Log In Sign Up

Relational Cost Analysis for Functional-Imperative Programs

by   Weihao Qu, et al.

Relational cost analysis aims at formally establishing bounds on the difference in the evaluation costs of two programs. As a particular case, one can also use relational cost analysis to establish bounds on the difference in the evaluation cost of the same program on two different inputs. One way to perform relational cost analysis is to use a relational type-and-effect system that supports reasoning about relations between two executions of two programs. Building on this basic idea, we present a type-and-effect system, called ARel, for reasoning about the relative cost of array-manipulating, higher-order functional-imperative programs. The key ingredient of our approach is a new lightweight type refinement discipline that we use to track relations (differences) between two arrays. This discipline combined with Hoare-style triples built into the types allows us to express and establish precise relative costs of several interesting programs which imperatively update their data.


page 1

page 2

page 3

page 4


Divergences on Monads for Relational Program Logics

Several relational program logics have been introduced for integrating r...

Differential Cost Analysis with Simultaneous Potentials and Anti-potentials

We present a novel approach to differential cost analysis that, given a ...

Reasoning about the garden of forking paths

Lazy evaluation is a powerful tool for functional programmers. It enable...

Bidirectional Type Checking for Relational Properties

Relational type systems have been designed for several applications incl...

Quantum Relational Hoare Logic with Expectations

We present a variant of the quantum relational Hoare logic from (Unruh, ...

Denotational recurrence extraction for amortized analysis

A typical way of analyzing the time complexity of functional programs is...

Scheduling Complexity of Interleaving Search

miniKanren is a lightweight embedded language for logic and relational p...