A Combinatory Logic Approach to Higher-order E-unification (Extended Abstract)
The case in which E admits presentation as a convergent term rewriting system is treated in detail: in this situation, a modification of ordinary narrowing is shown to be a complete method for enumerating higher-order E-unifiers.
A Combinatory Logic Approach to Higher-Order E-Unification
- MathematicsTheor. Comput. Sci.
Higher-Order and Semantic Unification
- Computer ScienceFSTTCS
It is shown that this standard unification procedure, with slight modifications, can be used to solve the satisfiability problem in combinatory logic with a convergent set of algebraic axioms R, thus resulting in a complete higher-order unification procedure for R.
Generating Compressed Combinatory Proof Structures: An Approach to Automated First-Order Theorem Proving
- Computer SciencePAAR@IJCAR
This “combinator term as proof structure” approach to automated first-order proving is introduced, an implementation and first experimental results are presented and features known from the connection structure calculus are realized.
First-order unification using variable-free relational algebra
- Computer ScienceLog. J. IGPL
We present a framework for the representation and resolution of first-order unification problems and their abstract syntax in a variable-free relational formalism which is an executable variant of…
Unification for \lambda -calculi Without Propagation Rules
- Computer ScienceICTAC
The unification procedure was developed for the calculi with ES that belong to the paradigm known as “act at a distance”, and explicit substitutions are not propagated to the level of variables, as usual.
A Functional Logic Language Based on Higher Order Narrowing
- Computer ScienceFunctional Programming
This work presents the functional logic language Higher Order Babel which provides higher order unification for parameter passing and solving equations and replaces the expensive β-reduction by the more efficient combinator reduction.
Superposition for Lambda-Free Higher-Order Logic
- Computer ScienceIJCAR
Refutationally complete superposition calculi for intentional and extensional \(\lambda \)-free higher-order logic, two formalisms that allow partial application and applied variables, appear promising as a stepping stone towards complete, efficient automatic theorem provers for full higher- order logic.
Superposition with Lambdas
- Computer ScienceCADE
A superposition calculus for a clausal fragment of extensional polymorphic higher-order logic that includes anonymous functions but excludes Booleans is designed and implemented in the Zipperposition prover and evaluated on TPTP and Isabelle benchmarks.
Superposition for Lambda-Free Higher-Order Logic ( Technical Report )
- Computer Science
Refutationally complete superposition calculi for intentional and extensional λ-free higher-order logic, two formalisms that allow partial application and applied variables, appear promising as a stepping stone towards complete, efficient automatic theorem provers for full higher- order logic.
SHOWING 1-10 OF 28 REFERENCES
Higher-Order Unification, Polymorphism, and Subsorts (Extended Abstract)
- Computer ScienceCTRS
This paper analyzes the problems that arise in extending Huet's higher-order unification algorithm from the simply typed λ-calculus to one with type variables and suggests a new type system for the λ -calculus which may pave the way to a complete unification algorithm for polymorphic terms.
Introduction to combinators and λ-calculus
- Computer ScienceActa Applicandae Mathematicae
These notes form a simple introduction to the two topics, suitable for a reader who has no previous knowledge of combinatory logic, but has taken an undergraduate course in predicate calculus and recursive functions.
Mechanizing omega-Order Type Theory Through Unification
- Mathematics, Computer ScienceTheor. Comput. Sci.
Higher Order E-Unification
- Computer ScienceCADE
An investigation of Higher-Order E-Unification, which consists of unifying typed lambda terms in the context of a first-order set of equations E, and a set of inference rules for higher-order E-unification and a proof of its soundness and completeness.
An Efficient Unification Algorithm
- Computer ScienceTOPL
A new unification algorithm, characterized by having the acyclicity test efficiently embedded into it, is derived from the nondeterministic one, and a PASCAL implementation is given.
Polymorphic Rewriting Conserves Algebraic Strong Normalization
- MathematicsTheor. Comput. Sci.
Combining algebra and higher-order types
- Computer Science, Mathematics Proceedings. Third Annual Information Symposium on Logic in Computer Science
The author shows that provability in the higher-order equational proof system obtained by adding the simply typed beta and eta axions to some many-sorted algebraic proof system is effectively reducible to Provability in that algebraicProof system.
A Complete Mechanization of Second-Order Type Theory
- Computer ScienceJACM
A generalization of the resolution method for higher order logic is presented and it is established that the author's generalized resolution procedure is complete with respect to a natural notion of validity based on Henkin's general validity for type theory.
Higher-order Unification with Dependent Function Types
- Computer ScienceRTA
In spite of the undecidability of this problem, Huet's algorithm for unification in the simply typed λ-calculus (λ→) is quite usable in practice.