# [plt-scheme] Problem with Contracts - HtDP 21.1.3

 From: David Yrueta (dyrueta at gmail.com) Date: Thu Nov 6 22:53:42 EST 2008 Previous message: [plt-scheme] SLaTeX: getting it to work Next message: [plt-scheme] Problem with Contracts - HtDP 21.1.3 Messages sorted by: [date] [thread] [subject] [author]

```If function "natural-f" --
;apply function f to x n times with a base case of TH where n=0
;(check-expect (natural-f cons 'x empty 5) (list 'x 'x 'x 'x 'x))
;(check-expect (natural-f + 1 5 9) 14)
(define (natural-f f x TH n)
(cond
[(zero? n) TH]
[else (f x
(natural-f f x TH (sub1 n) ))]))

-- properly abstracts over the the functions

;; copy : *N* X  ->  (listof X);; to create a list that contains;; obj n times
(define (copy n obj)
(cond
[(zero? n) empty]
[else (cons obj
(copy (sub1 n) obj))]))

;; n-adder : *N* number  ->  number;; to add n to x using;; (+ 1 ...) only
(cond
[(zero? n) x]
[else (+ 1

--then what is the general contract for "natural-f"?

Considering "natural-f" as an abstraction of function "n-adder" above, the
resulting contract would be:
(number number -> number) number number number -> number
(ex. (check-expect (natural-f + 1 5 9) 14)

But what would the contract for "natural-f" be if it was viewed as an
abstraction of function "copy?"
(ex.(check-expect (natural-f cons 'x empty 5) (list 'x 'x 'x 'x 'x))

In that case, argument "f" would take the value of "cons," so the question
(for me) comes down to how to represent the primitive "cons" as a function
type within a contract.

Is "cons" represented as (X Y -> Y)
where X is any Scheme ITEM, Y is the Scheme-value list, and the result is
basic type Y (Scheme-value list)?

Or is "cons" represented as  (X list -> (listof X)
where X is any Scheme ITEM, "list" is Scheme-value list, and the result is
defined type (listof X)?

The difference between the two contracts appears to be in the output types.
The first output type is basic, which is consistent with the contract
output for "n-adder"; the second output type is defined, which conflicts
with "n-adder."  Avoiding conflict means choosing the first representation
of "cons" in place of f in "natural-f"'s contract. S my guess is that the
proper general contract for "natural-f" would be:

;natural-f: (X Y -> Y) X Y number -> Y

Is this right? If not, where am I going wrong?

Thanks,
Dave
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