We present a generic framework for specifying and implementing ooine partial evaluators. The framework provides the infrastructure for specializing higher-order programs with computational effects speciied through a monad. It performs sound specialization for all monadic instances and is evaluation-order independent. It subsumes most previously published partial evaluators for higher-order func...

Abstract We develop the Scott model of programming language PCF in univalent type theory. Moreover, we work constructively and predicatively. To account for non-termination PCF, use lifting monad (also known as partial map classifier monad) from topos theory, which has been extended to theory by Escardó Knapp. Our results show that is a viable approach partiality can be constructed predicative ...

Abstract The algebraic properties of the combination probabilistic choice and nondeterministic have long been a research topic in program semantics. This paper explains formalization Coq proof assistant monad equipped with both choices: geometrically convex monad. has an immediate application: it provides model for that implements nontrivial interface, which allows proofs by equational reasonin...

This paper describes LPS, a Language Prototyping System that facilitates the modular development of interpreters from semantic building blocks. The system is based on the integration of ideas from Modular Monadic Semantics and Generic Programming. To define a new programming language, the abstract syntax is described as the fixpoint of non-recursive pattern functors. For each functor an algebra...

Coalgebras in a Kleisli category yield a generic definition of trace semantics for various types of labelled transition systems. In this paper we apply this generic theory to generative probabilistic transition systems, short PTS, with arbitrary (possibly uncountable) state spaces. We consider the sub-probability monad and the probability monad (Giry monad) on the category of measurable spaces ...

The exception monad, while an adequate mechanism for providing the denotational semantics of exceptions, is somewhat awkward to program with. Just as any other monad, it forces a programming style in which exceptional computations are explicitly sequentialized in the program text. In addition, values of computation types must usually be tested before use, in order to determine if they correspon...

Completely iterative algebras (cias) are those algebras in which recursive equations have unique solutions. In this paper we study complete iterativity for algebras with computational effects (described by a monad). First, we prove that for every analytic endofunctor on Set there exists a canonical distributive law over any commutative monad M , hence a lifting of that endofunctor to the Kleisl...

Modules over monads (or: actions of monads on endofunctors) are structures in which a monad interacts with an endofunctor, composed either on the left or on the right. Although usually not explicitly identified as such, modules appear in many contexts in programming and semantics. In this paper, we investigate the elementary theory of modules. In particular, we identify the monad freely generat...

We introduce the notion of an equational lifting monad: a commutative strong monad satisfying one additional equation (valid for monads arising from partial map classifiers). We prove that any equational lifting monad has a representation by a partial map classifier such that the Kleisli category of the former fully embeds in the partial category of the latter. Thus equational lifting monads pr...

We show that techniques for monad composition can be used nicely for modeling object oriented programming concepts In this functional setting we develop a new model for composing objects from individual features in a modular way Features are similar to abstract subclasses but separate the core functionality of a subclass from overwriting meth ods We view method overwriting more generally as res...