We show that the call-by-name monad translation of simply typed lambda calculus extended with sum and product types extends to special and general inductive and coinductive types so that its crucial property of preserving typings and βand commuting reductions is maintained. Specific similar-purpose translations such as CPS translations follow from the general monad translations by specializatio...

In this paper we use techniques for monad compositions in order to provide a basis for categorical unification in the framework of generalised terms. In particular, we provide results for many-valued sets of terms, and show that this composition of set functors can be extended to a monad.

The lift monad is the construction which to a poset freely adjoins a bottom element to it, or equivalently (from the classical viewpoint), the construction which freely adjoins suprema for subsets with at most one element. In constructive mathematics (i.e. inside a topos), these two constructions are no longer equivalent, since the equivalence is based on the boolean reasoning that a set with a...

The barbarians are at the gates. Hordes of Java programmers are being exposed to generics and delegates; hundreds of packages have been uploaded to Hackage; the Haskell IRC channel has nearly hit 500 users; and it's only a matter of time before Microsoft seals that multi-billion dollar bid for Hayoo. The time has come to retreat and climb higher into our ivory tower: we need to design a languag...

Several special-purpose systems have been proposed to analyze programs in JavaScript and other dynamically typed languages. However, none of these prior systems support automated, modular verification for both higher-order and stateful features. This paper proposes a new refinement of the state monad, the Dijkstra state monad, as a way of structuring specifications for higher-order, stateful pr...

The probability measures on compact Hausdorff spaces K form a compact convex subset PK of the space of measures with the vague topology. Every continuous map f : K → L of compact Hausdorff spaces induces a continuous affine map Pf : PK → PL extending P. Together with the canonical embedding ε : K → PK associating to every point its Dirac measure and the barycentric map β associating to every pr...