相关论文: An Elementary Fragment of Second-Order Lambda Calc…

We describe an ACL2 package for defining partial recursive functions that also supports efficient execution. While packages for defining partial recursive functions already exist for other theorem provers, they often require inductive…

This paper is a concise and painless introduction to the $\lambda$-calculus. This formalism was developed by Alonzo Church as a tool for studying the mathematical properties of effectively computable functions. The formalism became popular…

Alternating quantifier depth is a natural measure of difficulty required to express first order logical sentences. We define a sequence of first order properties on rooted, locally finite trees in a recursive manner, and provide rigorous…

Linear logic provides a framework to control the complexity of higher-order functional programs. We present an extension of this framework to programs with multithreading and side effects focusing on the case of elementary time. Our main…

It is shown that quantization of the dynamical systems with second class constraints actually can be reduced to quantization of the systems with first class constraints. The motion of the non-relativistic particle along the plane curve and…

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…

We propose a way to unify two approaches of non-cloning in quantum lambda-calculi: logical and algebraic linearities. The first approach is to forbid duplicating variables, while the second is to consider all lambda-terms as…

Functions with fixed initial coefficient have been widely studied. A new methodology is proposed in this paper by making appropriate modifications and improvements to the theory of second-order differential subordination. Several…

A genoid is a category of two objects such that one is the product of itself with the other. A genoid may be viewed as an abstract substitution algebra. It is a remarkable fact that such a simple concept can be applied to present a unified…

Iterated functions system (IFS) is defined by specifying a set of functions in a classical phase space, which act randomly on an initial point. In an analogous way, we define a quantum iterated functions system (QIFS), where functions act…

The study of various decision problems for logic fragments has a long history in computer science. This paper is on the membership problem for a fragment of first-order logic over infinite words; the membership problem asks for a given…

Godel's theory T can be understood as a theory of the simply-typed lambda calculus that is extended to include the constant 0, the successor function S, and the operator R_tau for primitive recursion on objects of type tau. It is known that…

The calculus of Dependent Object Types (DOT) has enabled a more principled and robust implementation of Scala, but its support for type-level computation has proven insufficient. As a remedy, we propose $F^\omega_{..}$, a rigorous…

A system of linear dependent types for the lambda calculus with full higher-order recursion, called dlPCF, is introduced and proved sound and relatively complete. Completeness holds in a strong sense: dlPCF is not only able to precisely…

We consider the untyped lambda calculus with constructors and recursively defined constants. We construct a domain-theoretic model such that any term not denoting bottom is strongly normalising provided all its `stratified approximations'…

This paper is about a categorical approach to model a very simple Semantically Linear lambda calculus, named Sll-calculus. This is a core calculus underlying the programming language SlPCF. In particular, in this work, we introduce the…

We describe a new quantifier elimination algorithm for real closed fields based on Thom encoding and sign determination. The complexity of this algorithm is elementary recursive and its proof of correctness is completely algebraic. In…

The categorical models of the differential lambda-calculus are additive categories because of the Leibniz rule which requires the summation of two expressions. This means that, as far as the differential lambda-calculus and differential…

We present a unified theory for formal mathematical systems including recursive systems closely related to formal grammars, including the predicate calculus as well as a formal induction principle. We introduce recursive systems generating…

The lambda-PRK-calculus is a typed lambda-calculus that exploits the duality between the notions of proof and refutation to provide a computational interpretation for classical propositional logic. In this work, we extend lambda-PRK to…