Logical Pseudocode: Connecting Algorithms with Proofs

TL;DR

This paper introduces logical pseudocodes, a formal framework connecting imperative algorithms with proofs, ensuring correctness and safety, and extending computability logic with forward reasoning capabilities.

Contribution

It generalizes pseudocodes into logical pseudocodes linked to proofs, providing correctness guarantees and extending computability logic with new reasoning features.

Findings

Logical pseudocodes correspond to proofs with cuts.

Statements in logical pseudocodes are guaranteed correct and safe.

Extension of computability logic with forward reasoning.

Abstract

Proofs (sequent calculus, natural deduction) and imperative algorithms (pseudocodes) are two well-known coexisting concepts. Then what is their relationship? Our answer is that \[ imperative\ algorithms\ =\ proofs\ with\ cuts \] This observation leads to a generalization to pseudocodes which we call {\it logical pseudocodes}. It is similar to natural deduction proof of computability logic\cite{Jap03,Jap08}. Each statement in it corresponds to a proof step in natural deduction. Therefore, the merit over pseudocode is that each statement is guaranteed to be correct and safe with respect to the initial specifications. It can also be seen as an extension to computability logic web (\colw) with forward reasoning capability.