Ben,
Thanks, changing "stream" to "stream apply" does solve the issue.
I tried to push it further little bit with the following code to see if
typed racket can support generic like Haskell or Scala:
#lang typed/racket
(require pfds/stream)
(define-type (OverFoldable A) (-> (Listof A) A))
(define-type (FibStreamCons A) (-> (Listof A) (Stream A)))
(define-type (FibStream A) (-> (OverFoldable A) (Listof A) (Stream A)))
(: sum (OverFoldable Number))
(define (sum xs) (apply + xs))
(: gfib_2 (All (A) (FibStream A)))
(define (gfib_2 f xs)
(: gfib_t (All (A) (FibStreamCons A)))
(define (gfib_t ys)
(stream-cons (last ys) (gfib_t (append (cdr ys) (list (f ys))))))
(stream-append (apply stream (drop-right xs 1)) (gfib_t xs)))
However, I got the following error message:
; /home/kiong-ge/Programming/Racket/typed_racket_test.rkt:28:61: Type
Checker: type mismatch
; expected: (Listof A)
; given: (Listof A)
; in: ys
But, according to this error message, expected and given types are exactly
the same, not sure how to deal with this issue.
Thanks,
Kiong-Gē.
On Monday, July 12, 2021 at 10:03:42 AM UTC-5 Ben Greenman wrote:
> On 7/11/21, Kiong-Gē Liāu <[email protected]> wrote:
> > Hi, in non-typed racket, I can define a generalized Fibonacci sequence
> >
> > X[n+k] = f(X[n], X[n+1], ...., X[n+k-1])
> >
> > using the following code
> >
> > #lang racket
> >
> > (require racket/stream)
> >
> > (define (gfib f xs)
> > (define (gfib_t xs)
> > (stream-cons (last xs) (gfib_t (append (cdr xs) (list (f xs))))))
> > (stream-append (drop-right xs 1) (gfib_t xs)))
> >
> > (define (sum xs) (apply + xs))
> > ;; Example of a (0, 1) initialized Fibonacci sequence
> > (define gfib20 (gfib sum '(0 1 )))
> >
> > But using typed racket, the following code
> >
> > #lang typed/racket
> >
> > (require pfds/stream)
> >
> > (define (sum [xs : (Listof Number)] ) (apply + xs))
> >
> > (define (gfib [f : (-> (Listof Number) Number)] [xs : (Listof Number)] )
> > (define (gfib_t [ys : (Listof Number)] )
> > (stream-cons (last ys) (gfib_t (append (cdr ys) (list (f ys))))))
> > (stream-append (stream (drop-right xs 1)) (gfib_t xs)))
> >
> > leads to error message
> >
> > ; /home/kiong-ge/Programming/Racket/typed_racket_test.rkt:8:11: Type
> > Checker: insufficient type information to typecheck. please add more type
> > annotations
> > ; in: gfib_t
> >
> > How should I set the type signature in the typed racket in order to get
> the
> > same result generated non-typed racket code ?
> >
> > Thanks,
> > Kiong-Ge.
>
> First, gfib_t needs a return type annotation. You can either add `:
> (Stream Number)` to the end of the line, or write a full signature
> above the define
>
> (: gfib_t (-> (Listof Number) (Stream Number)))
> (define (gfib_t ys)
>
> After this, the typechecker can run. But it finds a problem with
> stream-append. The issue here is that the two arguments to
> stream-append have different types. One contains lists of numbers and
> the other contains numbers.
>
> typed.rkt:11:2: Type Checker: Polymorphic function `stream-append'
> could not be applied to arguments:
> Argument 1:
> Expected: (Rec Stream (U (Boxof (U (-> (Pairof A Stream)) (Pairof
> A Stream))) Null))
> Given: (Rec x₀ (U (Boxof (U (-> (Pairof (Listof Number) x₀))
> (Pairof (Listof Number) x₀))) Null))
> Argument 2:
> Expected: (Rec Stream (U (Boxof (U (-> (Pairof A Stream)) (Pairof
> A Stream))) Null))
> Given: (Rec x₀ (U (Boxof (U (-> (Pairof Number x₀)) (Pairof
> Number x₀))) Null))
>
> in: (stream-append (stream (drop-right xs 1)) (gfib_t xs))
>
> Change (stream (drop-right xs 1)) to (apply stream (drop-right xs 1))
> and you should be OK.
>
> (It might be possible to call stream-append with a list and a stream
> --- like the untyped code does --- but I haven't figured out how to do
> that. Better stick with the Stream datatype.)
>
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