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Today's Topics:
1. Quickcheck: pushing element onto stack increases stack size
(PATRICK BROWNE)
2. Re: Quickcheck: pushing element onto stack increases stack
size (David McBride)
3. Re: Quickcheck: pushing element onto stack increases stack
size (PATRICK BROWNE)
4. Runge-Kutta and vectors (mike h)
----------------------------------------------------------------------
Message: 1
Date: Thu, 11 May 2017 20:38:59 +0100
From: PATRICK BROWNE <[email protected]>
To: The Haskell-Beginners Mailing List - Discussion of primarily
beginner-level topics related to Haskell <[email protected]>
Subject: [Haskell-beginners] Quickcheck: pushing element onto stack
increases stack size
Message-ID:
<cagflrkfxmavbqbwqwmi81uadkpglkwfornnaak-aykshapp...@mail.gmail.com>
Content-Type: text/plain; charset="utf-8"
Hi,
I am trying to use Quickcheck to check that pushing an element increases
the size of a stack.
Something like:
prop_size2 x s = (size (Push x s)) > (size s)
Is this possible? Below is my effort using an empty stack.
Thanks in advance,
Pat
module Stack (empty, push, pop, top, isEmpty) where
import Test.QuickCheck
data Stack a = Empty | Push a (Stack a) deriving Show
empty :: Stack a
empty = Empty
push :: a -> Stack a -> Stack a
push x ss = Push x ss
pop :: Stack a -> Stack a
pop Empty = error "pop emptyStack"
pop (Push x ss) = ss
top :: Stack a -> a
top Empty = error "top emptyStack"
top (Push x ss) = x
isEmpty :: Stack a -> Bool
isEmpty Empty = True
isEmpty (Push x ss) = False
size :: (Stack a) -> Int
size Empty = 0
size (Push x ss) = succ (size ss)
prop_size x = (size (Push x Empty)) > (size Empty)
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Message: 2
Date: Thu, 11 May 2017 16:00:57 -0400
From: David McBride <[email protected]>
To: [email protected], The Haskell-Beginners Mailing List -
Discussion of primarily beginner-level topics related to Haskell
<[email protected]>
Subject: Re: [Haskell-beginners] Quickcheck: pushing element onto
stack increases stack size
Message-ID:
<can+tr42capno62-g7sgfwu7wfy1ceyk3l1shcm-t2mzv-jd...@mail.gmail.com>
Content-Type: text/plain; charset="UTF-8"
First you need a way to generate an arbitrary stack. Here's a simple
method that just gives you a 50% chance at each level of generating an
extra layer.
instance Arbitrary a => Arbitrary (Stack a) where
arbitrary = oneof [return Empty, Push <$> arbitrary <*> arbitrary ]
prop_size_succeeds x s = size (Push x s) > size s
prop_size_fails x s = size s > size Empty
>quickCheck prop_size_fails
*** Failed! Falsifiable (after 6 tests):
()
Empty
On Thu, May 11, 2017 at 3:38 PM, PATRICK BROWNE <[email protected]> wrote:
> Hi,
> I am trying to use Quickcheck to check that pushing an element increases the
> size of a stack.
> Something like:
> prop_size2 x s = (size (Push x s)) > (size s)
>
> Is this possible? Below is my effort using an empty stack.
> Thanks in advance,
> Pat
>
>
> module Stack (empty, push, pop, top, isEmpty) where
> import Test.QuickCheck
>
> data Stack a = Empty | Push a (Stack a) deriving Show
>
> empty :: Stack a
> empty = Empty
>
> push :: a -> Stack a -> Stack a
> push x ss = Push x ss
>
> pop :: Stack a -> Stack a
> pop Empty = error "pop emptyStack"
> pop (Push x ss) = ss
>
> top :: Stack a -> a
> top Empty = error "top emptyStack"
> top (Push x ss) = x
>
> isEmpty :: Stack a -> Bool
> isEmpty Empty = True
> isEmpty (Push x ss) = False
>
>
> size :: (Stack a) -> Int
> size Empty = 0
> size (Push x ss) = succ (size ss)
>
>
> prop_size x = (size (Push x Empty)) > (size Empty)
>
> This email originated from DIT. If you received this email in error, please
> delete it from your system. Please note that if you are not the named
> addressee, disclosing, copying, distributing or taking any action based on
> the contents of this email or attachments is prohibited. www.dit.ie
>
> Is ó ITBÁC a tháinig an ríomhphost seo. Má fuair tú an ríomhphost seo trí
> earráid, scrios de do chóras é le do thoil. Tabhair ar aird, mura tú an
> seolaí ainmnithe, go bhfuil dianchosc ar aon nochtadh, aon chóipeáil, aon
> dáileadh nó ar aon ghníomh a dhéanfar bunaithe ar an ábhar atá sa ríomhphost
> nó sna hiatáin seo. www.dit.ie
>
> Tá ITBÁC ag aistriú go Gráinseach Ghormáin – DIT is on the move to
> Grangegorman
>
>
> _______________________________________________
> Beginners mailing list
> [email protected]
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>
------------------------------
Message: 3
Date: Thu, 11 May 2017 22:55:55 +0100
From: PATRICK BROWNE <[email protected]>
To: David McBride <[email protected]>
Cc: The Haskell-Beginners Mailing List - Discussion of primarily
beginner-level topics related to Haskell <[email protected]>
Subject: Re: [Haskell-beginners] Quickcheck: pushing element onto
stack increases stack size
Message-ID:
<CAGFLrKfBf=aXq-z+Nqhn=x83bjgvq68qbqr4xaqcuwx7f84...@mail.gmail.com>
Content-Type: text/plain; charset="utf-8"
David,
Thanks for the help.
Much appreciated,
Pat
On 11 May 2017 at 21:00, David McBride <[email protected]> wrote:
> First you need a way to generate an arbitrary stack. Here's a simple
> method that just gives you a 50% chance at each level of generating an
> extra layer.
>
> instance Arbitrary a => Arbitrary (Stack a) where
> arbitrary = oneof [return Empty, Push <$> arbitrary <*> arbitrary ]
>
> prop_size_succeeds x s = size (Push x s) > size s
> prop_size_fails x s = size s > size Empty
>
> >quickCheck prop_size_fails
> *** Failed! Falsifiable (after 6 tests):
> ()
> Empty
>
>
> On Thu, May 11, 2017 at 3:38 PM, PATRICK BROWNE <[email protected]>
> wrote:
> > Hi,
> > I am trying to use Quickcheck to check that pushing an element increases
> the
> > size of a stack.
> > Something like:
> > prop_size2 x s = (size (Push x s)) > (size s)
> >
> > Is this possible? Below is my effort using an empty stack.
> > Thanks in advance,
> > Pat
> >
> >
> > module Stack (empty, push, pop, top, isEmpty) where
> > import Test.QuickCheck
> >
> > data Stack a = Empty | Push a (Stack a) deriving Show
> >
> > empty :: Stack a
> > empty = Empty
> >
> > push :: a -> Stack a -> Stack a
> > push x ss = Push x ss
> >
> > pop :: Stack a -> Stack a
> > pop Empty = error "pop emptyStack"
> > pop (Push x ss) = ss
> >
> > top :: Stack a -> a
> > top Empty = error "top emptyStack"
> > top (Push x ss) = x
> >
> > isEmpty :: Stack a -> Bool
> > isEmpty Empty = True
> > isEmpty (Push x ss) = False
> >
> >
> > size :: (Stack a) -> Int
> > size Empty = 0
> > size (Push x ss) = succ (size ss)
> >
> >
> > prop_size x = (size (Push x Empty)) > (size Empty)
> >
> > This email originated from DIT. If you received this email in error,
> please
> > delete it from your system. Please note that if you are not the named
> > addressee, disclosing, copying, distributing or taking any action based
> on
> > the contents of this email or attachments is prohibited. www.dit.ie
> >
> > Is ó ITBÁC a tháinig an ríomhphost seo. Má fuair tú an ríomhphost seo trí
> > earráid, scrios de do chóras é le do thoil. Tabhair ar aird, mura tú an
> > seolaí ainmnithe, go bhfuil dianchosc ar aon nochtadh, aon chóipeáil, aon
> > dáileadh nó ar aon ghníomh a dhéanfar bunaithe ar an ábhar atá sa
> ríomhphost
> > nó sna hiatáin seo. www.dit.ie
> >
> > Tá ITBÁC ag aistriú go Gráinseach Ghormáin – DIT is on the move to
> > Grangegorman
> >
> >
> > _______________________________________________
> > Beginners mailing list
> > [email protected]
> > http://mail.haskell.org/cgi-bin/mailman/listinfo/beginners
> >
>
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seolaí ainmnithe, go bhfuil dianchosc ar aon nochtadh, aon chóipeáil, aon
dáileadh nó ar aon ghníomh a dhéanfar bunaithe ar an ábhar atá sa
ríomhphost nó sna hiatáin seo. www.dit.ie
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------------------------------
Message: 4
Date: Fri, 12 May 2017 08:49:12 +0100
From: mike h <[email protected]>
To: The Haskell-Beginners Mailing List - Discussion of primarily
beginner-level topics related to Haskell <[email protected]>
Subject: [Haskell-beginners] Runge-Kutta and vectors
Message-ID: <[email protected]>
Content-Type: text/plain; charset=utf-8
Having looked at 'Learn Physics by Programming in Haskell’ I became quite
wobbly with excitement! :)
So I took and implemented some of their ideas. My University level maths is
around 40 years old and so I struggled
with some of the later things - but it's slowly coming back!
(I have a copy at
https://github.com/banditpig/vectors/blob/master/LearnPhysics.pdf)
So I have
type Scalar = Double
type XYZ = (Scalar, Scalar, Scalar)
newtype Vector = V { xyz :: XYZ}
and set of vector operations
(^+^) :: Vector -> Vector -> Vector
(^-^) :: Vector -> Vector -> Vector
(*^) :: Scalar -> Vector -> Vector
(^*) :: Vector -> Scalar -> Vector
(^/) :: Vector -> Scalar -> Vector
(>.<) :: Vector -> Vector -> Scalar -- dot
(><) :: Vector -> Vector -> Vector -- cross
etc
I then have
type Time = Double
type Displacement = Vector
type Velocity = Vector
type State = (Time, Displacement, Velocity)
eulerStep :: (State -> Vector) -> Double -> State -> State
eulerStep f dt st@(t, r, v) = (t', r', v') where
t' = t + dt
r' = r ^+^ v ^* dt
v' = v ^+^ f st ^* dt
and so for a given acceleration function, time step and start state a solution
is given by
solution :: (State -> Vector) -> Double -> State -> [State]
solution a dt = iterate (eulerStep a dt)
What I'm trying to do is replace the Euler method of solving with the
Rung-Kutta method.
I'm really struggling in seeing how the Rung-Kutta examples I've seen are
implemented using vectors.
How should I progress? Any advice would be welcome! (I really want to implement
it using the types I have rather than using an external library )
Many Thanks
Mike
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