What the article calls "loci" satisfy the axioms of an affine space, with the exception (for example in the case of pointer arithmetic) that the base set might

What the article calls "loci" satisfy the axioms of an affine space, with the exception (for example in the case of pointer arithmetic) that the base set might not be a field but only a ring, and therefore it would be a "pseudo-affine" space based on a module rather than a vector space. Programming by specifying algebraic properties is very easy and natural, but in most languages it's a pain to encode in the type system.