Lambda the Ultimate

Has anyone worked with a lambda calculus variant in which divergence is present as a value but different from bottom?

It seems like that might be a useful variant for me, so I wanted to see if it's been done or is obviously broken before hammering out the details.

Thanks

Draining the Swamp: Micro Virtual Machines as Solid Foundation for Language Development
Kunshan Wang, Yi Lin, Stephen Blackburn, Michael Norrish, Antony Hosking
2015

Many of today's programming languages are broken. Poor performance, lack of features and hard-to-reason-about semantics can cost dearly in software maintenance and inefficient execution. The problem is only getting worse with programming languages proliferating and hardware becoming more complicated. An important reason for this brokenness is that much of language design is implementation-driven. The difficulties in implementation and insufficient understanding of concepts bake bad designs into the language itself. Concurrency, architectural details and garbage collection are three fundamental concerns that contribute much to the complexities of implementing managed languages. We propose the micro virtual machine, a thin abstraction designed specifically to relieve implementers of managed languages of the most fundamental implementation challenges that currently impede good design. The micro virtual machine targets abstractions over memory (garbage collection), architecture (compiler backend), and concurrency. We motivate the micro virtual machine and give an account of the design and initial experience of a concrete instance, which we call Mu, built over a two year period. Our goal is to remove an important barrier to performant and semantically sound managed language design and implementation.

Inside you will find the specification of an LLVM-inspired virtual instruction set with a memory model (enables proper GC support) including a specification of concurrent weak-memory operations (reusing C(++)11, a debatable choice), relatively rich control-flow primitive (complete stack capture enabling coroutines or JIT-style de-optimization), and live code update.