A language of constructions for minimal logic is the -calculus, where cut-elimination is encoded as fi-reduction. We examine corresponding languages for the minimal version of the modal logic S4, with notions of reduction that encodes cut-elimination for the corresponding sequent system. It turns out that a natural interpretation of the latter constructions is a -calculus extended by an idealized version of Lisp's eval and quote constructs. In this Part IIIa, we examine the termination and confluence properties of the evQ and evQ H -calculi. Most results are negative: the typed calculi do not terminate, the subsystems \Sigma and \Sigma H that propagate substitutions, quotations and evaluations downwards do not terminate either in the untyped case, and the untyped evQ H -calculus is not confluent. However, the typed versions of \Sigma and \Sigma H do terminate, so the typed evQ-calculus is confluent. It follows that the typed evQ-calculus is a conservative extension of the typed S4-cal...