call by name, assignment, and the lambda calculus
We define an extension of the call-by-name lambda calculus with additional constructs and reduction rules that represent mutable variables and assignments. The extended calculus has neither a concept of an explicit store nor a concept of evaluation order; nevertheless, we show that programs in the calculus can be implemented using a single-threaded store. We also show that the new calculus has the Church-Rosser property and that it is a conservative extension of classical lambda calculus with respect to operational equivalence; that is, all algebraic laws of the functional subset are preserved.
assignment lambda calculus extensibility reduction rules variability concept evaluation program functional