michael rice nowgate at yahoo.com
Wed Dec 22 01:30:01 CET 2010

Thanks, Ryan.

I rewrote it yesterday. Here's my updated version.

Better?

Michael

==============

import Data.Functor ((<\$>))
import System.Random

data Craps a = Roll a | Win a | Lose a deriving (Show)

-- Returns an infinite list of die throws
rollDice :: IO [Int]
rollDice =  randomRs (1,6) <\$> newStdGen

-- fmap g rollDice -> an infinite list of double dice throws.

g :: [Int] -> [Int]
g (x:y:rest) = (x+y) : (g rest)

h :: Craps [Int] -> [Int] -> [Craps [Int]]
h (Roll []) (2:ys) = (Lose [2]) : (h (Roll []) ys)
h (Roll []) (3:ys) = (Lose [3]) : (h (Roll []) ys)
h (Roll []) (7:ys) = (Win [7]) : (h (Roll []) ys)
h (Roll []) (11:ys) = (Win [11]) : (h (Roll []) ys)
h (Roll []) (y:ys) = h (Roll [y]) ys
h (Roll z@(x:xs)) (y:ys) = if y == 7
then (Lose (z ++ [y])) : (h (Roll []) ys)
else
if x == y
then (Win (z ++ [y])) : (h (Roll []) ys)
else h (Roll (z ++ [y])) ys

progressive ((x:xs),won) (Win _) = let bet = x + (last xs)
in (init xs,won+bet)
progressive (z@(x:xs),won) (Lose _) = let bet = x + (last xs)
in (z ++ [bet],won-bet)
martingale (won,lost) (Win _) = let bet = max 1 (2*lost)
in (won+bet,0)
martingale (won,lost) (Lose _) = let bet = max 1 (2*lost)
in (won,lost+bet)

-- Play
-- n : throw cycles
-- f : betting system
-- x : starting condition
playCraps n f x = let r = fmap ((take n) . (h (Roll [])) . g) rollDice
in fmap (foldl f x) r

{-
*Main> playCraps 5 progressive ([1..10],0)
([5,6,7],37)
*Main> playCraps 5 martingale (0,0)
(7,1)
-}

--- On Tue, 12/21/10, Ryan Ingram <ryani.spam at gmail.com> wrote:

From: Ryan Ingram <ryani.spam at gmail.com>
To: "michael rice" <nowgate at yahoo.com>
Date: Tuesday, December 21, 2010, 7:00 PM

-- State :: (s -> (a,s)) -> State s a
-- random :: Random a => StdGen -> (a, StdGen)
genRandom :: Random a => GeneratorState a

genRandom = State random

-- similar
genRandomR :: Random a => (a,a) -> GeneratorState a
genRandomR = State . randomR

rollDie :: GeneratorState Int
rollDie = genRandomR (1,6)

roll2Dice :: GeneratorState Int

roll2Dice = liftM2 (+) die die

These can be used to simplify a lot of the code here.

-- ryan

On Fri, Dec 17, 2010 at 5:55 PM, michael rice <nowgate at yahoo.com> wrote:

Paul Graham refers to all those features as "orthogonality" ("On Lisp", pg. 63) and you're right, Haskell has it in spades, but it takes time to understand all of it and even more time to use it effectively. One almost needs a checklist.

But I think I'm catching on. I programmed this craps simulation last week. It's a problem from "Problems For Computer Solution", Gruenberger & Jaffray, 1965, The RAND Corp.

import System.Random

type
GeneratorState = State StdGen
data Craps a = Roll a | Win a | Lose a deriving (Show)

f :: Craps [Int] -> GeneratorState (Craps [Int])

f (Roll []) = do g0 <- get
let (d1,g1) = randomR (1,6) g0

(d2,g2) = randomR (1,6) g1
t1 = d1+d2

put g2
case t1 of

2 -> return (Lose [t1])
3 -> return (Lose [t1])

7 -> return (Win [t1])
11 -> return (Win [t1])

_ -> do g2 <- get
let (d3,g3) = randomR (1,6) g2

(d4,g4) = randomR (1,6) g3
t2 = d3+d4

put g4
if t2 == t1

then do
return (Win [t1,t2])

else
if t2 == 7

then do
return (Lose [t1,t2])

else
f (Roll [t2,t1])

f (Roll l) = do g0 <- get
let (d1,g1) = randomR (1,6) g0

(d2,g2) = randomR (1,6) g1
t = d1+d2

if t == (last l)
then do

put g2
return (Win (reverse (t:l)))

else
if t == 7

then do
put g2

return (Lose (reverse (t:l)))
else do

put g2
f (Roll (t:l))

progressive (z@(x:xs),n) (Win _) = let b = x + (last
xs)
in (init xs,n+b)
progressive (z@(x:xs),n) (Lose _) = let b = x + (last xs)
in (z ++ [b],n-b)

*Main> let r = evalState (sequence \$ replicate 6 (f (Roll []))) (mkStdGen 987)

*Main> r
[Win
[8,12,10,3,8],Win [5,9,10,11,12,11,8,9,5],Win [7],Lose [9,7],Win [5,5],Win [5,2,6,4,6,8,5]]
*Main> foldl progressive ([1..10],0) r

([6],49)

Function f generates the roll cycle outcomes which are then folded with the progressive betting system.

In the final answer, the [6] is what's left of the original betting list [1..10]. The betting list is used to determine the bet: always bet the (first + last) of betting list. If a win, delete the first and last. If a loss, add loss to end of betting list. The 49 is winnings, initially 0.

There's no explanation in the book of what should happen if the betting list becomes empty, or a singleton, but that could be fixed by
making it longer.

Comments, criticism, and better ways of doing it are welcome.

Michael

--- On Fri, 12/17/10, David Leimbach <leimy2k at gmail.com> wrote:

From: David Leimbach <leimy2k at gmail.com>

To: "michael rice" <nowgate at yahoo.com>

Date: Friday, December 17, 2010, 7:45 PM

No problem.  Haskell is a different animal than even other functional languages in my experience, and it takes time to get used to the coolness in the type system, the lazy evaluation, the point free style, functional composition and all the other interesting techniques you now
have at your fingertips for writing very expressive code :-).

Do that for a while then go back to algol based languages, and wonder why the heck anyone uses those on purpose :-).  (yeah there's good reasons to use them, but it starts to feel confining)

Dave
On Fri, Dec 17, 2010 at 4:28 PM, michael rice <nowgate at yahoo.com> wrote:

Hi, all.

Putting the list in the IO monad was deliberate. Another one I was looking at was

f :: String -> IO String
f s = do return s

main = do ios <- f "hello"
fmap tail ios

which worked fine

So, the big error was trying to add  1 + [1,2,3,4,5].

I considered that I needed an additional fmap and thought I had tried

fmap (fmap (1+)) iol

but must have messed it up, because I got an error. I guess I was on the right track.

I like to try various combinations to test my understanding. It's kind of embarrassing when I get stumped by something simple like this, but that's how one learns.

Thanks again,

Michael

--- On Fri, 12/17/10, Daniel Fischer

From: Daniel Fischer <daniel.is.fischer at googlemail.com>

Cc: "michael rice" <nowgate at yahoo.com>

Date: Friday, December 17, 2010, 4:24 PM

On Friday 17 December 2010 18:04:20, michael rice wrote:
> I don't understand this error message. Haskell appears not to understand

> that 1 is a Num.
>
> Prelude> :t 1
> 1 :: (Num t) => t
> Prelude> :t [1,2,3,4,5]
> [1,2,3,4,5] :: (Num t) => [t]
> Prelude>

>
>
Michael
>
> ===================
>
> f :: [Int] -> IO [Int]
> f lst = do return lst
>
> main = do let lst = f [1,2,3,4,5]
>           fmap (+1) lst

The fmap is relative to IO, your code is equivalent to

do let lst = (return [1,2,3,4,5])
fmap (+1) lst

~>

fmap (+1) (return [1,2,3,4,5])

~>

do lst <- return [1,2,3,4,5]
return \$ (+1) lst

but there's no instance Num [Int] in scope

You probably
meant

do let lst = f [1,2,3,4,5]
fmap (map (+1)) lst

>
> ===============================
>
> Prelude> :l test

> [1 of 1] Compiling Main             ( test.hs, interpreted )
>
> test.hs:5:17:
>     No instance for (Num [Int])
>       arising from the literal `1' at test.hs:5:17

>     Possible fix: add an instance declaration for (Num [Int])
>     In the second argument of `(+)', namely `1'
>     In the first argument of
`fmap', namely `(+ 1)'
>     In the expression: fmap (+ 1) lst
> Prelude>

--- On Fri, 12/17/10, Daniel Fischer <daniel.is.fischer at googlemail.com> wrote:

From: Daniel Fischer <daniel.is.fischer at googlemail.com>

Cc: "michael rice" <nowgate at yahoo.com>

Date: Friday, December 17, 2010, 4:24 PM

On Friday 17 December 2010 18:04:20, michael rice wrote:
> I don't understand this error message. Haskell appears not to understand
> that 1 is a Num.

>
> Prelude> :t 1
> 1 :: (Num t) => t
> Prelude> :t [1,2,3,4,5]
>
[1,2,3,4,5] :: (Num t) => [t]
> Prelude>
>
> Michael
>
> ===================
>
> f :: [Int] -> IO [Int]
> f lst = do return lst
>
> main = do let lst = f [1,2,3,4,5]

>           fmap (+1) lst

The fmap is relative to IO, your code is equivalent to

do let lst = (return [1,2,3,4,5])
fmap (+1) lst

~>

fmap (+1) (return [1,2,3,4,5])

~>

do lst <- return [1,2,3,4,5]
return \$ (+1) lst

but there's no instance Num [Int] in scope

You probably meant

do let lst = f [1,2,3,4,5]
fmap (map (+1)) lst

>
> ===============================
>
> Prelude> :l test
> [1 of 1] Compiling Main             ( test.hs, interpreted
)
>
> test.hs:5:17:
>     No instance for (Num [Int])
>       arising from the literal `1' at test.hs:5:17
>     Possible fix: add an instance declaration for (Num [Int])
>     In the second argument of `(+)', namely `1'

>     In the first argument of `fmap', namely `(+ 1)'
>     In the expression: fmap (+ 1) lst
> Prelude>

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