Let-Binding in a Linear Lambda Calculus with First-Class Continuations

In our previous work, we proposed a linear lambda calculus with first-class continuations. In the usual lambda calculus, an argument value can be duplicated and deleted, but the continuation cannot. In our calculus, a value is allowed to be neither duplicated nor deleted, but a continuation is allowed, so it can be considered to be dual with the usual lambda calculus. In this paper, we extend a linear lambda calculus with first-class continuations by adding let-binding. We define a syntax, a call-by-value reduction, and a type system of the calculus. Then, we discuss the let-polymorphism in our calculus.