1. Functions, Patterns and Datatypes
Creating New Functions
Composition
Currying
Recursive Functions
Patterns
Programmer-defined Datatypes
CSE S. Tanimoto Functions, Patterns , and Types

2. Composition and Currying in ML
Combining two functions to create a new function by composition. h(x) = g(f(x))
ML provides the built in operator “o”
Combining a function and one value to create a new function by currying.
h(x) = f(a, x)
ML does it implicitly.
CSE S. Tanimoto Functions, Patterns , and Types

3. CSE 341 -- S. Tanimoto Functions, Patterns , and Types
Composition in ML
fun f x = x+1;
val f = fn : int -> int
fun g y = 2*y;
val g = fn : int -> int
val h = g o f;
val h = fn : int -> int
h 5;
val it = 12
CSE S. Tanimoto Functions, Patterns , and Types

4. CSE 341 -- S. Tanimoto Functions, Patterns , and Types
Currying in ML
fun times x y = x*y;
val times = fn : int * int -> int
val times10 = times 10;
val times10 = fn : int -> int
times10 5;
val it = 50
CSE S. Tanimoto Functions, Patterns , and Types

5. Recursive Functions in ML
fun fact n = if n = 0 then 1
else n * fact (n-1);
val fact = fn : int -> int
fact 5;
val it = 120
fact 100;
uncaught exception overflow
raised at <file stdin>
CSE S. Tanimoto Functions, Patterns , and Types

6. Recursive Functions Using Patterns
fun fact 0 = 1 |
fact n = n * fact(n-1);
val fact = fn : int -> int
fact 5;
val it = 120
CSE S. Tanimoto Functions, Patterns , and Types

7. Reversing a List: Using if
fun rev lst = if lst = nil then nil
else
val rev : fn ''a list -> ''a list
rev [1, 2, 3, 4];
val it = [4, 3, 2, 1] : int list
rev [“nice”, “feature”, “recursion”];
val it = [“recursion”, “feature”, “nice”] : string list
rev [1.0, 2.0, 3.0];
Error: operator and operand don’t agree (equality type required)
CSE S. Tanimoto Functions, Patterns , and Types

8. Reversing a List: Using Patterns
fun rev2(nil) = nil |
rev2(a::b) =
val rev2 : fn 'a list -> 'a list
rev2 [1, 2, 3, 4];
val it = [4, 3, 2, 1] : int list
rev2 [1.0, 1.2, 1.3];
val it = [1.3, 1.2, 1.0] : real list
CSE S. Tanimoto Functions, Patterns , and Types

9. Programmer-Defined “Types”
Use type to create a synonym or abbreviation for an existing type
type piles = int list list;
type piles = int list list
val somepiles : piles = [[1,2,3],[4,5],[6,7]];
val sompiles = [[1,2,3],[4,5],[6,7]] : piles
CSE S. Tanimoto Functions, Patterns , and Types

10. Programmer-Defined “Datatypes”
Use datatype to create an entirely new type -- one which could not be expressed using only the basic types, tuples, and lists.
datatype color = Red | Yellow | Green;
datatype color Green | Red | Yellow
val mycolor = Red;
val mycolor = Red : color
fun okToGo c = if c = Green then true else false;
val okToGo fn : color -> bool
okToGo(Red);
val it = false : bool
CSE S. Tanimoto Functions, Patterns , and Types

11. Datatypes with Constructors
datatype tnode =
L of int |
I of int * tnode * tnode |
NULL;
(A tree node is either a Leaf containing an integer,
an interior node containing an int and two tree nodes,
or it’s NULL -- representing an empty tree.)
CSE S. Tanimoto Functions, Patterns , and Types

12. Working with Datatypes
(* tree.ml *)
(* Create a binary tree, test whether an element occurs in the tree, and insert an element *)
val mytree = I(50,I(25,L(10),L(40)),I(75,L(60),L(90)));
fun member (i, NULL) = false |
member (i, L(j)) = (i = j) |
member (i, I(j, ls, rs)) =
if i = j then true
else if i < j then member (i, ls)
else member (i, rs);
CSE S. Tanimoto Functions, Patterns , and Types

13. Working with Datatypes (Cont)
fun
insert (i, NULL) = L(i) |
insert (i, L(j)) =
if i < j then I(j,L(i),NULL)
else I(j,NULL,L(i)) |
insert (i, I(j, ls, rs)) =
if i=j then I(j, ls, rs)
else if i < j then I(j, insert(i,ls),rs)
else I(j, ls, insert(i, rs));
CSE S. Tanimoto Functions, Patterns , and Types