We have definitionally extended Isabelle/HOLCF to support axiomatic Haskell-style constructor classes. We have subsequently defined the functor and monad classes, together with their laws, and implemented state and resumption monad transformers as generic constructor class instances. This is a step towards our goal of giving modular denotational semantics for concurrent lazy functional programm...

We define the category of tidy symmetric multicategories. We construct for each tidy symmetric multicategory Q a cartesian monad (EQ, TQ) and extend this assignation to a functor. We exhibit a relationship between the slice construction on symmetric multicategories, and the ‘free operad’ monad construction on suitable monads. We use this to give an explicit description of the relationship betwe...

Limitations of monad stacks get in the way of developing highly modular programs with effects. This pearl demonstrates that Functional Programming’s abstraction tools are up to the challenge. Of course, abstraction must be followed by clever instantiation: Huet’s zipper for the monad stack makes components jump through unanticipated hoops.

Are we interested in choice functions or function for choice? Was it my choice or did I choose? In the end it is all about sorts and operators, terms as given by the term monad over the appropriate category, and variable substitutions as morphisms in the Kleisli category of that particular term monad.

We prove that iteration theories can be introduced as algebras for the monad Rat on the category of signatures assigning to every signature Σ the rationalΣ-tree signature. This supports the result that iteration theories axiomatize precisely the equational properties of least fixed points in domain theory: Rat is the monad of free rational theories and every free rational theory has a continuou...

In this chapter we explain constructive methods for computing the cohomol-ogy of a sheaf on a projective variety. We also give a construction for the Beilinson monad, a tool for studying the sheaf from partial knowledge of its cohomology. Finally, we give some examples illustrating the use of the Beilinson monad.

Article history: Received 30 October 2014 Accepted 6 January 2015 Available online xxxx Communicated by Ross Street MSC: 18A32 18B15

We propose an intermediate form based on monad-algebra comprehensions (to represent queries), folds (to represent computation), and setoids over polynomial datatypes (to represent data), suitable for use in collection processing. Such an intermediate form captures, in a uniform way, large fragments of many recent largescale collection processing languages such as MapReduce, PIG, DryadLINQ, and ...

Spans are pairs of arrows with a common domain. Despite their symmetry, spans are frequently viewed as oriented transitions from one of the codomains to the other codomain. The transition along an oriented span might be thought of as transitioning backwards along the first arrow (sometimes called ‘leftwards’) and then, having reached the common domain, forwards along the second arrow (sometimes...

In our recent work [5] on automating Isabelle proofs, we discovered that several proof search problems can be elegantly expressed as a monadic program. Unfortunately, Standard ML does not natively support the kinds of polymorphism required to easily express a Monad abstraction, nor similar abstractions such as Applicative and Functor . In this paper, we present a technique for encoding construc...