Pattern matching as computation

[David Storrs]

This works:

(match (vector 1 2 3 4)

 [(vector a b (app add1 c) d)

  (list a b c d)])

; => '(1 2 4 4)

Suppose instead I wanted to have a pattern like so (this does not work):

(match (vector 1 2 3 4)

  [(vector a (app + b ..2 x) c) (list a b c x)]

; => '(1 (2 3) 4 5))  ;  NB:  does not work

Is there a way to do this?

Less trivially, I'd like to be able to do something like this:

#lang racket

(struct person (name age) #:prefab)
(struct horse (color owner) #:prefab)

; The following does not work

(match (vector 'brown 'bob 23)
  [(vector the-color (app (curry apply person) args ... the-owner))

   (horse the-color the-owner)])

I've been through the pattern matching docs in some detail and tried various things, but my brain-fu is weak.

[Eric Griffis]

On Thu, Jun 27, 2019 at 11:56 AM David Storrs <david....@gmail.com> wrote:
>
> Suppose instead I wanted to have a pattern like so (this does not work):
>
> (match (vector 1 2 3 4)
>   [(vector a (app + b ..2 x) c) (list a b c x)]
> ; => '(1 (2 3) 4 5))  ;  NB:  does not work

We have a few problems here.

The pattern (vector a ? c) does not match the shape of the val-expr
(vector 1 2 3 4).

In the second sub-pattern (app + b ..2 x), Racket complains `..2' is an
"incorrect use of ... in pattern" because every sub-pattern of `app' must
independently match the result of (+ 2).

To get the expected result '(1 (2 3) 4 5) from the actual result (list a b
c x), we'd need the following bindings:

a --> 1
b --> '(2 3)
c --> 4
x --> 5

At this point, I'm not sure what you're trying to do. Maybe you're trying
to bind `b' to '(2 3), then `x' with the sum (+ 2 3), then `c' with 4.

Here's one way to do it from within a single pattern:

(match (vector 1 2 3 4)

  [(and (vector a _ _ c)
        (app (λ (vec)
               (match vec
                 [(vector _ p q _)
                  (list (list p q) (+ p q))]))
             (list b x)))
   (list a b c x)])

> Less trivially, I'd like to be able to do something like this:
>
> #lang racket
> (struct person (name age) #:prefab)
> (struct horse (color owner) #:prefab)
>
> ; The following does not work
> (match (vector 'brown 'bob 23)
>   [(vector the-color (app (curry apply person) args ... the-owner))
>    (horse the-color the-owner)])

Here's an adaptation of the above technique that works:

(match (vector 'brown 'bob 23)

  [(and (vector the-color _ _)
        (app (λ (vec)
               (match vec
                 [(vector _ name age)
                  (person name age)]))

             the-owner))
   (horse the-color the-owner)])

Incidentally, Algebraic Racket is designed for this:

#lang algebraic/racket/base

(require (prefix-in algebraic- algebraic/racket/base/forms))

(algebraic-case (vector 1 2 3 4)
  [#(a p q c)
   #:with b (list p q)
   #:with x (+ p q)
   (list a b c x)])

(algebraic-case (vector 'brown 'bob 23)
  [#(the-color name age)
   #:with the-owner (person name age)
   (horse the-color the-owner)])

If a #:with directive fails, the overall match fails:

(algebraic-case (vector 'brown 'bob 23)
  [#(the-color name age)
   #:with the-owner #f
   #:with (person _ _) the-owner
   (horse the-color the-owner)])

Eric

[David Storrs]

On Thu, Jun 27, 2019 at 5:13 PM Eric Griffis <ded...@gmail.com> wrote:

On Thu, Jun 27, 2019 at 11:56 AM David Storrs <david....@gmail.com> wrote:
>

> Suppose instead I wanted to have a pattern like so (this does not work):
>
> (match (vector 1 2 3 4)
>   [(vector a (app + b ..2 x) c) (list a b c x)]
> ; => '(1 (2 3) 4 5))  ;  NB:  does not work

We have a few problems here.

The pattern (vector a ? c) does not match the shape of the val-expr
(vector 1 2 3 4).

In the second sub-pattern (app + b ..2 x), Racket complains `..2' is an
"incorrect use of ... in pattern" because every sub-pattern of `app' must
independently match the result of (+ 2).

To get the expected result '(1 (2 3) 4 5) from the actual result (list a b
c x), we'd need the following bindings:

a --> 1
b --> '(2 3)
c --> 4
x --> 5

At this point, I'm not sure what you're trying to do. Maybe you're trying
to bind `b' to '(2 3), then `x' with the sum (+ 2 3), then `c' with 4.

Here's one way to do it from within a single pattern:

(match (vector 1 2 3 4)

  [(and (vector a _ _ c)
        (app (λ (vec)
               (match vec
                 [(vector _ p q _)
                  (list (list p q) (+ p q))]))
             (list b x)))

   (list a b c x)])

> Less trivially, I'd like to be able to do something like this:
>
> #lang racket
> (struct person (name age) #:prefab)
> (struct horse (color owner) #:prefab)
>
> ; The following does not work
> (match (vector 'brown 'bob 23)
>   [(vector the-color (app (curry apply person) args ... the-owner))
>    (horse the-color the-owner)])

Here's an adaptation of the above technique that works:

(match (vector 'brown 'bob 23)

  [(and (vector the-color _ _)
        (app (λ (vec)
               (match vec
                 [(vector _ name age)
                  (person name age)]))

             the-owner))
   (horse the-color the-owner)])

Makes sense -- it's two matches,  but still within one sexp.  Thanks.

Incidentally, Algebraic Racket is designed for this:

#lang algebraic/racket/base

(require (prefix-in algebraic- algebraic/racket/base/forms))

(algebraic-case (vector 1 2 3 4)
  [#(a p q c)
   #:with b (list p q)
   #:with x (+ p q)
   (list a b c x)])

(algebraic-case (vector 'brown 'bob 23)
  [#(the-color name age)
   #:with the-owner (person name age)
   (horse the-color the-owner)])

If a #:with directive fails, the overall match fails:

(algebraic-case (vector 'brown 'bob 23)
  [#(the-color name age)
   #:with the-owner #f
   #:with (person _ _) the-owner
   (horse the-color the-owner)])

That is drop-dead sexy.  Thanks, Eric.

Eric

[Sorawee Porncharoenwase]

If you want only one match, it seems what you really want is ~seq-like form from syntax/parse. E.g.,

#lang racket

(require syntax/parse)

(define ->value syntax->datum)

(define (apply-lift op args)
  (datum->syntax #f (apply op (->value args))))

(syntax-parse (vector 1 2 3 4)
  [#(a {~and {~seq {~between b 2 2} ...}
             {~bind [x (apply-lift + #'(b ...))]}} c)
   (->value #'(a (b ...) c x))])
;; => '(1 (2 3) 4 5)

(struct person (name age) #:prefab)
(struct horse (color owner) #:prefab)

(syntax-parse (vector 'brown 'bob 23)
  [#(the-color {~and {~seq args ...}
                     {~bind [the-owner (apply-lift person #'(args ...))]}})
   (->value (apply-lift horse #'(the-color the-owner)))])
;; => '#s(horse brown #s(person bob 23))

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[David Storrs]

Oh, neat.  Thank you, Sorawee.