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Today's Topics:
1. Tree-like Structure with unique elements on each level (martin)
2. Re: Tree-like Structure with unique elements on each level
(Imants Cekusins)
3. Implementing instance of '^' operator (pmcil...@gmail.com)
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Message: 1
Date: Sat, 2 Jan 2016 20:53:24 +0100
From: martin <martin.drautzb...@web.de>
To: The Haskell-Beginners Mailing List - Discussion of primarily
beginner-level topics related to Haskell <beginners@haskell.org>
Subject: [Haskell-beginners] Tree-like Structure with unique elements
on each level
Message-ID: <56882ab4.2090...@web.de>
Content-Type: text/plain; charset=utf-8
Hello all,
I recently modeled a tree like this:
data Predicate a = Any | Pred (S.Set a)
data Product a = Pany | Prod (S.Set(Predicate a, S.Set(Product a)))
What I wanted to achieve was to have each element only once on each level.
Hence the Sets. But this structure does not
achieve this. I can easily duplicate elements on a level as long as their
subordinates are different, so I might as well
give up working with sets.
Is there a way to construct a tree where each element can occur only once on
each level?
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Message: 2
Date: Sat, 2 Jan 2016 22:12:57 +0100
From: Imants Cekusins <ima...@gmail.com>
To: The Haskell-Beginners Mailing List - Discussion of primarily
beginner-level topics related to Haskell <beginners@haskell.org>
Subject: Re: [Haskell-beginners] Tree-like Structure with unique
elements on each level
Message-ID:
<CAP1qinagm=rsfzhr9w1v37b_m6utukqt2jjk52lyjoymhcj...@mail.gmail.com>
Content-Type: text/plain; charset="utf-8"
> data Predicate a = Any | Pred (S.Set a)
data Product a = Pany | Prod (S.Set(Predicate a, S.Set(Product a)))
Does this fit:
data Predicate a = Any | Pred a
data Product a = Pred' (Predicate a) | Prod (Product a)
?
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Message: 3
Date: Sat, 2 Jan 2016 22:55:41 -0800
From: <pmcil...@gmail.com>
To: "beginners@haskell.org" <beginners@haskell.org>
Subject: [Haskell-beginners] Implementing instance of '^' operator
Message-ID: <5688c5ec.e93e420a.22e11.5...@mx.google.com>
Content-Type: text/plain; charset="utf-8"
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
? Defining non-trivial implementations, where constructor must be private, etc.
? Invoking an abstract superclass concrete instance method from within the
subclass method definition
The latter appears not to be possible in Haskell. Is this true?
Here?s the basic code, but I punted on x^n. It looks like I?d have to paste in
the entire original definition of ?^?.
data Modp a = Modp a a deriving (Eq, Show)
mkModp p n | isPrime p = Modp p (n `mod` p)
| otherwise = error $ show p ++ " is not a prime"
instance Integral a => Num (Modp a) where
(Modp q n) + (Modp p m) | p==q = Modp p $ (n+m) `mod` p
| otherwise = error $ "unequal moduli"
(Modp p n) * (Modp q m) | p==q = Modp p $ (n*m) `mod` p
| otherwise = error $ "unequal moduli"
negate (Modp p n) = Modp p (p-n)
-- can't reuse base because ^ is impl. directly in prelude
{- (Modp p x) ^ n | n <= p = (Modp p x) `baseExp` n
| n1 == 0 = (Modp p x)
| n > p = x ^ n1
where baseExp = ^ in Num
n1 = n `mod` p
-}
instance Integral a => Fractional (Modp a) where
recip (Modp p n) = (Modp p n)^(p-2)
isPrime p = True -- stub
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