Initial Semantics aims at characterizing the syntax associated to a signature as the initial object of some category. We present an initial semantics result for typed syntax with variable binding together with its formalization in the Coq proof assistant. The main theorem was first proved on paper in the second authorâ€™s PhD thesis in 2010, and verifiedâ€¦ (More)

The theorem of three circles in real algebraic geometry guarantees the termination and correctness of an algorithm of isolating real roots of a univariate polynomial. The main idea of its proof is to consider polynomials whose roots belong to a certain area of the complex plane delimited by straight lines. After applying a transformation involving inversionâ€¦ (More)

We present an initial semantics result for typed higher-order syntax based on monads and modules over monads. The notion of module generalizes the substitution structure of monads. For a simply typed binding signature S we define a representation of S to be a monad equipped with a morphism of modules for each of its arities. The monad of abstract syntax ofâ€¦ (More)