This paper presents equational-based logics for proving first order properties of programming languages involving effects. We propose two dual inference system patterns that can be instanciated with monads or comonads in order to be used for proving properties of different effects. The first pattern provides inference rules which can be interpreted in the Kleisli category of a monad and the coK...

A combinatorial criterium is given when a monadic quantiier is expressible by means of universe-independent monadic quantiiers of width n. It is proved that the corresponding hierarchy does not collapse. As an application, it is shown that the second resumption (or vectorization) of the HH artig quantiier is not deenable by monadic quantiiers. The techniques rely on Ramsey theory.

A formula ψ(Y ) is a selector for a formula φ(Y ) in a structure M if there exists a unique Y that satisfies ψ in M and this Y also satisfies φ. A formula ψ(X,Y ) uniformizes a formula φ(X, Y ) in a structure M if for every X there exists a unique Y such that ψ(X,Y ) holds in M and for this Y , φ(X,Y ) also holds in M. In this paper we survey some fundamental algorithmic questions and recent re...

We describe how to perform monadic computations over recursive data structures with fine grained control over the evaluation strategy. This solves the issue that the definition of a recursive monadic function already determines the evaluation strategy due to the necessary sequencing of the monadic operations. We show that compositional data types already provide the structure needed in order to...

The present paper gives a classification of the expressive power of two-variable least fixed-point logics. The main results are: 1. The two-variable fragment of monadic least fixed-point logic with parameters is as expressive as full monadic least fixed-point logic (on binary structures). 2. The two-variable fragment of monadic least fixed-point logic without parameters is as expressive as the ...