Automated deduction by theory resolution
Journal of Automated Reasoning
Completion of a set of rules modulo a set of equations
SIAM Journal on Computing
An introduction to mathematical logic and type theory: to truth through proof
An introduction to mathematical logic and type theory: to truth through proof
Proofs and types
A representation of Lambda terms suitable for operations on their intensions
LFP '90 Proceedings of the 1990 ACM conference on LISP and functional programming
Combinatory reduction systems: introduction and survey
Theoretical Computer Science - A collection of contributions in honour of Corrado Bo¨hm on the occasion of his 70th birthday
Confluence properties of weak and strong calculi of explicit substitutions
Journal of the ACM (JACM)
A notation for lambda terms. A generalization of environment
Theoretical Computer Science
Tree-Manipulating Systems and Church-Rosser Theorems
Journal of the ACM (JACM)
Complete Sets of Reductions for Some Equational Theories
Journal of the ACM (JACM)
Higher order unification via explicit substitutions
Information and Computation
Typed lambda-calculi with explicit substitutions may not terminate
TLCA '95 Proceedings of the Second International Conference on Typed Lambda Calculi and Applications
Higher-Order Equational Unification via Explicit Substitutions
ALP '97-HOA '97 Proceedings of the 6th International Joint Conference on Algebraic and Logic Programming
Rewriting modulo a rewrite system
Rewriting modulo a rewrite system
Constrained resolution: a complete method for higher-order logic.
Constrained resolution: a complete method for higher-order logic.
Rewriting logic: roadmap and bibliography
Theoretical Computer Science - Rewriting logic and its applications
Binding Logic: Proofs and Models
LPAR '02 Proceedings of the 9th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning
Algebraic Structures and Dependent Records
TPHOLs '02 Proceedings of the 15th International Conference on Theorem Proving in Higher Order Logics
From Higher-Order to First-Order Rewriting
RTA '01 Proceedings of the 12th International Conference on Rewriting Techniques and Applications
Deduction versus Computation: The Case of Induction
AISC '02/Calculemus '02 Proceedings of the Joint International Conferences on Artificial Intelligence, Automated Reasoning, and Symbolic Computation
Higher-order unification and matching
Handbook of automated reasoning
Journal of Automated Reasoning
Nominal logic, a first order theory of names and binding
Information and Computation - TACS 2001
Definitions by rewriting in the Calculus of Constructions
Mathematical Structures in Computer Science
Closed reduction: explicit substitutions without $\alpha$-conversion
Mathematical Structures in Computer Science
Eigenvariables, bracketing and the decidability of positive minimal predicate logic
Theoretical Computer Science
On the Convergence of Reduction-based and Model-based Methods in Proof Theory
Electronic Notes in Theoretical Computer Science (ENTCS)
Cut Elimination in Deduction Modulo by Abstract Completion
LFCS '07 Proceedings of the international symposium on Logical Foundations of Computer Science
Types for Proofs and Programs
Annals of Mathematics and Artificial Intelligence
Journal of Automated Reasoning
The stratified foundations as a theory modulo
TLCA'01 Proceedings of the 5th international conference on Typed lambda calculi and applications
A finite first-order presentation of set theory
TYPES'02 Proceedings of the 2002 international conference on Types for proofs and programs
Embedding pure type systems in the lambda-pi-calculus modulo
TLCA'07 Proceedings of the 8th international conference on Typed lambda calculi and applications
A simple proof that super-consistency implies cut elimination
RTA'07 Proceedings of the 18th international conference on Term rewriting and applications
Truth values algebras and proof normalization
TYPES'06 Proceedings of the 2006 international conference on Types for proofs and programs
A finite first-order theory of classes
TYPES'06 Proceedings of the 2006 international conference on Types for proofs and programs
Automating theories in intuitionistic logic
FroCoS'09 Proceedings of the 7th international conference on Frontiers of combining systems
All about maude - a high-performance logical framework: how to specify, program and verify systems in rewriting logic
Embedding deduction modulo into a prover
CSL'10/EACSL'10 Proceedings of the 24th international conference/19th annual conference on Computer science logic
Rule-based programming and proving: the ELAN experience outcomes
ASIAN'04 Proceedings of the 9th Asian Computing Science conference on Advances in Computer Science: dedicated to Jean-Louis Lassez on the Occasion of His 5th Cycle Birthday
What do we know when we know that a theory is consistent?
CADE' 20 Proceedings of the 20th international conference on Automated Deduction
Unbounded proof-length speed-up in deduction modulo
CSL'07/EACSL'07 Proceedings of the 21st international conference, and Proceedings of the 16th annuall conference on Computer Science Logic
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We give a first-order presentation of higher-order logic based on explicit substitutions. This presentation is intentionally equivalent to the usual presentation of higher-order logic based on λ-calculus, that is, a proposition can be proved without the extensionality axioms in one theory if and only if it can be in the other. We show that the Extended Narrowing and Resolution first-order proof-search method can be applied to this theory. In this way we get a step-by-step simulation of higher-order resolution. Hence, expressing higher-order logic as a first-order theory and applying a first-order proof search method is a relevant alternative to a direct implementation. In particular, the well-studied improvements of proof search for first-order logic could be reused at no cost for higher-order automated deduction. Moreover, as we stay in a first-order setting, extensions, such as equational higher-order resolution, may be easier to handle.