354 research outputs found
Type-Based Termination, Inflationary Fixed-Points, and Mixed Inductive-Coinductive Types
Type systems certify program properties in a compositional way. From a bigger
program one can abstract out a part and certify the properties of the resulting
abstract program by just using the type of the part that was abstracted away.
Termination and productivity are non-trivial yet desired program properties,
and several type systems have been put forward that guarantee termination,
compositionally. These type systems are intimately connected to the definition
of least and greatest fixed-points by ordinal iteration. While most type
systems use conventional iteration, we consider inflationary iteration in this
article. We demonstrate how this leads to a more principled type system, with
recursion based on well-founded induction. The type system has a prototypical
implementation, MiniAgda, and we show in particular how it certifies
productivity of corecursive and mixed recursive-corecursive functions.Comment: In Proceedings FICS 2012, arXiv:1202.317
Synthesizing Probabilistic Invariants via Doob's Decomposition
When analyzing probabilistic computations, a powerful approach is to first
find a martingale---an expression on the program variables whose expectation
remains invariant---and then apply the optional stopping theorem in order to
infer properties at termination time. One of the main challenges, then, is to
systematically find martingales.
We propose a novel procedure to synthesize martingale expressions from an
arbitrary initial expression. Contrary to state-of-the-art approaches, we do
not rely on constraint solving. Instead, we use a symbolic construction based
on Doob's decomposition. This procedure can produce very complex martingales,
expressed in terms of conditional expectations.
We show how to automatically generate and simplify these martingales, as well
as how to apply the optional stopping theorem to infer properties at
termination time. This last step typically involves some simplification steps,
and is usually done manually in current approaches. We implement our techniques
in a prototype tool and demonstrate our process on several classical examples.
Some of them go beyond the capability of current semi-automatic approaches
Fair Termination of Binary Sessions
A binary session is a private communication channel that connects two processes, each adhering to a protocol description called session type. In this work, we study the first type system that ensures the fair termination of binary sessions. A session fairly terminates if all of the infinite executions admitted by its protocol are deemed ‘unrealistic’ because they violate certain fairness assumptions. Fair termination entails the eventual completion of all pending input/output actions, including those that depend on the completion of an unbounded number of other actions in possibly different sessions. This form of lock freedom allows us to address a large family of natural communication patterns that fall outside the scope of existing type systems. Our type system is also the first to adopt fair subtyping, a liveness-preserving refinement of the standard subtyping relation for session types that so far has only been studied theoretically. Fair subtyping is surprisingly subtle not only to characterize concisely but also to use appropriately, to the point that the type system must carefully account for all usages of fair subtyping to avoid compromising its liveness-preserving properties
Functional Ownership through Fractional Uniqueness
Ownership and borrowing systems, designed to enforce safe memory management
without the need for garbage collection, have been brought to the fore by the
Rust programming language. Rust also aims to bring some guarantees offered by
functional programming into the realm of performant systems code, but the type
system is largely separate from the ownership model, with type and borrow
checking happening in separate compilation phases. Recent models such as
RustBelt and Oxide aim to formalise Rust in depth, but there is less focus on
integrating the basic ideas into more traditional type systems. An approach
designed to expose an essential core for ownership and borrowing would open the
door for functional languages to borrow concepts found in Rust and other
ownership frameworks, so that more programmers can enjoy their benefits.
One strategy for managing memory in a functional setting is through
uniqueness types, but these offer a coarse-grained view: either a value has
exactly one reference, and can be mutated safely, or it cannot, since other
references may exist. Recent work demonstrates that linear and uniqueness types
can be combined in a single system to offer restrictions on program behaviour
and guarantees about memory usage. We develop this connection further, showing
that just as graded type systems like those of Granule and Idris generalise
linearity, Rust's ownership model arises as a graded generalisation of
uniqueness. We combine fractional permissions with grading to give the first
account of ownership and borrowing that smoothly integrates into a standard
type system alongside linearity and graded types, and extend Granule
accordingly with these ideas.Comment: 23 pages + references. In submissio
Terminological reasoning with constraint handling rules
Constraint handling rules (CHRs) are a flexible means to implement \u27user-defined\u27 constraints on top of existing host languages (like Prolog and Lisp). Recently, M. Schmidt-Schauß and G. Smolka proposed a new methodology for constructing sound and complete inference algorithms for terminological knowledge representation formalisms in the tradition of KLONE. We propose CHRs as a flexible implementation language for the consistency test of assertions, which is the basis for all terminological reasoning services.
The implementation results in a natural combination of three layers: (i) a constraint layer that reasons in well- understood domains such as rationals or finite domains, (ii) a terminological layer providing a tailored, validated vocabulary on which (iii) the application layer can rely. The flexibility of the approach will be illustrated by extending the formalism, its implementation and an application example (solving configuration problems) with attributes, a new quantifier and concrete domains
Observational equivalences for linear logic CC languages
Linear logic Concurrent Constraint programming (LCC) is an extension of
concurrent constraint programming (CC) where the constraint system is based on
Girard's linear logic instead of the classical logic. In this paper we address
the problem of program equivalence for this programming framework. For this
purpose, we present a structural operational semantics for LCC based on a label
transition system and investigate different notions of observational
equivalences inspired by the state of art of process algebras. Then, we
demonstrate that the asynchronous \pi-calculus can be viewed as simple
syntactical restrictions of LCC. Finally we show LCC observational equivalences
can be transposed straightforwardly to classical Concurrent Constraint
languages and Constraint Handling Rules, and investigate the resulting
equivalences.Comment: 17 page
A Declarative Semantics for CLP with Qualification and Proximity
Uncertainty in Logic Programming has been investigated during the last
decades, dealing with various extensions of the classical LP paradigm and
different applications. Existing proposals rely on different approaches, such
as clause annotations based on uncertain truth values, qualification values as
a generalization of uncertain truth values, and unification based on proximity
relations. On the other hand, the CLP scheme has established itself as a
powerful extension of LP that supports efficient computation over specialized
domains while keeping a clean declarative semantics. In this paper we propose a
new scheme SQCLP designed as an extension of CLP that supports qualification
values and proximity relations. We show that several previous proposals can be
viewed as particular cases of the new scheme, obtained by partial
instantiation. We present a declarative semantics for SQCLP that is based on
observables, providing fixpoint and proof-theoretical characterizations of
least program models as well as an implementation-independent notion of goal
solutions.Comment: 17 pages, 26th Int'l. Conference on Logic Programming (ICLP'10
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