26 research outputs found
Importing SMT and Connection proofs as expansion trees
Different automated theorem provers reason in various deductive systems and,
thus, produce proof objects which are in general not compatible. To understand
and analyze these objects, one needs to study the corresponding proof theory,
and then study the language used to represent proofs, on a prover by prover
basis. In this work we present an implementation that takes SMT and Connection
proof objects from two different provers and imports them both as expansion
trees. By representing the proofs in the same framework, all the algorithms and
tools available for expansion trees (compression, visualization, sequent
calculus proof construction, proof checking, etc.) can be employed uniformly.
The expansion proofs can also be used as a validation tool for the proof
objects produced.Comment: In Proceedings PxTP 2015, arXiv:1507.0837
Towards the Integration of an Intuitionistic First-Order Prover into Coq
An efficient intuitionistic first-order prover integrated into Coq is useful
to replay proofs found by external automated theorem provers. We propose a
two-phase approach: An intuitionistic prover generates a certificate based on
the matrix characterization of intuitionistic first-order logic; the
certificate is then translated into a sequent-style proof.Comment: In Proceedings HaTT 2016, arXiv:1606.0542
A Deep Reinforcement Learning Approach to First-Order Logic Theorem Proving
Automated theorem provers have traditionally relied on manually tuned
heuristics to guide how they perform proof search. Deep reinforcement learning
has been proposed as a way to obviate the need for such heuristics, however,
its deployment in automated theorem proving remains a challenge. In this paper
we introduce TRAIL, a system that applies deep reinforcement learning to
saturation-based theorem proving. TRAIL leverages (a) a novel neural
representation of the state of a theorem prover and (b) a novel
characterization of the inference selection process in terms of an
attention-based action policy. We show through systematic analysis that these
mechanisms allow TRAIL to significantly outperform previous
reinforcement-learning-based theorem provers on two benchmark datasets for
first-order logic automated theorem proving (proving around 15% more theorems)
Dedukti: a Logical Framework based on the -Calculus Modulo Theory
Dedukti is a Logical Framework based on the -Calculus Modulo
Theory. We show that many theories can be expressed in Dedukti: constructive
and classical predicate logic, Simple type theory, programming languages, Pure
type systems, the Calculus of inductive constructions with universes, etc. and
that permits to used it to check large libraries of proofs developed in other
proof systems: Zenon, iProver, FoCaLiZe, HOL Light, and Matita
Scalable Fine-Grained Proofs for Formula Processing
We present a framework for processing formulas in automatic theorem provers, with generation of detailed proofs. The main components are a generic contextual recursion algorithm and an extensible set of inference rules. Clausification, skolemization, theory-specific simplifications, and expansion of 'let' expressions are instances of this framework. With suitable data structures, proof generation adds only a linear-time overhead, and proofs can be checked in linear time. We implemented the approach in the SMT solver veriT. This allowed us to dramatically simplify the code base while increasing the number of problems for which detailed proofs can be produced, which is important for independent checking and reconstruction in proof assistants