5 Higher order Functions on Lists

1. try:

   use list;
   
   double:num -> num;
   double(n) <= n*n;
   
   map double [1,2,3,4];
   
   map (lambda x => x*x) [1,2,3,4];
   

2. try

   use list;
   
   type string == list(char);
   
   type student == string X string;
   
   type class == list(student X num);
   
   c:class;
   
   c <= [(("Fred","Jones"),66),(("Ali","Mohamed"),76),(("Mary","Ward"),92),(("Colin","Gold"),31)];
   
   
   map (lambda ((x,y),z) => x) c;
   
   
   map (lambda ((x,y),z) => z) c;
   
   foldr  (0 ,(+))  (map (lambda ((x,y),z) => z) c);
   
   (foldr  (0 ,(+))  (map (lambda ((x,y),z) => z) c))/length(c);
   
   
   averageClass: class -> num;
   averageClass k <= (foldr  (0 ,(+))  (map (lambda ((x,y),z) => z) k))/length(k);
   
   
   averageClass	 c;
   
   type course == string X class;
   
   c1: course;
   
   c1 <=("CS1", c);
   
   c2: course;
   
   c2 <=("Maths", [(("Fred","Jones"),36),(("Ali","Mohamed"),56),(("Mary","Ward"),45),(("Colin","Gold"),71)]);
   
   averageCourse:course -> num;
   averageCourse(x,y) <= averageClass(y);
   
   averageCourse c1;
   
   type degreeprogramme == list(course);
   
   cs:degreeprogramme;
   cs <= [c1,c2];
   
   cs;
   
   map averageCourse cs;
   map (lambda (x,y) => (x, averageCourse (x,y))) cs;
   

3. Redo all last week's exercises using higher order functions.

4. Look at the files on igor in directory: /usr/local/share/hope/lib. That explains the point of use list; at the beginning of the above.