as a Model of Computation in Coq

We formalise a weak call-by-value lambda-calculus we call L in the constructive type theory of Coq and study it as a minimal functional programming language and as a model of computation. We show key results including (1) semantic properties of procedures are undecidable, (2) the class of total procedures is not recognisable, (3) a class is decidable if it is recognisable, corecognisable, and logically decidable, and (4) a class is recognisable if and only if it is enumerable. Most of the results require a step-indexed self-interpreter. All results are verified formally and constructively, which is the challenge of the project. The verification techniques we use for procedures will apply to call-by-value functional programming languages formalised in Coq in general.

- Paper, Extended Journal version
- Browse the sources (with proof-state, might be slow)
- Download sources (compile with Coq 8.6 and 8.7)
- Dependency graph of Coq files