255 research outputs found
Introduction to the Literature On Programming Language Design
This is an introduction to the literature on programming language design and related topics. It is intended to cite the most important work, and to provide a place for students to start a literature search
On Spatial Conjunction as Second-Order Logic
Spatial conjunction is a powerful construct for reasoning about dynamically
allocated data structures, as well as concurrent, distributed and mobile
computation. While researchers have identified many uses of spatial
conjunction, its precise expressive power compared to traditional logical
constructs was not previously known. In this paper we establish the expressive
power of spatial conjunction. We construct an embedding from first-order logic
with spatial conjunction into second-order logic, and more surprisingly, an
embedding from full second order logic into first-order logic with spatial
conjunction. These embeddings show that the satisfiability of formulas in
first-order logic with spatial conjunction is equivalent to the satisfiability
of formulas in second-order logic. These results explain the great expressive
power of spatial conjunction and can be used to show that adding unrestricted
spatial conjunction to a decidable logic leads to an undecidable logic. As one
example, we show that adding unrestricted spatial conjunction to two-variable
logic leads to undecidability. On the side of decidability, the embedding into
second-order logic immediately implies the decidability of first-order logic
with a form of spatial conjunction over trees. The embedding into spatial
conjunction also has useful consequences: because a restricted form of spatial
conjunction in two-variable logic preserves decidability, we obtain that a
correspondingly restricted form of second-order quantification in two-variable
logic is decidable. The resulting language generalizes the first-order theory
of boolean algebra over sets and is useful in reasoning about the contents of
data structures in object-oriented languages.Comment: 16 page
An abstract interpretation for SPMD divergence on reducible control flow graphs
Vectorizing compilers employ divergence analysis to detect at which program point a specific variable is uniform, i.e. has the same value on all SPMD threads that execute this program point. They exploit uniformity to
retain branching to counter branch divergence and defer computations to scalar processor units. Divergence
is a hyper-property and is closely related to non-interference and binding time. There exist several divergence,
binding time, and non-interference analyses already but they either sacrifice precision or make significant
restrictions to the syntactical structure of the program in order to achieve soundness.
In this paper, we present the first abstract interpretation for uniformity that is general enough to be applicable to reducible CFGs and, at the same time, more precise than other analyses that achieve at least the
same generality.
Our analysis comes with a correctness proof that is to a large part mechanized in Coq. Our experimental
evaluation shows that the compile time and the precision of our analysis is on par with LLVM’s default
divergence analysis that is only sound on more restricted CFGs. At the same time, our analysis is faster and
achieves better precision than a state-of-the-art non-interference analysis that is sound and at least as general
as our analysis
On Role Logic
We present role logic, a notation for describing properties of relational
structures in shape analysis, databases, and knowledge bases. We construct role
logic using the ideas of de Bruijn's notation for lambda calculus, an encoding
of first-order logic in lambda calculus, and a simple rule for implicit
arguments of unary and binary predicates. The unrestricted version of role
logic has the expressive power of first-order logic with transitive closure.
Using a syntactic restriction on role logic formulas, we identify a natural
fragment RL^2 of role logic. We show that the RL^2 fragment has the same
expressive power as two-variable logic with counting C^2 and is therefore
decidable. We present a translation of an imperative language into the
decidable fragment RL^2, which allows compositional verification of programs
that manipulate relational structures. In addition, we show how RL^2 encodes
boolean shape analysis constraints and an expressive description logic.Comment: 20 pages. Our later SAS 2004 result builds on this wor
Really Natural Linear Indexed Type Checking
Recent works have shown the power of linear indexed type systems for
enforcing complex program properties. These systems combine linear types with a
language of type-level indices, allowing more fine-grained analyses. Such
systems have been fruitfully applied in diverse domains, including implicit
complexity and differential privacy. A natural way to enhance the
expressiveness of this approach is by allowing the indices to depend on runtime
information, in the spirit of dependent types. This approach is used in DFuzz,
a language for differential privacy. The DFuzz type system relies on an index
language supporting real and natural number arithmetic over constants and
variables. Moreover, DFuzz uses a subtyping mechanism to make types more
flexible. By themselves, linearity, dependency, and subtyping each require
delicate handling when performing type checking or type inference; their
combination increases this challenge substantially, as the features can
interact in non-trivial ways. In this paper, we study the type-checking problem
for DFuzz. We show how we can reduce type checking for (a simple extension of)
DFuzz to constraint solving over a first-order theory of naturals and real
numbers which, although undecidable, can often be handled in practice by
standard numeric solvers
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