PL-SML3: Functions

Functional programming

1. Avoid mutation

2. Functions as values

3. Laziness

4. First-class functions: can using functions wherever we use values.
   Higher-order functions: accepts functions as arguments and return functions as results.

5. Function closure: Functions can use bindings from outsides the function definition (in scope where function is defined)
   --code
   --environment

6. lexical scope: using environment where function is defined.
   Dynamic scope: using environment where function is called.

Why lexical scope ?

• Function meaning does not depend on variable names used.
• Function can be type-checked and reasoned where defined.
• Closures can easily store the data they need.

Currying

• Every function just takes one argument.
• Caller and callee must use the same technique (currying).
• A famous example:
  fun foldl (f, acc, xs) =
  case xs of
  null => acc
  | x::xs=> foldl (f, f(acc, x), xs)
  fun foldr (f, acc, xs) =
  case xs of
  null => acc
  | x::xs=> f (foldr (f, acc, xs), x)

Value restriction

When you get a warning/error, you should just turn var-binding back into fun-binding.

Continuation

Reference

ref e to create a reference with initial contents e
e1 := e2 to update contents
!e to retrieve contents
val x = ref [] value restriction

call-back