Readable semi-automatic formal proofs of Depth-First Search in graphs using Why3

Ran Chen (1) , Jean-Jacques Levy (2)

1 Institute of Software
2 PI.R2 - Design, study and implementation of languages for proofs and programs

Quite often formal proofs are not published in conferences or journal articles, because formal proofs are usually too long. A typical article states the ability of having implemented a formal proof, but the proof itself is often sketched in terms of a natural language. At best, some formal lemmas and definitions are stated. Can we do better ? We try here to publish the details of a formal proof of the white-paths theorem about depth-first search in graphs. We use Why3 as the proving platform, because Why3 uses first-order logic augmented with inductive definitions of predicates and because Why3 makes possible to delegate bits of proofs to on-the-shelf automatic provers at same time as Why3 provides interfaces with interactive proof checkers such that Coq, PVS or Isabelle. Algorithms on graphs are also a good testbed since graphs are combinatorial structures whose algebraic properties are not fully obvious. Depth-first search may look over-simple, but it is the first step of the construction of a library of readable formal proofs for more complex algorithms on graphs with more realistic data structures.

Mots clés: Logic and computation; Proof certification; Graph Algorithms

Domaines: Informatique et langage [cs.CL]

Ran Chen, Jean-Jacques Levy. Readable semi-automatic formal proofs of Depth-First Search in graphs using Why3. 2015. ⟨hal-01253136⟩