Programming Language Notes

A programming language is a mathematical calculus, or formal language. Its goal is to express algorithms in a manner that is unambiguous to people and machines. Like any calculus, a language’s notation contains both syntax and semantics. Since syntax can be easily translated, the semantics are more fundamental. Church and Turing showed that the minimal semantics of the Lambda Calculus and Universal Turing Machine are sufficient to emulate the semantics of any more complicated programming language or machine. Reducing a particular language to the Lambda Calculus may require holistic restructuring of programs in that language. We say that a particular language feature (e.g., continuations, macros, garbage collection) is expressive if it cannot be emulated without restructuring programs that use it.