General Computer Science 320201 GenCS I & II Lecture ... - Kwarc

- fun both_plus (x:int,y:int) = fn (z:int) => x + y + z;
val both_plus int * int -> int -> int
cascaded_plus 4 5;
Another simplification (related to those above)
- fun cascaded_plus x y = x + y;
val cascaded_plus : int -> int -> int
c○: Michael Kohlhase 70
e EdNote: Generla Problem: how to mark up SML syntax?
Folding Procedures
Definition 102 SML provides the left folding operator to realize a recurrent computation
schema
foldl : (’a * ’b -> ’b) -> ’b -> ’a list -> ’b
foldl f s [x1,x2,x3] = f(x3,f(x2,f(x1,s)))
We call the procedure f the iterator and s the start value
Example 103 Folding the iterator op+ with start value 0:
foldl op+ 0 [x1,x2,x3] = x3+(x2+(x1+0))
x3
x3
f
x2
+
x2
f
x1
+
f
+
s
x1 0
Thus the procedure fun plus xs = foldl op+ 0 xs adds the elements of integer lists.
Folding Procedures (continued)
Example 104 (Reversing Lists)
c○: Michael Kohlhase 71
foldl op:: nil [x1,x2,x3]
= x3 :: (x2 :: (x1:: nil))
Thus the procedure fun rev xs = foldl op:: nil xs reverses a list
c○: Michael Kohlhase 72
40
x3
::
x2
::
::
x1 n