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#+TITLE: About Coq

Coq is a formal proof management system which provides a pure
functional language with nice dependent types together with an
environment for writing machine-checked proofs.

- [[./posts/StronglySpecifiedFunctions.org][A Series on Strongly-Specified Funcions in Coq]] ::
  Using dependent types and the ~Prop~ sort, it becomes possible to specify
  functions whose arguments and results are constrained by properties.
  Using such a “strongly-specified” function requires to provide a proof that
  the supplied arguments satisfy the expected properties, and allows for soundly
  assuming the results are correct too. However, implementing dependently-typed
  functions can be challenging.

- [[./posts/Ltac.org][A Series on Ltac]] ::
  Ltac is the “tactic language” of Coq. It is commonly advertised as the common
  approach to write proofs, which tends to bias how it is introduced to new Coq
  users (/e.g./, in Master courses). In this series, we present Ltac as the
  metaprogramming tool it is, since fundamentally it is an imperative language
  which allows for constructing Coq terms interactively and incrementally.

- [[./posts/RewritingInCoq.html][Rewriting in Coq]] ::
  The ~rewrite~ tactics are really useful, since they are not limited to the Coq
  built-in equality relation.

- [[./posts/ClightIntroduction.html][A Study of Clight and its Semantics]] ::
  Clight is a “simplified” C AST used by CompCert, the certified C compiler. In
  this write-up, we prove a straighforward functional property of a small C
  function, as an exercise to discover the Clight semantics.

- [[./posts/AlgebraicDatatypes.html][Proving Algebraic Datatypes are “Algebraic”]] ::
  The set of types which can be defined in a language together with ~+~ and ~*~
  form an “algebraic structure” in the mathematical sense, hence the name. It
  means the definitions of ~+~ and ~*~ have to satisfy properties such as
  commutativity or the existence of neutral elements.

- [[./posts/Coqffi.org][A Series on ~coqffi~]] ::
  ~coqffi~ generates Coq FFI modules from compiled OCaml interface
  modules (~.cmi~). In practice, it greatly reduces the hassle to
  together OCaml and Coq modules within the same codebase, especially
  when used together with the ~dune~ build system.