Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userCertifying and reasoning about cost annotations of functional programs
200
0
0.0
(
0
)
Added by
Yann Regis-Gianas
Publication date
2011
fields
Informatics Engineering
and research's language is
English
Authors
Roberto M. Amadio
Ask ChatGPT about the research
No Arabic abstract
We present a so-called labelling method to insert cost annotations in a higher-order functional program, to certify their correctness with respect to a standard compilation chain to assembly code including safe memory management, and to reason on them in a higher-order Hoare logic.
rate research
Read More
Most modern (classical) programming languages support recursion. Recursion has also been successfully applied to the design of several quantum algorithms and introduced in a couple of quantum programming languages. So, it can be expected that recursion will become one of the fundamental paradigms of quantum programming. Several program logics have been developed for verification of quantum while-programs. However, there are as yet no general methods for reasoning about (mutual) recursive procedures and ancilla quantum data structure in quantum computing (with measurement). We fill the gap in this paper by proposing a parameterized quantum assertion logic and, based on which, designing a quantum Hoare logic for verifying parameterized recursive quantum programs with ancilla data and probabilistic control. The quantum Hoare logic can be used to prove partial, total, and even probabilistic correctness (by reducing to total correctness) of those quantum programs. In particular, two counterexamples for illustrating incompleteness of non-parameterized assertions in verifying recursive procedures, and, one counterexample for showing the failure of reasoning with exact probabilities based on partial correctness, are constructed. The effectiveness of our logic is shown by three main examples -- recursive quantum Markov chain (with probabilistic control), fixed-point Grovers search, and recursive quantum Fourier sampling.
A software analysis is a computer program that takes some representation of a software product as input and produces some useful information about that product as output. A software product line encompasses emph{many} software product variants, and thus existing analyses can be applied to each of the product variations individually, but not to the entire product line as a whole. Enumerating all product variants and analyzing them one by one is usually intractable due to the combinatorial explosion of the number of product variants with respect to product line features. Several software analyses (e.g., type checkers, model checkers, data flow analyses) have been redesigned/re-implemented to support variability. This usually requires a lot of time and effort, and the variability-aware version of the analysis might have new errors/bugs that do not exist in the original one. Given an analysis program written in a functional language based on PCF, in this paper we present two approaches to transforming (lifting) it into a semantically equivalent variability-aware analysis. A light-weight approach (referred to as emph{shallow lifting}) wraps the analysis program into a variability-aware version, exploring all combinations of its input arguments. Deep lifting, on the other hand, is a program rewriting mechanism where the syntactic constructs of the input program are rewritten into their variability-aware counterparts. Compositionally this results in an efficient program semantically equivalent to the input program, modulo variability. We present the correctness criteria for functional program lifting, together with correctness proof sketches of our program transformations. We evaluate our approach on a set of program analyses applied to the BusyBox C-language product line.
Accurate programming is a practical approach to producing high quality programs. It combines ideas from test-automation, test-driven development, agile programming, and other state of the art software development methods. In addition to building on approaches that have proven effective in practice, it emphasizes concepts that help programmers sharpen their understanding of both the problems they are solving and the solutions they come up with. This is achieved by encouraging programmers to think about programs in terms of properties.
A quantum circuit is a computational unit that transforms an input quantum state to an output one. A natural way to reason about its behavior is to compute explicitly the unitary matrix implemented by it. However, when the number of qubits increases, the matrix dimension grows exponentially and the computation becomes intractable. In this paper, we propose a symbolic approach to reasoning about quantum circuits. It is based on a small set of laws involving some basic manipulations on vectors and matrices. This symbolic reasoning scales better than the explicit one and is well suited to be automated in Coq, as demonstrated with some typical examples.
Program slicing provides explanations that illustrate how program outputs were produced from inputs. We build on an approach introduced in prior work by Perera et al., where dynamic slicing was defined for pure higher-order functional programs as a Galois connection between lattices of partial inputs and partial outputs. We extend this approach to imperative functional programs that combine higher-order programming with references and exceptions. We present proofs of correctness and optimality of our approach and a proof-of-concept implementation and experimental evaluation.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
