Re: Domains? [Re: r28597 - docs/Perl6/Spec/S32-setting-library]
On Tue, 13 Oct 2009 09:21 +0200, "Michael Zedeler" wrote: > 'a' .. 'z' followed by 'ä', 'ö', 'å' (Swedish) 'a' .. 'z', 'å', 'ä', 'ö' (Finnish) 'a' .. 's', 'š', 'z', 'ž', 't' .. 'w', 'õ', 'ä', 'ö', 'ü', 'x', 'y' (Estonian) So yes, you are definitely on the right track with Domains. Regards, Ville Koskinen
Domains? [Re: r28597 - docs/Perl6/Spec/S32-setting-library]
yary wrote: ... Also, the domain should define how to compare objects and could provide details about whether the set is finite, countable or uncountable. ... Sounds like a role "Domain" that provides methods (off the top of my head)- ordering - returns Nil if the domain is unordered, or a method implementing "cmp" if it is ordered succ, pred- returns Nil if the domain is uncountable, or method implementing "next item", "prior item" if countable. Exactly. count - returns Inf if it's an infinite domain, or count of objects if finite. What if counting is an expensive operation? In most cases, the developer will know whether the domain is infinite and just hardwire the result to Inf. Then the .. operator can accept anything that does Domain where ordering is non-Nil, and the ... operator can add the condition that succ/pred are non-Nil. Yes. Moreover, I have realized that Domains can solve a lot of other problems, such as collations. In English, it makes sense to write something like 'a' .. 'z' but the Danish and Swedish counterparts are 'a' .. 'z' followed by 'æ', 'ø', 'å' (Danish) and 'a' .. 'z' followed by 'ä', 'ö', 'å' (Swedish) since there is only one 'z' in unicode (for obvious reasons), collation is something separate from the charset, which can be provided in a domain. Also, encoding magical month names becomes easy (the double parens here are casting to a domain): my $month = ((DateDomain['en_US', '%b']))'Jan'; $month++; say $month; # Feb ...and even... my $date = ((DateDomain['en_US', '%D']))'01/14/2001'; $date++; say $date; # 01/15/2001 Also, this is an extension of the notion of subtypes, augmenting it with ordering and some other relations. Next question is whether the domain shouldn't also provide arithmetic. There is a lot of plumbing to do to fully use this concept, but I believe it could be really useful. Regards, Michael. where
Re: r28597 - docs/Perl6/Spec/S32-setting-library
... > Also, the domain should define how to compare objects and could provide > details about whether the set is finite, countable or uncountable. ... Sounds like a role "Domain" that provides methods (off the top of my head)- ordering - returns Nil if the domain is unordered, or a method implementing "cmp" if it is ordered succ, pred- returns Nil if the domain is uncountable, or method implementing "next item", "prior item" if countable. count - returns Inf if it's an infinite domain, or count of objects if finite. What if counting is an expensive operation? perhaps there should also be an "is_infinite" method that returns true or false. Then the .. operator can accept anything that does Domain where ordering is non-Nil, and the ... operator can add the condition that succ/pred are non-Nil.
Re: r28597 - docs/Perl6/Spec/S32-setting-library
David Green wrote: On 2009-Oct-4, at 2:07 pm, Moritz Lenz wrote: Michael Zedeler wrote: It doesn't, because succ should always give the next, smallest possible element given some ordering relation. Where's that definition from? The dictionary. =) It would be confusing to have a "successor" method for something that isn't orderable and discrete. An ordered continuous type like Real could have .inc and .dec; it just happens that in the common case of Ints, .succ and .inc mean the same thing. Complex could have an .inc method, but I don't think there's any especially obvious choice (because .inc probably wants an ordered type). Would it add 1? or 1+i? Better to spell it out explicitly. Well, Real implies ordering (at least to me ;-), I don't think we have a class or role for countability. A Discrete role would be useful, but is Set good enough for that? Sets could be acting as domains for things such as Integers, so we are on two different abstraction levels there (having Integer implement Set would probably never make much sense, but an Integer object can be part of a Set). Integers, strings and other types have a succ and pred method, but you could say that they draw upon a set (acting as their domain) when they decide the successor and predecessor of any given element. In mathematical terms it makes sense, but I am aware that from an implementation perspective, it sounds somewhat odd. It does, however solve some of the current problems that we have with iterating on Ranges and various other things. Also, the domain should define how to compare objects and could provide details about whether the set is finite, countable or uncountable. Does anyone know if there has been any prior discussions of such an approach? I started changing the spec, but decided against it since I have some 10 years of design discussion to catch up on first. Links to prior discussions will be greatly appreciated. Regards, Michael.
Re: r28597 - docs/Perl6/Spec/S32-setting-library
Michael Zedeler writes: > Moritz Lenz wrote: >> Jon Lang wrote: >> >>> How do pred and succ work when given Complex values? >>> >> By adding/substracting 1 from the real part, I'd say. Don't know if that >> actually makes sense. >> > It doesn't, because succ should always give the next, smallest possible > element given some ordering relation. Neither does it make sense for > real numbers. Same thing applies to pred. And yet, you somehow manage to fit an infinite number of strings between a string and its «successor» ... Likewise, you could choose to define .succ for reals. Eirik, for reals! -- The price of success in philosophy is triviality. -- C. Glymour.
Re: r28597 - docs/Perl6/Spec/S32-setting-library
On 2009-Oct-4, at 2:07 pm, Moritz Lenz wrote: Michael Zedeler wrote: It doesn't, because succ should always give the next, smallest possible element given some ordering relation. Where's that definition from? The dictionary. =) It would be confusing to have a "successor" method for something that isn't orderable and discrete. An ordered continuous type like Real could have .inc and .dec; it just happens that in the common case of Ints, .succ and .inc mean the same thing. Complex could have an .inc method, but I don't think there's any especially obvious choice (because .inc probably wants an ordered type). Would it add 1? or 1+i? Better to spell it out explicitly. Well, Real implies ordering (at least to me ;-), I don't think we have a class or role for countability. A Discrete role would be useful, but is Set good enough for that? -David
Re: r28597 - docs/Perl6/Spec/S32-setting-library
Jon Lang wrote: > Moritz Lenz wrote: >> Jon Lang wrote: >>> typos: s[Nuermic] = "Numeric" >> >> You do have a pugs commit bit, don't you? > > A what? AFAICT, I don't have any way of editing the Synopses; You have now (sorry for assuming earlier that you had). A username and password should be on the way to your email address. svn co http://svn.pugscode.org/pugs/docs/Perl6/Spec/ cd Spec # hack away svn ci Cheers, Moritz
Re: r28597 - docs/Perl6/Spec/S32-setting-library
Moritz Lenz wrote: > Jon Lang wrote: >> typos: s[Nuermic] = "Numeric" > > You do have a pugs commit bit, don't you? A what? AFAICT, I don't have any way of editing the Synopses; all I can do is to comment on what I find. -- Jonathan "Dataweaver" Lang
Re: r28597 - docs/Perl6/Spec/S32-setting-library
Michael Zedeler wrote: > Moritz Lenz wrote: >> Jon Lang wrote: >> >>> How do pred and succ work when given Complex values? >>> >> By adding/substracting 1 from the real part, I'd say. Don't know if that >> actually makes sense. >> > It doesn't, because succ should always give the next, smallest possible > element given some ordering relation. Where's that definition from? For me .succ was just the backend for prefix and postfix ++, which desugar to $thing += 1 (except for strings, where it's magic). > Neither does it make sense for > real numbers. Same thing applies to pred. > > It may be necessary to move methods in the Numeric class that require > ordering and countability to somewhere else. Well, Real implies ordering (at least to me ;-), I don't think we have a class or role for countability. >> You do have a pugs commit bit, don't you? >> If you find errors, feel free to correct them in the synopsis. > I do. If anyone doesn't object, I'd be happy to move the methods down to > a subclass (or -role) - at least in the spec (not sure what to do with > the code as of now). The code and tests are later adapted at whim, or so ;-) Cheers, Moritz
Re: r28597 - docs/Perl6/Spec/S32-setting-library
Moritz Lenz wrote: Jon Lang wrote: How do pred and succ work when given Complex values? By adding/substracting 1 from the real part, I'd say. Don't know if that actually makes sense. It doesn't, because succ should always give the next, smallest possible element given some ordering relation. Neither does it make sense for real numbers. Same thing applies to pred. It may be necessary to move methods in the Numeric class that require ordering and countability to somewhere else. You do have a pugs commit bit, don't you? If you find errors, feel free to correct them in the synopsis. I do. If anyone doesn't object, I'd be happy to move the methods down to a subclass (or -role) - at least in the spec (not sure what to do with the code as of now). Regards, Michael.
Re: r28597 - docs/Perl6/Spec/S32-setting-library
Jon Lang wrote: > How do pred and succ work when given Complex values? By adding/substracting 1 from the real part, I'd say. Don't know if that actually makes sense. > More generally: if Complex does Numeric, then Numeric doesn't include > Ordered (or whatever it's called), because Complex doesn't do Ordered. > As such, you can't used Numeric for any function that depends on the > value being Ordered. Correct, that's what Real is for. > On Sun, Oct 4, 2009 at 10:15 AM, wrote: >> @@ -255,7 +284,7 @@ >> >> =item I >> >> - Num multi method func ( Num $x: TrigBase $base = $?TRIGBASE ) is export >> + Nuermic multi method func ( Nuermic $x: TrigBase $base = $?TRIGBASE ) is >> export > > typos: s[Nuermic] = "Numeric" You do have a pugs commit bit, don't you? If you find errors, feel free to correct them in the synopsis. Cheers, Moritz
Re: r28597 - docs/Perl6/Spec/S32-setting-library
How do pred and succ work when given Complex values? More generally: if Complex does Numeric, then Numeric doesn't include Ordered (or whatever it's called), because Complex doesn't do Ordered. As such, you can't used Numeric for any function that depends on the value being Ordered. On Sun, Oct 4, 2009 at 10:15 AM, wrote: > @@ -255,7 +284,7 @@ > > =item I > > - Num multi method func ( Num $x: TrigBase $base = $?TRIGBASE ) is export > + Nuermic multi method func ( Nuermic $x: TrigBase $base = $?TRIGBASE ) is > export typos: s[Nuermic] = "Numeric" > where I is one of: > sin, cos, tan, asin, acos, atan, sec, cosec, cotan, asec, acosec, > @@ -281,14 +310,58 @@ > > =item atan2 > > - our Num multi method atan2 ( Num $y: Num $x = 1 ) > - our Num multi atan2 ( Num $y, Num $x = 1 ) > + our Nuermic multi method atan2 ( Nuermic $y: Nuermic $x = 1 ) > + our Nuermic multi atan2 ( Nuermic $y, Nuermic $x = 1 ) More typos: s[Nuermic] = "Numeric" -- Jonathan "Dataweaver" Lang
r28597 - docs/Perl6/Spec/S32-setting-library
Author: moritz Date: 2009-10-04 19:15:53 +0200 (Sun, 04 Oct 2009) New Revision: 28597 Modified: docs/Perl6/Spec/S32-setting-library/Numeric.pod Log: [S32/Numeric] major overhaul * Most methods that were in Num are now Numeric * sign() and the rounding methods are now in Real * document (at least partially) Rat, Num and Int Modified: docs/Perl6/Spec/S32-setting-library/Numeric.pod === --- docs/Perl6/Spec/S32-setting-library/Numeric.pod 2009-10-04 17:15:43 UTC (rev 28596) +++ docs/Perl6/Spec/S32-setting-library/Numeric.pod 2009-10-04 17:15:53 UTC (rev 28597) @@ -28,7 +28,7 @@ repository under /docs/Perl6/Spec/S32-setting-library/Numeric.pod so edit it there in the SVN repository if you would like to make changes. -This documents Bit, Int, Num, Rat, Complex, and Bool. +This documents Bit, Int, Numeric, Rat, Complex, and Bool. XXX So where are Bit, Int, and Rat @@ -52,13 +52,17 @@ =back -=head2 Num +=head2 Numeric -The following are all defined in the C role: +C is a role for everything that's a scalar number. So C, C, +C, C and other numeric types do that role. However it is an +abstract interface, so C<$number.WHAT> will never return C. Users who +provide their own scalar numeric types are encouraged to implement the +C role. -B: L +The following are all defined in the C role: -C provides some constants in addition to the basic +C provides some constants in addition to the basic mathematical functions. constant pi is export = 3.14159_26535_89793_23846_26433_83279_50288; @@ -68,74 +72,43 @@ =item succ - our Num multi method succ ( Num $x: ) is export - our Int multi method succ ( Int $x: ) is export + our Numeric multi method succ ( Numeric $x: ) is export + our Int multi method succ ( Int $x: ) is export Returns the successor of C<$x>. This method is used by C<< prefix:<++> >> and C<< postfix:<++> >> to increment the value in a container. =item pred - our Num multi method pred ( Num $x: ) is export - our Int multi method pred ( Int $x: ) is export + our Numeric multi method pred ( Numeric $x: ) is export + our Int multi method pred ( Int $x: ) is export Returns the predeccessor of C<$x>. This method is used by C<< prefix:<--> >> and C<< postfix:<--> >> to decrement the value in a container. =item abs - our Num multi method abs ( Num $x: ) is export + our Numeric multi method abs ( Numeric $x: ) is export Absolute Value. -=item floor - - our Int multi method floor ( Num $x: ) is export - -Returns the highest integer not greater than C<$x>. - -=item ceiling - - our Int multi method ceiling ( Num $x: ) is export - -Returns the lowest integer not less than C<$x>. - -=item round - - our Int multi method round ( Num $x: ) is export - -Returns the nearest integer to C<$x>. The algorithm is C. -(Other rounding algorithms will be given extended names beginning with "round".) - -=item truncate - - our Int multi method truncate ( Num $x: ) is export - -Returns the closest integer to C<$x> whose absolute value is not greater -than the absolute value of C<$x>. (In other words, just chuck any -fractional part.) This is the default rounding function used by -implicit integer conversions. - -You may also truncate using explicit integer casts, either C for -an arbitrarily large integers, or C for native integers. - =item exp - our Num multi method exp ( Num $exponent: Num :$base = Num::e ) is export + our Numeric multi method exp ( Numeric $exponent: Numeric :$base = Num::e ) is export Performs similar to C<$base ** $exponent>. C<$base> defaults to the constant I. =item log - our Num multi method log ( Num $x: Num $base = Num::e ) is export + our Numeric multi method log ( Numeric $x: Numeric $base = Num::e ) is export Logarithm of base C<$base>, default Natural. Calling with C<$x == 0> is an error. =item log10 - our Num multi method log10 (Num $x:) is export + our Numeric multi method log10 (Numeric $x:) is export A base C<10> logarithm, othewise identical to C. @@ -148,34 +121,9 @@ unary C function in Perl 6, so just multiply C by your desired multiplier. For picking a random integer you probably want to use something like C<(1..6).pick> instead. - -=item sign - - our Int multi method sign ( Num $x: ) is export - -Returns 1 when C<$x> is greater than 0, -1 when it is less than 0, 0 when it -is equal to 0, or undefined when the value passed is undefined. - -=item srand - - multi method srand ( Num $seed: ) - multi srand ( Num $seed = default_seed_algorithm()) - -Seed the generator C uses. C<$seed> defaults to some combination -of various platform dependent characteristics to yield a non-deterministic seed. -Note that you get one C for free when you start a Perl program, so -you I call C yourself if you wish to specify a deterministic seed -(or if you wish to be differently nondeterministic). - -=item sqrt - - our Num multi method sqrt (
