1) (color-r tuple2))

            (proc (color-g tuple1) (color-g tuple2))

            (proc (color-b tuple1) (color-b tuple2)))]))

(define (tuple-op-by-constant op tuple c)

  (tuple-map-elementwise (λ (e) (op e c)) tuple))

(define (tuple-op-pairwise op t1 t2 . tuples)

  (cond [(empty? tuples) (tuple-map-pairwise op t1 t2)]

        [else (apply tuple-op-pairwise op

                     (tuple-map-pairwise op t1 t2)

                     (car tuples)

                     (cdr tuples))]))

(define (vector+c v c)

  (tuple-op-by-constant + v c))

(define (vector*c v c)

  (tuple-op-by-constant * v c))

(define (vector+ u v . vectors)

  (apply tuple-op-pairwise + u v vectors))

(define (vector- u v . vectors)

  (apply tuple-op-pairwise - u v vectors))

Then I'll do something similar for points and colors. This library will probably be converted to Typed Racket, so the contracts are only temporary.

This seems to be the cleanest solution I think, and it's actually quite similar to the F# code I've written for the same project.

I know this seems simple, but wanted to check on people's thoughts on idiomatic ways in Racket, and to make sure I wasn't missing some secret sauce of structs or something else.

[jackh...@gmail.com]

To make your vector+ operation take an arbitrary number of arguments, this is what I'd do:

(define (vector+ . vectors)
  (vector
    (for/sum ([v (in-list vectors)]) (vector-i v))
    (for/sum ([v (in-list vectors)]) (vector-j v))
    (for/sum ([v (in-list vectors)]) (vector-k v))))

(module+ test
  (test-case "vector+"
    (check-equal? (vector+) (vector 0 0 0))
    (check-equal? (vector+ (vector 1 2 3)) (vector 1 2 3))
    (check-equal? (vector+ (vector 1 2 3) (vector 4 5 6)) (vector 5 7 9))))

I can see some value in abstracting over this, if you've got a lot of structs with mathy variable-arity operations on them. I personally might try to do something with reducers. I'm not fully sure how I'd go about it though. Rather than experiment with that I'd probably just prefer to write the boring boilerplate code.