The unification problem and several variants are presented. Various algorithms and data structures are discussed. Research on unification arising in several areas of computer science is surveyed, these areas include theorem proving, logic programming, and natural language processing. Sections of the paper include examples that highlight particular uses

Type inference is the compile-time process of reconstructing missing type information in a program based on the usage of its variables. ML and Haskell are two languages where this aspect of compilation has enjoyed some popularity, allowing type information to be omitted while static type checking is still performed. Type inference may be expected to have some application in the prototyping and scripting languages which are becoming increasingly popular. A difficulty with type inference is the confusing and sometimes counter-intuitive diagnostics produced by the type checker as a result of type errors. A modification of the Hindley-Milner type inference algorithm is presented, which allows the specific reasoning which led to a program variable having a particular type to be recorded for type explanation. This approach is close to the intuitive process used in practice for debugging type errors. 1 Introduction Type inference refers to the compile-time process of reconstructing missing t...

. Term matching has become one of the most important primitive operations for symbolic computation. This paper describes the extension of the object-oriented symbolic computation system AlgBench with pattern matching and unification facilities. The various pattern objects are organized in subclasses of the class of the composite expressions. This leads to a clear design and to a distributed implementation of the pattern matcher in the subclasses. New pattern object classes can consequently be added easily to the system. Huet's and our simple mark and retract algorithm for standard unification as well as Stickel's algorithm for associative commutative unification have been implemented in an objectoriented style. Unifiers are selected at runtime. We extend Mathematica's type-constrained pattern matching by taking into account inheritance information from a user-defined hierarchy of object types. The argument unification is basically instance variable unification. The improvement of the ...

We have become so used to viewing natural language in computational terms that we need occasionally to remind ourselves of the methodological commitment this view entails. That commitment is this: we assume that to understand linguistic tasks—tasks such as recognizing sentences, determining their structure, extracting their meaning, and manipulating the information they contain—is to discover the algorithms required to perform those tasks, and to investigate their computational properties. To be sure, the physical realization of the corresponding processes in humans is a legitimate study too, but one from which the computational investigation of language may be pursued in Splendid Isolation. Complexity Theory is the mathematical study of the resources—both in time and space—required to perform computational tasks. What bounds can we place—from above or below—on the number of steps taken to compute such-and-such a function, or a function belonging to such-and-such a class? What bounds can we place on the amount of memory required? It is not surprising, therefore, that in the study of natural language, complexity-theoretic issues abound. Since any computational task can be the object of complexity-theoretic investigation, it would be hopeless even to attempt a complete survey of Complexity Theory in the study of natural language. We focus therefore on a selection of topics in natural language where there has been a particular accumulation of complexity-theoretic results. Section 2 discusses parsing and recognition; Section 3 discusses the computation of logical form; and Section 4 discusses the problem of determining logical relationships between sentences in natural language. But we begin with a brief review of the Complexity Theory itself. A draft chapter for the Blackwell Computational Linguistics and Natural Language Processing Handbook, edited by Alex Clark, Chris Fox and Shalom Lappin.