This repository contains a Coq formalization and proof of soundness for :

• recursive Hoare triple verification with a verification condition generator on a simple language with procedures and aliasing;
• a method for verifying relational properties using a verification condition generator, without relying on code transformation (such as self-composition) or making additional separation hypotheses in case of aliasing;

This project was developed and tested with Coq version 8.13.0. To run the whole proof, run

make

Then, to observe the proof step-by-step for some file, run

coqide <filename.v>

for example, coqide Hoare_Triple.v

• Loc.v: definition of locations.
• Sigma.v: definition of memory state.
• Proc.v: definition of procedure names.
• Aexp.v: definition of arithmetic expressions.
• Bexp.v: definition of boolean expressions.
• Com.v: definition of commands and proof of useful property.
• Inliner.v: definintion of inliner for procedures and proof of useful property.
• Hoare_Triple.v: definintion of Hoare Triples and proof of useful property.
• Vcg.v and Vcg_Opt.v: definition of respectively a naive verification condition genrator and a optimized version and proof of useful property.
• Correct.v: proof that Hoare Triples can be verified using verification condition generator.
• Rela.v: definition of relational properties and proof of useful property.
• Vcg_Rela.v: definition of a verification condition generator for Relational Properties using the verification condition generator define in Vcg.v and proof of useful property.
• Correct_Rela.v: proofs that Relational Properties can be verified using verification condition generator.
• Examples.v: some examples.