[plt-scheme] macro question

On Jun 10, 2008, at 3:03 PM, Jos Koot wrote:

>>
>>> My personal opinion is that types do not significantly improve  
>>> readability of programs. A good similarity between data  
>>> structure  and the structure of the procedures acting on these  
>>> data is far  more important, I think (this I did experience, but  
>>> not invent by  myself, of course)
>>
>> If your comments on data defs and your program organization  
>> disagree, which one is right? Who is going to point out the  
>> discrepancy? If you  had types, the type checker would. That's how  
>> types contribute to  readability (among other things).
>
> Of course it is nice having a type checker pointing to the  
> discrepancy. I agree that explicit formulation of the intentions of  
> the programmer can improve readability, but only with the condition  
> that the code is not overloaded with an abundance of lines that  
> interrupt the story of the algorithms. When possible, I try to  
> separate algorithms from data representation. I.e. When I do a  
> serious job, I try to write algorithms as abstractions over the  
> representation. This is called ADT if I am not mistaken :)


Before we talk too abstractly here, let's look at an example:

UNTYPED

> #lang scheme
>
> ;; An A is one of:
> ;; -- Number
> ;; -- Boolean
> ;; -- (cons A A)
>
> ;; A -> Number
> ;; compute the sum of all numbers in the tree
> (define (Sigma tree)
>   (cond
>     [(number? tree) tree]
>     [(boolean? tree) 0]
>     [else (+ (Sigma (car tree)) (Sigma (cdr tree)))]))
>
> (= (Sigma (cons (cons #t 5) 0)) 5)

TYPED:

> #lang typed-scheme
>
> (define-type-alias A (mu A (U Number Boolean (cons A A))))
>
> (: Sigma (A -> Number))
> ;; compute the sum of all numbers in the tree
> (define (Sigma tree)
>   (cond
>     [(number? tree) tree]
>     [(boolean? tree) 0]
>     [else (+ (Sigma (car tree)) (Sigma (cdr tree)))]))
>
> (= (Sigma (cons (cons #t 5) 0)) 5)
>


In general, Typed Scheme is as compact as untyped Scheme in HtDP  
style. And it is checked for you. -- Matthias