David Turner gives a condensed summary of the lambda calculus and functional programming in this paper on Churchâ€™s Thesis and Functional Programming.
The lambda-calculus, which Church developed during the period of convergence from which the Thesis emerged, has influenced almost every aspect of the development of programming and programming languages. It is the basis of functional programming, which after a long infancy is entering adulthood as a practical alternative to traditional ad-hoc imperative programming languages. Many important ideas in mainstream programming languagesâ€”recursion, procedures as parameters, linked lists and trees, garbage collectors â€” came by cross fertilization from functional programming. Moreover the main schools of both operational and denotational semantics are lambda-calculus based and amount to using functional programming to explain other programming systems.
The original project from whose wreckage by paradox lambda-calculus survived, to unify logic with an account of computable functions, appears to have been reborn in unexpected form, via the propositions-as-types paradigm.
Many of the PLT topics mentioned on LtU are covered - PLT in 20 pages or less. I'm still hoping for someone to publish a pop-PLT book that takes something like these 20 pages and turns them into a 800 page novel. In the meantime, this is a nice roadmap for PLT that helps provide the connections between such things as Curry-Howard, Coq, System F. (About as close to a cheatsheet for LtU that I've come across).