Modules over monads and operational semantics (expanded version)

Abstract

This paper is a contribution to the search for efficient and high-level mathematical tools to specify and reason about (abstract) programming languages or calculi. Generalising the reduction monads of Ahrens et al., we introduce transition monads, thus covering new applications such as lambda-bar-mu-calculus, pi-calculus, Positive GSOS specifications, differential lambda-calculus, and the big-step, simply-typed, call-by-value lambda-calculus. Moreover, we design a suitable notion of signature for transition monads.

Variable binding and substitution for (nameless) dummies

“…(Indeed, values are closed under value substitution.) For this monad, the situation is more complex, as already exposed in[HHL22].…”

Variable binding and substitution for (nameless) dummies

“…However, 𝑋 fails to be a De Bruijn monad because there are no term variables. One way of understanding this is that values form an untyped De Bruijn monad, and terms form a module over it [HHL20,HHL22]. We present a simply-typed version of this approach in detail below in §7.5.…”