2,724 research outputs found
A Denotational Semantics for First-Order Logic
In Apt and Bezem [AB99] (see cs.LO/9811017) we provided a computational
interpretation of first-order formulas over arbitrary interpretations. Here we
complement this work by introducing a denotational semantics for first-order
logic. Additionally, by allowing an assignment of a non-ground term to a
variable we introduce in this framework logical variables.
The semantics combines a number of well-known ideas from the areas of
semantics of imperative programming languages and logic programming. In the
resulting computational view conjunction corresponds to sequential composition,
disjunction to ``don't know'' nondeterminism, existential quantification to
declaration of a local variable, and negation to the ``negation as finite
failure'' rule. The soundness result shows correctness of the semantics with
respect to the notion of truth. The proof resembles in some aspects the proof
of the soundness of the SLDNF-resolution.Comment: 17 pages. Invited talk at the Computational Logic Conference (CL
2000). To appear in Springer-Verlag Lecture Notes in Computer Scienc
Mechanized semantics
The goal of this lecture is to show how modern theorem provers---in this
case, the Coq proof assistant---can be used to mechanize the specification of
programming languages and their semantics, and to reason over individual
programs and over generic program transformations, as typically found in
compilers. The topics covered include: operational semantics (small-step,
big-step, definitional interpreters); a simple form of denotational semantics;
axiomatic semantics and Hoare logic; generation of verification conditions,
with application to program proof; compilation to virtual machine code and its
proof of correctness; an example of an optimizing program transformation (dead
code elimination) and its proof of correctness
Semantics for a Quantum Programming Language by Operator Algebras
This paper presents a novel semantics for a quantum programming language by
operator algebras, which are known to give a formulation for quantum theory
that is alternative to the one by Hilbert spaces. We show that the opposite
category of the category of W*-algebras and normal completely positive
subunital maps is an elementary quantum flow chart category in the sense of
Selinger. As a consequence, it gives a denotational semantics for Selinger's
first-order functional quantum programming language QPL. The use of operator
algebras allows us to accommodate infinite structures and to handle classical
and quantum computations in a unified way.Comment: In Proceedings QPL 2014, arXiv:1412.810
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