Sémantique Axiomatique ou Logique de Hoare - Ensiie

The rule (axiom) for the assignment statement
{P[x ← e]}x := e{P}
P[x → e] : it is the formula P where all the free occurrences of x
are replaced by e.
e.g. x > 1[x ← x + 1] is x + 1 > 1.
Assignments change the state so we expect Hoare triples for
assignments always to reflect that change.
The meaning of this rule is clearer when read from right to left.
Intuition :
If we want x to have some property Q after the assignment, then
that property must hold for the value (e) being assigned to x
before the assignment is executed.
{(x +1) > 5} x := x+1 {x > 5} is an instance of the assignment
axiom
(ENSIIE) Hoare 17 / 52