We introduce an axiomatic extension of Höhle’s Monoidal Logic called Semi–divisible Monoidal Logic, and prove that it is complete by showing that semi–divisibility is preserved in MacNeille completion. Moreover, we introduce Strong semi– divisible Monoidal Logic and conjecture that a predicate formula α is derivable in Strong Semi–divisible Monadic logic if, and only if its double negation ¬¬α ...

The main goal of this paper is to introduce and investigate the related theory on monadic effect algebras. First, we design axiomatic system existential quantifiers algebras then use it give definition universal quantifier Then, relatively complete subalgebra prove that there exists a one-to-one correspondence between set all subalgebras. Moreover, characterize generated formula ideals Riesz co...

This paper investigates corecursive deenitions which are at the same time monadic. This corresponds to functions that generate a data structure following a corecursive process, while producing a computational eeect modeled by a monad. We introduce a functional, called monadic anamorphism, that captures deenitions of this kind. We also explore another class of monadic recursive functions, corres...

The first-order theory of linear order is far from trivia!. The monadic (secondorder) theory of linear order is much stronger. Stil~ surpr,Mng decidability results were proven in that direction. Rabin proved in [10i that the monadic theory of the rational chain is decidable. Hence the monadic theory of all countable linear orders is decidable. Biichi proved in [I] that the monadic theory of ord...

Most of the existing literature about monadic programming focuses on theory but does not address issues of software engineering. Using monadic parsing as a running example, we demonstrate monadic programs written in a typical style, recognize how they violate abstraction boundaries, and recover clean abstraction crossings through monadic reflection. Once monadic reflection is made explicit, it ...

Given a complete and cocomplete symmetric monoidal closed category V and a symmetric monoidal V -category C with cotensors and a strong V -monad T on C, we investigate axioms under which an ObCindexed family of operations of the form αx : (Tx) v −→ (Tx)w provides semantics for algebraic operations, which may be used to extend the usual monadic semantics of the computational λ-calculus uniformly...