386 research outputs found
Proving termination of evaluation for System F with control operators
We present new proofs of termination of evaluation in reduction semantics
(i.e., a small-step operational semantics with explicit representation of
evaluation contexts) for System F with control operators. We introduce a
modified version of Girard's proof method based on reducibility candidates,
where the reducibility predicates are defined on values and on evaluation
contexts as prescribed by the reduction semantics format. We address both
abortive control operators (callcc) and delimited-control operators (shift and
reset) for which we introduce novel polymorphic type systems, and we consider
both the call-by-value and call-by-name evaluation strategies.Comment: In Proceedings COS 2013, arXiv:1309.092
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
Answer-Type Modification without Tears: Prompt-Passing Style Translation for Typed Delimited-Control Operators
The salient feature of delimited-control operators is their ability to modify
answer types during computation. The feature, answer-type modification (ATM for
short), allows one to express various interesting programs such as typed printf
compactly and nicely, while it makes it difficult to embed these operators in
standard functional languages.
In this paper, we present a typed translation of delimited-control operators
shift and reset with ATM into a familiar language with multi-prompt shift and
reset without ATM, which lets us use ATM in standard languages without
modifying the type system. Our translation generalizes Kiselyov's direct-style
implementation of typed printf, which uses two prompts to emulate the
modification of answer types, and passes them during computation. We prove that
our translation preserves typing. As the naive prompt-passing style translation
generates and passes many prompts even for pure terms, we show an optimized
translation that generate prompts only when needed, which is also
type-preserving. Finally, we give an implementation in the tagless-final style
which respects typing by construction.Comment: In Proceedings WoC 2015, arXiv:1606.0583
Perspectives for proof unwinding by programming languages techniques
In this chapter, we propose some future directions of work, potentially
beneficial to Mathematics and its foundations, based on the recent import of
methodology from the theory of programming languages into proof theory. This
scientific essay, written for the audience of proof theorists as well as the
working mathematician, is not a survey of the field, but rather a personal view
of the author who hopes that it may inspire future and fellow researchers
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
On the Expressive Power of User-Defined Effects: Effect Handlers, Monadic Reflection, Delimited Control
We compare the expressive power of three programming abstractions for
user-defined computational effects: Bauer and Pretnar's effect handlers,
Filinski's monadic reflection, and delimited control without
answer-type-modification. This comparison allows a precise discussion about the
relative expressiveness of each programming abstraction. It also demonstrates
the sensitivity of the relative expressiveness of user-defined effects to
seemingly orthogonal language features. We present three calculi, one per
abstraction, extending Levy's call-by-push-value. For each calculus, we present
syntax, operational semantics, a natural type-and-effect system, and, for
effect handlers and monadic reflection, a set-theoretic denotational semantics.
We establish their basic meta-theoretic properties: safety, termination, and,
where applicable, soundness and adequacy. Using Felleisen's notion of a macro
translation, we show that these abstractions can macro-express each other, and
show which translations preserve typeability. We use the adequate finitary
set-theoretic denotational semantics for the monadic calculus to show that
effect handlers cannot be macro-expressed while preserving typeability either
by monadic reflection or by delimited control. We supplement our development
with a mechanised Abella formalisation
On Subexponentials, Synthetic Connectives, and Multi-level Delimited Control
International audienceWe construct a partially-ordered hierarchy of delimited control operators similar to those of the CPS hierarchy of Danvy and Filinski. However, instead of relying on nested CPS translations, these operators are directly interpreted in linear logic extended with subexponentials (i.e., multiple pairs of ! and ?). We construct an independent proof theory for a fragment of this logic based on the principle of focusing. It is then shown that the new constraints placed on the permutation of cuts correspond to multiple levels of delimited control
A Functional Abstraction of Typed Invocation Contexts
In their paper "A Functional Abstraction of Typed Contexts", Danvy and
Filinski show how to derive a monomorphic type system of the shift and reset
operators from a CPS semantics. In this paper, we show how this method scales
to Felleisen's control and prompt operators. Compared to shift and reset,
control and prompt exhibit a more dynamic behavior, in that they can manipulate
a trail of contexts surrounding the invocation of previously captured
continuations. Our key observation is that, by adopting a functional
representation of trails in the CPS semantics, we can derive a type system that
encodes all and only constraints imposed by the CPS semantics
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