1111課題 - wwes @ ウィキ

課題１

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sumlist

定義
fun sumList nil = 0

 | sumList (a::b) = a + sumList b;

実行例

• val t = [2,3,4];

val t = [2,3,4] : int list

• sumList t;

val it = 9 : int

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member

定義
fun member (E, nil) = false

 | member (E, h::t) = E = h orelse member (E,t);

実行例
val it = [2,5,5] : int list

• member(2,t);

val it = true : bool

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unique

定義
fun unique nil = []

| unique (a::A) = if member(a,A) = true
                  then unique A
                  else a::unique A;

実行例

• unique [3,2,3,4,2,5];

val it = [3,4,2,5] : int list

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filter

定義
fun filter (f,nil) = []

| filter(f,a::A) = if f(a) = true
                   then a::filter(f,A)
                   else filter(f,A)

実行例

• fun t x = if x = 2 then true else false;

val t = fn : int -> bool

• filter(t,[2,1,2,1,2,1,3,3,2]);

val it = [2,2,2,2] : int list

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delete

定義
fun delete (D, nil) = []

 | delete (D,h::H) = if h == D
             then delete (D,H)
             else h::delete (D, H);

実行例

• val t = [2,3,3,3,3,3,3,5,5];

val t = [2,3,3,3,3,3,3,5,5] : int list

• delete (3,t);

val it = [2,5,5] : int list

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課題２
difference(差集合)
定義
fun difference ([],B) = []

| difference(a::A,B) = if member(a,B) = true
                   then difference(A,B)
                   else a::difference(A,B);

実行例

• val n = [1,2,3,4,5];

val n = [1,2,3,4,5] : int list

• val m = [4,5,6,7];

val m = [4,5,6,7] : int list

• difference (n,m);

val it = [1,2,3] : int list

fun intersection ([],ys)=[]
| intersection(x::xs,ys)=if member(x,ys) =true

		   then x::intersection (xs,ys)
		   else intersection (xs,ys);

fun union (xs,ys)= unique(xs@ys);

fun subseteq ([],ys)= true
| subseteq (x::xs,ys)= if member(x,ys)=true

		 then subseteq(xs,ys)
		 else false;

• intersection([1,2,3],[1,3,5,7]);

val it = [1,3] : int list

• union([1,2,3],[1,3,5,7]);

val it = [2,1,3,5,7] : int list

• subseteq ([1,2,3],[1,3,5,7]);

val it = false : bool

• subseteq ([1,2,3],[1,3]);

val it = false : bool

• subseteq ([1,2,3],[1,2,3]);

val it = true : bool

• subseteq ([1,3],[1,2,3]);

val it = true : bool