200 research outputs found
The solid surface combustion space shuttle experiment hardware description and ground-based test results
The Lewis Research Center is developing a series of microgravity combustion experiments for the Space Shuttle. The Solid Surface Combustion Experiment (SSCE) is the first to be completed. SSCE will study flame spreading over thermally thin fuels (ashless filter paper) under microgravity conditions. The flight hardware consists of a combustion chamber containing the sample and a computer which takes the data and controls the experiment. Experimental data will include gas-phase and solid-phase temperature measurements and motion pictures of the combustion process. Flame spread rates will be determined from the motion pictures
Opposed-Flow Flame Spreading in Reduced Gravity
Experimental results obtained in drop towers and in Space Shuttle based experiments coupled with modelling efforts are beginning to provide information that is allowing an understanding to be developed of the physics of opposed-flow flame spread at reduced gravity where the spread rate and flow velocity are comparable and of the role played by radiative and diffusive processes in flame spreading in microgravity. Here we describe one Space Shuttle based experiment on flame spreading in a quiescent environment, the Solid Surface Combustion Experiment, SSCE, one planned microgravity experiment on flame spreading in a radiatively-controlled, forced opposing flow environment, the Diffusive and Radiative Transport in Fires Experiment, DARTFire, modelling efforts to support these experiments, and some results obtained to date
An experimental study of the influence of elevated buoyancy levels on flame spread rate over thermally thin cellulosic materials
The role of buoyancy on the flame spread rate over paper and its effect on extinction was studied by changing the gravity level and pressure. It was found that the flame spread rate decreases as the buoyancy induced flow increases. A method for correlating flame spread data using dimensionless parameters is presented. The Damkohler number is shown to be the dependent variable
The Effect of Ambient Pressure on Flame Spread over Thin Cellulosic Fuel in a Quiescent Microgravity Environment
Quotient inductive-inductive types
Higher inductive types (HITs) in Homotopy Type Theory (HoTT) allow the definition of datatypes which have constructors for equalities over the defined type. HITs generalise quotient types and allow to define types which are not sets in the sense of HoTT (i.e. do not satisfy uniqueness of equality proofs) such as spheres, suspensions and the torus. However, there are also interesting uses of HITs to define sets, such as the Cauchy reals, the partiality monad, and the internal, total syntax of type theory. In each of these examples we define several types that depend on each other mutually, i.e. they are inductive-inductive definitions. We call those HITs quotient inductive-inductive types (QIITs).
Although there has been recent progress on the general theory of HITs, there isn't yet a theoretical foundation of the combination of equality constructors and induction-induction, despite having many interesting applications. In the present paper we present a first step towards a semantic definition of QIITs. In particular, we give an initial-algebra semantics and show that this is equivalent to the section induction principle, which justifies the intuitively expected elimination rules
Generic Fibrational Induction
This paper provides an induction rule that can be used to prove properties of
data structures whose types are inductive, i.e., are carriers of initial
algebras of functors. Our results are semantic in nature and are inspired by
Hermida and Jacobs' elegant algebraic formulation of induction for polynomial
data types. Our contribution is to derive, under slightly different
assumptions, a sound induction rule that is generic over all inductive types,
polynomial or not. Our induction rule is generic over the kinds of properties
to be proved as well: like Hermida and Jacobs, we work in a general fibrational
setting and so can accommodate very general notions of properties on inductive
types rather than just those of a particular syntactic form. We establish the
soundness of our generic induction rule by reducing induction to iteration. We
then show how our generic induction rule can be instantiated to give induction
rules for the data types of rose trees, finite hereditary sets, and
hyperfunctions. The first of these lies outside the scope of Hermida and
Jacobs' work because it is not polynomial, and as far as we are aware, no
induction rules have been known to exist for the second and third in a general
fibrational framework. Our instantiation for hyperfunctions underscores the
value of working in the general fibrational setting since this data type cannot
be interpreted as a set.Comment: For Special Issue from CSL 201
Needle & knot : binder boilerplate tied up
To lighten the burden of programming language mechanization, many approaches have been developed that tackle the substantial boilerplate which arises from variable binders. Unfortunately, the existing approaches are limited in scope. They typically do not support complex binding forms (such as multi-binders) that arise in more advanced languages, or they do not tackle the boilerplate due to mentioning variables and binders in relations. As a consequence, the human mechanizer is still unnecessarily burdened with binder boilerplate and discouraged from taking on richer languages.
This paper presents Knot, a new approach that substantially extends the support for binder boilerplate. Knot is a highly expressive language for natural and concise specification of syntax with binders. Its meta-theory constructively guarantees the coverage of a considerable amount of binder boilerplate for well-formed specifications, including that for well-scoping of terms and context lookups. Knot also comes with a code generator, Needle, that specializes the generic boilerplate for convenient embedding in COQ and provides a tactic library for automatically discharging proof obligations that frequently come up in proofs of weakening and substitution lemmas of type-systems.
Our evaluation shows, that Needle & Knot significantly reduce the size of language mechanizations (by 40% in our case study). Moreover, as far as we know, Knot enables the most concise mechanization of the POPLmark Challenge (1a + 2a) and is two-thirds the size of the next smallest. Finally, Knot allows us to mechanize for instance dependentlytyped languages, which is notoriously challenging because of dependent contexts and mutually-recursive sorts with variables
Equality, Quasi-Implicit Products, and Large Eliminations
This paper presents a type theory with a form of equality reflection:
provable equalities can be used to coerce the type of a term. Coercions and
other annotations, including implicit arguments, are dropped during reduction
of terms. We develop the metatheory for an undecidable version of the system
with unannotated terms. We then devise a decidable system with annotated terms,
justified in terms of the unannotated system. Finally, we show how the approach
can be extended to account for large eliminations, using what we call
quasi-implicit products.Comment: In Proceedings ITRS 2010, arXiv:1101.410
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