1,922 research outputs found
Predicate Abstraction for Linked Data Structures
We present Alias Refinement Types (ART), a new approach to the verification
of correctness properties of linked data structures. While there are many
techniques for checking that a heap-manipulating program adheres to its
specification, they often require that the programmer annotate the behavior of
each procedure, for example, in the form of loop invariants and pre- and
post-conditions. Predicate abstraction would be an attractive abstract domain
for performing invariant inference, existing techniques are not able to reason
about the heap with enough precision to verify functional properties of data
structure manipulating programs. In this paper, we propose a technique that
lifts predicate abstraction to the heap by factoring the analysis of data
structures into two orthogonal components: (1) Alias Types, which reason about
the physical shape of heap structures, and (2) Refinement Types, which use
simple predicates from an SMT decidable theory to capture the logical or
semantic properties of the structures. We prove ART sound by translating types
into separation logic assertions, thus translating typing derivations in ART
into separation logic proofs. We evaluate ART by implementing a tool that
performs type inference for an imperative language, and empirically show, using
a suite of data-structure benchmarks, that ART requires only 21% of the
annotations needed by other state-of-the-art verification techniques
Bounded Refinement Types
We present a notion of bounded quantification for refinement types and show
how it expands the expressiveness of refinement typing by using it to develop
typed combinators for: (1) relational algebra and safe database access, (2)
Floyd-Hoare logic within a state transformer monad equipped with combinators
for branching and looping, and (3) using the above to implement a refined IO
monad that tracks capabilities and resource usage. This leap in expressiveness
comes via a translation to "ghost" functions, which lets us retain the
automated and decidable SMT based checking and inference that makes refinement
typing effective in practice.Comment: 14 pages, International Conference on Functional Programming, ICFP
201
Practical Subtyping for System F with Sized (Co-)Induction
We present a rich type system with subtyping for an extension of System F.
Our type constructors include sum and product types, universal and existential
quantifiers, inductive and coinductive types. The latter two size annotations
allowing the preservation of size invariants. For example it is possible to
derive the termination of the quicksort by showing that partitioning a list
does not increase its size. The system deals with complex programs involving
mixed induction and coinduction, or even mixed (co-)induction and polymorphism
(as for Scott-encoded datatypes). One of the key ideas is to completely
separate the induction on sizes from the notion of recursive programs. We use
the size change principle to check that the proof is well-founded, not that the
program terminates. Termination is obtained by a strong normalization proof.
Another key idea is the use symbolic witnesses to handle quantifiers of all
sorts. To demonstrate the practicality of our system, we provide an
implementation that accepts all the examples discussed in the paper and much
more
Modular session types for objects
Session types allow communication protocols to be specified
type-theoretically so that protocol implementations can be verified by static
type checking. We extend previous work on session types for distributed
object-oriented languages in three ways. (1) We attach a session type to a
class definition, to specify the possible sequences of method calls. (2) We
allow a session type (protocol) implementation to be modularized, i.e.
partitioned into separately-callable methods. (3) We treat session-typed
communication channels as objects, integrating their session types with the
session types of classes. The result is an elegant unification of communication
channels and their session types, distributed object-oriented programming, and
a form of typestate supporting non-uniform objects, i.e. objects that
dynamically change the set of available methods. We define syntax, operational
se-mantics, a sound type system, and a sound and complete type checking
algorithm for a small distributed class-based object-oriented language with
structural subtyping. Static typing guarantees that both sequences of messages
on channels, and sequences of method calls on objects, conform to
type-theoretic specifications, thus ensuring type-safety. The language includes
expected features of session types, such as delegation, and expected features
of object-oriented programming, such as encapsulation of local state.Comment: Logical Methods in Computer Science (LMCS), International Federation
for Computational Logic, 201
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