Free S-Monoids: A Higher-Order Syntax with Metavariables
نویسنده
چکیده
The notion of Σ-monoids is proposed by Fiore, Plotkin and Turi, to give abstract algebraic model of languages with variable binding and substitutions. In this paper, we give a free construction of Σ-monoids. The free Σ-monoid over a given presheaf serves a well-structured term language involving binding and substitutions. Moreover, the free Σ-monoid naturally contains interesting syntactic objects which can be viewed as “metavariables” and “environments”. We analyse the term language of the free Σ-monoid by relating it with several concrete systems, especially the λ-calculus extended with contexts.
منابع مشابه
Left I-quotients of band of right cancellative monoids
Let $Q$ be an inverse semigroup. A subsemigroup $S$ of $Q$ is a left I-order in $Q$ and $Q$ is a semigroup of left I-quotients of $S$ if every element $qin Q$ can be written as $q=a^{-1}b$ for some $a,bin S$. If we insist on $a$ and $b$ being $er$-related in $Q$, then we say that $S$ is straight in $Q$. We characterize semigroups which are left I-quotients of left regular bands of right cancell...
متن کاملOn Regularity of Acts
In this article we give a characterization of monoids for which torsion freeness, ((principal) weak, strong) flatness, equalizer flatness or Condition (E) of finitely generated and (mono) cyclic acts and Condition (P) of finitely generated and cyclic acts implies regularity. A characterization of monoids for which all (finitely generated, (mono) cyclic acts are regular will be given too. We als...
متن کامل-torsion free Acts Over Monoids
In this paper firt of all we introduce a generalization of torsion freeness of acts over monoids, called -torsion freeness. Then in section 1 of results we give some general properties and in sections 2, 3 and 4 we give a characterization of monoids for which this property of their right Rees factor, cyclic and acts in general implies some other properties, respectively.
متن کاملZappa-Szép products of free monoids and groups
We prove that left cancellative right hereditary monoids satisfying the dedekind height property are precisely the Zappa-Szép products of free monoids and groups. The ‘fundamental’ monoids of this type are in bijective correspondence with faithful self-similar group actions. 2000 AMS Subject Classification: 20M10, 20M50. 1 A class of left cancellative monoids This paper develops some ideas that...
متن کاملFree Variables and Subexpressions in Higher-Order Meta Logic
This paper addresses the problem of how to represent free variables and subexpressions involving-bindings. The aim is to apply what is known as higher-order abstract syntax to higher-order term rewriting systems. Directly applying-reduction for the purpose of subterm-replacement is incompatible with the requirements of term-rewriting. A new meta-level representation of subterms is developed tha...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2004