Jewels of the lambda calculus: scope

If abstraction is the grand prize-winning jewel of the lambda calculus, then scope is the first runner-up. Mitch Wand teaches his graduate students that the scoping properties of a language are one of the Four Questions we ask in order to understand its semantics ("why is this language different from all other languages?").

Scope is the first static property of any programming language. Lexical scope gives us a static context in which to understand a fragment of a program. Within the following program:

λy.λx.y

we can look at the inner portion, λx.y, and in order to understand what portion of the program gives meaning to its body, we must understand that y is bound to--i.e., will receive its runtime meaning from--the static context of the fragment that binds it, i.e., the outer binding.

The static aspects of a program are what communicate its properties to the reader, allowing the reader to understand its behavior logically, as opposed to experimentally. Scope is the property that communicates the relationships between fragments of a program, whether through arguments, module imports, or class hierarchies. Scope is the static assignment of responsibility to these units of the program for communicating dynamic information.