A Calculus of Lambda Calculus Contexts

The calculus λc serves as a general framework for representing contexts. Essential features are control over variable capturing and the freedom to manipulate contexts before or after hole filling, by a mechanism of delayed substitution. The context calculus λc is given in the form of an extension of the lambda calculus. Many notions of context can be represented within the framework; a particular variation can be obtained by the choice of a pretyping, which we illustrate by three examples.