A Unification Algorithm for Typed lambda-Calculus

  title={A Unification Algorithm for Typed lambda-Calculus},
  author={G{\'e}rard P. Huet},
  journal={Theor. Comput. Sci.},
  • G. Huet
  • Published 1 June 1975
  • Computer Science
  • Theor. Comput. Sci.

Unification in Typed Lambda Calculus

  • G. Huet
  • Computer Science
    Lambda-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

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

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

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

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,

Decidability of bounded higher-order unification

An Efficient Unification Algorithm

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

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

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

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.



A complete mechanization of (ω) -order type theory

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

Automatic Program Synthesis in Second-Order Logic

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

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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

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

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

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.


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

  • A. Church
  • Mathematics
    Journal 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.