**Abstract** : Consider a world where exporting proof evidence into a well defined,
universal, and permanent format is taken as "feature zero" for
computational logic systems. In such a world, provers will
communicate and share theorems and proofs; libraries will archive and
organize proofs; and marketplaces of proofs would be open to any
prover that admits checkable proof objects. In that world, proof
checkers will be the new gatekeepers: they will be entrusted with the
task of checking that claimed proof evidence elaborates into a formal
proof.
Logicians and proof theorists have worked on defining notions of proof
that are not based on technology and do not have version numbers
attached to them. There are many such proof systems in the
literature: Hilbert-Frege proofs, Gentzen's sequent calculus proofs,
Prawitz's natural deduction proofs, etc. Each of these proof systems
have been given precise syntax and meaning. While such well studied
proof descriptions exist, a quick review of the current state of
automated and interactive theorem provers reveals that provers seldom
output their "proof evidence" using such proof systems. While there
is a lot of interest in having provers share and trust each other's
proofs most of that work has been based on building bridges between
two specific provers: a change in the version number of one prover can
cause that bridge to collapse.
The ProofCert project has as one of its goals the development of a
flexible framework for defining the semantics of a wide range of proof
evidence in such a way that provers would define the meaning of their
own proof evidence and trusted proof checkers would be able to
interpret that meaning and check its formal correctness. To achieve
this goal, we must first be able to separate proof evidence from its
provenance and then provide a formal and clear framework for defining
the semantics of proof evidence. The ProofCert project is focused on
the problem of checking formal proof: there is no assumption made that
such formal proofs are actually readable by humans.