While the study of quantale-like structures goes back up to the 1930’s (notwithstanding that the term itself was introduced in [2] in connection with certain aspects of C∗-algebras), there has recently been much interest in quantales in a variety of contexts. The most important connection probably is with Girard’s linear logic. In particular, one can enunciate the following slogan: Quantales ar...

Combining monadic computations may induce a significant syntactic overhead. To allow monadic programming in direct style, we have developed Coco, a type-based tool that automatically rewrites ML code inserting necessary binds, unit, and morphisms between monads. This tool demonstration will show how to take advantage of Coco to facilitate using monadic libraries in practice, and will discuss po...

A fundamental result of Büchi states that the set of monadic second-order formulas true in the structure (Nat,<) is decidable. A natural question is: what monadic predicates (sets) can be added to (Nat,<) while preserving decidability? Elgot and Rabin found many interesting predicates P for which the monadic theory of 〈Nat,<,P〉 is decidable. The Elgot and Rabin automata theoretical method has b...

Monads are becoming an increasingly important tool for structural functional programming, because they provide a uniform framework for describing a wide range of programming language features. To facilitate program transformation, Fokkinga derived a su cient assumption under which there is a kind of socalled monadic catamorphisms which satisfy several general laws useful for the transformation ...

We study the expressiveness of finite message-passing automata with a priori unbounded channels and show them to capture exactly the class of MSC languages that are definable in existential monadic second-order logic interpreted over MSCs. Moreover, we prove the monadic quantifier-alternation hierarchy over MSCs to be infinite and conclude that the class of MSC languages accepted by message-pas...

Node selection in trees is a fundamental operation to XML databases, programming languages, and information extraction. We propose a new class of querying languages to define n-ary node selection queries as compositions of monadic queries. The choice of the underlying monadic querying language is parametric. We show that compositions of monadic MSO-definable queries capture n-ary MSO-definable ...

We show, for an arbitrary adjunction F U : B → A with B Cauchy complete, that the functor F is comonadic if and only if the monad T on A induced by the adjunction is of effective descent type, meaning that the free T-algebra functor F : A → AT is comonadic. This result is applied to several situations: In Section 4 to give a sufficient condition for an exponential functor on a cartesian closed ...