Added CP examples.

IntegerLineMPD/prob1.lhs

@@ -35,6 +35,19 @@ What is the probability of ~a~?  (If ~a~ is not in the support of pd, we "round"
 >   lookup a [(_, p)] = p
 >   lookup a ((a', p):rest) = if a <= a' then p else lookup a rest
 
+Probabilities:
+
+> prob :: (a -> Bool) -> PD a -> Double
+> prob e (PD aps) = sum [p | (a, p) <- aps, e a == True]
+
+> lift :: (Bool -> Bool -> Bool) -> (a -> Bool) -> (a -> Bool) -> (a -> Bool)
+> lift op f g = \ a -> op (f a) (g a) 
+
+> condProb :: (a -> Bool) -> (a -> Bool) -> PD a -> Maybe Double
+> condProb e1 e2 pd = let pe2 = prob e2 pd in
+>                     if pe2 == 0.0 
+>                     then Nothing
+>                     else Just (prob (lift (&&) e1 e2) pd / pe2)
 
 Cummulative probabilities:
 
@@ -51,6 +64,7 @@ Expected value:
 > expectation :: PD Double -> Double
 > expectation (PD as) = sum (map (uncurry (*)) as) 
 
+
 Some distributions
 
 > bernoulli :: Double -> PD Double
@@ -195,19 +209,9 @@ What is the probability of the first flip being a head given that there are at l
 >         then return a 
 >         else twoOutOfThree
 
-> toss3 :: PD (Double, Double, Double)
-> toss3 = PD [((x, y, z), p) | x <- s, y <- s, z <- s]
->   where p = 0.5 * 0.5 * 0.5
->         s = [0.0, 1.0]
-
-> prob :: (a -> Bool) -> PD a -> Double
-> prob e (PD aps) = sum [p | (a, p) <- aps, e a == True]
-
-> cprob :: (a -> Bool) -> (a -> Bool) -> PD a -> Maybe Double
-> cprob e1 e2 pd = let pe2 = prob e2 pd in
->                  if pe2 == 0.0 
->                  then Nothing
->                  else Just (prob (\ a -> e1 a && e2 a) pd / pe2)
+> fstHtwoHs1 :: Nat -> Double
+> fstHtwoHs1 n = let pd = PD (get_pd n twoOutOfThree) in
+>                get_prob 1.0 pd
 
 > fstH :: (Double, Double, Double) -> Bool
 > fstH (x, _, _) = x == 1.0
@@ -215,7 +219,28 @@ What is the probability of the first flip being a head given that there are at l
 > twoHs :: (Double, Double, Double) -> Bool
 > twoHs (x, y, z) = x + y + z >= 2.0
 
-> lala = cprob fstH twoHs toss3
+> toss3 :: RV (Double, Double, Double)
+> toss3 = do a <- toss 0.5
+>            b <- toss 0.5
+>            c <- toss 0.5
+>            return (a, b, c)
+
+> fstHtwoHs2 :: Nat -> Maybe Double
+> fstHtwoHs2 n = let pd = PD (get_pd n toss3) in
+>                condProb fstH twoHs pd
+
+> fstHtwoHs3 :: Nat -> Maybe Double
+> fstHtwoHs3 n = let t1 = get_pd n (toss 0.5) in
+>                let pd = PD [((x, y, z), px * py * pz) | (x, px) <- t1, (y, py) <- t1, (z, pz) <- t1] in
+>                condProb fstH twoHs pd
+
+> fstHtwoHs4 :: Maybe Double
+> fstHtwoHs4 = let t1 = pd2List (bernoulli 0.5) in
+>              let pd = PD [((x, y, z), px * py * pz) | (x, px) <- t1, (y, py) <- t1, (z, pz) <- t1] in
+>              condProb fstH twoHs pd
+
+
+
 
 
 3.2 Factor