Postscript
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
- 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.
Resources
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 (https://stackoverflow.com/questions/tagged/coq)
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.
https://deepspec.org/event/dsss17/index.html