Coroutines are a general control flow construct that can eliminate control flow fragmentation inherent in event-driven programs, and are still missing in many popular languages. Coroutines with snapshots are a first-class, type-safe, stackful coroutine model, which unifies many variants of suspendable computing, and is sufficiently general to express iterators, single-assignment variables, async-await, actors, event streams, backtracking, symmetric coroutines and continuations. In this paper, we develop a formal model called $lambda_{rightsquigarrow}$ (lambda-squiggly) that captures the essence of type-safe, stackful, delimited coroutines with snapshots. We prove the standard progress and preservation safety properties. Finally, we show a formal transformation from the $lambda_{rightsquigarrow}$ calculus to the simply-typed lambda calculus with references.
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