## 476 Citations

### Unification in Typed Lambda Calculus

- Computer ScienceLambda-Calculus and Computer Science Theory
- 1975

This paper discusses the problem of finding common instances to terms in typed λ-calculus. It is shown that here the notion of most general unifier must be extended. Complete sets of unifiers are…

### Unification in a l-calculus with intersection types

- Computer ScienceICLP 1993
- 1993

The unification and constraint simplification algorithms described here lay the groundwork for a mechanization of such frameworks as constraint logic programming languages and theorem provers.

### A Unification Algorithms for Confluent Theories

- Computer ScienceICALP
- 1987

A correct and complete unification algorithm for confluent theories that is demand driven and can handle infinite and partial instantiated objects and thus can be used as a means to integrate functional and logic programming.

### Unification of Higher-Order patterns in a Simply Typed Lambda-Calculus with Finite Products and terminal Type

- Computer Science, MathematicsRTA
- 1996

This work develops a higher-order unification algorithm for a restricted class of simply typed lambda terms with function space and product type constructors that terminates on each input and produces a most general unifier if one exists.

### The Undecidability of Typability in the Lambda-Pi-Calculus

- Computer ScienceTLCA
- 1993

The set of pure terms which are typable in the λII-calculus in a given context is not recursive. So there is no general type inference algorithm for the programming language Elf and, in some cases,…

### 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.

### Functional unification of higher-order patterns

- Computer ScienceLICS 1993
- 1993

The complete development of a unification algorithm for so-called higher-order patterns, a subclass of lambda -terms, is presented and the result is a directly executable functional program in de Bruijn's (1972) notation.

### Unification in Lambda-Calculus

- Computer Science
- 1991

This unification algorithm can be used to generalize first-order proof- search algorithms to second-order logic, making possible for example a straighforward treatment of McCarthy's circumscription schema.

### Unification in Lambda-Calculi with if-then-else

- Computer ScienceCADE
- 1998

This unification algorithm can be used to generalize first-order proofsearch algorithms to second-order logic, making possible for example a straighforward treatment of McCarthy's circumscription schema.

## References

SHOWING 1-10 OF 11 REFERENCES

### A complete mechanization of (ω) -order type theory

- PhilosophyACM Annual Conference
- 1972

We present a complete unification algorithm for logic with the language of all finite types. In addition, we show how this procedure can be used with a generalized resolution principle which does not…

### Mechanizing omega-Order Type Theory Through Unification

- Mathematics, Computer ScienceTheor. Comput. Sci.
- 1976

### Automatic Program Synthesis in Second-Order Logic

- ChemistryIJCAI
- 1973

A resolution-based theorem prover, incorporating a restricted higher-order unification algorithm, has been applied to the automatic synthesis of SNOBOL-4 programs. The set of premisses includes…

### A mechanization of type theory

- PhilosophyIJCAI 1973
- 1973

A refutational system of logic for a language of order is presented, in the sense that a refutation of a set of sentences exists if and only if this set does not possess a general Henkin model.

### Resolution in Type Theory

- PhilosophyJ. Symb. Log.
- 1971

In [8] J. A. Robinson introduced a complete refutation procedure called resolution for first order predicate calculus. Resolution is based on ideas in Herbrand's Theorem, and provides a very…

### 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.

### A Machine-Oriented Logic Based on the Resolution Principle

- MathematicsJACM
- 1965

The paper concludes with a discussion of several principles which are applicable to the design of efficient proof-procedures employing resolution as the basle logical process.

### AUTOMATED LOGIC FOR SEMI-AUTOMATED MATHEMATICS

- Computer Science
- 1964

Six formal systems of logic, S sub 1 through S sub 6, for which proof procedures or partial proof procedures are readily contrived are defined and described in order to simplify the descriptions of S sub 5 and SSub 6.

### A formulation of the simple theory of types

- MathematicsJournal of Symbolic Logic
- 1940

A formulation of the simple theory oftypes which incorporates certain features of the calculus of λ-conversion into the theory of types and is offered as being of interest on this basis.