Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Proof-relevant $\pi$-calculus: a constructive account of concurrency and
  causality   We present a formalisation in Agda of the theory of concurrent transitions,
residuation, and causal equivalence of traces for the pi-calculus. Our
formalisation employs de Bruijn indices and dependently-typed syntax, and
aligns the "proved transitions" proposed by Boudol and Castellani in the
context of CCS with the proof terms naturally present in Agda's representation
of the labelled transition relation. Our main contributions are proofs of the
"diamond lemma" for the residuals of concurrent transitions and a formal
definition of equivalence of traces up to permutation of transitions.
  In the pi-calculus transitions represent propagating binders whenever their
actions involve bound names. To accommodate these cases, we require a more
general diamond lemma where the target states of equivalent traces are no
longer identical, but are related by a braiding that rewires the bound and free
names to reflect the particular interleaving of events involving binders. Our
approach may be useful for modelling concurrency in other languages where
transitions carry metadata sensitive to particular interleavings, such as
dynamically allocated memory addresses.

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The categories of this paper are: q-bio
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The categories of this paper are: hep-ph
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The categories of this paper are: econ
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The categories of this paper are: chao-dyn
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The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
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The categories of this paper are: eess
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The categories of this paper are: quant-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-th
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The categories of this paper are: math
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The categories of this paper are: patt-sol
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The categories of this paper are: funct-an