## 34 Citations

### A Combinatory Logic Approach to Higher-order E-unification (Extended Abstract)

- MathematicsCADE
- 1992

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.

### Higher-Order and Semantic Unification

- Computer ScienceFSTTCS
- 1993

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
- 2022

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
- 2011

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
- 2016

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
- 1995

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
- 2018

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
- 2019

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
- 2018

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.

## References

SHOWING 1-10 OF 28 REFERENCES

### Higher-Order Unification, Polymorphism, and Subsorts (Extended Abstract)

- Computer ScienceCTRS
- 1990

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
- 1990

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.
- 1976

### Higher Order E-Unification

- Computer ScienceCADE
- 1990

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
- 1982

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.
- 1991

### Combining algebra and higher-order types

- Computer Science, Mathematics[1988] Proceedings. Third Annual Information Symposium on Logic in Computer Science
- 1988

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
- 1973

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
- 1989

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.