[Haskell-cafe] Haskell is a declarative language? Let's see how easy it is to declare types of things.
alex.solla at gmail.com
Fri Apr 5 03:15:57 CEST 2013
On Thu, Apr 4, 2013 at 3:29 PM, Albert Y. C. Lai <trebla at vex.net> wrote:
> On 13-04-04 01:07 AM, wren ng thornton wrote:
>> When the quantifiers are implicit, we can rely on the unique human ability
>> to DWIM. This is a tremendous advantage when first teaching people about
>> mathematical concerns from a logical perspective. However, once people
>> move beyond the basics of quantification (i.e., schemata, rank-1
>> polymorphism, etc), things get really hairy and this has lead to no end of
>> quibbles in philosophy and semantics, where people seem perversely
>> attached to ill-specified and outdated logics.
>> On the other hand, with explicit quantification you can't rely on DWIM and
>> must teach people all the gritty details up front--- since the application
>> of those details is being made explicit. This is an extremely difficult
>> task for people who are new to symbolic reasoning/manipulation in the
>> first place. In my experience, it's better to get people fluently
>> comfortable with symbolic manipulations before even mentioning
> I agree with most of it. I disagree with the first two sentences. With
> only one variable, therefore only one implicit quantifier, and even being
> told that this quantifier is placed outermost, it is already hairy enough.
> The unique human ability to DWIM (do what *I* mean) as opposed to DWYM (do
> what *you* mean) can be relied upon for confusion, frustration, students
> and teachers being at each others' throats, and needing to quibble in
> semantics which is WDYM (what do you mean) afterall.
Students need to learn to do what the professor means. That is what they
are paying for.
Let me tell you a short story about the first college math class I ever
took. It was a course in introductory analysis, where we started by
constructing the natural numbers, and slowly introducing the field axioms,
and finally constructing R and C. Well, sometime during the first week, we
encountered "0", a symbol I had obviously seen before. And I used some
properties I knew about zero in a proof. My professor called me into his
office, and told me to treat the circular thing he was talking about in
class as, essentially, a symbol whose semantics we are /determining/ in
terms of the axioms introduced.
This is the very paradigm of "semantic quibbling" -- what does "0" MEAN?
It depends! And not just on the axioms in play, but also on the community
of language speakers/math doers, and the contexts in which they are
discussing a problem. (Indeed, a week later, I had proved enough about the
symbol 0 that it /BECAME/ the zero I knew and loved in high school.
> In IRC channel #haskell, beginners write like the following and ask why it
> is a type error:
> f :: Bool -> t
> f True = 'x'
> f False = 'y'
> You may think you know what's wrong, but you don't actually know until you
> know how to clarify to the beginners. Note: harping on the word "any" does
> not clarify, for the beginners exactly say this:
> "Yeah, t can be *any* type, therefore *I* am making it Char. Isn't that
> what *any* means?"
Indeed. And this confusion would continue to exist if the quantifier was
made explicit. Notice that the confusion is about what "any" means, and
not what "upside-down A" means, or what a "missing" upside-down A means.
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