Proving Performance Properties of Higher-order Functions with Memoization
Ravi Madhavan
EPFL
20 Dec 2016, 11:30 am - 12:30 pm
Kaiserslautern building G26, room 112
simultaneous videocast to Saarbrücken building E1 5, room 029
simultaneous videocast to Saarbrücken building E1 5, room 029
SWS Colloquium
Static verification of performance properties of programs is an important
problem that has attracted great deal of research. However, most existing tools
infer best-effort upper bounds and hope that they match users expectations. In
this talk, I will present a system for specifying and verifying bounds on
resources such as the number of evaluation steps and heap-allocated objects,
for functional Scala programs that may rely on lazy evaluation and memoization.
In our system, users can specify the desired resource bound as a template with
numerical holes in the contracts of functions e.g. ...
Static verification of performance properties of programs is an important
problem that has attracted great deal of research. However, most existing tools
infer best-effort upper bounds and hope that they match users expectations. In
this talk, I will present a system for specifying and verifying bounds on
resources such as the number of evaluation steps and heap-allocated objects,
for functional Scala programs that may rely on lazy evaluation and memoization.
In our system, users can specify the desired resource bound as a template with
numerical holes in the contracts of functions e.g. as "steps <= ? * size(list)
?", along with other functional properties necessary for establishing the
bounds. The system automatically infers values for the holes that will make the
templates hold for all executions of the functions. For example, the property
that a function converting a propositional formula f into negation-normal form
(NNF) takes time linear in the size of f can be expressed in the
post-condition of the function using the predicate "steps <= ? * size(f) ?",
where size is a user-defined function counting the number of nodes in the
syntax tree of the formula.
Using our tool, we have verified asymptotically precise bounds of several
algorithms and data structures that rely on complex sharing of higher-order
functions and memoization. Our benchmarks include balanced search trees like
red-black trees and AVL trees, Okasaki’s constant-time queues, deques, lazy
data structures based on numerical representations such as lazy binomial heaps,
cyclic streams, and dynamic programming algorithms.
Some of the benchmarks have posed serious challenges to automatic as well as
manual reasoning.
The system is a part of the Leon verifier and can be tried online at
"http://leondev.epfl.ch" ("Resource bounds" section).
Read more