18,400 research outputs found
Extending the Extensional Lambda Calculus with Surjective Pairing is Conservative
We answer Klop and de Vrijer's question whether adding surjective-pairing
axioms to the extensional lambda calculus yields a conservative extension. The
answer is positive. As a byproduct we obtain a "syntactic" proof that the
extensional lambda calculus with surjective pairing is consistent.Comment: To appear in Logical Methods in Computer Scienc
An Invariant Cost Model for the Lambda Calculus
We define a new cost model for the call-by-value lambda-calculus satisfying
the invariance thesis. That is, under the proposed cost model, Turing machines
and the call-by-value lambda-calculus can simulate each other within a
polynomial time overhead. The model only relies on combinatorial properties of
usual beta-reduction, without any reference to a specific machine or evaluator.
In particular, the cost of a single beta reduction is proportional to the
difference between the size of the redex and the size of the reduct. In this
way, the total cost of normalizing a lambda term will take into account the
size of all intermediate results (as well as the number of steps to normal
form).Comment: 19 page
A correspondence between rooted planar maps and normal planar lambda terms
A rooted planar map is a connected graph embedded in the 2-sphere, with one
edge marked and assigned an orientation. A term of the pure lambda calculus is
said to be linear if every variable is used exactly once, normal if it contains
no beta-redexes, and planar if it is linear and the use of variables moreover
follows a deterministic stack discipline. We begin by showing that the sequence
counting normal planar lambda terms by a natural notion of size coincides with
the sequence (originally computed by Tutte) counting rooted planar maps by
number of edges. Next, we explain how to apply the machinery of string diagrams
to derive a graphical language for normal planar lambda terms, extracted from
the semantics of linear lambda calculus in symmetric monoidal closed categories
equipped with a linear reflexive object or a linear reflexive pair. Finally,
our main result is a size-preserving bijection between rooted planar maps and
normal planar lambda terms, which we establish by explaining how Tutte
decomposition of rooted planar maps (into vertex maps, maps with an isthmic
root, and maps with a non-isthmic root) may be naturally replayed in linear
lambda calculus, as certain surgeries on the string diagrams of normal planar
lambda terms.Comment: Corrected title field in metadat
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