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There is a green room backstage with two stage entrances just off of the theater. It contains two large countertops with mirrors, as well as a sink. Monitors provide an audio feed from the theatre. The green room also provides a route to the restrooms and water fountains without passing through the theatre.
As a blackbox-style theatre, there is not a dedicated stage, which means the addition of more chairs will reduce the available space for a performance or presentation. Up to two rows of chairs can be placed on risers to create a stadium-seating feel.
Separation of macros into blackbox ones and whitebox ones is a feature of Scala 2.11.x and Scala 2.12.x. The blackbox/whitebox separation is not supported in Scala 2.10.x. It is also not supported in macro paradise for Scala 2.10.x.
With macros becoming a part of the official Scala 2.10 release, programmers in research and industry have found creative ways of using macros to address all sorts of problems, far extending our original expectations.
In fact, macros became an important part of our ecosystem so quickly that just a couple of months after the release of Scala 2.10, when macros were introduced in experimental capacity, we had a Scala language team meeting and decided to standardize macros and make them a full-fledged feature of Scala by 2.12.
UPDATE It turned out that it was not that simple to stabilize macros by Scala 2.12. Our research into that has resulted in establishing a new metaprogramming foundation for Scala, called scala.meta, whose first beta is expected to be released simultaneously with Scala 2.12 and might later be included in future versions of Scala. In the meanwhile, Scala 2.12 is not going to see any changes to reflection and macros - everything is going to stay experimental as it was in Scala 2.10 and Scala 2.11, and no features are going to be removed. However, even though circumstances under which this document has been written have changed, the information still remains relevant, so please continue reading.
Macro flavors are plentiful, so we decided to carefully examine them to figure out which ones should be put in the standard. This entails answering a few important questions. Why are macros working so well? Why do people use them?
Our hypothesis is that this happens because the hard to comprehend notion of metaprogramming expressed in def macros piggybacks on the familiar concept of a typed method call. Thanks to that, the code that users write can absorb more meaning without becoming bloated or losingcomprehensibility.
This curious feature provides additional flexibility, enabling fake type providers, extended vanilla materialization, fundep materialization and extractor macros, but it also sacrifices clarity - both for humans and for machines.
In the 2.11 release, we take first step of standardization by expressing the distinction between blackbox and whitebox macros in signatures of def macros, so that scalac can treat such macros differently. This is just a preparatory step, so both blackbox and whitebox macros remain experimental in Scala 2.11.
We express the distinction by replacing scala.reflect.macros.Context with scala.reflect.macros.blackbox.Context and scala.reflect.macros.whitebox.Context. If a macro impl is defined with blackbox.Context as its first argument, then macro defs that are using it are considered blackbox, and analogously for whitebox.Context. Of course, the vanilla Context is still there for compatibility reasons, but it issues a deprecation warning encouraging to choose between blackbox and whitebox macros.
Whitebox def macros work exactly like def macros used to work in Scala 2.10. No restrictions of any kind get applied, so everything that could be done with macros in 2.10 should be possible in 2.11 and 2.12.
By a blackbox theorem I mean a theorem that is often applied but whose proof is understood in detail by relatively few of those who use it. A prototypical example is the Classification of Finite Simple Groups (assuming the proof is complete). I think very few people really know the nuts and bolts of the proof but it is widely applied in many areas of mathematics. I would prefer not to include as a blackbox theorem exotic counterexamples because they are not usually applied in the same sense as the Classification of Finite Simple Groups.
The graph minor theorem and the graph structure theorem are two results which are invoked quite often in combinatorics/graph theory. Much like the classification of finite simple groups they are excellent ways of sweeping hundreds of pages of technical proofs under just a few sentences.
Deligne's Theorem, found at Wikipedia under the heading of Weil conjectures, which is the Riemann Hypothesis for zeta-functions of algebraic varieties over finite fields, is often applied to estimate exponential sums in Number Theory, I suspect often by people (like me) who haven't gone through a proof in detail.
Low dimensional topology is unfortunately full of such theorems. Maybe the archetypal example is the Kirby Theorem, which states that surgery on two framed links in S3 give diffeomorphic 3-manifolds if and only if the links are related by a specific set of combinatorial moves. The result is used routinely, in order to prove that invariants of framed links descend to topological invariants of the manifold (e.g. Reshetikhin-Turaev invariants).
All known proofs of Kirby's Theorem are a nightmare (see this MO question). You need to use some heavy tool (Cerf's Theorem/ explicit presentation of Mapping Class Groups) in order to show that some expansion of the space of Morse functions (a Frechet space) is path connected. This is outside the toolbox of most topologists.
There are more mild examples too. The proof that PL 3-manifolds can be smoothed, and that the resulting smooth structure is unique up to isotopy (the exact statement is in Kirby-Seibenmann), is used routinely as though it were obvious, but it is actually quite a hard theorem which is not covered in any of the standard textbooks (Thurston's "3-Manifolds" being an exception). See Lurie's 2009 notes.
I think the Uniformization theorem is an example of blackbox theorem : any simply connected Riemann surface is conformally equivalent to either the open unit disk, the complex plane or the Riemann sphere.
Faltings' Theorem, to the effect that a curve of genus greater than 1 over the rationals has only finitely many rational points, is often invoked, I suspect often by people who haven't gone through a proof in detail.
It is used in harmonic analysis and number theory. It is not so difficult a result to state but a proof is not so commonly seen in books. The measure allows one to define an integral on the group and do analysis.
In the spectral sequences example, I feel like many people once learned the background, and then forgot it (perhaps could reconstruct if forced). But regardless, they still know how to apply the machines in the problems relevant to them.
This topology theorem states that a looped continuous path in the plane partitions the points of the plane, such that any continuous path going from a point in one partition to a point in the other intersects the loop.
There seem to be a lot of theorems in calculus of which I don't fully understand the proof, though some of this shows my ignorance of calculus. Jordan's theorem seem to be an extreme example though. Let me list some other examples.
By combining Nagata embedding with Hironaka's resolution of singularities (mentioned in another answer), you get "any smooth variety over a characteristic zero field admits an open immersion into a proper smooth variety", which is concise enough that people often use it without citing the authors' hard work.
Almost anyone working in algebraic number theory uses the main results of class field theory regularly. However, even if many people have sat through a course going through the proofs of the theorems, very few people remember the proofs, and even fewer use them.
While it is somewhat instructive to know what goes into the proofs of the main theorems (e.g., to see what obstacles prevent the proofs from being entirely constructive), it cannot be said that the grungy details of these proofs are particularly relevant to using the theory in practice. Thus, in the first half of the course we will emphasize an understanding of the statements of the main results (in their many different forms) and will not place much emphasis on how the main theorems are proven; precise references will be given for those who wish to read the details of the proofs of the main theorems. Once we have spent some time digesting what class field theory tells us, we will study some applications of the theory, such as in the context of imaginary quadratic fields and abelian coverings of algebraic curves.
The existence of Hilbert and Quot schemes. These are arguably the most important objects in moduli/deformation theory but the proof of their existence is almost never even presented in books on the topic, let alone needed or used. All the properties and applications follow formally so the existence is used as a black box.
Many texts on algebraic geometry take this as a black box, quoting standard sources of commutative algebra. The reason seems to be that you don't have to understand the methods of the proof (e.g. Koszul homology) in order to apply these results.
Faltings' almost purity theorem. The proof given, for the smooth case, in $p$-adic Hodge theory has some problems, and the proof of the general case in the Asterisque paper Almost tale Extensions is completely unreadable (at least to me) and also contains some mistakes. We now finally have a very good proof (by Peter Scholze), but the almost purity theorem has been used as a black box for years.
The well-definedness of the connected sum of two manifolds. After all, we choose two arbitrary balls for gluing; why should the result be independent? The proof depends on the nontrivial Disc theorem.
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