Reasoning About MLIR Semantics Through Effects and Handlers 

MLIR is a novel framework for developing intermediate representations (IRs) of compilers. At its core, MLIR is a framework for the specification of syntax fragments (dialects) and optimisations, which can be combined à-la-carte to form customised IRs. Through this, MLIR allows IR abstractions to be shared across different domains. With rapid adoption of MLIR across industry, techniques for formalised semantics which matches the flexibility and extensibility 
offered by MLIR are urgently needed. We propose a framework for MLIR semantics based on effect handlers, which allows for dialect semantics to be specified in a modular and composable way, parallel to MLIR. We also describe several research directions continuing on from handlers-based MLIR semantics.