Values

34, 1.09, “IMT Atlantique” or false are values that can be integrated into calculus, as for instance 34 * 1.09 to get the conversion into euros of 34 dollars using a rate of 1.09.

Variables

• Variables are names that refer to values, while constants are fixed.

• Always favor variables over reuses of the same value.

• Values have an associated type, which defines possible operations on them.

• Programming languages define several elementary types (booleans, integers, real numbers, strings, etc.) and allow us to create your own composite types.

• Data structures allow to group simple types into collections.

Variables

The type of a variable determines:

• which operations can be applied on it,
• the space used in memory to store its associated value,
• if its value may evolve.

The location where a variable is defined determine its visibility:

• as a global or local variable.

The toolbox to write algorithms is very basic.

• defining variables / assigning values
• conditions
• loops
• defining / calling functions (focus of next session)

Managing variables

• declare variables
• assign (calculated) values to variables

a : int = 34 * nb

Conditions

Conditional statements (if) are used to split the sequential execution of the algorithm based on a Boolean condition.

if est - reel < epsilon: 
    print("Estimation found ", est)
else:
    print("Continuation")

Loops

Loops make it possible to define cycles in the execution flow of an algorithm.

# Initialize a few variables
v : List[int] = [1, 5, -5, 15, 0]
maxv : int = v[O] if len(v) > 0 else None
i : int = 0

# A loop that will iterate n times
for i in range(len(v)):
    if v[i] > max:
        max = v[i] 

An invariant is used to prove by induction that a loop effectively reaches an expected state from an initial state.

    maxv == max v[0:i]