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Lecture1-2.md

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Lecture 1.2

Elements of Programming

Non-trivial programming languages provide:

  1. primitive expressions representing the simplest elements
  2. ways to combine and abstract expressions; Abstract expression means giving a name to expression and referring them later on.

Opening the REPL from sbt

sbt console

Primitive expression

Non-primitive expression evaluated as follow:

  1. Take the leftmost operator
  2. Evaluate the operand (left before right)
  3. Apply the operator to the operands

A name in the expression will be evaluated by replacing it with the right hand side of its definition.

Evaluation stops when the process results in a value.

Example

(2 * pi) * radius

(2 * 3.14) * radius

(6.28) * radius

(6.28) * 3

18.84

Parameters

Definitions can have parameters. Parameters are defined as below.

def Square(x: Int):Int = x * x

def sumOfSquare(x: Int, y: Int) = square(x) + square(y)

Definition parameters are defined inside parenthesis; parameter name is followed by :(colon) then space then datatype.

Datatypes in Scala
  1. Int, --- 32 bit integer
  2. Double, and -- 64 bit floating point number
  3. Boolean (true or false)

Evaluation of functional application

  1. Evaluate all function arguments (from left to right)
  2. Replace all the function application by right-hand side and at the same time
  3. Replace formal parameters of the function by actual arguments
Example
sumOfSquares(3, 2+2)
sumofSquares(3, 4) ---> Step 1 (Evaluate all function arguments)
square(3) + square(4) ---> Step 2 (Replace all function application by right-hand side)
3 * 3 + square(4) ---> Step 3 (Replace formal parameters of the function by actual arguments)
9 + square(4)
9 + 4 * 4
9 + 16
25

This scheme of evaluation is called substitution model; idea underlying in this model is reduce an expression to a value.

Avoid side effect

For example,

c++

In the above expression, there is no better way to use substitution model to reduce it to a value because it changes value of c in a single expression.

Alternative evaluation strategy

Instead of evaluating the function arguments at first, apply the right-hand side of the function application with unreduced arguments

Example

sumOfSquares(2, 3 + 3)
square(2) + square( 3 + 3 )
2 * 2 + square( 3 + 3)
4 + square( 3 + 3)
4 + (3+3) * (3 + 3)
4 + 6 * (3 + 3)
4 + 6 * 6
4 + 36
40

There are two ways to evaluate a function; call-by-value and call-by-name

Both evaluation reduces to same value if the reduced expression consists of pure function and both evaluation terminates.

Advantages

call-by-value evaluates the function arguments only once. call-by-name does not evaluates unused arguments