Comments I think there s a fundamental disconnect with this article and it starts with piece on lambda calculus There is need of a bridge between the historical work and computing languages Ada Byron developed some notation for the algorithmic computing so programming paradigms should trace back at least to her In 1963 John McCarthy wrote a seminal paper A basis for a mathematical theory of computation found In Computer Programming and formal systems North Holland McCarthy s paper is a bridge from what we have today and the Church Turing Kleene work McCarthy s basic argument was that recursive functions were the natural setting Denotational semantics is the natural outgrowth of McCarthy s ideas by way of Strachey and Scott