An imperative language uses a sequence of statements to determine how to reach a certain goal. (Eg. C, C++, Java). Eg. Below, each statement changes the state of the program, from assigning values to each variable to the final addition of those values.

int total = 0;
int number1 = 5;
int number2 = 10;
total = number1 + number2; 

As seen imperative programming involves modifying mutable variables, using assignments, control structures like if-else, for, break, continue, etc.

Problem:
The imperative programming is what programmers use mostly in their day to day life. The problem is scaling. Imperative programming conceptualizes programs word by word. To solve this, we need higher level abstractions of collections, polynomials, geometric shapes, etc. Hence we come to Functional Programming.

A functional language takes functional approach to problem solving i.e. based on functions. Functions are first class citizens i.e. whatever you can do with data i.e. declare it anywhere, pass it as parameters, return them from functions, use operators on them, etc, you can do that on Functions and thus use functions to form the program. Eg. List, Python, Scala. Note that Lisp is a functional programming language in a restricted sense. Python and Scala are functional programming languages in a wider sense meaning they also count as object oriented languages. Functional programming is becoming popular due to:

• simpler reasoning principles
• better modularity
• good for exploiting parallelism for multicore and cloud computing. Watch https://www.youtube.com/watch?v=3jg1AheF4n0 for information on this by Martin Odersky.

Any program written in a logic programming language is a set of sentences in logical form, expressing facts and rules about some problem domain. The rules are written in the form of clauses (Eg. Prolog, Datalog).

A OOP language takes an object based approach to problem solving. Objects are first class citizens i.e. whatever you can do with data i.e. declare it anywhere, pass it as parameters, use operators on them, etc, you can do that on Objects and thus use objects to form the program. (Eg. Java)

Doing concurrent programming in Java requires writing and managing threads, async blocks, locks and releasing locks, etc. Scala makes this simple by providing parallel collections and lambda expressions.

Note: Java8 tries to improve on this problem in Java by introducing lambda expressions.

b + 1 is and expression, while a = b + 1; is a statement. A statement forms a complete unit of execution.

Functional programming is like a calculator. An interactive shell lets one write expressions and responds with their value (REPL: Read-Eval-Print-Loop).

Scala uses def to define variables. The definitions can have parameters:

def example = 2      // evaluated when called
val example = 2      // evaluated immediately
lazy val example = 2 // evaluated once when needed

def square(x: Double) = x * x
# return type can be specified:
def square(x: Double): Double = x * x

Note: Specifying return type for functions is optional, but if the function is recursive then its mandatory. Primitive datatypes are same as in Java but capitalized: Int, Double, Boolean

It looks like if - else for Java but is used for expressions and not statements.

def abs(x: Int) = if (x >= 0) x else -x

Sometimes && or || do not require the right-hand operand to be evaluated. This is called as short-circuit evaluation

true || e  // is true irrespective of e
false || e // is false irrespective of e

Scala allows Nested Functions so that the functions that are not supposed to be accessed by the user can be nested inside the ones that are accessible.

A block is defined using curly braces: { .... }. The last element of a block is an expression that defines its value i.e. return expression. The word return is optional. Blocks are themselves expressions; a block may appear everywhere an expression can.

// This block is invalid:
def x = {
    def y = {
      5
    }
}

// These are valid
def x = {
    def y = 5
}
def x = {
    def y = {
      5
    }
    y
}

The definitions inside a block are only visible from inside that block. The definitions inside a block shadow definitions of the same names outside the block.

val x = 0
def f(y: Int) = y + 1
val result = {
  val x = f(3); // f is not shadowed inside the block, x is.
  x * x
} + x

// Here result = 16

** Semicolons ** are optional, used to separate multiple expressions written on the same line.

Expressions extending to multiple lines can be written by using curly braces:

( expression1 
+ expression2 )

Or, the operator can be written as the end of first line indicating that the operation is not yet finished.

expression1 + 
expression2

In Scala, an expression can be:

• An identifier such as x, isGoodEnough
• A literal, like 0, 1.0, "abc"
• A function application, like sqrt(x)
• An operator application, like -x, y + x
• A selection, like math.abs
• A conditional expression, like if (x < 0) -x else x
• A block, like { val x = math.abs(y) ; x * 2 }
• An anonymous function, like x => x + 1.