  interpreters are tools to compute approximations for behaviors of a program.
These approximations can then be used for optimisation or for error detection.
In this paper, we show how to describe an abstract interpreter using the
type-theory based theorem prover Coq, using inductive types for syntax and
structural recursive programming for the abstract interpreter's kernel. The
abstract interpreter can then be proved correct with respect to a Hoare logic
for the programming language.
