Congratulations: We've made it to the end of Logical Foundations!

Looking Back

We've covered quite a bit of ground so far. Here's a quick review...
  • Functional programming:
    • "declarative" programming style (recursion over immutable data structures, rather than looping over mutable arrays or pointer structures)
    • higher-order functions
    • polymorphism
  • Logic, the mathematical basis for software engineering:
                   logic                        calculus
            --------------------   ~   ----------------------------
            software engineering       mechanical/civil engineering
    • inductively defined sets and relations
    • inductive proofs
    • proof objects
  • Coq, an industrial-strength proof assistant
    • functional core language
    • core tactics
    • automation

Looking Forward

If what you've seen so far has whetted your interest, you have several choices for further reading in later volumes of the Software Foundations series. Some of these are intended to be accessible to readers immediately after finishing Logical Foundations; others require a few chapters from Volume 2, Programming Language Foundations. The Preface chapter in each volume gives details about prerequisites.


Here are some other good places to learn more...
  • This book includes some optional chapters covering topics that you may find useful. Take a look at the table of contents and the chapter dependency diagram to find them.
  • For questions about Coq, the #coq area of Stack Overflow ( is an excellent community resource.
  • Here are some great books on functional programming
    • Learn You a Haskell for Great Good, by Miran Lipovaca [Lipovaca 2011].
    • Real World Haskell, by Bryan O'Sullivan, John Goerzen, and Don Stewart [O'Sullivan 2008]
    • ...and many other excellent books on Haskell, OCaml, Scheme, Racket, Scala, F sharp, etc., etc.
  • And some further resources for Coq:
    • Certified Programming with Dependent Types, by Adam Chlipala [Chlipala 2013].
    • Interactive Theorem Proving and Program Development: Coq'Art: The Calculus of Inductive Constructions, by Yves Bertot and Pierre Casteran [Bertot 2004].
  • If you're interested in real-world applications of formal verification to critical software, see the Postscript chapter of Programming Language Foundations.
  • For applications of Coq in building verified systems, the lectures and course materials for the 2017 DeepSpec Summer School are a great resource.
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