stschaef / ivy_semantics

Formal Semantics of Ivy

This repository contains some small-step structural operational semantics of the Ivy programming language. The semantics are given as formal inference rules and are implemented in Coq.

Setup

To make imports work using coqtop inside VSCode I had to adjust my coq.coqProjectRoot and coqtop.binPath settings.

For instance on my laptop, I have the following settings added to my settings.json:

"coqtop.binPath": "/opt/homebrew/bin",
"coq.coqProjectRoot": "/Users/stevenschaefer/ivy_semantics/coq",

So Far

A slimmed down typechecker and small step interpreter has been implemented so far in Coq. To execute this, I extract OCaml from the Coq code and then connect this to a parser made via ocamlyacc.

This is still very much a work in progress and does not fully work. However, the typechecker currently works. Additionally, a slimmed down interpreter with only variables and type declarations currently works.

TODOs

• Get rid of Maps.v import. It is only useful for ensuring eqb works as expected. This should be easily fixable with the proper imports.
• Get rid of double import warning.
• Implement function symbols properly.
• Prove type preservation/progress for expressions and commands
• Prove that commands are well-formed if the underlying expressions are well-typed, and vice versa
• Need to refactor nondeterminism. Probably as maps out of the unit type?
• Incorporate assertions (axioms and pre-/post-conditions) into the interpreter
• Properly scope variables
• Actions need to be implemented. For now we are only handling void actions; however, at some point it might be worth working in (multiple) return types. There is a decent argument to be made that these multiple return types are just syntactic sugar anyway, and they don't seem to show up in the code we care about (say Aman's ivybench)
• Probably separate the use of a function as a location and as an actual function
• In the parser, add the syntactic sugar where capital letters are implicitly quantified. Ideally add enough sugar to be able to run all of the benchmarks without too much headache.
• Implement modules to serve as axiom schemas.