Burning more bridges (mostly numeric ones)

[Ivan Lazar Miljenovic]

On 23 March 2014 11:58, Bart Massey <bart at cs.pdx.edu> wrote:
> My complaint with numeric-prelude is that it doesn't (and arguably
> can't) fix the problems that for me make Haskell borderline usable for
> actual engineering work involving actual "normal" numbers, and
> genuinely somewhat unusable for teaching: Off the top of my head:
>
> * The lack of implicit conversions (except for the weird defaulting of
> literals, which means that I am constantly writing `fromIntegral` and
> `toRealFrac` in places where there is only one reasonable choice of
> type conversion, and occasionally having things just malfunction
> because I didn't quite understand what these conversion functions
> would give me as a result.
>
>     Prelude> 3 + 3.5
>     6.5
>     Prelude> let x = 3
>     Prelude> x + 3.5
>
>     <interactive>:4:5:
>         No instance for (Fractional Integer) arising from the literal `3.5'
>         Possible fix: add an instance declaration for (Fractional Integer)
>         In the second argument of `(+)', namely `3.5'
>         In the expression: x + 3.5
>         In an equation for `it': it = x + 3.5
>     Prelude>
>
> I mean, seriously? We expect newbies to just roll with this kind of thing?

Isn't this more of a ghci issue than a Haskell issue?

I actually think it's good behaviour that - in actual code, not
defaulted numerals in ghci - we need to explicitly convert between
types rather than have a so-far-Integer-value automagically convert to
Double.

>
> Even worse, the same sort of thing happens when trying to add a
> `Data.Word.Word` to an `Integer`. This is a totally safe conversion if
> you just let the result be `Integer`.

What would be the type of such an operation be? I think we'd need some
kind of new typeclass to denote the "base value", which would make the
actual type signature be much more hairy.

>
> * The inability of Haskell to handle unary negation sanely, which
> means that I and newbies alike are constantly having to figure things
> out and parenthesize. From my observations of students, this is a huge
> barrier to Haskell adoption: people who can't write 3 + -5 just give
> up on a language. (I love the current error message here, "cannot mix
> `+' [infixl 6] and prefix `-' [infixl 6] in the same infix
> expression", which is about as self-diagnosing of a language failing
> as any error message I've ever seen.)

This is arguably the fault of mathematics for overloading the - operator :p

>
> * The multiplicity of exponentiation functions, one of which looks
> exactly like C's XOR operator, which I've watched trip up newbies a
> bunch of times. (Indeed, NumericPrelude seems to have added more of
> these, including the IMHO poorly-named (^-) which has nothing to do
> with numeric negation as far as I can tell. See "unary negation"
> above.)
>
> * The incredible awkwardness of hex/octal/binary input handling, which
> requires digging a function with an odd and awkward return convention
> (`readHex`) out of an oddly-chosen module (or rolling my own) in order
> to read a hex value. (Output would be just as bad except for
> `Text.Printf` as a safety hatch.) Lord knows what you're supposed to
> do if your number might have a C-style base specifier on the front,
> other than the obvious ugly brute-force thing?
>
> * Defaulting numeric types with "-Wall" on producing scary warnings.
>
>     Prelude> 3 + 3
>
>     <interactive>:2:3: Warning:
>         Defaulting the following constraint(s) to type `Integer'
>           (Num a0) arising from a use of `+'
>         In the expression: 3 + 3
>         In an equation for `it': it = 3 + 3
>
>     <interactive>:2:3: Warning:
>         Defaulting the following constraint(s) to type `Integer'
>           (Num a0) arising from a use of `+' at <interactive>:2:3
>           (Show a0) arising from a use of `print' at <interactive>:2:1-5
>         In the expression: 3 + 3
>         In an equation for `it': it = 3 + 3
>     6
>
> and similarly for 3.0 + 3.0. If you can't even write simple addition
> without turning off or ignoring warnings, well, I dunno. Something.
> Oh, and try to get rid of those warnings. The only ways I know are `3
> + 3 :: Integer` or `(3 :: Integer) + 3`, both of which make code read
> like a bad joke.

So above you didn't like how ghci defaulted to types too early, now
you're complaining that it's _not_ defaulting?  Or just that it gives
you a warning that it's doing the defaulting?

>
> Of course, if you write everything to take specific integral or
> floating types rather than `Integral` or `RealFloat` or `Num` this
> problem mostly goes away. So everyone does, turning potentially
> general code into needlessly over-specific code.
>
>
> Not sure I'm done, but running out of steam. But yeah, while I'm fine
> with fancy algebraic stuff getting fixed, I'd also like to see simple
> grade-school-style arithmetic work sanely. That would let me teach
> Haskell more easily as well as letting me write better, clearer, more
> correct Haskell for that majority of my real-world problems that
> involve grade-school numbers.
>
> --Bart
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-- 
Ivan Lazar Miljenovic
Ivan.Miljenovic at gmail.com
http://IvanMiljenovic.wordpress.com