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We incorporate higher-order functions and state monads in Maude, thereby embedding a higher-order functional language with imperative features in the Maude framework. We illustrate, via simple programs in the resulting language: the concrete and symbolic execution of programs; their verification with respect to properties expressed in Reachability Logic, a language-parametric generalisation of Hoare...
One main challenge of the theory of computational effects is to understand how to combine various notions of effects in a meaningful way. Here, we study the particular case of the local state monad, which we would like to express as the result of combining together a family of global state monads parametrized by the number of available registers. To that purpose, we develop a notion of indexed monad...
Every finitary monad T on the category of sets is described by an algebraic theory whose n-ary operations are the elements of the free algebra Tn generated by n letters. This canonical presentation of the monad (called its Lawvere theory) offers a precious guideline in the search for an intuitive presentation of the monad by generators and relations. Hence, much work has been devoted to extend this...
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