A Metalanguage for Guarded Iteration

Abstract

Notions of guardedness serve to delineate admissible recursive definitions in various settings in a compositional manner. In recent work, we have introduced an axiomatic notion of guardedness in symmetric monoidal categories, which serves as a unifying framework for various examples from program semantics, process algebra, and beyond. In the present paper, we propose a generic metalanguage for guarded iteration based on combining this notion with the fine-grain callby-value paradigm, which we intend as a unifying programming language for guarded and unguarded iteration in the presence of computational effects. We give a generic (categorical) semantics of this language over a suitable class of strong monads supporting guarded iteration, and show it to be in touch with the standard operational behaviour of iteration by giving a concrete big-step operational semantics for a certain specific instance of the metalanguage and establishing soundness and (computational) adequacy for this case.

An Adequate While-Language for Hybrid Computation

“…Next we build a syntax-independent, denotational counterpart to the operational semantics previously introduced. In order to achieve this, we will take advantage of the general principles of fine-grain call-by-value [15,18,27], and thus introduce a monad for the duration semantics. Recall that (−) ⋆ denotes the Kleisli lifting of a monad T, the set R + denotes the non-negative real numbers and the set R+ denotes the non-negative real numbers with infinity.…”

“…The submonad H + of H that arises from this restriction, was studied in [16] and enjoys better properties than H; we expect our adequacy result to restrict accordingly. This task is however not entirely trivial, as it requires a considerable adaptation of the language to keep track of progressiveness of terms, yet a systematic approach to this issue was proposed recently [18].…”