Sources: background card; Lattner et al., MLIR: A Compiler Infrastructure for the End of Moore’s Law, arXiv:2002.11054
Theory (CT-ML wiki): Compiler Correctness · Double-Pushout Rewriting
Lowering is the process of converting operations from a higher-level MLIR Dialect into operations from a lower-level one — e.g. linalg (linear algebra) → scf (loops) → cf (branches) → llvm dialect → LLVM IR. Each step is typically implemented as a set of pattern-based rewrite rules run by a conversion pass, similar in spirit to an LLVM Pass but operating dialect-to-dialect instead of IR-to-IR.
A single program is usually lowered through several dialects in sequence rather than jumping straight to LLVM, because each intermediate level is still a good place to run optimizations that only make sense at that level (e.g. loop tiling makes sense on scf/linalg, but not once everything has become flat LLVM instructions).
This progressive, multi-level lowering is a close structural analogue to what The Original Idea describes wanting: multiple ASTs at different levels (source language, typed IR, LLVM/MLIR) connected by transformations, all persisted as one graph.