LETn

LETn is a formal binding construct used in theoretical computer science and language design to denote the simultaneous binding of n variables within a single expression. The designation emphasizes that exactly n bindings are introduced in one grouped form, generalizing the ordinary let-binding which typically binds a single variable. LETn is often discussed in the context of specification languages, functional languages, and formal calculi where concise multi-binding expressions can improve readability and reflect parallel binding intentions.

The general syntax of LETn can be described as a binding block of the form LETn ((x1 = e1, x2 = e2, ..., xn = en)) IN body, where the xi are bound to the corresponding ei, and body is evaluated in the extended environment that includes these bindings. Some languages prefer a flatter syntax such as LETn ⟨x1, x2, ..., xn⟩ = ⟨e1, e2, ..., en⟩ IN body. In many formal settings, the default interpretation is non-recursive (the bindings are evaluated in parallel and are not allowed to refer to each other within the same block). A recursive variant, sometimes called LETrec or LETn-rec, allows the bound variables to be defined in terms of each other.

Semantics can vary by language, but common themes include parallel binding, where all ei are evaluated in the outer environment and then xi are bound, and optional recursive semantics that enable mutual reference. LETn is valued for expressing multiple related bindings succinctly and for modeling environments in formal specifications.

Examples illustrate parallel binding (x=1, y=2 in body x+y) and the way dependencies are handled under different semantic choices. See also let, let rec, and parallel binding.