《Two Dozen Short Lessons in Haskell》（二十四）代数类型
这是《Two Dozen Short Lessons in Haskell》这本书的最后一章，第23章没有习题。
这一章里介绍了Haskell如果自定义一种类型，并且用一个双人博弈游戏为例子讲解了如何使用这些类型，里面简单介绍了Minimax算法。
至此，这本书全部学完，当然还没用Haskell写过什么大一点的程序，只是掌握了其基本概念。
1 A tree, in computer science, is an entity
a with a root and two subtrees
b with a root and a collection of subtrees, each of which is also a tree
c with a collection of subtrees, each of which has one or more roots
d described in a diagram with circles, lines, and random connections
2 A sequence, in Haskell, is an entity
a with one or more elements
b that is empty or has a first element followed by a sequence of elements
c whose elements are also sequences
d with a head and one or more tails
3 The following definition specifies
HASKELL DEFINITION • data WeekDay =
HASKELL DEFINITION • Monday | Tuesday | Wednesday | Thursday | Friday
a a type with five constructors
b a type with five explicit constructors and two implicit ones
c a tree with five roots
d a sequence with five elements
4 Given the definition in the preceding question, what is the type of the following function f?
HASKELL DEFINITION • f Tuesday = "Belgium"
a f :: WeekDay –> String
b f :: Tuesday -> "Belgium"
c f :: Day –> Country
d type of f cannot be determined
5 Types defined in Haskell scripts with the data keyword
a must begin with a capital letter
b may be imported from modules
c must be used consistently in formulas, just like intrinsic types
d all of the above
6 What kind of structure does the following type represent?
HASKELL DEFINITION • data BinaryTree = Branch BinaryTree BinaryTree | Leaf String
a a type with four constructors
b a digital structure
c a tree made up of ones and zeros
d a tree in which each root has either two subtrees or none
7 Given the preceding definition of the type BinaryTree, which of the following defines a function that computes
the total number of Branch constructors in an entity of type BinaryTree?
a branches binaryTree = 2
b branches (Branch left right) = 2
branches (Leaf x) = 0
c branches (Branch left right) = 1 + branches left + branches right
branches (Leaf x) = 0
d branches (Branch left right) = 2*branches left + 2*branches right
branches (Leaf x) = 1
8 The formula xs!!(length xs - 1)
a is recursive
b has the same type as xs
c delivers the same result as last xs
d none of the above
9 Given the definition of the function pam in the module SequenceUtilities, the formula
pam (map (+) [1 . . 5]) 10
a delivers the same result as map (1+) [1 . . 5]
b delivers the same result as pam [1 .. 5] (map (1+))
c delivers the result [11, 12, 13, 14, 15]
d all of the above
10 Given the Grid [1,3,0, 0,0,0, 0,0,2] (as in the tic-tac-toe script), what is the status of the game?
a game over, X wins
b game over, O wins
c O’s turn to play
d X’s turn to play
11 Which of the following formulas extracts the diagonal of a grid (as in the tic-tac-toe program)?
a (take 3 . map head . iterate(drop 4)) grid
b [head grid, head(drop 4 grid), head(drop 8 grid)]
c [head grid, grid!!4, last(grid)]
d all of the above
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答案
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1 b
数据结构中“树”的定义，一个根及多个子树
2 b
列表有可能是空的
3 a
data可以来自定义一种类型（也就是面向对象语言中的类），这里有五个构造器constructor。只是这里的构造器都没有带参数。
4 a
这个简单，定义好的类型可以像内置的Haskell类型一样来用。
5 d
类型名称必须是大写字母开头的；可以导入模块中；可以像内置的类型一样用。
6 d
就是二叉树的定义
7 c
求二叉树的分支总数。叶子节点分支为0，否则为左子树的分支数+右子树的分支数。
8 c
!!用来取出一个列表中指定位置上的元素。这里就是取最后一个元素，与last函数一样。
9 c？
还没搞明白pam的意思。
10 c
先走画X，后走的画O。该O方走棋。
130 XX.
000 …
002 ..O
11 b？
答案是b，我认为是d。感觉这些表示方法都正确，答案a中的函数写得相当牛X，不知道为什么不正确？