Procedure ConstraintPropagation(ℛ, x̄i)

input: A constraint network ℛ = 〈X, D, C〉; a partial assignment path x̄i to variable Xi.

output: reduced domain Di of Xi; reduced domains of future variables; newly inferred constraints.

This is a generic procedure that performs the desired level of constraint propagation, for example forward checking, unit propagation, arc consistency over the constraint network ℛ and conditioned on x̄i.

return reduced domain of Xi