5,081 research outputs found
Semantics of a Typed Algebraic Lambda-Calculus
Algebraic lambda-calculi have been studied in various ways, but their
semantics remain mostly untouched. In this paper we propose a semantic analysis
of a general simply-typed lambda-calculus endowed with a structure of vector
space. We sketch the relation with two established vectorial lambda-calculi.
Then we study the problems arising from the addition of a fixed point
combinator and how to modify the equational theory to solve them. We sketch an
algebraic vectorial PCF and its possible denotational interpretations
Linear-algebraic lambda-calculus
With a view towards models of quantum computation and/or the interpretation
of linear logic, we define a functional language where all functions are linear
operators by construction. A small step operational semantic (and hence an
interpreter/simulator) is provided for this language in the form of a term
rewrite system. The linear-algebraic lambda-calculus hereby constructed is
linear in a different (yet related) sense to that, say, of the linear
lambda-calculus. These various notions of linearity are discussed in the
context of quantum programming languages. KEYWORDS: quantum lambda-calculus,
linear lambda-calculus, -calculus, quantum logics.Comment: LaTeX, 23 pages, 10 figures and the LINEAL language
interpreter/simulator file (see "other formats"). See the more recent
arXiv:quant-ph/061219
Reconciling positional and nominal binding
We define an extension of the simply-typed lambda calculus where two
different binding mechanisms, by position and by name, nicely coexist. In the
former, as in standard lambda calculus, the matching between parameter and
argument is done on a positional basis, hence alpha-equivalence holds, whereas
in the latter it is done on a nominal basis. The two mechanisms also
respectively correspond to static binding, where the existence and type
compatibility of the argument are checked at compile-time, and dynamic binding,
where they are checked at run-time.Comment: In Proceedings ITRS 2012, arXiv:1307.784
On Role Logic
We present role logic, a notation for describing properties of relational
structures in shape analysis, databases, and knowledge bases. We construct role
logic using the ideas of de Bruijn's notation for lambda calculus, an encoding
of first-order logic in lambda calculus, and a simple rule for implicit
arguments of unary and binary predicates. The unrestricted version of role
logic has the expressive power of first-order logic with transitive closure.
Using a syntactic restriction on role logic formulas, we identify a natural
fragment RL^2 of role logic. We show that the RL^2 fragment has the same
expressive power as two-variable logic with counting C^2 and is therefore
decidable. We present a translation of an imperative language into the
decidable fragment RL^2, which allows compositional verification of programs
that manipulate relational structures. In addition, we show how RL^2 encodes
boolean shape analysis constraints and an expressive description logic.Comment: 20 pages. Our later SAS 2004 result builds on this wor
Map Calculus in GIS: a proposal and demonstration
This paper provides a new representation for fields (continuous surfaces) in Geographical Information Systems (GIS), based on the notion of spatial functions and their combinations. Following Tomlin's (1990) Map Algebra, the term 'Map Calculus' is used for this new representation. In Map Calculus, GIS layers are stored as functions, and new layers can be created by combinations of other functions. This paper explains the principles of Map Calculus and demonstrates the creation of function-based layers and their supporting management mechanism. The proposal is based on Church's (1941) Lambda Calculus and elements of functional computer languages (such as Lisp or Scheme)
- …