Intersection Types and Computational Rules

The invariance of the meaning of a λ-term by reduction/expansion w.r.t. the considered computational rules is one of the minimal requirements one expects to hold for a λ-model. Being the intersection type systems a general framework for the study of semantic domains for the Lambda-calculus, the present paper provides a characterisation of “meaning invariance” in terms of characterisation results for intersection type systems enabling typing invariance of terms w.r.t. various notions of reduction/expansion, like β, η and a number of relevant restrictions of theirs.