Distilling the Requirements of Gödel’s Incompleteness Theorems with a Proof Assistant

Formalization of Shannon’s Theorems Using the Coq Proof-Assistant

概 要 Proofs in information theory can be very technical, to the point that the exposition of details must sometimes be sacrificed for the sake of clarity. The only way to provide complete proofs without impairing understanding is to formalize them with the help of dedicated computer software: proof-assistants. In this tutorial, we demonstrate formal proof for information theory. First, we explai...

A Machine-Assisted Proof of Gödel's Incompleteness theorems for the Theory of Hereditarily Finite Sets

A formalization of Gödel’s incompleteness theorems using the Isabelle proof assistant is described. This is apparently the first mechanical verification of the second incompleteness theorem. The work closely follows Świerczkowski (2003), who gave a detailed proof using hereditarily finite set theory. The adoption of this theory is generally beneficial, but it poses certain technical issues that...

Defending the Bank with a Proof Assistant

We show how the proof-assistant Coq helped us formally verify security properties of an API. As far as we know, this is the rst mathematical proof of security properties of an API. The API we veried is a xed version of Bond's modelization of IBM's Common Cryptographic Architecture. We explain the methodology we followed, sketch our proof and explain the points the formal veri cation raised.

Poitín: Distilling Theorems From Conjectures

In this paper, we describe a new fully automatic theorem prover called Poit́ın which makes use of a novel transformation algorithm called distillation to prove input conjectures. The input conjectures are defined in a functional language and are transformed using the distillation algorithm. The result of this transformation can be easily inspected to see whether the original conjecture is true. ...

Arithmetic and the Incompleteness Theorems