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Pattern Unification for the Lambda Calculus with Linear and. Affine Types∗. Anders Schack-Nielsen Carsten Sch¨urmann. IT University of Copenhagen.

A semi-decision algorithm is presented, to search for unification of formulas in typed ω-order λ-calculus, and its correctness is proved.

Again from the Preface of \Lambda-Calculus and Combinators, an Introduction". The -calculus was invented around 1930 by an American logician Alonzo Church, as part of a comprehensive logical system which included higher-order operators (operators which act on other operators)::: Combinatory logic has the same aims as -calculus, andcan

We will present a definition of the unification algorithm for the particular case where the terms we want to unify are simple types. Page 7. 40. 5. The typed λ- ...

Nov 22, 2005 · Unification in typed lambda calculus Authors Authors and affiliations Gérard Huet Conference paper First Online: 22 November 2005 3 Citations 2.1k Downloads Part of the Lecture Notes in Computer Science book series (LNCS, volume 37) Abstract This paper discusses the problem of finding common instances to terms in typed λ-calculus.

Jan 03, 2022 · Unification is an algorithmic process of solving equations between symbolic expressions. I have solved a few execercises in FOL: f (x,b ()) = f (a (),y) has one unifier: [a ()/x,b ()/y], Is it possible to use Unification for Lambda Calculus terms? For example (= means beta reduces to): Equation: (λx.T) b = a b. Solve for T. Solution: [ (a x)/T].

08.11.2016 · In my understanding, if a unification solves equations of terms that are not higher-order terms, then it is a first-order unification. If a unification solves equations of terms that are higher-order terms, then it is a higher-order unification. Therefore a unification solves equations of $\lambda$-terms should be a higher-order Unification.

CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): Abstract. A new unification algorithm is introduced, which (unlike pre-vious algorithms for unification in λ-calculus) shares the pleasant proper-ties of first-order unification.

CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): We propose related algorithms for unification and constraint simplification in !& , a refinement of the simply-typed -calculus with subtypes and bounded intersection types.

Abstract. A new unification algorithm is introduced, which (unlike pre- vious algorithms for unification in λ-calculus) shares the pleasant proper-.

01.06.1975 · A semi-decision algorithm is presented, to search for unification of formulas in typed ω -order λ -calculus, and its correctness is proved. It is shown that the search space is significantly smaller than the one for finding the most general unifiers. In particular, our search is not redundant.

the Lambda-Calculus and Combinatory Logic Masahiko Sato Graduate School of Informatics, Kyoto University j.w.w. Takafumi Sakurai and Helmut Schwichtenberg TPP 2018 RIEC, Tohoku University November 21, 2018. Objects, Concepts and Notations Natural numbers: 0, 1, 2+3, Rational numbers: 1/3, 2/6,

01.03.1988 · Unification delays are formalised independently of any context, by defining a lambda calculus where a unification constraint forms an integral part of each term. This calculus is shown to support an unusually simple unification theory, where most general unifiers trivially always exist.

CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): Abstract. A new unification algorithm is introduced, which (unlike pre-vious algorithms for unification in λ-calculus) shares the pleasant proper-ties of first-order unification. Proofs of these properties are given, in par-ticular uniqueness of the answer and the most-general-unifier property.

It is shown that the search space for unification of formulas in typed ω -order λ -calculus is significantly smaller than the one for ...

Formally, a unification approach presupposes An infinite set of variables. For higher-order unification, it is convenient to choose disjoint from the set of lambda-term bound variables. A set of terms such that . For first-order unification, is usually the set of first-order terms (terms built from variable and function symbols).

Again from the Preface of \Lambda-Calculus and Combinators, an Introduction". The -calculus was invented around 1930 by an American logician Alonzo Church, as part of a comprehensive logical system which included higher-order operators (operators which act on other operators)::: Combinatory logic has the same aims as -calculus, andcan

In this paper we prove the coherence of a class of lambda-calculus-based languages that use the intersection type discipline, including both a purely functional …

What are the Lambda-Calculus and Combinatory Logic? The Preface of \Lambda-Calculus and Combinators, an Introduction" by J.R. Hindley and J.P. Seldin says: The -calculus and combinatory logic aretwosystems of logic which can also serve as abstract programming languages. They both aim to describe some very general properties of programs that

03.01.2022 · Unification is an algorithmic process of solving equations between symbolic expressions.. I have solved a few execercises in FOL: f(x,b()) = f(a(),y) has one unifier: [a()/x,b()/y], Is it possible to use Unification for Lambda Calculus terms? For example (= …

operators)... Page 7. History of the calculi. Again from the Preface of “Lambda-Calculus ...

A proof that higher order matching (unification where only one term contains existential variables) is decidable was announced by Colin Stirling in 2006, and a ...

The λ-calculus and combinatory logic are two systems of logic which can also serve as abstract programming languages. They.

22.11.2005 · Cite this paper as: Huet G. (1975) Unification in typed lambda calculus. In: Böhm C. (eds) λ-Calculus and Computer Science Theory. LCCST 1975.

Title:Pattern Unification for the Lambda Calculus with Linear and Affine Types ; Subjects: Logic in Computer Science (cs.LO) ; ACM classes: F.4.1; ...

lambda-calculus unification · Unification is an algorithmic process of solving equations between symbolic expressions.