At Thu, 13 Feb 2014 16:22:35 -0500, Bloch Stephen wrote: > > [1 <multipart/signed (7bit)>] > [1.1 <multipart/alternative (7bit)>] > [1.1.1 <text/plain; us-ascii (quoted-printable)>] > > On Feb 13, 2014, at 2:51 PM, Sam Tobin-Hochstadt wrote: > > >> (for/sum: : Flonum [[ii : Index 300]] > >> pi) > >> > >> and I get the type error "Expected Flonum, but got Zero". Where is there a > >> zero anywhere in this code? And even if there were a zero, shouldn't Zero > >> be a subtype of Flonum? > >> > >> Don't tell me the Zero I'm running into is the initial value of for/sum's > >> hidden accumulator.... > > > > Unfortunately, that's exactly what I'm going to tell you. Typed > > Racket isn't smart enough to know that the initial value is never > > used, and so 0 is thought to be a possibility. > > Doesn't that make for/sum: useless for anything other than exact integers?
`for/sum:' is also useful for any return type that includes exact integers (well, that include at least exact zero), such as `Real'. `Flonum' (and `Single-Flonum') are the only types for which it won't work. > Couldn't for/sum: initialize its accumulator to a Real-Zero rather > than the overly-specified type Zero? (That would rule out complexes, > but it would be a big step in the right direction.) (Should there be > a Complex-Zero type?) > > Even better, could for/sum: look at the annotation type and decide > what initial value (0 or #i0.0) to use? That would solve this problem, but would have some potentially undesirable side effects. For example, the return value of `for/sum:' of an empty sequence would depend on the type annotation. This would also be a divergence from untyped Racket's behavior, which Typed Racket aims to always be consistent with. At Thu, 13 Feb 2014 16:30:50 -0500, Bloch Stephen wrote: > On Feb 13, 2014, at 2:56 PM, Vincent St-Amour wrote: > > 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? Yes. The `Real' type includes integers as well as floating point numbers (and also exact rationals (i.e. fractions)). > 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). Exactly. > Even though AFAIK anything plus a Flonum produces either a Flonum or > an error. That's true for addition (but not for, say, multiplication). However, as far as the typechecker knows, there may never actually be any additions performed. If the input sequence is empty, the initial value of the accumulator will get returned right away. In your case, that can't happen, but the typechecker doesn't know that. > I'm so confused.... If you need help navigating types, Typed Racket provides some type exploring facilities: http://doc.racket-lang.org/ts-reference/Exploring_Types.html You can do things like querying a function's type to know, say, the return type you would get given argument types, and vice versa. You can also expand union types (like `Real') to see what they contain. For a more detailed description of the design principles of the Typed Racket numeric tower, we wrote a paper on the topic: http://www.ccs.neu.edu/racket/pubs/padl12-stff.pdf Vincent ____________________ Racket Users list: http://lists.racket-lang.org/users
