Lab 3: Lambda Calculus and Currying functions (map, foldr, foldl)

1. Lambda Calculus
2. map

   - map;
   val it = fn : ('a -> 'b) -> 'a list -> 'b list
   - map ~ [1, 2, 3, 4];
   val it = [~1,~2,~3,~4] : int list
   - map not [false, true];
   val it = [true,false] : bool list
   - map (fn x => x*x) [1, 2, 3, 4];
   val it = [1,4,9,16] : int list
   - map (fn x => print (x ^ "\n")) ["1", "2", "3", "4"];
   1
   2
   3
   4
   val it = [(),(),(),()] : unit list
   - 
     

3. foldr

   - foldr;
   val it = fn : ('a * 'b -> 'b) -> 'b -> 'a list -> 'b
   - foldr (fn(a, b) => a - b) 0 [1, 2, 3, 4];
   val it = ~2 : int
   - fun sub(a, b) = a - b;
   val sub = fn : int * int -> int
   - sub(1, sub(2, sub(3, sub(4, 0))));
   val it = ~2 : int
   - foldr (op -) 0 [1, 2, 3, 4];
   val it = ~2 : int
   - 
     

4. foldl

   - foldl;
   val it = fn : ('a * 'b -> 'b) -> 'b -> 'a list -> 'b
   - foldl (fn(a, b) => a - b) 0 [1, 2, 3, 4];
   val it = 2 : int
   - fun sub(a, b) = a - b;
   val sub = fn : int * int -> int
   - sub(4, sub(3, sub(2, sub(1, 0))));
   val it = 2 : int
   - foldl (op -) 0 [1, 2, 3, 4];
   val it = 2 : int
   - 
     

5. Examples
   1. max()
   2. isMember()
   3. union()
   4. intersect()
6. SML Exercises
   1. Write a function il2rl that converts an int list to a real list.
   2. Write a function dupList that takes [1, 2, 3] and produces [1, 1, 2, 2, 3, 3].
   3. Define a function mymap with the same type and behavior as map.
   4. Define a function myfoldr with the same type and behavior as foldr.
   5. Define a function myfoldl with the same type and behavior as foldl.