From: Jim Pryor <profjim@jimpryor.net>
Date: Sun, 12 Dec 2010 06:48:41 +0000 (-0500)
Subject: starting assignment 10
X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=commitdiff_plain;h=61144e14eacb1ce6fdd602962f5d77c11deed156

starting assignment 10

Signed-off-by: Jim Pryor <profjim@jimpryor.net>
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+-- from the Glasgow Haskell Compiler sources (/Control/Monad/State/Strict.hs)
+
+-- An example from /The Craft of Functional Programming/, Simon
+-- Thompson (<http://www.cs.kent.ac.uk/people/staff/sjt/>),
+-- Addison-Wesley 1999: \"Given an arbitrary tree, transform it to a
+-- tree of integers in which the original elements are replaced by
+-- natural numbers, starting from 0.  The same element has to be
+-- replaced by the same number at every occurrence, and when we meet
+-- an as-yet-unvisited element we have to find a \'new\' number to match
+-- it with:\"
+--
+-- > data Tree a = Nil | Node a (Tree a) (Tree a) deriving (Show, Eq)
+-- > type Table a = [a]
+--
+-- > numberTree :: Eq a => Tree a -> State (Table a) (Tree Int)
+-- > numberTree Nil = return Nil
+-- > numberTree (Node x t1 t2)
+-- >        =  do num <- numberNode x
+-- >              nt1 <- numberTree t1
+-- >              nt2 <- numberTree t2
+-- >              return (Node num nt1 nt2)
+-- >     where
+-- >     numberNode :: Eq a => a -> State (Table a) Int
+-- >     numberNode x
+-- >        = do table <- get
+-- >             (newTable, newPos) <- return (nNode x table)
+-- >             put newTable
+-- >             return newPos
+-- >     nNode::  (Eq a) => a -> Table a -> (Table a, Int)
+-- >     nNode x table
+-- >        = case (findIndexInList (== x) table) of
+-- >          Nothing -> (table ++ [x], length table)
+-- >          Just i  -> (table, i)
+-- >     findIndexInList :: (a -> Bool) -> [a] -> Maybe Int
+-- >     findIndexInList = findIndexInListHelp 0
+-- >     findIndexInListHelp _ _ [] = Nothing
+-- >     findIndexInListHelp count f (h:t)
+-- >        = if (f h)
+-- >          then Just count
+-- >          else findIndexInListHelp (count+1) f t
+--
+-- numTree applies numberTree with an initial state:
+--
+-- > numTree :: (Eq a) => Tree a -> Tree Int
+-- > numTree t = evalState (numberTree t) []
+--
+-- > testTree = Node "Zero" (Node "One" (Node "Two" Nil Nil) (Node "One" (Node "Zero" Nil Nil) Nil)) Nil
+-- > numTree testTree => Node 0 (Node 1 (Node 2 Nil Nil) (Node 1 (Node 0 Nil Nil) Nil)) Nil
+--
+-- sumTree is a little helper function that does not use the State monad:
+--
+-- > sumTree :: (Num a) => Tree a -> a
+-- > sumTree Nil = 0
+-- > sumTree (Node e t1 t2) = e + (sumTree t1) + (sumTree t2)