1、用ML編寫正確的程序ML Programming Correctly汪旻51103790361函數(shù)式程序設計過程式語言面向命令，函數(shù)式語言面向表達式函數(shù)式語言避免繁瑣的內存管理函數(shù)式語言要求寫出可靠正確的程序函數(shù)式語言的幾個概念函數(shù)，遞歸，模式匹配，多態(tài)類型檢測，高階函數(shù)，無窮數(shù)據結構，惰性求值2ML與純函數(shù)式編程語言的區(qū)別ML是非純函數(shù)式語言熱情求值沒有無窮數(shù)據結構模塊多態(tài)類型檢測異常處理簡單的IO指令3ML的誕生ML(Meta-Language) 是一個通用的函數(shù)式編程語言，它是由愛丁堡大學的Robin Milner在二十世紀七十年代晚期開發(fā)的，現(xiàn)在流行的方言有Standard ML和Ca

2、ml.啟發(fā)語言：ISWIM影響語言：Miranda, Haskell, Cyclone, C+, F#, Clojure, Felix, Opa, Erlang 設計初衷：LCF定理證明機中尋找證明策略ML大多被用于語言設計和操作（編譯器、分析器、定理證明機）， 但是它作為通用語言也被用于生化，金融系統(tǒng)，和宗譜數(shù)據庫，一個P2P的客戶服務器程序等等。4Level 0Hello world“Hello world!”; (*make a string*)print it; (*output it*)階乘函數(shù)fun fac 0 = 1 | fac n = n * fac (n - 1);LV.0M

3、L Programmer猿LV.1ML ProgrammerLevel Up!5Level 1值的聲明命名常量val pi = 3.14159;聲明函數(shù)fun circle_area (r) = pi*r*r;標識符字母開頭，允許數(shù)字、下劃線、撇號!%&$#+_*/:?|6Level 1基本類型數(shù)int, real + - * div mod 負號類型約束字符串連接符#”0”和“0”真值orelse, andalso, notif E then E1 else E2- fun square x = x*x;- fun square x = x*x :real;7Level 1序偶、元組、記錄序

4、偶向量(2.5 , 1.2) : real*realtype vec = real * real;記錄val ZS = name=“Zhang San”, age=20, major=“CS”;#age ZS; 20 : intLV.1ML Programmer猿LV.2ML ProgrammerLevel Up!8Level 2表達式中綴操作符(infix operator)及其優(yōu)先級、結合方式傳值調用(add.)局部聲明let . in . endlocal . in . end支持嵌套9(* Example for infix operator *)infix xor;fun (p xo

5、r q) = (p orelse q) andalso not (p andalso q);(* 中綴優(yōu)先級 *)infix 7 times;(* 傳值調用 *)sqr(sqr(sqr(2)=sqr(sqr(2*2)=sqr(sqr(4)=sqr(4*4)=sqr(16)=16*16=256 .zero(sqr(sqr(sqr(2)=zero(sqr(sqr(2*2)=zero(sqr(sqr(4)=zero(sqr(4*4)=zero(sqr(16)=zero(16*16)=zero(256)=010(* Example for let . in . end *)fun fraction (

6、n,d) = let val com = gcd(n,d) in (n div com, d div com) end; val fraction = fn : int * int - int * int(* Example for local . in . end *)local fun itfib (n, prev, curr) : int = if n=1 then curr else itfib (n-1, curr, prev+curr)in fun fib (n) = itfib(n, 0, 1)end; val fib = fn ; int - intLV.2ML Program

7、mer猿LV.3ML ProgrammerLevel Up!11 Level 3模塊系統(tǒng)結構通過Conplex.zero這樣的形式來訪問不同結構里的標識符可以相同簽名12structure Complex : ARITH = struct type t = real*real; val zero = (0.0, 0.0); fun sum (x,y), (x,y) = (x+x, y+y) : t; fun diff (x,y), (x,y) = (x-x, y-y) : t; fun prod (x,y), (x,y) = (x*x - y*y, x*y + x*y) : t; fun re

8、cip (x,y) = let val t:real = x*x + y*y in (x/t, y/t) end fun quo (z,z) = prod(z, recip z); end;signature ARITH = sig type t val zero : t val sum : t * t - t val diff : t * t - t val prod : t * t - t val quo : t * t - t end;LV.3ML Programmer猿LV.4ML ProgrammerLevel Up!13Level 4多態(tài)類型檢測多態(tài)類型的聲明關于算法（Damas(

9、1985)的博士論文）- fun pairself x = (x,x); val pairself = fn : a - a * afun fst (x,y) = x; val fst = fn : a * b - afun snd (x,y) = y; val snd = fn : a * b - bLV.4ML Programmer猿LV.5ML ProgrammerLevel Up!14Level 5List順序 3, 4可重復 3, 4, 3元素類型任意 (1,”one”),(2,”two”),(3,”three”) : (int*string) list: 右結合中綴操作符cons

10、在表前加入一個元素_通配符LV.5ML Programmer猿LV.6ML ProgrammerLevel Up!15Level 6數(shù)據類型聲明datatype person = King | Peer of string*string*int | Knight of string | Peasant of string;fun title King = His Majesty the King“ | title (Peer(deg,terr,_) = The deg of terr | title (Knight name) = Sir name | title (Peasant name)

11、 = name;16Level 6樹節(jié)點=節(jié)點+子樹or葉子datatype a tree = Lf | Br of a tree * a tree;size(tree)應用17val tree2 = Br(2, Br(1,Lf,Lf), Br(3,Lf,Lf);val tree5 = Br(5, Br(6,Lf,Lf), Br(7,Lf,Lf);val tree4 = Br(4, tree2, tree5);421356718（* make a tree *）datatype a tree = Lf | Br of a * a tree * a tree;structure Tree = s

12、tructfun size Lf = 0 | size (Br(v,t1,t2) = 1 + size t1 + size t2;fun size Lf = 0 | size (Br(v,t1,t2) = 1 + size t1 + size t2;fun depth Lf = 0 | depth (Br(v,t1,t2) = 1 + Int.max (depth t1, depth t2); fun reflect Lf = Lf | reflect (Br(v,t1,t2) = Br(v, reflect t2, reflect t1);.end;19（* 二叉查找樹 *）(* Dicti

13、onaries as Binary search trees *)signature DICTIONARY = sig type key(*type of keys*) type a t(*type of tables*) exception E of key(*errors in lookup, insert*) val empty: a t(*the empty dictionary*) val lookup: a t * key - a val insert: a t * key * a - a t val update: a t * key * a - a t end;(*Struct

14、ure Order can vary; Tree avoids referring to a free structure. *)structure Dict : DICTIONARY = struct type key = string; type a t = (key * a) tree; exception E of key; val empty = Lf; 20fun lookup (Lf, b) = raise E b | lookup (Br (a,x),t1,t2), b) =(case Spare(a,b) of GREATER = lookup(t1, b) | EQUAL

15、= x | LESS = lookup(t2, b); fun insert (Lf, b, y) = Br(b,y), Lf, Lf) | insert (Br(a,x),t1,t2), b, y) =(case Spare(a,b) of GREATER = Br (a,x), insert(t1,b,y), t2) | EQUAL = raise E b | LESS = Br (a,x), t1, insert(t2,b,y); fun update (Lf, b, y) = Br(b,y), Lf, Lf) | update (Br(a,x),t1,t2), b, y) =(case

16、 Spare(a,b) of GREATER = Br (a,x), update(t1,b,y), t2) | EQUAL = Br (a,y), t1, t2) | LESS = Br (a,x), t1, update(t2,b,y); end;LV.6ML Programmer猿LV.7ML ProgrammerLevel Up!21后期升級攻略函數(shù)與算子實現(xiàn)惰性求值實現(xiàn)搜索策略函數(shù)式程序正確性的證明抽象類型（用于建立大型系統(tǒng)）ML中的命令式程序設計應用：LAMBDA演算解釋器22總結用ML可以很容易寫出清晰、可靠的程序。值得作為函數(shù)式編程的入門語言。在犧牲部分效率的情況下，提升程序的安全性是十分必要的。因為在函數(shù)式編程里，正確性第一，清晰性次之，效率排在第三位。ML在運行前會檢查所有的類型和接口以防止出錯，讓程序員將更多的精力放在豐富語言上，而不是冗長又無用的調試和測試。ML遠沒有這次所展示的這么少，它的強大之處還待繼續(xù)去深入地了解。23參考資料ML for the Working