• Imperative: how to execute logic
• Declarative: what to compute

• How to execute program logic
• Defines control flow as sequence of statements
• Language examples
  • Procedural: C, Pascal
  • Object-oriented: C++, Java, PHP, Python, Ruby
  • Parallel-processing: NESL

int total = 0;
for (int i = 0; i <= 5; i++) {
    total += i;
}
System.out.println(total);

• What to execute
• Defines program logic instead of control flow
• Language examples
  • Logic: Prolog
  • Functional: Lisp, Scala, Julia, Haskell, R, Matlab
  • Database: SQL

select * from users

def fib(n: Int) : Long = n match {
  case 0 | 1 => n
  case _ => fib(n-1) + fib(n-2)
}

• Control flow in program steps
• Decomposes software top to bottom into procedures
• Subroutines or functions
• Features
  • Simplicity in small-scale programs
  • Easy to match with execution in processor
  • Mutable data

program Fibonacci;
function fib(n: Integer): Integer;
var a: Integer = 1;
    b: Integer = 1;
    f: Integer;
    i: Integer
begin
    if (n=1) or (n=2) then fib := 1
    else begin
        for i := 3 to n do begin
            f := a+b;
            b := a;
            a := f;
        end;
        fib := f;
    end;
end;

• Evaluate mathematical functions
• Functions: pure without side effects, side-effecting, higher-order
• Features
  • Clear responsibilities
  • Immutable data
  • Contracts and correctness

def fib(n: Int): Int = 
    if n <= 1 then n
    else fib(n-1) + fib(n-2)

def fib(n: Int) : Long = n match {
  case 0 | 1 => n
  case _ => fib(n-1) + fib(n-2)
}