Effects Without Monads: Non-determinism – Back to the Meta Language

Abstract

We reflect on programming with complicated effects, recalling an undeservingly forgotten alternative to monadic programming and checking to see how well it can actually work in modern functional languages.We adopt and argue the position of factoring an effectful program into a first-order effectful DSL with a rich, higher-order 'macro' system. Not all programs can be thus factored. Although the approach is not general-purpose, it does admit interesting programs. The effectful DSL is likewise rather problem-specific and lacks general-purpose monadic composition, or even functions. On the upside, it expresses the problem elegantly, is simple to implement and reason about, and lends itself to non-standard interpretations such as code generation (compilation) and abstract interpretation. A specialized DSL is liable to be frequently extended; the experience with the tagless-final style of DSL embedding shown that the DSL evolution can be made painless, with the maximum code reuse.We illustrate the argument on a simple but representative example of a rather complicated effect -non-determinism, including committed choice. Unexpectedly, it turns out we can write interesting non-deterministic programs in an ML-like language just as naturally and elegantly as in the functional-logic language Curry -and not only run them but also statically analyze, optimize and compile. The richness of the Meta Language does, in reality, compensate for the simplicity of the effectful DSL.The key idea goes back to the origins of ML as the Meta Language for the Edinburgh LCF theorem prover. Instead of using ML to build theorems, we now build (DSL) programs.

The optics of language-integrated query

“…3.2. Quoting from [47], "extensibility is the strong suite of the tagless-final embedding"; therefore, this task should be easy. Indeed, we simply need to declare a new type class where we have a component containing an entry for each domain optic in the model, as shown in Fig.…”