254 research outputs found
Relational Parametricity and Control
We study the equational theory of Parigot's second-order
λμ-calculus in connection with a call-by-name continuation-passing
style (CPS) translation into a fragment of the second-order λ-calculus.
It is observed that the relational parametricity on the target calculus induces
a natural notion of equivalence on the λμ-terms. On the other hand,
the unconstrained relational parametricity on the λμ-calculus turns
out to be inconsistent with this CPS semantics. Following these facts, we
propose to formulate the relational parametricity on the λμ-calculus
in a constrained way, which might be called ``focal parametricity''.Comment: 22 pages, for Logical Methods in Computer Scienc
An estimation for the lengths of reduction sequences of the -calculus
Since it was realized that the Curry-Howard isomorphism can be extended to
the case of classical logic as well, several calculi have appeared as
candidates for the encodings of proofs in classical logic. One of the most
extensively studied among them is the -calculus of Parigot. In this
paper, based on the result of Xi presented for the -calculus Xi, we
give an upper bound for the lengths of the reduction sequences in the
-calculus extended with the - and -rules.
Surprisingly, our results show that the new terms and the new rules do not add
to the computational complexity of the calculus despite the fact that
-abstraction is able to consume an unbounded number of arguments by virtue
of the -rule
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
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