Related papers: Is alpha-conversion easy?
We present some lambda calculus with explicit substitutions and named variables. The characteristic feature of this calculus is as follows: renaming of bound variables when performing substitutions is done using special reductions and may…
Using explicit weakenings, we can define alpha-conversion by simple equations without any mention of free variables.
Safety is a syntactic condition of higher-order grammars that constrains occurrences of variables in the production rules according to their type-theoretic order. In this paper, we introduce the safe lambda calculus, which is obtained by…
In this work we provide alternative formulations of the concepts of lambda theory and extensional theory without introducing the notion of substitution and the sets of all, free and bound variables occurring in a term. We also clarify the…
A non-deterministic call-by-need lambda-calculus \calc with case, constructors, letrec and a (non-deterministic) erratic choice, based on rewriting rules is investigated. A standard reduction is defined as a variant of left-most outermost…
Many different systems with explicit substitutions have been proposed to implement a large class of higher-order languages. Motivations and challenges that guided the development of such calculi in functional frameworks are surveyed in the…
The formal system lambda-delta is a typed lambda calculus that pursues the unification of terms, types, environments and contexts as the main goal. lambda-delta takes some features from the Automath-related lambda calculi and some from the…
Closure conversion is a program transformation at work in compilers for functional languages to turn inner functions into global ones, by building closures pairing the transformed functions with the environment of their free variables.…
The linear-algebraic lambda-calculus and the algebraic lambda-calculus are untyped lambda-calculi extended with arbitrary linear combinations of terms. The former presents the axioms of linear algebra in the form of a rewrite system, while…
This paper concerns the explicit treatment of substitutions in the lambda calculus. One of its contributions is the simplification and rationalization of the suspension calculus that embodies such a treatment. The earlier version of this…
Call a semantics for a language with variables absolute when variables map to fixed entities in the denotation. That is, a semantics is absolute when the denotation of a variable a is a copy of itself in the denotation. We give a trio of…
A comparison of Landin's form of lambda calculus with Church's shows that, independently of the lambda calculus, there exists a mechanism for converting functions with arguments indexed by variables to the usual kind of function where the…
Environments and closures are two of the main ingredients of evaluation in lambda-calculus. A closure is a pair consisting of a lambda-term and an environment, whereas an environment is a list of lambda-terms assigned to free variables. In…
We address the problem of complementing higher-order patterns without repetitions of existential variables. Differently from the first-order case, the complement of a pattern cannot, in general, be described by a pattern, or even by a…
Terms in the lambda-calculus can be represented as planar trees decorated with symbols for abstraction and application, and having variables as leaves. In this paper, we concentrate on the branches of such trees, rather than on the trees…
Divergences are fundamental to the information criteria that underpin most signal processing algorithms. The alpha-beta family of divergences, designed for non-negative data, offers a versatile framework that parameterizes and continuously…
The confluence of untyped \lambda-calculus with unconditional rewriting is now well un- derstood. In this paper, we investigate the confluence of \lambda-calculus with conditional rewriting and provide general results in two directions.…
The lambda-calculus is a peculiar computational model whose definition does not come with a notion of machine. Unsurprisingly, implementations of the lambda-calculus have been studied for decades. Abstract machines are implementations…
Conventional machine learning studies generally assume close-environment scenarios where important factors of the learning process hold invariant. With the great success of machine learning, nowadays, more and more practical tasks,…
The confluence of untyped lambda-calculus with unconditional rewriting has already been studied in various directions. In this paper, we investigate the confluence of lambda-calculus with conditional rewriting and provide general results in…