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/// Original C++ implementation found at http://www.wilmott.com/messageview.cfm?catid=10&threadid=38771
/// C# implementation found at http://weblogs.asp.net/esanchez/archive/2010/07/29/a-quick-and-dirty-implementation-of-excel-norminv-function-in-c.aspx
/*
 *     Compute the quantile function for the normal distribution.
 *
 *     For small to moderate probabilities, algorithm referenced
 *     below is used to obtain an initial approximation which is
 *     polished with a final Newton step.
 *
 *     For very large arguments, an algorithm of Wichura is used.

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Generalized Algebraic Data Types in Scala

Basic GADTs

Here's an ADT which is not a GADT, in Haskell:

data Expr = IntExpr Int | BoolExpr Bool

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Monocle, like many other Scala FP libraries, was inspired by Haskell. In our case, it is the Lens library by Edward Kmett and al.

In Monocle, we experimented with various optics encoding: pair of functions, Van Laarhoven, profunctor (see LensImpl). The JVM and Haskell runtime are hugely different, and an encoding that works well in Haskell can be inefficient in Scala. For example, Haskell relies on zero cost wrapper (newtype) to effectively select typeclass instances, but we don't have an equivalent in Scala/JVM yet (opaque types may help). You can find some of the benchmarks we made for Lenses in 2015 here.

However, something we didn't do very well was to adapt the API to the specificity of Scala. If you look at Monocle 1.x or 2.x, it has the same interface as Haskell's Lens but in much more clunky way. The example

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-----BEGIN PRIVATE KEY-----
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