A Unification Algorithm for Typed lambda-Calculus

@article{Huet1975AUA,
  title={A Unification Algorithm for Typed lambda-Calculus},
  author={G{\'e}rard P. Huet},
  journal={Theor. Comput. Sci.},
  year={1975},
  volume={1},
  pages={27-57}
}
  • 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

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

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.
...

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  • 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.