68,901 research outputs found
Initial Semantics for Reduction Rules
We give an algebraic characterization of the syntax and operational semantics
of a class of simply-typed languages, such as the language PCF: we characterize
simply-typed syntax with variable binding and equipped with reduction rules via
a universal property, namely as the initial object of some category of models.
For this purpose, we employ techniques developed in two previous works: in the
first work we model syntactic translations between languages over different
sets of types as initial morphisms in a category of models. In the second work
we characterize untyped syntax with reduction rules as initial object in a
category of models. In the present work, we combine the techniques used earlier
in order to characterize simply-typed syntax with reduction rules as initial
object in a category. The universal property yields an operator which allows to
specify translations---that are semantically faithful by construction---between
languages over possibly different sets of types.
As an example, we upgrade a translation from PCF to the untyped lambda
calculus, given in previous work, to account for reduction in the source and
target. Specifically, we specify a reduction semantics in the source and target
language through suitable rules. By equipping the untyped lambda calculus with
the structure of a model of PCF, initiality yields a translation from PCF to
the lambda calculus, that is faithful with respect to the reduction semantics
specified by the rules.
This paper is an extended version of an article published in the proceedings
of WoLLIC 2012.Comment: Extended version of arXiv:1206.4547, proves a variant of a result of
PhD thesis arXiv:1206.455
Initiality for Typed Syntax and Semantics
We give an algebraic characterization of the syntax and semantics of a class
of simply-typed languages, such as the language PCF: we characterize
simply-typed binding syntax equipped with reduction rules via a universal
property, namely as the initial object of some category. For this purpose, we
employ techniques developed in two previous works: in [2], we model syntactic
translations between languages over different sets of types as initial
morphisms in a category of models. In [1], we characterize untyped syntax with
reduction rules as initial object in a category of models. In the present work,
we show that those techniques are modular enough to be combined: we thus
characterize simply-typed syntax with reduction rules as initial object in a
category. The universal property yields an operator which allows to specify
translations - that are semantically faithful by construction - between
languages over possibly different sets of types.
We specify a language by a 2-signature, that is, a signature on two levels:
the syntactic level specifies the types and terms of the language, and
associates a type to each term. The semantic level specifies, through
inequations, reduction rules on the terms of the language. To any given
2-signature we associate a category of models. We prove that this category has
an initial object, which integrates the types and terms freely generated by the
2-signature, and the reduction relation on those terms generated by the given
inequations. We call this object the (programming) language generated by the
2-signature.
[1] Ahrens, B.: Modules over relative monads for syntax and semantics (2011),
arXiv:1107.5252, to be published in Math. Struct. in Comp. Science
[2] Ahrens, B.: Extended Initiality for Typed Abstract Syntax. Logical
Methods in Computer Science 8(2), 1-35 (2012)Comment: presented at WoLLIC 2012, 15 page
Classical logic, continuation semantics and abstract machines
One of the goals of this paper is to demonstrate that denotational semantics is useful for operational issues like implementation of functional languages by abstract machines. This is exemplified in a tutorial way by studying the case of extensional untyped call-by-name λ-calculus with Felleisen's control operator 𝒞. We derive the transition rules for an abstract machine from a continuation semantics which appears as a generalization of the ¬¬-translation known from logic. The resulting abstract machine appears as an extension of Krivine's machine implementing head reduction. Though the result, namely Krivine's machine, is well known our method of deriving it from continuation semantics is new and applicable to other languages (as e.g. call-by-value variants). Further new results are that Scott's D∞-models are all instances of continuation models. Moreover, we extend our continuation semantics to Parigot's λμ-calculus from which we derive an extension of Krivine's machine for λμ-calculus. The relation between continuation semantics and the abstract machines is made precise by proving computational adequacy results employing an elegant method introduced by Pitts
An interactive semantics of logic programming
We apply to logic programming some recently emerging ideas from the field of
reduction-based communicating systems, with the aim of giving evidence of the
hidden interactions and the coordination mechanisms that rule the operational
machinery of such a programming paradigm. The semantic framework we have chosen
for presenting our results is tile logic, which has the advantage of allowing a
uniform treatment of goals and observations and of applying abstract
categorical tools for proving the results. As main contributions, we mention
the finitary presentation of abstract unification, and a concurrent and
coordinated abstract semantics consistent with the most common semantics of
logic programming. Moreover, the compositionality of the tile semantics is
guaranteed by standard results, as it reduces to check that the tile systems
associated to logic programs enjoy the tile decomposition property. An
extension of the approach for handling constraint systems is also discussed.Comment: 42 pages, 24 figure, 3 tables, to appear in the CUP journal of Theory
and Practice of Logic Programmin
Mechanized semantics
The goal of this lecture is to show how modern theorem provers---in this
case, the Coq proof assistant---can be used to mechanize the specification of
programming languages and their semantics, and to reason over individual
programs and over generic program transformations, as typically found in
compilers. The topics covered include: operational semantics (small-step,
big-step, definitional interpreters); a simple form of denotational semantics;
axiomatic semantics and Hoare logic; generation of verification conditions,
with application to program proof; compilation to virtual machine code and its
proof of correctness; an example of an optimizing program transformation (dead
code elimination) and its proof of correctness
Connectors meet Choreographies
We present Cho-Reo-graphies (CR), a new language model that unites two
powerful programming paradigms for concurrent software based on communicating
processes: Choreographic Programming and Exogenous Coordination. In CR,
programmers specify the desired communications among processes using a
choreography, and define how communications should be concretely animated by
connectors given as constraint automata (e.g., synchronous barriers and
asynchronous multi-casts). CR is the first choreography calculus where
different communication semantics (determined by connectors) can be freely
mixed; since connectors are user-defined, CR also supports many communication
semantics that were previously unavailable for choreographies. We develop a
static analysis that guarantees that a choreography in CR and its user-defined
connectors are compatible, define a compiler from choreographies to a process
calculus based on connectors, and prove that compatibility guarantees
deadlock-freedom of the compiled process implementations
Lazy Evaluation and Delimited Control
The call-by-need lambda calculus provides an equational framework for
reasoning syntactically about lazy evaluation. This paper examines its
operational characteristics. By a series of reasoning steps, we systematically
unpack the standard-order reduction relation of the calculus and discover a
novel abstract machine definition which, like the calculus, goes "under
lambdas." We prove that machine evaluation is equivalent to standard-order
evaluation. Unlike traditional abstract machines, delimited control plays a
significant role in the machine's behavior. In particular, the machine replaces
the manipulation of a heap using store-based effects with disciplined
management of the evaluation stack using control-based effects. In short, state
is replaced with control. To further articulate this observation, we present a
simulation of call-by-need in a call-by-value language using delimited control
operations
The Sigma-Semantics: A Comprehensive Semantics for Functional Programs
A comprehensive semantics for functional programs is presented, which generalizes the well-known call-by-value and call-by-name semantics. By permitting a separate choice between call-by value and call-by-name for every argument position of every function and parameterizing the semantics by this choice we abstract from the parameter-passing mechanism. Thus common and distinguishing features of all instances of the sigma-semantics, especially call-by-value and call-by-name semantics, are highlighted. Furthermore, a property can be validated for all instances of the sigma-semantics by a single proof. This is employed for proving the equivalence of the given denotational (fixed-point based) and two operational (reduction based) definitions of the sigma-semantics. We present and apply means for very simple proofs of equivalence with the denotational sigma-semantics for a large class of reduction-based sigma-semantics. Our basis are simple first-order constructor-based functional programs with patterns
The Sigma-Semantics: A Comprehensive Semantics for Functional Programs
A comprehensive semantics for functional programs is presented, which generalizes the well-known call-by-value and call-by-name semantics. By permitting a separate choice between call-by value and call-by-name for every argument position of every function and parameterizing the semantics by this choice we abstract from the parameter-passing mechanism. Thus common and distinguishing features of all instances of the sigma-semantics, especially call-by-value and call-by-name semantics, are highlighted. Furthermore, a property can be validated for all instances of the sigma-semantics by a single proof. This is employed for proving the equivalence of the given denotational (fixed-point based) and two operational (reduction based) definitions of the sigma-semantics. We present and apply means for very simple proofs of equivalence with the denotational sigma-semantics for a large class of reduction-based sigma-semantics. Our basis are simple first-order constructor-based functional programs with patterns
- …