We consider the problem of establishing a relationship between two interpretations of base type terms of a λc-calculus extended with algebraic operations. We show that the given relationship holds if it satisfies a set of natural conditions. We apply this result to 1) comparing two monadic semantics related by a strong monad morphism, and 2) comparing two monadic semantics of fresh name creatio...

An algebra is called corecursive if from every coalgebra a unique coalgebra-toalgebra homomorphism exists into it. We prove that free corecursive algebras are obtained as coproducts of the terminal coalgebra (considered as an algebra) and free algebras. The monad of free corecursive algebras is proved to be the free corecursive monad, where the concept of corecursive monad is a generalization o...

For a monad S on a categoryK whose Kleisli category is a quantaloid, we introduce the notion of modularity, in such a way that morphisms in the Kleisli category may be regarded as V(bi)modules (= profunctors, distributors), for some quantale V . The assignment S // V is shown to belong to a global adjunction which, in the opposite direction, associates with every (commutative, unital) quantale ...

The main result of this paper shows how coalgebraic traces, in suitable Kleisli categories, give rise to traced monoidal structure in those Kleisli categories, with finite coproducts as monoidal structure. At the heart of the matter lie partially additive monads inducing partially additive structure in their Kleisli categories. By applying the standard “Int” construction one obtains compact clo...

This article demonstrates how a powerful and expressive abstraction from concurrency theory plays a dual rôle as a programming tool for concurrent applications and as a foundation for their verification. This abstraction—monads of resumptions expressed using monad transformers—is cheap: it is easy to understand, easy to implement, and easy to reason about. We illustrate the expressiveness of th...

We investigate similarities between non-deterministic and probabilistic ways of describing a system in terms of computation trees. We first show that the construction of traces for both kinds of relations follow the same principles of construction (which could be described in terms of monads, but this does not happen here). Finally representations of measurable trees in terms of probabilistic r...

The simplicial category ∆ plays many roles all over mathematics. In one of these roles it is a monad freely generated by a single object (see [9], Section 3, [2], Section 4, and references therein). That ∆ is isomorphic to this free monad may be understood as a coherence result connecting the syntax brought by the equational presentation of monads and the semantics given by the order preserving...

The Dijkstra monad has been introduced recently for capturing weakest precondition computations within the context of program verification, supported by a theorem prover. Here we give a more general description of such Dijkstra monads in a categorical setting. We first elaborate the recently developed view on program semantics in terms of a triangle of computations, state transformers, and pred...

The usual monad laws can directly be used as rewrite rules for Isabelle’s simplifier to normalise monadic HOL terms and decide equivalences. In a commutative monad, however, the commutativity law is a higher-order permutative rewrite rule that makes the simplifier loop. This AFP entry implements a simproc that normalises monadic expressions in commutative monads using ordered rewriting. The sim...

A symbol is a tool used by the author in conveying his messages to reader. Symbols are also an aesthetic for authors. This study aims reveal symbolic rationality collection of Heaven Sungsang stories Triyanto Triwikromo. In this study, authors use new theory namely Critical Semiotics. The semiotics has its roots merging Northrop Frye's semiotic and Jurgen Habermas's Theory. emphasis point on Se...