[racket] Another basic TR question

On Feb 13, 2014, at 2:56 PM, Vincent St-Amour wrote:

> At Thu, 13 Feb 2014 14:45:08 -0500,
> Bloch Stephen wrote:
>> Don't tell me the Zero I'm running into is the initial value of
>> for/sum's hidden accumulator....
> 
> Yes, that's where the Zero comes from.
> 
>> And even if there were a zero, shouldn't Zero be a subtype of Flonum?
> 
> Zero is the type of the exact integer 0, but the Flonum type only
> includes floating-point numbers. The two are not related by subtyping.

Yes, actually I figured that part out... but why is the accumulator initialized to something that might be the wrong type?

> You can use `assert' to check, at run-time, that you do always get a
> Flonum:
> 
>    (assert (for/sum: : Real [[ii : Index 300]]
>              pi)
>            flonum?)
> 
> This expression typechecks at type Flonum.

Hmm.  So just changing the annotation type from Flonum to Real does the trick?

for/sum: initializes its accumulator to an exact 0, which is of type Zero, which is a subtype of Real but not of Flonum.
It then adds pi, which is a Flonum, which is also a subtype of Real, and it has no problem proving the answer to be a Real (just not a Flonum).  Even though AFAIK anything plus a Flonum produces either a Flonum or an error.

I'm so confused....

Anyway, thanks!


Stephen Bloch
sbloch at adelphi.edu
GPG  key at http://adelphi.edu/sbloch/sbloch.pubkey.asc

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