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Today's Topics:
1. Re: Implementing instance of '^' operator (Chadda? Fouch?)
2. Re: Ambiguous module name `Prelude': it was found in
multiple packages (trying to install HXQ) (Chadda? Fouch?)
3. proving fmap law for recursive data types (???)
4. Re: proving fmap law for recursive data types (Kim-Ee Yeoh)
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Message: 1
Date: Sat, 16 Jan 2016 21:05:06 +0000
From: Chadda? Fouch? <chaddai.fou...@gmail.com>
To: The Haskell-Beginners Mailing List - Discussion of primarily
beginner-level topics related to Haskell <beginners@haskell.org>
Subject: Re: [Haskell-beginners] Implementing instance of '^' operator
Message-ID:
<canfjzraowmcyh8kr30txuq3mttf0bsureuax_hnwnxqspfp...@mail.gmail.com>
Content-Type: text/plain; charset="utf-8"
(^) is _not_ a method of Num, it is simply a function with a Num
constraint. It will work on your new numbers as well as it would on any
other that implements (*) correctly, you don't need to rewrite it.
By the way, your functions are dangerously partial, it would seem useful to
put the prime into the type so that you can't add or multiply different Mod
p. Of course this demands a bit more knowledge of Haskell type system than
is likely in a beginner, but if you're motivated, I encourage you to look
at numbers in type (see GHC.TypeLits maybe).
--
Jeda?
Le dim. 3 janv. 2016 ? 14:07, Harald Hanche-Olsen <han...@math.ntnu.no> a
?crit :
> -----Original Message-----
> From: pmcil...@gmail.com <pmcil...@gmail.com>
> Date: 3 January 2016 at 07:55:53
>
> > As a ?hello world? example for type definitions, I like to define a
> numeric type that can
> > handle the mod p multiplicative group, where p is prime. This requires:
> > ? Implementing interface functions
>
> [?]
>
> I can?t help with the question you?re asking, but I have a minor nitpick:
> You want to have
> negate (Modp p 0) = Modp p 0,
> and not Modp p p as in your current implementation.
>
> ? Harald
> _______________________________________________
> Beginners mailing list
> Beginners@haskell.org
> http://mail.haskell.org/cgi-bin/mailman/listinfo/beginners
>
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Message: 2
Date: Sat, 16 Jan 2016 21:14:47 +0000
From: Chadda? Fouch? <chaddai.fou...@gmail.com>
To: The Haskell-Beginners Mailing List - Discussion of primarily
beginner-level topics related to Haskell <beginners@haskell.org>
Subject: Re: [Haskell-beginners] Ambiguous module name `Prelude': it
was found in multiple packages (trying to install HXQ)
Message-ID:
<CANfjZRZknV4TV5yxy=frfjbrehbny1ac7zrv6iyfi_zmzea...@mail.gmail.com>
Content-Type: text/plain; charset="utf-8"
Le mar. 5 janv. 2016 ? 22:16, Henk-Jan van Tuyl <hjgt...@chello.nl> a
?crit :
> You can do "cabal unpack hxq" and update the file hxq.cabal; I tried it
> and there are many more things that need updates. Your best bet would be
> to ask the author to update the package. Otherwise, you could ask the
> Haskell Caf? if someone would like to take over maintenance of HXQ.
Apparently someone did update HXQ : Leonidas Fegaras, the original
maintainer, updated HXQ on the 7 january 2016. I can only assume that
Stanislaw contacted him directly.
Just to conclude the discussion on a positive note !
--
Jeda?
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Message: 3
Date: Sat, 16 Jan 2016 19:17:59 -0800
From: ??? <traqueofzi...@gmail.com>
To: beginners@haskell.org
Subject: [Haskell-beginners] proving fmap law for recursive data types
Message-ID:
<CAMjcG+HazdkDXyjKwMURRiJmCBSjW=f+e06xmujvsvhs81z...@mail.gmail.com>
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Hi,
Suppose you have something like:
data Tree a = Leaf a | Branch (Tree a) (Tree a)
instance Functor Tree where
fmap f (Leaf a) = Leaf $ f a
fmap f (Branch l r) = Branch (fmap f l) (fmap f r)
To check that fmap id = id, I can see that the case for Leaf is ok:
fmap id (Leaf a) = Leaf $ id a = Leaf a
How would you prove it for the second case? Is some sort of inductive proof
necessary? I found this:
http://ssomayyajula.github.io/posts/2015-11-07-proofs-of-functor-laws-with-Haskell.html,
which goes over an inductive (on the length of the list) proof for the list
type, but I'm not sure how to do it for a Tree.
Thanks,
toz
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Message: 4
Date: Sun, 17 Jan 2016 11:47:33 +0700
From: Kim-Ee Yeoh <k...@atamo.com>
To: The Haskell-Beginners Mailing List - Discussion of primarily
beginner-level topics related to Haskell <beginners@haskell.org>
Subject: Re: [Haskell-beginners] proving fmap law for recursive data
types
Message-ID:
<capy+zdrbwxhygen8phu6z35osecqqsqhxx5lbvzvep+c--0...@mail.gmail.com>
Content-Type: text/plain; charset="utf-8"
On Sun, Jan 17, 2016 at 10:17 AM, ??? <traqueofzi...@gmail.com> wrote:
How would you prove it for the second case? Is some sort of inductive proof
> necessary? I found this:
> http://ssomayyajula.github.io/posts/2015-11-07-proofs-of-functor-laws-with-Haskell.html,
> which goes over an inductive (on the length of the list) proof for the list
> type, but I'm not sure how to do it for a Tree.
>
You've got the right idea. The general outline of a simple inductive proof
is this:
1. Prove for the smallest case (in this case, a tree with just one Leaf)
2. While assuming that the hypothesis holds for a small case, prove
hypothesis for the next case one up in size
3. Put 1 and 2 together to claim hypothesis for all cases
You've done 1.
You're stuck at 2 because you haven't yet found some measure of a "size" of
a Tree.
What are some common Tree measures you've seen?
-- Kim-Ee
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