A higher-order logic as the basis for logic programming
A higher-order logic as the basis for logic programming
Mechanical procedure for proof construction via closed terms in typed &lgr; calculus
Journal of Automated Reasoning
Partial polymorphic type inference and higher-order unification
LFP '88 Proceedings of the 1988 ACM conference on LISP and functional programming
Higher-order unification revisited: Complete sets of transformations
Journal of Symbolic Computation
Higher-order unification with dependent function types
RTA-89 Proceedings of the 3rd international conference on Rewriting Techniques and Applications
Journal of the ACM (JACM)
Logic programming in the LF logical framework
Logical frameworks
Simple second-order languages for which unification is undecidable
Theoretical Computer Science
Unification under a mixed prefix
Journal of Symbolic Computation
Higher-order unification via combinators
Theoretical Computer Science
Theoretical Computer Science
Higher-order equational logic programming
POPL '94 Proceedings of the 21st ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Second-order unification and type inference for Church-style polymorphism
POPL '98 Proceedings of the 25th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Higher-order rewrite systems and their confluence
Theoretical Computer Science - Special issue: rewriting systems and applications
A Complete Mechanization of Second-Order Type Theory
Journal of the ACM (JACM)
Higher order unification via explicit substitutions
Information and Computation
Reasoning with higher-order abstract syntax in a logical framework
ACM Transactions on Computational Logic (TOCL)
Solving Higher-Order Equations: From Logic to Programming
Solving Higher-Order Equations: From Logic to Programming
Deaccenting and Higher-Order Unification
Journal of Logic, Language and Information
Higher-Order Rigid E-Unification
LPAR '94 Proceedings of the 5th International Conference on Logic Programming and Automated Reasoning
Dynamic Memory Management for Sequential Logic Programming Languages
IWMM '92 Proceedings of the International Workshop on Memory Management
The Undecidability of Typability in the Lambda-Pi-Calculus
TLCA '93 Proceedings of the International Conference on Typed Lambda Calculi and Applications
Third-Order Matching in the Presence of Type Constructors
TLCA '95 Proceedings of the Second International Conference on Typed Lambda Calculi and Applications
Primitive Recursion for Higher-Order Abstract Syntax
TLCA '97 Proceedings of the Third International Conference on Typed Lambda Calculi and Applications
Decidability of All Minimal Models
TYPES '95 Selected papers from the International Workshop on Types for Proofs and Programs
Linear Interpolation for the Higher-Order Matching Problem
TAPSOFT '97 Proceedings of the 7th International Joint Conference CAAP/FASE on Theory and Practice of Software Development
Implementation of Higher-Order Unification Based on Calculus of Explicit Substitution
SOFSEM '95 Proceedings of the 22nd Seminar on Current Trends in Theory and Practice of Informatics
Linear Second-Order Unification and Context Unification with Tree-Regular Constraints
RTA '00 Proceedings of the 11th International Conference on Rewriting Techniques and Applications
Modular Higher-Order E-Unification
RTA '91 Proceedings of the 4th International Conference on Rewriting Techniques and Applications
Higher-Order Rewrite Systems (Abstract)
RTA '95 Proceedings of the 6th International Conference on Rewriting Techniques and Applications
Linear Second-Order Unification
RTA '96 Proceedings of the 7th International Conference on Rewriting Techniques and Applications
Higher Order Conditional Rewriting and Narrowing
CCL '94 Proceedings of the First International Conference on Constraints in Computational Logics
Modular AC Unification of Higher-Order Patterns
CCL '94 Proceedings of the First International Conference on Constraints in Computational Logics
Higher-Order Equational Unification via Explicit Substitutions
ALP '97-HOA '97 Proceedings of the 6th International Joint Conference on Algebraic and Logic Programming
Higher-Order Matching and Tree Automata
CSL '97 Selected Papers from the11th International Workshop on Computer Science Logic
Third-Order Matching in the Polymorphic Lambda Calculus
HOA '95 Selected Papers from the Second International Workshop on Higher-Order Algebra, Logic, and Term Rewriting
Specifying Theorem Provers in a Higher-Order Logic Programming Language
Proceedings of the 9th International Conference on Automated Deduction
Programming by Example and Proving by Example Using Higher-order Unification
Proceedings of the 10th International Conference on Automated Deduction
Proceedings of the 10th International Conference on Automated Deduction
A Combinatory Logic Approach to Higher-order E-unification (Extended Abstract)
CADE-11 Proceedings of the 11th International Conference on Automated Deduction: Automated Deduction
Representing Proof Transformations for Program Optimizations
CADE-12 Proceedings of the 12th International Conference on Automated Deduction
Decidable Higher-Order Unification Problems
CADE-12 Proceedings of the 12th International Conference on Automated Deduction
Unification in an Extensional Lambda Calculus with Ordered Function Sorts and Constant Overloading
CADE-12 Proceedings of the 12th International Conference on Automated Deduction
Theory and Practice of Minimal Modular Higher-Order E-Unification
CADE-12 Proceedings of the 12th International Conference on Automated Deduction
Extensional Higher-Order Resolution
CADE-15 Proceedings of the 15th International Conference on Automated Deduction: Automated Deduction
System Description: Teyjus - A Compiler and Abstract Machine Based Implementation of lambda-Prolog
CADE-16 Proceedings of the 16th International Conference on Automated Deduction: Automated Deduction
Solvability of Context Equations with Two Context Variables is Decidable
CADE-16 Proceedings of the 16th International Conference on Automated Deduction: Automated Deduction
System Description: Twelf - A Meta-Logical Framework for Deductive Systems
CADE-16 Proceedings of the 16th International Conference on Automated Deduction: Automated Deduction
Higher-order unification and matching
Handbook of automated reasoning
Linear higher-order pre-unification
LICS '97 Proceedings of the 12th Annual IEEE Symposium on Logic in Computer Science
Constrained resolution: a complete method for higher-order logic.
Constrained resolution: a complete method for higher-order logic.
Extensions and applications of higher-order unification
Extensions and applications of higher-order unification
Some uses of higher-order logic in computational linguistics
ACL '86 Proceedings of the 24th annual meeting on Association for Computational Linguistics
Higher-Order Coloured Unification and natural language semantics
ACL '96 Proceedings of the 34th annual meeting on Association for Computational Linguistics
Focus and Higher-Order Unification
COLING '96 Proceedings of the 16th conference on Computational linguistics - Volume 1
Higher-order beta matching with solutions in long beta-eta normal form
Nordic Journal of Computing - Selected papers of the 17th nordic workshop on programming theory (NWPT'05), October 19-21, 2005
Practical type inference for arbitrary-rank types
Journal of Functional Programming
One-and-a-Halfth Order Terms: Curry-Howard and Incomplete Derivations
WoLLIC '08 Proceedings of the 15th international workshop on Logic, Language, Information and Computation
A formal calculus for informal equality with binding
WoLLIC'07 Proceedings of the 14th international conference on Logic, language, information and computation
Capture-avoiding substitution as a nominal algebra
ICTAC'06 Proceedings of the Third international conference on Theoretical Aspects of Computing
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The talk will present a survey of higher order unification, covering an outline of its historical development, a summary of its applications to three fields: automated theorem proving, and more generally engineering of proof assistants, programming environments and software engineering, and finally computational linguistics. It concludes by a presentation of open problems, and a few prospective remarks on promising future directions. This presentation assumes as background the survey by Gilles Dowek in the Handbook of automated theorem proving [28].