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Beyond Notations: Hygienic Macro Expansion for Theorem Proving Languages

ABSTRACT: In interactive theorem provers (ITPs), extensible syntax is not only crucial to lower the cognitive burden of manipulating complex mathematical objects, but plays a critical role in developing reusable abstractions in libraries. Most ITPs support such extensions in the form of restrictive “syntax sugar” substitutions and other ad hoc mechanisms, which are too rudimentary to support many desirable abstractions. As a result, libraries are littered with unnecessary redundancy. Tactic languages in these systems are plagued by a seemingly unrelated issue: accidental name capture, which often produces unexpected and counterintuitive behavior. We take ideas from the Scheme family of programming languages and solve these two problems simultaneously by proposing a novel hygienic macro system custom-built for ITPs. We further describe how our approach can be extended to cover type-directed macro expansion resulting in a single, uniform system offering multiple abstraction levels that range from supporting simplest syntax sugars to elaboration of formerly baked-in syntax. We have implemented our new macro system and integrated it into the upcoming version (v4) of the Lean theorem prover. Despite its expressivity, the macro system is simple enough that it can easily be integrated into other systems. Electronic supplementary material The online version of this chapter (10.1007/978-3-030-51054-1_10) contains supplementary material, which is available to authorized users.

SUBMITTER: Peltier N

PROVIDER: S-EPMC7324063 | biostudies-literature | 2020 Jun

REPOSITORIES: biostudies-literature

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Project description:BackgroundHygienic behavior is a complex, genetically-based quantitative trait that serves as a key defense mechanism against parasites and diseases in Apis mellifera. Yet, the genomic basis and functional pathways involved in the initiation of this behavior are still unclear. Deciphering the genomic basis of hygienic behavior is a prerequisite to developing an extensive repertoire of genetic markers associated to the performance level of this quantitative trait. To fill this knowledge gap, we performed an RNA-seq on brain samples of 25 honeybees per hives from five hygienic and three non-hygienic hives.ResultsThis analysis revealed that a limited number of functional genes are involved in honeybee hygienic behavior. The genes identified, and especially their location in the honeybee genome, are consistent with previous findings. Indeed, the genomic sequences of most differentially expressed genes were found on the majority of the QTL regions associated to the hygienic behavior described in previous studies. According to the Gene Ontology annotation, 15 genes are linked to the GO-terms DNA or nucleotide binding, indicating a possible role of these genes in transcription regulation. Furthermore, GO-category enrichment analysis revealed that electron carrier activity is over-represented, involving only genes belonging to the cytochrome P450. Cytochrome P450 enzymes' overexpression can be explained by a disturbance in the regulation of expression induced by changes in transcription regulation or sensitivity to xenobiotics. Over-expressed cytochrome P450 enzymes could potentially degrade the odorant pheromones or chemicals that normally signal the presence of a diseased brood before activation of the removal process thereby inhibit hygienic behavior.ConclusionsThese findings improve our understanding on the genetics basis of the hygienic behavior. Our results show that hygienic behavior relies on a limited set of genes linked to different regulation patterns (expression level and biological processes) associated with an over-expression of cytochrome P450 genes.

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Beyond Notations: Hygienic Macro Expansion for Theorem Proving Languages

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