Every dialogue category comes equipped with a continuation monad defined by applying the negation functor twice. In this paper, we advocate that this double negation monad should be understood as part of a larger parametric monad (or a lax action) with parameter taken in the opposite of the dialogue category. This alternative point of view has one main conceptual benefit: it reveals that the st...

Pattern discovery in unaligned DNA sequences is a fundamental problem in computational biology with important applications in finding regulatory signals. Current approaches to pattern discovery focus on monad patterns that correspond to relatively short contiguous strings. However, many of the actual regulatory signals are composite patterns that are groups of monad patterns that occur near eac...

Increased stabilization of mRNA coding for key cancer genes can contribute to invasiveness. This is achieved by down-regulation of exosome cofactors, which bind to 3'-UTR in cancer-related genes. Here, we identified amphiregulin, an EGFR ligand, as a target of WD repeat protein Monad, a component of R2TP/prefoldin-like complex, in MDA-MB-231 breast cancer cells. Monad specifically interacted wi...

For programmers, Monads are a well-known way to represent an abstract data structure, but without knowing its true nature. Admittedly, the definition of Monads in Category Theory is too subtle and obscure so makes people to avoid from trying to understand them. In this paper, we attempt to explore popular Monads in a purely functional programming language, Haskell, with a Category-theoretic min...

Probability is often counter-intuitive, and it always involves a great deal of math. This is unfortunate, because many applications in robotics and AI increasingly rely on probability theory. We introduce a modular toolkit for constructing probability monads, and show that it can be used for everything from discrete distributions to weighted particle filtering. This modular approach allows us t...

Even a functor without an adjoint induces a monad, namely, its codensity monad; this is subject only to the existence of certain limits. We clarify the sense in which codensity monads act as substitutes for monads induced by adjunctions. We also expand on an undeservedly ignored theorem of Kennison and Gildenhuys: that the codensity monad of the inclusion of (finite sets) into (sets) is the ult...

In this article we give a construction of a polynomial 2-monad from an operad and describe the algebras of the 2-monads which then arise. This construction is different from the standard construction of a monad from an operad in that the algebras of our associated 2-monad are the categorified algebras of the original operad. Moreover it enables us to characterise operads as categorical polynomi...

The Dijkstra and Hoare monads have been introduced recently for capturing weakest precondition computations and computations with preand post-conditions, within the context of program verification, supported by a theorem prover. Here we give a more general description of such monads in a categorical setting. We first elaborate the recently developed view on program semantics in terms of a trian...

Many program optimisations involve transforming a program in direct style to an equivalent program in continuation-passing style. This paper investigates the theoretical underpinnings of this transformation in the categorical setting of monads. We argue that so-called absolute Kan Extensions underlie this program optimisation. It is known that every Kan extension gives rise to a monad, the code...

These two quotations represent the key ideas behind two major research agendas. The first captures the essence of monadic I/O, which is the fundamental abstraction used to provide input/output and concurrency in the lazy, purely-functional language (Concurrent) Haskell. The second captures the essence of first-class synchronous events, which is the fundamental abstraction used to provide concur...