Call-by-Value λ-calculus and LJQ

LJQ is a focused sequent calculus for intuitionistic logic, with a simple restriction on the first premiss of the usual left introduction rule for implication. In a previous paper we discussed its history (going back to about 1950, or beyond) and presented its basic theory and some applications; here we discuss in detail its relation to call-by-value reduction in lambda calculus, establishing a connection between LJQ and the CBV calculus λC of Moggi. In particular, we present an equational correspondence between these two calculi forming a bijection between the two sets of normal terms, and allowing reductions in each to be simulated by reductions in the other.