Advanced Functional Programming in Scala

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Advanced Functional
Programming in Scala
Patrick Nicolas
Oct 2013
Rev. July 2015
patricknicolas.blogspot.com
www.slideshar...

This is an overview of some interesting advanced
features of Scala. It is not meant to be a tutorial and
assume that you a...

Scala has a lot of features …..
Actors
Composed futures
F-bound
Reactive
Advanced functional programming?
... among them

Higher kind projection
Contravariant functors
Monadic composition
Streams
Views
Type classes
Stacked mixins models
Cake pa...

Functors and monads are defined as single type higher kinds:
M[_]. The problem is to define monadic composition for
object...

Higher kind projection
Let us consider a covariant functor F that applies a morphism f
within a category C defined as
∀𝑎, ...

Higher kind projection
How can we define a functor for classes that have multiple
parameterized type?
Let’s consider the d...

Higher kind projection
The implementation of the functor for the Vector type uses the
projection of the higher kind Functi...

Higher kind projection
Contravariant functors
Monadic composition
Streams
Views
Type classes
Stacked mixins models
Cake pa...

Contravariant functors
Some categories of objects such as covariant tensors or
function parameterized on the input or cont...

Contravariant functors
Let us consider a contravariant functor F that applies a
morphism f within a category C defined as
...

Contravariant functors
The implementation of the contravariant functor for the CoVector
type uses the projection of the hi...

Higher kind projection
Contravariant functors
Monadic composition
Streams
Views
Type classes
Stacked mixins models
Cake pa...

It is quite common to compose, iteratively or recursively
functions, methods or data transformations.
Monadic composition
...

Monads are abstract structures in algebraic topology related to
the category theory.
A category C is a structure which has...

Let’s consider the definition of a kernel function Kf as the composition
of 2 functions g o h.
𝒦𝑓 𝐱, 𝐲 = 𝑔(
𝑖
ℎ(𝑥𝑖, 𝑦𝑖))
M...

A monad extends a functor with binding method (flatMap)
The monadic definition of the kernel function component h
Monadic ...

Example of Kernel functions
𝒦 𝐱, 𝐲 = 𝑒
−
1
2
𝐱−𝐲
𝜎
2
h: 𝑥, 𝑦 → 𝑥 − 𝑦 g: 𝑥 → 𝑒
−
1
2𝜎2( 𝑥)2
Polynomial kernel
𝒦 𝐱, 𝐲 = (1 +...

The monadic composition consists of chaining the flatMap invocation
on the functor, map, that preserves morphisms on kerne...

Higher kind projection
Contravariant functors
Monadic composition
Streams
Views
Type classes
Stacked mixins models
Cake pa...

Streams
Streams reduce memory consumption by allocating and
releasing chunk of data (or slice or time series) while allowi...

The large data set is converted into a stream then broken
down into manageable slices. The slices are instantiated,
proces...

Slices of NOBS observations are allocated one at the time, (take)
processed, then released (drop) at the time.
Views and s...

The reference streamRef has to be weak, in order to have the slices
garbage collected. Otherwise the memory consumption in...

Comparing list, stream and stream with weak references.
Views and streams
Operating zone

Higher kind projection
Contravariant functors
Monadic composition
Streams
Views
Type classes
Stacked mixins models
Cake pa...

Views
Scientific computations require chaining complex data
transformations on large data set. There is not always a
need ...

Views
Accessing an element of the list requires allocating
the entire list in memory.
Accessing an element of the view req...

Higher kind projection
Contravariant functors
Monadic composition
Streams
Views
Type classes
Stacked mixins models
Cake pa...

Type classes
Scala libraries classes cannot always be sub-classed.
Wrapping library component in a helper class clutters t...

Let’s consider the definition of a tensor as being either a vector
or a covector.
Type classes
Let’s extend the concept of...

Type classes
The inner object Metric define the implicit conversion

Higher kind projection
Contravariant functors
Monadic composition
Streams
Views
Type classes
Stacked mixins models
Cake pa...

Stacked mixins models
Scala stacked traits and abstract values preserve the core
formalism of mathematical expressions.
Tr...

𝑓 ∈ ℝ 𝑛
→ ℝ 𝑛
𝑓 𝑥 = 𝑒 𝑥
𝑔 ∈ ℝ 𝑛 → ℝ
ℎ = 𝑔𝑜𝑓
g 𝒙 = 𝑖 𝑥𝑖
Declaration
Model
Instantiation
Stacked mixins models

Higher kind projection
Contravariant functors
Monadic composition
Streams
Views
Type classes
Stacked mixins models
Cake pa...

Stacked mixins models
Building machine learning apps requires configurable,
dynamic workflows
Leverage mixins, inheritance...

Stacked mixins models
Multiple models and algorithms are typically evaluated by
weaving computation tasks.
A learning plat...

Even the simplest workflow, defined as a pipeline of data transformations
requires a flexible design …
Stacked mixins mode...

Stacked mixins models
Summary of the 3 configurability layers of Cake pattern
1. Given the objective of the computation, s...

Implementation of Preprocessing module
Stacked mixins models

Implementation of Preprocessing module using discrete Fourier
… and discrete Kalman filter
Stacked mixins models

d
d
Preprocessing
Loading
Reducing Training
Validating
Preprocessor
DFTFilter
Kalman
EM
PCA SVM
MLP
Reducer Supervisor
Clu...

A simple clustering workflow requires a preprocessor &
reducer. The computation sequence exec transform a time
series of e...

A model is created by processing the original time series of type TS[T]
through a preprocessor, a training supervisor and ...

Putting all together for a conditional path execution …
Stacked mixins models

Higher kind projection
Contravariant functors
Monadic composition
Streams
Views
Type classes
Stacked mixins models
Cake pa...

Magnet pattern
Method overloading in Scala has limitations:
• Type erasure in the JVM causes collision of type of
argument...

Magnet pattern
Let’s consider the following three incarnations of the method test
These methods have different return type...

Magnet pattern
Step 1: Define generic return type and constructor
Step 2: Implement the test methods as implicits

Magnet pattern
Step 3: Implement the lifted function test as follows
The first call invokes the implicit fromTN and the se...

Higher kind projection
Contravariant functors
Monadic composition
Streams
Views
Type classes
Stacked mixins models
Cake pa...

View bound
Context bound cannot be used to bind the parameterized
type of a generic class to a primitive type.
Scala view ...

View bound
Let’s consider a class which parameterized type can be
manipulate as a Float.
Context bound is not permissible
...

View bound
The solution is to bind the class type to a Float using an
implicit conversion (or view)
The <% directive is th...

Higher kind projection
Contravariant functors
Monadic composition
Streams
Views
Type classes
Stacked mixins models
Cake pa...

F-Bound polymorphism is a parametric type polymorphism
that constrains the subtypes to themselves using bounds.
It is impo...

F-Bound polymorphism
Let’s create a trait that define a discriminative learning model
with method to manipulate data.
The ...

F-Bound polymorphism
One solution is to restrict (or bound) the type to a Discriminative
class
It prevents a new class to ...

F-Bound polymorphism
The self reference guarantee the integrity of each existing
and new subclass. F-Bound polymorphism is...

Higher kind projection
Contravariant functors
Monadic composition
Streams
Views
Type classes
Stacked mixins models
Cake pa...

Data flow back pressure
A data flow control mechanism handling back pressure
on bounded mail boxes of upstream actors.
Sca...

Data flow back pressure
Actor-based workflow has to consider
- Cascading failures => supervision strategy
- Cascading bott...

Messages passing scheme to process various data streams
with transformations.
Dataset
Workers
Controller
Watcher
Load->
Co...

Worker actors processes data chunk msg.xt sent by the
controller with the transformation msg.fct
Message sent by collector...

Watcher actor monitors messages queues report to collector with
Status message.
GetStatus message sent by the collector ha...

Controller creates the workers, bounded mailbox for each worker
actor (msgQueues) and the watcher actor.
Data flow back pr...

The Controller loads the data sets per chunk upon receiving the
message Load from the main program. It processes the resul...

The Load message is implemented as a loop that create data chunk
which size is adjusted according to the load computed by ...

Simple throttle increases/decreases size of the batch of
observations given the current load and specified watermark.
Data...

Feedback control loop adjusts the size of the batches given the
load in mail boxes and complexity of the computation
Data ...

• Feedback control loop should be smoothed (moving
average, Kalman…)
• A larger variety of data flow control actions such ...

Higher kind projection
Contravariant functors
Monadic composition
Streams
Views
Type classes
Stacked mixins models
Cake pa...

Delimited continuation
Continuation Passing Style (CPS) is a technique that
abstracts computation unit as a data structure...

Delimited continuation
A data transformation (or computation unit) can be
extended (continued) with another transformation...

Delimited continuation
A delimited continuation is a section of the workflow that
is reified into a function returning a v...

More Scala nuggets…
• Domain specific language
• Reactive streams
• Back-pressure strategy using connection state
Wait a m...

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