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Today's Topics:
1. Re: Problem with minimax with alpha beta pruning (Maxim Frolov)
2. Re: Lambda expression currying (Lawrence Bottorff)
3. Another currying and lambda question (Lawrence Bottorff)
4. Re: Another currying and lambda question (Francesco Ariis)
5. Re: Another currying and lambda question (Lawrence Bottorff)
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Message: 1
Date: Tue, 22 Dec 2020 13:18:56 +0000
From: Maxim Frolov <[email protected]>
To: The Haskell-Beginners Mailing List - Discussion of primarily
beginner-level topics related to Haskell <[email protected]>
Subject: Re: [Haskell-beginners] Problem with minimax with alpha beta
pruning
Message-ID: <7fb37eab-89cd-4559-9c92-5dcb68c7f20b@Spark>
Content-Type: text/plain; charset="utf-8"
Got it. Thank you Kim-Ee!
On 22 Dec 2020, 08:28 +0000, Kim-Ee Yeoh <[email protected]>, wrote:
> Hi Maxim,
>
> The scope of this question falls outside this beginners list, which tends
> toward questions about haskell syntax (see other active thread).
>
> You will typically find more response on the haskell-cafe list, which you
> might want to resend your query to.
>
> > On Mon, Dec 21, 2020 at 11:01 PM Maxim Frolov <[email protected]>
> > wrote:
> > > Hi All,
> > >
> > > I am new to Haskell and got stuck while experimenting with minimax
> > > algorithm (tic-tac-toe game). Just for learning I am trying to avoid
> > > external modules and use only the standard Prelude library.
> > >
> > > Here is the code snippet:
> > >
> > > type Pos = (Int,Int)
> > > -- Players are O (minimizing) and X (maximizing), B is for the draw
> > > (blank), I and J are used for -INF and +INF respectively
> > > data Player = I | O | B | X | J
> > > deriving (Eq, Ord, Show)
> > > type Grid = [(Pos,Player)]
> > > data Tree a = Node a [Tree a]
> > > deriving Show
> > >
> > > minimax :: Player -> Player -> Tree Grid -> Tree (Grid, Player)
> > > minimax _ _ (Node g [])
> > > | wins X g = Node (g,X) []
> > > | wins O g = Node (g,O) []
> > > | otherwise = Node (g,B) []
> > > minimax a b (Node g ts)
> > > | turn g == X =
> > > let ts' = [minimax alpha b t | t <- ts, alpha < b]
> > > ps = [p | Node (_,p) _ <- ts']
> > > alpha = maximum (a:ps)
> > > in Node (g, alpha) ts'
> > > | turn g == O =
> > > let ts' = [minimax a beta t | t <- ts, a < beta]
> > > ps = [p | Node (_,p) _ <- ts']
> > > beta = minimum (b:ps)
> > > in Node (g, beta) ts'
> > >
> > >
> > > The function call is like:
> > >
> > > minimax I J tree
> > >
> > >
> > > It looks like I got a recursion loop. Could someone advise how to
> > > approach the problem?
> > >
> > > Thank you,
> > > Max
> > >
> > >
> > > _______________________________________________
> > > Beginners mailing list
> > > [email protected]
> > > http://mail.haskell.org/cgi-bin/mailman/listinfo/beginners
> --
> -- Kim-Ee
> _______________________________________________
> Beginners mailing list
> [email protected]
> http://mail.haskell.org/cgi-bin/mailman/listinfo/beginners
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Message: 2
Date: Tue, 22 Dec 2020 10:00:22 -0600
From: Lawrence Bottorff <[email protected]>
To: The Haskell-Beginners Mailing List - Discussion of primarily
beginner-level topics related to Haskell <[email protected]>
Subject: Re: [Haskell-beginners] Lambda expression currying
Message-ID:
<cafahfsueey9ez+vffdvmm2sj9d0wjy97uud_c2-s5jpbxsx...@mail.gmail.com>
Content-Type: text/plain; charset="utf-8"
Thanks, that's clearer now.
On Tue, Dec 22, 2020 at 12:55 AM Francesco Ariis <[email protected]> wrote:
> Hello Lawrence,
>
> Il 21 dicembre 2020 alle 23:59 Lawrence Bottorff ha scritto:
> > addThree :: (Num a) => a -> a -> a -> a
> > addThree = \x -> \y -> \z -> x + y + z
> > […]
> >
> > But how is the beta reduction happening with addThree?
>
> Should be:
>
> addThree = (\x -> \y -> \z -> x + y + z) 1 2 3
> = (\y -> \z -> 1 + y + z) 2 3 beta
> = (\z -> 1 + 2 + z) 3 beta
> = 1 + 2 + 3 beta
> = …
>
> Does that make sense?
> —F
> _______________________________________________
> Beginners mailing list
> [email protected]
> http://mail.haskell.org/cgi-bin/mailman/listinfo/beginners
>
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Message: 3
Date: Tue, 22 Dec 2020 11:48:02 -0600
From: Lawrence Bottorff <[email protected]>
To: The Haskell-Beginners Mailing List - Discussion of primarily
beginner-level topics related to Haskell <[email protected]>
Subject: [Haskell-beginners] Another currying and lambda question
Message-ID:
<cafahfsvv7a1qnn0e_dqbl2t7qfmbg7c5jnopowpbcc9wuh_...@mail.gmail.com>
Content-Type: text/plain; charset="utf-8"
In *Learn You... <http://learnyouahaskell.com/higher-order-functions> *I'm
seeing this
flipA :: (a -> b -> c) -> b -> a -> c
flipA f x y = f y x
and this
flipB :: (a -> b -> c) -> b -> a -> c
flipB f = \x y -> f y x
What is it specifically about currying that makes flipA possible? Also,
with flipB, could someone explain the beta reduction? It looks like f is
not being acted on, just passed along, Would it look more like this in
lambda calculus?
(\x \y -> f y x)
then
(\x \y -> f y x) g a b
gives
g b a ?
LB
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Message: 4
Date: Tue, 22 Dec 2020 18:59:21 +0100
From: Francesco Ariis <[email protected]>
To: [email protected]
Subject: Re: [Haskell-beginners] Another currying and lambda question
Message-ID: <20201222175921.GA3626@extensa>
Content-Type: text/plain; charset=utf-8
Il 22 dicembre 2020 alle 11:48 Lawrence Bottorff ha scritto:
> flipA :: (a -> b -> c) -> b -> a -> c
> flipA f x y = f y x
>
> What is it specifically about currying that makes flipA possible?
I do not see how currying is involved here! Maybe when you pass
a function to an higher order one?
> flipB :: (a -> b -> c) -> b -> a -> c
> flipB f = \x y -> f y x
>
> Also, with flipB, could someone explain the beta reduction? It looks
> like f is not being acted on, just passed along, Would it look more
> like this in lambda calculus?
Indeed `f` is not being acted on (i.e. it is «outside» of the lambda)
(λx. λy. f y x) b a
(λy. f y b) a beta
f a b beta
fully expressed with lambdas would be:
(λf. λx. λy. f y x) g b a
------------------------------
Message: 5
Date: Tue, 22 Dec 2020 15:15:42 -0600
From: Lawrence Bottorff <[email protected]>
To: The Haskell-Beginners Mailing List - Discussion of primarily
beginner-level topics related to Haskell <[email protected]>
Subject: Re: [Haskell-beginners] Another currying and lambda question
Message-ID:
<cafahfsuyrgcieajvo1c-ppqef+ayksjvbwopnwhejy9akdk...@mail.gmail.com>
Content-Type: text/plain; charset="utf-8"
Thanks again!
On Tue, Dec 22, 2020 at 11:59 AM Francesco Ariis <[email protected]> wrote:
> Il 22 dicembre 2020 alle 11:48 Lawrence Bottorff ha scritto:
> > flipA :: (a -> b -> c) -> b -> a -> c
> > flipA f x y = f y x
> >
> > What is it specifically about currying that makes flipA possible?
>
> I do not see how currying is involved here! Maybe when you pass
> a function to an higher order one?
>
> > flipB :: (a -> b -> c) -> b -> a -> c
> > flipB f = \x y -> f y x
> >
> > Also, with flipB, could someone explain the beta reduction? It looks
> > like f is not being acted on, just passed along, Would it look more
> > like this in lambda calculus?
>
> Indeed `f` is not being acted on (i.e. it is «outside» of the lambda)
>
> (λx. λy. f y x) b a
> (λy. f y b) a beta
> f a b beta
>
> fully expressed with lambdas would be:
>
> (λf. λx. λy. f y x) g b a
>
> _______________________________________________
> Beginners mailing list
> [email protected]
> http://mail.haskell.org/cgi-bin/mailman/listinfo/beginners
>
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