7,130 research outputs found
A Family Of Syntactic Logical Relations For The Semantics Of Haskell-Like Languages
Logical relations are a fundamental and powerful tool for reasoning about programs in languages with parametric polymorphism. Logical relations suitable for reasoning about observational behavior in polymorphic calculi supporting various programming language features have been introduced in recent years. Unfortunately, the calculi studied are typically idealized, and the results obtained for them over only partial insight into the impact of such features on observational behavior in implemented languages. In this paper we show how to bring reasoning via logical relations closer to bear on real languages by deriving results that are more pertinent to an intermediate language for the (mostly) lazy functional language Haskell like GHC Core. To provide a more ?ne-grained analysis of program behavior than is possible by reasoning about program equivalence alone, we work with an abstract notion of relating observational behavior of computations which has among its specializations both observational equivalence and observational approximation. We take selective strictness into account, and we consider the impact of different kinds of computational failure, e.g., divergence versus failed pattern matching, because such distinctions are significant in practice. Once distinguished, the relative de?nedness of different failure causes needs to be considered, because different orders here induce different observational relations on programs (including the choice between equivalence and approximation). Our main contribution is the construction of an entire family of logical relations, parameterized over a definedness order on failure causes, each member of which characterizes the corresponding observational relation. Although we deal with properties very much tied to types, we base our results on a type-erasing semantics since this is more faithful to actual implementations
Foundational Extensible Corecursion
This paper presents a formalized framework for defining corecursive functions
safely in a total setting, based on corecursion up-to and relational
parametricity. The end product is a general corecursor that allows corecursive
(and even recursive) calls under well-behaved operations, including
constructors. Corecursive functions that are well behaved can be registered as
such, thereby increasing the corecursor's expressiveness. The metatheory is
formalized in the Isabelle proof assistant and forms the core of a prototype
tool. The corecursor is derived from first principles, without requiring new
axioms or extensions of the logic
A Systematic Aspect-Oriented Refactoring and Testing Strategy, and its Application to JHotDraw
Aspect oriented programming aims at achieving better modularization for a
system's crosscutting concerns in order to improve its key quality attributes,
such as evolvability and reusability. Consequently, the adoption of
aspect-oriented techniques in existing (legacy) software systems is of interest
to remediate software aging. The refactoring of existing systems to employ
aspect-orientation will be considerably eased by a systematic approach that
will ensure a safe and consistent migration.
In this paper, we propose a refactoring and testing strategy that supports
such an approach and consider issues of behavior conservation and (incremental)
integration of the aspect-oriented solution with the original system. The
strategy is applied to the JHotDraw open source project and illustrated on a
group of selected concerns. Finally, we abstract from the case study and
present a number of generic refactorings which contribute to an incremental
aspect-oriented refactoring process and associate particular types of
crosscutting concerns to the model and features of the employed aspect
language. The contributions of this paper are both in the area of supporting
migration towards aspect-oriented solutions and supporting the development of
aspect languages that are better suited for such migrations.Comment: 25 page
Logical relations for coherence of effect subtyping
A coercion semantics of a programming language with subtyping is typically
defined on typing derivations rather than on typing judgments. To avoid
semantic ambiguity, such a semantics is expected to be coherent, i.e.,
independent of the typing derivation for a given typing judgment. In this
article we present heterogeneous, biorthogonal, step-indexed logical relations
for establishing the coherence of coercion semantics of programming languages
with subtyping. To illustrate the effectiveness of the proof method, we develop
a proof of coherence of a type-directed, selective CPS translation from a typed
call-by-value lambda calculus with delimited continuations and control-effect
subtyping. The article is accompanied by a Coq formalization that relies on a
novel shallow embedding of a logic for reasoning about step-indexing
Koka: Programming with Row Polymorphic Effect Types
We propose a programming model where effects are treated in a disciplined
way, and where the potential side-effects of a function are apparent in its
type signature. The type and effect of expressions can also be inferred
automatically, and we describe a polymorphic type inference system based on
Hindley-Milner style inference. A novel feature is that we support polymorphic
effects through row-polymorphism using duplicate labels. Moreover, we show that
our effects are not just syntactic labels but have a deep semantic connection
to the program. For example, if an expression can be typed without an exn
effect, then it will never throw an unhandled exception. Similar to Haskell's
`runST` we show how we can safely encapsulate stateful operations. Through the
state effect, we can also safely combine state with let-polymorphism without
needing either imperative type variables or a syntactic value restriction.
Finally, our system is implemented fully in a new language called Koka and has
been used successfully on various small to medium-sized sample programs ranging
from a Markdown processor to a tier-splitted chat application. You can try out
Koka live at www.rise4fun.com/koka/tutorial.Comment: In Proceedings MSFP 2014, arXiv:1406.153
Learning-Assisted Automated Reasoning with Flyspeck
The considerable mathematical knowledge encoded by the Flyspeck project is
combined with external automated theorem provers (ATPs) and machine-learning
premise selection methods trained on the proofs, producing an AI system capable
of answering a wide range of mathematical queries automatically. The
performance of this architecture is evaluated in a bootstrapping scenario
emulating the development of Flyspeck from axioms to the last theorem, each
time using only the previous theorems and proofs. It is shown that 39% of the
14185 theorems could be proved in a push-button mode (without any high-level
advice and user interaction) in 30 seconds of real time on a fourteen-CPU
workstation. The necessary work involves: (i) an implementation of sound
translations of the HOL Light logic to ATP formalisms: untyped first-order,
polymorphic typed first-order, and typed higher-order, (ii) export of the
dependency information from HOL Light and ATP proofs for the machine learners,
and (iii) choice of suitable representations and methods for learning from
previous proofs, and their integration as advisors with HOL Light. This work is
described and discussed here, and an initial analysis of the body of proofs
that were found fully automatically is provided
Structural Induction Principles for Functional Programmers
User defined recursive types are a fundamental feature of modern functional
programming languages like Haskell, Clean, and the ML family of languages.
Properties of programs defined by recursion on the structure of recursive types
are generally proved by structural induction on the type. It is well known in
the theorem proving community how to generate structural induction principles
from data type declarations. These methods deserve to be better know in the
functional programming community. Existing functional programming textbooks
gloss over this material. And yet, if functional programmers do not know how to
write down the structural induction principle for a new type - how are they
supposed to reason about it? In this paper we describe an algorithm to generate
structural induction principles from data type declarations. We also discuss
how these methods are taught in the functional programming course at the
University of Wyoming. A Haskell implementation of the algorithm is included in
an appendix.Comment: In Proceedings TFPIE 2013, arXiv:1312.221
Relative Effect Declarations for Lightweight Effect-Polymorphism
Type-and-effect systems are a well-studied approach for reasoning about the computational behavior of programs. A major roadblock in adopting effect systems in popular languages is the tradeoff between expressiveness and verbosity. In this technical report, we present a syntactically lightweight but expressive system for annotating effect-polymorphic behavior of functions. The presented system is independent from any specific effect domains and can be embedded in an extensible type-and-effect system
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