The center Z(C) of an autonomous category C is monadic over C (if certain coends exist in C). The notion of Hopf monad naturally arises if one tries to reconstruct the structure of Z(C) in terms of its monad Z: we show that Z is a quasitriangular Hopf monad on C and Z(C) is isomorphic to the braided category ZC of Z-modules. More generally, let T be a Hopf monad on an autonomous category C. We ...

We show the benefits of applying modular monadic semantics to compiler construction. Modular monadic semantics allows us to define a language with a rich set of features from reusable building blocks, and use program transformation and equational reasoning to improve code. Compared to denotational semantics, reasoning in monadic style offers the added benefits of highly modularized proofs and m...

Dependency analysis is vital to several applications in computer science. It lies at the essence of secure information flow analysis, binding-time etc. Various calculi have been proposed literature for analysing individual dependencies. Abadi et. al., by extending Moggi’s monadic metalanguage, unified these into Core Calculus (DCC). DCC has served as a foundational framework dependency last two...

We show the benefits of applying modular monadic semantics to compiler construction. Modular monadic semantics allows us to define a languagewith a rich set of features from reusable building blocks, and use program transformation and equational reasoning to improve code. Compared to denotational semantics, reasoning in monadic style offers the added benefits of highly modularized proofs and mo...

Cost monadic logic has been introduced recently as a quantitative extension to monadic second-order logic. A sentence in the logic defines a function from a set of structures to N∪{∞}, modulo an equivalence relation which ignores exact values but preserves boundedness properties. The rich theory associated with these functions has already been studied over finite words and trees. We extend the ...

A monadic formula ψ(Y) is a selector for a monadic formula φ(Y) in a structure M if ψ defines in M a unique subset P of the domain and this P also satisfies φ in M. If C is a class of structures and φ is a selector for ψ in every M ∈ C, we say φ is a selector for φ over C. For a monadic formula φ(X,Y) and ordinals α ≤ ω1 and δ < ω, we decide whether there exists a monadic formula ψ(X,Y) such th...

In this paper, we look at two categorical accounts of computational effects (strong monad as a model of the monadic metalanguage, adjunction as a model of call-bypush-value with stacks), and we adapt them to incorporate global exceptions. In each case, we extend the calculus with a construct, due to Benton and Kennedy, that fuses exception handling with sequencing. This immediately gives us an ...

Assume ZFC + "There is a weakly compact cardinal" is consistent. Then: (i) For every S c C), ZFC + "S and the monadic theory of o2 are recursive each in the other" is consistent; and (ii) ZFC + "The full second-order theory of w2 is interpretable in the monadic theory of W2" is consistent. Introduction. First we recall the definition of monadic theories. The monadic language corresponding to a ...

The paper gives a survey of known results related to computational devices (finite and push–down automata) recognizing monadic generalized quantifiers in finite models. Some of these results are simple reinterpretations of descriptive—feasible correspondence theorems from finite–model theory. Additionally a new result characterizing monadic quantifiers recognized by push down automata is proven...