Re: [Haskell-cafe] What is a number. (Was: Num instances for 2-dimensional types)
On Mon, Oct 5, 2009 at 11:02 AM, Sönke Hahn sh...@cs.tu-berlin.de wrote: On 5 Oct 2009, at 21:06, Lennart Augustsson wrote: OK, just pairs have no arithmetic, but one way of defining arithmetic is to treat the pairs as complex numbers. Or as mantissa and exponent. Or as something else. So there's nothing wrong, IMO, to make pairs an instance of Num if you so desire. (Though I'd probably introduce a new type.) I was looking for one intuitive way of instantiating pairs of numbers as Num. One where i wouldn't have to look in the documentation to remember what (+) does. So considering all these examples of what pairs of numbers could be, i agree with Miguel Mitrofanov: It's something that should not be done. Two questions remain, i think: 1. How can i have some notion of addition and subtraction for something that i don't want to put in the Num class? That's easy: I could just write a class that defines binary operators (like (+~) and (-~), for example). I don't get the fanciness of (+), but that's okay. I don't know how well it works in practice, but you could hide the prelude in your module and then import it qualified. This would allow your module to redefine the normal symbols as the operators you want them to be. 2. How can i use numeric literals to construct values, whose types are not in the Num class? This I don't know how to do without a pre-processor or maybe Template Haskell would work. Haskell could provide a class IsNumber (like IsString for string literals). Is that something we would want? Seems like IsBoolean would also be useful if you went this route. And perhaps, IsList :) I'm sure we could think of more. I can see how they would be handy for anyone making an eDSL, especially if combine with view patterns. Jason ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] What is a number. (Was: Num instances for 2-dimensional types)
On Mon, 5 Oct 2009, Jason Dagit wrote: 2. How can i use numeric literals to construct values, whose types are not in the Num class? Numeric literals are treated as Integer or Rational, and are then converted with the function fromInteger or fromRational, respectively, to the required type. Whatever fromInteger function is in scope, will be used. If fromInteger is in a class other than Num (in NumericPrelude it is Ring, but it can be also a function that is not a class method), then number literals have a type like: 2 :: MyNumClass a = a ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] What is a number. (Was: Num instances for 2-dimensional types)
Hi,
On Tue, Oct 6, 2009 at 2:37 AM, Henning Thielemann
lemm...@henning-thielemann.de wrote:
Numeric literals are treated as Integer or Rational, and are then converted
with the function fromInteger or fromRational, respectively, to the required
type. Whatever fromInteger function is in scope, will be used. If
fromInteger is in a class other than Num (in NumericPrelude it is Ring, but
it can be also a function that is not a class method), then number literals
have a type like:
2 :: MyNumClass a = a
This is only the case if you use GHC's NoImplicitPrelude extension,
otherwise the fromInteger of the Prelude is used, even if it is not
in scope. Here is an example:
module A where
boolLit :: Integer - Bool
boolLit 0 = False
boolLit _ = True
{-# LANGUAGE NoImplicitPrelude #-}
module Main where
import A(boolLit)
import Prelude(Integer,Bool,print)
fromInteger :: Integer - Bool
fromInteger = boolLit
main = print 0
Note that 0 means different things in the different modules!
-Iavor
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Re: [Haskell-cafe] What is a number. (Was: Num instances for 2-dimensional types)
jerzy.karczmarc...@info.unicaen.fr wrote: American people will call it a discussion about semantics, and we, European will not understand why this word is used in a pejorative context... Semantics *should* be a pejorative word unless it refers to something formally specified, and preferably executable or machine-checkable. Those subtle Contintental critics of informal semantics, namely Derrida, Irigaray, et al, showed us why. ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] What is a number. (Was: Num instances for 2-dimensional types)
Just pairs have no natural arithmetic upon them. Exactly my point. BTW. the missing term of M.M. is DUAL NUMBERS. Remembered this already. Thanks anyway. ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] What is a number. (Was: Num instances for 2-dimensional types)
OK, just pairs have no arithmetic, but one way of defining arithmetic is to treat the pairs as complex numbers. Or as mantissa and exponent. Or as something else. So there's nothing wrong, IMO, to make pairs an instance of Num if you so desire. (Though I'd probably introduce a new type.) On Mon, Oct 5, 2009 at 6:46 PM, Miguel Mitrofanov miguelim...@yandex.ru wrote: Just pairs have no natural arithmetic upon them. Exactly my point. BTW. the missing term of M.M. is DUAL NUMBERS. Remembered this already. Thanks anyway. ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] What is a number. (Was: Num instances for 2-dimensional types)
And I agree that sometimes it can be suitable. But simply defining an instance of Num without a single word on the problem one is trying to solve is not just pointless. It's something that should not be done. On 5 Oct 2009, at 21:06, Lennart Augustsson wrote: OK, just pairs have no arithmetic, but one way of defining arithmetic is to treat the pairs as complex numbers. Or as mantissa and exponent. Or as something else. So there's nothing wrong, IMO, to make pairs an instance of Num if you so desire. (Though I'd probably introduce a new type.) On Mon, Oct 5, 2009 at 6:46 PM, Miguel Mitrofanov miguelim...@yandex.ru wrote: Just pairs have no natural arithmetic upon them. Exactly my point. BTW. the missing term of M.M. is DUAL NUMBERS. Remembered this already. Thanks anyway. ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] What is a number. (Was: Num instances for 2-dimensional types)
On 5 Oct 2009, at 21:06, Lennart Augustsson wrote: OK, just pairs have no arithmetic, but one way of defining arithmetic is to treat the pairs as complex numbers. Or as mantissa and exponent. Or as something else. So there's nothing wrong, IMO, to make pairs an instance of Num if you so desire. (Though I'd probably introduce a new type.) I was looking for one intuitive way of instantiating pairs of numbers as Num. One where i wouldn't have to look in the documentation to remember what (+) does. So considering all these examples of what pairs of numbers could be, i agree with Miguel Mitrofanov: It's something that should not be done. Two questions remain, i think: 1. How can i have some notion of addition and subtraction for something that i don't want to put in the Num class? That's easy: I could just write a class that defines binary operators (like (+~) and (-~), for example). I don't get the fanciness of (+), but that's okay. 2. How can i use numeric literals to construct values, whose types are not in the Num class? Haskell could provide a class IsNumber (like IsString for string literals). Is that something we would want? BTW, interesting discussion, thanks! Sönke On Monday 05 October 2009 07:24:37 pm Miguel Mitrofanov wrote: And I agree that sometimes it can be suitable. But simply defining an instance of Num without a single word on the problem one is trying to solve is not just pointless. It's something that should not be done. On Mon, Oct 5, 2009 at 6:46 PM, Miguel Mitrofanov miguelim...@yandex.ru wrote: Just pairs have no natural arithmetic upon them. Exactly my point. BTW. the missing term of M.M. is DUAL NUMBERS. Remembered this already. Thanks anyway. ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
