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We propose a novel approach to soundly combining linear types with multi-shot effect handlers. Linear type systems statically ensure that resources such as file handles and communication channels are used exactly once. Effect handlers provide a rich modular programming abstraction for implementing features ranging from exceptions to concurrency to backtracking. Whereas conventional linear type systems bake in the assumption that continuations are invoked exactly once, effect handlers allow continuations to be discarded (e.g. for exceptions) or invoked more than once (e.g. for backtracking). This mismatch leads to soundness bugs in existing systems such as the programming language Links, which combines linearity (for session types) with effect handlers. We introduce control-flow linearity as a means to ensure that continuations are used in accordance with the linearity of any resources they capture, ruling out such soundness bugs. We formalise the notion of control-flow linearity in a System F-style core calculus Feff∘, equipped with linear types, an effect type system, and effect handlers. We define a linearity-aware semantics in order to formally prove that Feff∘ preserves the integrity of linear values in the sense that no linear value is discarded or duplicated. In order to show that control-flow linearity can be made practical, we adapt Links based on the design of Feff∘, in doing so fixing a long-standing soundness bug. Finally, to better expose the potential of control-flow linearity, we define an ML-style core calculus Qeff∘, based on qualified types, which requires no programmer provided annotations, and instead relies entirely on type inference to infer control-flow linearity. Both linearity and effects are captured by qualified types. Qeff∘ overcomes a number of practical limitations of Feff∘, supporting abstraction over linearity, linearity dependencies between type variables, and a much more fine-grained notion of control-flow linearity. 

WebAssembly (Wasm) is a low-level portable code format offering near native performance. It is intended as a compilation target for a wide variety of source languages. However, Wasm provides no direct support for non-local control flow features such as async/await, generators/iterators, lightweight threads, first-class continuations, etc. This means that compilers for source languages with such features must ceremoniously transform whole source programs in order to target Wasm. We present WasmFX an extension to Wasm which provides a universal target for non-local control features via effect handlers, enabling compilers to translate such features directly into Wasm. Our extension is minimal and only adds three main instructions for creating, suspending, and resuming continuations. Moreover, our primitive instructions are type-safe providing typed continuations which are well-aligned with the design principles of Wasm whose stacks are typed. We present a formal specification of WasmFX and show that the extension is sound. We have implemented WasmFX as an extension to the Wasm reference interpreter and also built a prototype WasmFX extension for Wasmtime, a production-grade Wasm engine, piggybacking on Wasmtime's existing fibers API. The preliminary performance results for our prototype are encouraging, and we outline future plans to realise a native implementation.