lab08: init

lab08/monadLab.lhs

@@ -0,0 +1,80 @@
+Below we have some mathematical binary arguments that you may recognize from homework 2.
+
+> data Binop =
+>     Plus     -- +  :: Int  -> Int  -> Int
+>   | Minus    -- -  :: Int  -> Int  -> Int
+>   | Times    -- *  :: Int  -> Int  -> Int
+>   | Divide   -- /  :: Int  -> Int  -> Int
+>   deriving (Show)
+
+applyOp performs these operations, but unlike in the homework,
+you now must consider errors (represented by 'Nothing').
+
+> applyOp :: Binop -> Maybe Int -> Maybe Int -> Maybe Int
+
+Plus is done for you.  Notice how code must check for 'Nothing'
+for each operand.
+
+> applyOp Plus mi mj =
+>   case mi of
+>     Nothing -> Nothing
+>     Just i ->
+>       case mj of
+>         Nothing -> Nothing
+>         Just j -> Just $ i + j
+
+Minus is also done for you.  This case **does** use monads,
+but without the do syntax.
+
+> applyOp Minus mi mj =
+>   mi >>= (\i -> mj >>= (\j -> Just $ i - j))
+
+Implement Times and Divide.  Try the Times case without monads (as we did with
+the Plus case).
+
+> applyOp Times mi mj = error "TBD"
+
+For the Divide case, use bind (>>=) as we did for Minus.
+On an attempt to divide by 0, return Nothing as the answer.
+
+> applyOp Divide mi mj = error "TBD"
+
+The following test cases will help you verify your changes.
+
+> testapp1 = applyOp Minus (applyOp Times (Just 3) (Just 4)) $ applyOp Divide (Just 8) (Just 2)
+> testapp2 = applyOp Minus (applyOp Times (Just 3) (Just 4)) $ applyOp Divide (Just 8) (applyOp Plus (Just 3) (Just (-3)))
+
+
+Now implement applyOp', which implements all methods using the do syntax.
+The Plus case is done for you once again.  Be sure to check for zero with Divide.
+
+> applyOp' :: Binop -> Maybe Int -> Maybe Int -> Maybe Int
+> applyOp' Plus mi mj = do
+>   i <- mi
+>   j <- mj
+>   return $ i + j
+> applyOp' Minus mi mj = error "TBD"
+> applyOp' Times mi mj = error "TBD"
+> applyOp' Divide mi mj  = error "TBD"
+
+More test cases:
+
+> testapp1' = applyOp' Minus (applyOp' Times (Just 3) (Just 4)) $ applyOp' Divide (Just 8) (Just 2)
+> testapp2' = applyOp' Minus (applyOp' Times (Just 3) (Just 4)) $ applyOp' Divide (Just 8) (applyOp' Plus (Just 3) (Just (-3)))
+
+
+Finally, note the following function for incrementing and decrementing ints.
+
+> mincr :: Int -> Maybe Int
+> mincr i = Just $ i + 1
+
+> mdecr :: Int -> Maybe Int
+> mdecr i = Just $ i - 1
+
+Experiment with these functions and the >>= syntax.
+Here is one example:
+
+> testIncDec = Just 7 >>= mincr >>= mincr >>= mincr >>= mdecr
+
+Does bind seem more natural in this case than using do?  Why or why not?
+