# Upcoming paper: The Theory of Call-by-Value Solvability at ICFP 2022

#### The Theory of Call-by-Value Solvability

The denotational semantics of the untyped $\lambda$-calculus is a well developed field built around the concept of solvable terms, which are elegantly characterized in many different ways. In particular, unsolvable terms provide a consistent notion of meaningless term. The semantics of the untyped call-by-value lambda-calculus is instead still in its infancy, because of some inherent difficulties but also because call-by-value solvable terms are less studied and understood than in call-by-name. On the one hand, we show that a carefully crafted presentation of call-by-value allows us to recover many of the properties that solvability has in call-by-name, in particular qualitative and quantitative characterizations via multi types. On the other hand, we stress that, in call-by-value, solvability plays a different role: identifying unsolvable terms as meaningless induces an inconsistent theory.