6,001 research outputs found
Deduction modulo theory
This paper is a survey on Deduction modulo theor
Several types of types in programming languages
Types are an important part of any modern programming language, but we often
forget that the concept of type we understand nowadays is not the same it was
perceived in the sixties. Moreover, we conflate the concept of "type" in
programming languages with the concept of the same name in mathematical logic,
an identification that is only the result of the convergence of two different
paths, which started apart with different aims. The paper will present several
remarks (some historical, some of more conceptual character) on the subject, as
a basis for a further investigation. The thesis we will argue is that there are
three different characters at play in programming languages, all of them now
called types: the technical concept used in language design to guide
implementation; the general abstraction mechanism used as a modelling tool; the
classifying tool inherited from mathematical logic. We will suggest three
possible dates ad quem for their presence in the programming language
literature, suggesting that the emergence of the concept of type in computer
science is relatively independent from the logical tradition, until the
Curry-Howard isomorphism will make an explicit bridge between them.Comment: History and Philosophy of Computing, HAPOC 2015. To appear in LNC
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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