Congratulations: We've made it to the end!

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 two choices for further reading in the Software Foundations series:
  • Programming Language Foundations (volume 2, by a set of authors similar to this book's) covers material that might be found in a graduate course on the theory of programming languages, including Hoare logic, operational semantics, and type systems.
  • Verified Functional Algorithms (volume 3, by Andrew Appel) builds on the themes of functional programming and program verification in Coq, addressing a range of topics that might be found in a standard data structures course, with an eye to formal verification.


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.

(* 30 Apr 2020 *)