This presentation takes you on a functional programming journey, it starts from basic Scala programming language design concepts and leads to a concept of Monads, how some of them designed in Scala and what is the purpose of them
Function Programming in Scala.
A lot of my examples here comes from the book
Functional programming in Scala By Paul Chiusano and Rúnar Bjarnason, It is a good book, buy it.
Function Programming in Scala.
A lot of my examples here comes from the book
Functional programming in Scala By Paul Chiusano and Rúnar Bjarnason, It is a good book, buy it.
In this presentation I have presented about the iPython, how to install iPython, how to start with iPython. How to plot graph, how to animate/design it, the different type of graphs. What all functions you can take help of with iPython
Function Programming in Scala.
A lot of my examples here comes from the book
Functional programming in Scala By Paul Chiusano and Rúnar Bjarnason, It is a good book, buy it.
This presentation takes you on a functional programming journey, it starts from basic Scala programming language design concepts and leads to a concept of Monads, how some of them designed in Scala and what is the purpose of them
Function Programming in Scala.
A lot of my examples here comes from the book
Functional programming in Scala By Paul Chiusano and Rúnar Bjarnason, It is a good book, buy it.
Function Programming in Scala.
A lot of my examples here comes from the book
Functional programming in Scala By Paul Chiusano and Rúnar Bjarnason, It is a good book, buy it.
In this presentation I have presented about the iPython, how to install iPython, how to start with iPython. How to plot graph, how to animate/design it, the different type of graphs. What all functions you can take help of with iPython
Function Programming in Scala.
A lot of my examples here comes from the book
Functional programming in Scala By Paul Chiusano and Rúnar Bjarnason, It is a good book, buy it.
Quicksort - a whistle-stop tour of the algorithm in five languages and four p...Philip Schwarz
Quicksort - a whistle-stop tour of the algorithm in five languages and four paradigms.
Programming Paradigms: Functional, Logic, Imperative, Imperative Functional
Languages: Haskell, Scala, Java, Clojure, Prolog
download for better quality - Learn about the sequence and traverse functions through the work of Runar Bjarnason and Paul Chiusano, authors of Functional Programming in Scala https://www.manning.com/books/functional-programming-in-scala, and Sam Halliday, author of "Functional Programming for Mortals with Scalaz" https://leanpub.com/fpmortals
download for better quality - Learn about the sequence and traverse functions
through the work of Runar Bjarnason and Paul Chiusano, authors of Functional Programming in Scala https://www.manning.com/books/functional-programming-in-scala
Download for better quality.
Functor Composition - including (starting from) the definition in Bartosz Milewski's Category Theory book. https://github.com/hmemcpy/milewski-ctfp-pdf
Download for better quality.
Monads do not Compose. Not in a generic way - There is no general way of composing monads.
A comment from Rúnar Bjarnason, coauthor of FP in Scala: "They do compose in a different generic way. For any two monads F and G we can take the coproduct which is roughly Free of Either F or G (up to normalization)".
Another comment from Sergei Winitzki (which caused me to upload https://www.slideshare.net/pjschwarz/addendum-to-monads-do-not-compose): "It is a mistake to think that a traversable monad can be composed with another monad. It is true that, given `Traversable`, you can implement the monad's methods (pure and flatMap) for the composition with another monad (as in your slides 21 to 26), but this is a deceptive appearance. The laws of the `Traversable` typeclass are far insufficient to guarantee the laws of the resulting composed monad. The only traversable monads that work correctly are Option, Either, and Writer. It is true that you can implement the type signature of the `swap` function for any `Traversable` monad. However, the `swap` function for monads needs to satisfy very different and stronger laws than the `sequence` function from the `Traversable` type class. I'll have to look at the "Book of Monads"; but, if my memory serves, the FPiS book does not derive any of these laws." See https://www.linkedin.com/feed/update/urn:li:groupPost:41001-6523141414614814720?commentUrn=urn%3Ali%3Acomment%3A%28groupPost%3A41001-6523141414614814720%2C6532108273053761536%29
Quicksort - a whistle-stop tour of the algorithm in five languages and four p...Philip Schwarz
Quicksort - a whistle-stop tour of the algorithm in five languages and four paradigms.
Programming Paradigms: Functional, Logic, Imperative, Imperative Functional
Languages: Haskell, Scala, Java, Clojure, Prolog
download for better quality - Learn about the sequence and traverse functions through the work of Runar Bjarnason and Paul Chiusano, authors of Functional Programming in Scala https://www.manning.com/books/functional-programming-in-scala, and Sam Halliday, author of "Functional Programming for Mortals with Scalaz" https://leanpub.com/fpmortals
download for better quality - Learn about the sequence and traverse functions
through the work of Runar Bjarnason and Paul Chiusano, authors of Functional Programming in Scala https://www.manning.com/books/functional-programming-in-scala
Download for better quality.
Functor Composition - including (starting from) the definition in Bartosz Milewski's Category Theory book. https://github.com/hmemcpy/milewski-ctfp-pdf
Download for better quality.
Monads do not Compose. Not in a generic way - There is no general way of composing monads.
A comment from Rúnar Bjarnason, coauthor of FP in Scala: "They do compose in a different generic way. For any two monads F and G we can take the coproduct which is roughly Free of Either F or G (up to normalization)".
Another comment from Sergei Winitzki (which caused me to upload https://www.slideshare.net/pjschwarz/addendum-to-monads-do-not-compose): "It is a mistake to think that a traversable monad can be composed with another monad. It is true that, given `Traversable`, you can implement the monad's methods (pure and flatMap) for the composition with another monad (as in your slides 21 to 26), but this is a deceptive appearance. The laws of the `Traversable` typeclass are far insufficient to guarantee the laws of the resulting composed monad. The only traversable monads that work correctly are Option, Either, and Writer. It is true that you can implement the type signature of the `swap` function for any `Traversable` monad. However, the `swap` function for monads needs to satisfy very different and stronger laws than the `sequence` function from the `Traversable` type class. I'll have to look at the "Book of Monads"; but, if my memory serves, the FPiS book does not derive any of these laws." See https://www.linkedin.com/feed/update/urn:li:groupPost:41001-6523141414614814720?commentUrn=urn%3Ali%3Acomment%3A%28groupPost%3A41001-6523141414614814720%2C6532108273053761536%29
Another episode in series of Functional Thinking in Scala. This episode relates to Referential Transparency, Substitution model, context dependence and error handling in Scala.
Presentation on handling non-existence of data in Java et. al. (e.g. the problem with pesky nulls) and an introduction to the Option monad in Scala as a "solution" to this problem.
I presented this talk June, 28th 2013 at CPH Scala Group meeting, and a week later, July 3rd, at the "Scala User Group Århus" meetup.
In this short introduction, I try to frame the problem, i.e. the large amounts of error-prone null-checking code we usually have to write in Java, and Introduce the Option monad (Some/None) in Scala, as a solution. I explain the basics of what the Option class provides, and various ways of using it, ranging from basic level isEmtpy, over pattern-matching to more advanced fully functional "collection-style" (e.g. map, flatMap) operations and finally by using the for-comprehension.
Also includes links to relevant resources for further reading on the last slide.
The objectives of the seminar are to shed a light on the premises of FP and give you a basic understanding of the pillars of FP so that you would feel enlightened at the end of the session. When you walk away from the seminar you should feel an inner light about the new way of programming and an urge & motivation to code like you never before did!
Functional programming should not be confused with imperative (or procedural) programming. Neither it is like object oriented programming. It is something different. Not radically so, since the concepts that we will be exploring are familiar programming concepts, just expressed in a different way. The philosophy behind how these concepts are applied to solving problems are also a little different. We shall learn and talk about essentially the fundamental elements of Functional Programming.
AdRoll Tech Talk Presentation:
In this talk I present three approaches to understanding monads:
- How Monads Arise Naturally
- Monads as Implemented in Haskell
- Monads in Category Theory
I am Britney. I am a Differential Equations Assignment Solver at mathhomeworksolver.com. I hold a Master's in Mathematics, from London, UK. I have been helping students with their assignments for the past 10 years. I solved assignments related to Differential Equations Assignment.
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I am Steven M. I am a Maths Assignment Expert at mathsassignmenthelp.com. I hold a Master's in Mathematics from Ryerson University. I have been helping students with their assignments for the past 10 years. I solve assignments related to Maths.
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You can also call +1 678 648 4277 for any assistance with Maths Assignments.
Integral Calculus. - Differential Calculus - Integration as an Inverse Process of Differentiation - Methods of Integration - Integration using trigonometric identities - Integrals of Some Particular Functions - rational function - partial fraction - Integration by partial fractions - standard integrals - First and second fundamental theorem of integral calculus
It includes all the basics of calculus. It also includes all the formulas of derivatives and how to carry it out. It also includes function definition and different types of function along with relation.
About
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
Technical Specifications
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
Key Features
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface
• Compatible with MAFI CCR system
• Copatiable with IDM8000 CCR
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
Application
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
Welcome to WIPAC Monthly the magazine brought to you by the LinkedIn Group Water Industry Process Automation & Control.
In this month's edition, along with this month's industry news to celebrate the 13 years since the group was created we have articles including
A case study of the used of Advanced Process Control at the Wastewater Treatment works at Lleida in Spain
A look back on an article on smart wastewater networks in order to see how the industry has measured up in the interim around the adoption of Digital Transformation in the Water Industry.
Quality defects in TMT Bars, Possible causes and Potential Solutions.PrashantGoswami42
Maintaining high-quality standards in the production of TMT bars is crucial for ensuring structural integrity in construction. Addressing common defects through careful monitoring, standardized processes, and advanced technology can significantly improve the quality of TMT bars. Continuous training and adherence to quality control measures will also play a pivotal role in minimizing these defects.
Cosmetic shop management system project report.pdfKamal Acharya
Buying new cosmetic products is difficult. It can even be scary for those who have sensitive skin and are prone to skin trouble. The information needed to alleviate this problem is on the back of each product, but it's thought to interpret those ingredient lists unless you have a background in chemistry.
Instead of buying and hoping for the best, we can use data science to help us predict which products may be good fits for us. It includes various function programs to do the above mentioned tasks.
Data file handling has been effectively used in the program.
The automated cosmetic shop management system should deal with the automation of general workflow and administration process of the shop. The main processes of the system focus on customer's request where the system is able to search the most appropriate products and deliver it to the customers. It should help the employees to quickly identify the list of cosmetic product that have reached the minimum quantity and also keep a track of expired date for each cosmetic product. It should help the employees to find the rack number in which the product is placed.It is also Faster and more efficient way.
CFD Simulation of By-pass Flow in a HRSG module by R&R Consult.pptxR&R Consult
CFD analysis is incredibly effective at solving mysteries and improving the performance of complex systems!
Here's a great example: At a large natural gas-fired power plant, where they use waste heat to generate steam and energy, they were puzzled that their boiler wasn't producing as much steam as expected.
R&R and Tetra Engineering Group Inc. were asked to solve the issue with reduced steam production.
An inspection had shown that a significant amount of hot flue gas was bypassing the boiler tubes, where the heat was supposed to be transferred.
R&R Consult conducted a CFD analysis, which revealed that 6.3% of the flue gas was bypassing the boiler tubes without transferring heat. The analysis also showed that the flue gas was instead being directed along the sides of the boiler and between the modules that were supposed to capture the heat. This was the cause of the reduced performance.
Based on our results, Tetra Engineering installed covering plates to reduce the bypass flow. This improved the boiler's performance and increased electricity production.
It is always satisfying when we can help solve complex challenges like this. Do your systems also need a check-up or optimization? Give us a call!
Work done in cooperation with James Malloy and David Moelling from Tetra Engineering.
More examples of our work https://www.r-r-consult.dk/en/cases-en/
Democratizing Fuzzing at Scale by Abhishek Aryaabh.arya
Presented at NUS: Fuzzing and Software Security Summer School 2024
This keynote talks about the democratization of fuzzing at scale, highlighting the collaboration between open source communities, academia, and industry to advance the field of fuzzing. It delves into the history of fuzzing, the development of scalable fuzzing platforms, and the empowerment of community-driven research. The talk will further discuss recent advancements leveraging AI/ML and offer insights into the future evolution of the fuzzing landscape.
Overview of the fundamental roles in Hydropower generation and the components involved in wider Electrical Engineering.
This paper presents the design and construction of hydroelectric dams from the hydrologist’s survey of the valley before construction, all aspects and involved disciplines, fluid dynamics, structural engineering, generation and mains frequency regulation to the very transmission of power through the network in the United Kingdom.
Author: Robbie Edward Sayers
Collaborators and co editors: Charlie Sims and Connor Healey.
(C) 2024 Robbie E. Sayers
Forklift Classes Overview by Intella PartsIntella Parts
Discover the different forklift classes and their specific applications. Learn how to choose the right forklift for your needs to ensure safety, efficiency, and compliance in your operations.
For more technical information, visit our website https://intellaparts.com
Water scarcity is the lack of fresh water resources to meet the standard water demand. There are two type of water scarcity. One is physical. The other is economic water scarcity.
Final project report on grocery store management system..pdfKamal Acharya
In today’s fast-changing business environment, it’s extremely important to be able to respond to client needs in the most effective and timely manner. If your customers wish to see your business online and have instant access to your products or services.
Online Grocery Store is an e-commerce website, which retails various grocery products. This project allows viewing various products available enables registered users to purchase desired products instantly using Paytm, UPI payment processor (Instant Pay) and also can place order by using Cash on Delivery (Pay Later) option. This project provides an easy access to Administrators and Managers to view orders placed using Pay Later and Instant Pay options.
In order to develop an e-commerce website, a number of Technologies must be studied and understood. These include multi-tiered architecture, server and client-side scripting techniques, implementation technologies, programming language (such as PHP, HTML, CSS, JavaScript) and MySQL relational databases. This is a project with the objective to develop a basic website where a consumer is provided with a shopping cart website and also to know about the technologies used to develop such a website.
This document will discuss each of the underlying technologies to create and implement an e- commerce website.
2. Format of Talk
1. Introduce definition from Category Theory
2. Use something from Scala as an example
3. Show it satisfies the definition.
4. Do ^^ until Monad defined
5. Prove that definition given in FP is equivalent to
definition given in Category Theory
Plus random points about application and practicalities
along the way
3. Note about foundations
● Category Theory is itself a foundation of mathematics,
and strictly speaking you don’t need Set Theory to do
Category Theory
● Nevertheless a lot of examples and language used to
explain Category Theory is actually borrowed from Set
Theory
● I will do the same as it makes things much easier
(strictly speaking I’m using the von Neumann–Bernays–Gödel (NBG) set theory Axiomatization, which
is a conservative extension of ZFC that allows us to talk about Proper Classes (e.g. Class of all Sets)
4. Definition - Category
1. a class ob(C) of objects
2. a class hom(C) of morphisms, or arrows, or maps, between the objects. Each morphism f has a unique
source object a and target object b where a and b are in ob(C). We write f: a → b, and we say "f is a morphism
from a to b".
3. for every three objects a, b and c, a binary operation hom(a, b) × hom(b, c) → hom(a, c) called composition
of morphisms; the composition of f : a → b and g : b → c is written as g ∘ f or gf. (Some authors use
"diagrammatic order", writing f;g or fg.)
such that the following axioms hold:
a. (associativity) if f : a → b, g : b → c and h : c → d then h ∘ (g ∘ f) = (h ∘ g) ∘ f, and
b. (identity) for every object x, there exists a morphism 1x
: x → x (some authors write idx
) called the identity morphism for x, such
that for every morphism f : a → b, we have 1b
∘ f = f = f ∘ 1a
.
5. Example - Scala S
Let the set of Types in Scala be Ob(C)
Let the set of 1 param Functions in Scala be hom(C)
NOTATION: Methods of a Type A, that return a type B that take no params can
be equivalently considered as 1 param functions f: A -> B. Therefore I will
interchange method invocation and function application henceforth.
Composition o is defined as simply normal function composition, now
For any f, g, h (types obv) we have
(h o (g o f))(x) = (g o f)(h(x)) = f(g(h(x))) = f((h o g)(x)) = ((h o g) o f)(x) -
associativity
For any T, id_T : T -> T is defined by for any x is a T, id_T(x) = x, clearly this is
an identity
7. Example - Parameterized Types
Many parameterized types in Scala can be viewed as Functors with their map operation;
Let S be the Scala Category, and F: S -> S
associate any T in Ob(S) to List[T] in Ob(S)
associate any f: A -> B (for any A, B in Ob(S)) to map(f): List[A] -> List[B]. Now for any T in Ob(S)
F(id_T)(someList) = someList.map(x => x) = (x => x)(someList) = id_List[T] = id_F[T]
- so satisfies identity preservation
And it’s obvious that someList.map(f).map(g) = someList.map(g o f), so satisfies composition
preservation
Practical Point
When you write a parameterized type in an API in Scala with a map function, you are telling the API
user that map(f).map(g) is the same as map(f o g). So in Scalding, it’s often convenient to chain map
operations together for readability, rather than compose the functions - but Scalding is clever, it will
compose the functions for you so that your still O(N) not O(2N), O(3N) etc.
8. Definition - Natural Transformation
.If F and G are functors between the categories C and D, then a natural transformation η from F to G associates to every object X in C a
morphism ηX
: F(X) → G(X) between objects of D, called the component of η at X, such that for every morphism f : X → Y in C we have:
9. Example - Flatten
Let F: S -> S and G: S -> S be the Option[Option[ _ ]] Functor and Option[ _ ] Functor respectively.
NOTATION: will be sloppy henceforth
Let f: X -> Y in Hom(S)
So F(f): Option[Option[ X ]] -> Option[Option[ Y ] is .map(_.map(f))
G(f): Option[X] -> Option[Y] is .map(f)
10. Example - Flatten - Continued
Let N_x be .flatten[x], then flatten is a Natural Transformation:
N_Y = flatten[Y]: Option[Option[Y]] -> Option[Y]
N_X = flatten[X]: Option[Option[X]] -> Option[X]
So N_Y o F(f) = .map(_.map(f)).flatten
and G(f) o N_X = .flatten.map(f). Now
Some(Some(x)).map(_.map(f)).flatten = Some(Some(x).map(f)).flatten = Some(Some(f(x)).flatten
= Some(f(x)) = Some(x).map(f) = Some(Some(x)).flatten.map(f)
Note there are many more natural transformations, like if we defined toList on Option.
Practical Point
Knowing an operation is a natural transformation makes refactoring easier.
12. Example - Option Monad
Let F be the Option Functor, then combined with the flatten natural transformation M we have a
monad: For any X in Ob(S)
F(M_X) = map(_.flatten) : Option[Option[Option[X]]] -> Option[Option[X]]
M_F(X) = M_Option[X] = flatten[Option[X]]: Option[Option[Option[X]]] -> Option[Option[X]]
so
M_X o F(M_X) = .map(_.flatten).flatten : Option[Option[Option[X]]] -> Option[X]
M_X o M_F(X) = .flatten.flatten : Option[Option[Option[X]]] -> Option[X]
Let’s check these are equal
Some(Some(Some(x))).map(_.flatten).flatten = Some(Some(Some(x)).flatten).flatten
= Some(Some(x)).flatten = Some(x) = Some(Some(x)).flatten =
Some(Some(Some(x))).flatten.flatten
Therefore we have the first coherence condition ...
13. Example - Option Monad continued
Now our Identity natural transformation will be the Some function, i.e.
N_X = Some: X -> Option[X] (which is the same as Id(X) -> Option[X])
so
F(N_X) = .map(Some), so
M_X o F(N_X) = .map(Some).flatten, which is clearly the identity Functor (other way round - exercise)
14. Definition - Monad in FP
In functional programming a monadic Type M is simply defined in terms of
flatMap, where:
For any f: X -> M[Y], g: Y -> M[Z], and any x: M[X]
x.flatMap(f).flatMap(g) = x.flatMap(f(_).flatMap(g))
and there exists a neutral element N: X -> M[X], where
x.flatMap(N) = x
15. Theorem - Equivalence
The two previous definitions are equivalent when we make the following substitution
.map(f).flatten for flatMap(f) - (*)
Proof:
.flatten.flatten = .map(_.flatten).flatten - Monad Category Theory
=> .map(f(_).map(g)).flatten.flatten = .map(f(_).map(g)).map(_.flatten).flatten
- by substituting in .map(f(_).map(g))
Now RHS = .map(f(_).map(g).flatten).flatten - by Functor Composition Preservation
= .flatMap(f(_).map(g).flatten) - by (*)
= .flatMap(f(_).flatMap(g)) - by (*)
...
16. Proof continued
Now LHS = x.map(f(_)).map(_.map(g)).flatten.flatten - by Functor Composition Preservation
= x.map(f).flatten.map(g).flatten - since flatten is a natural transformation (recall earlier slide)
= x.flatMap(f).flatMap(g) - by (*) twice.
Therefore
.flatMap(f(_).flatMap(g)) = .flatMap(f).flatMap(g)
It remains to show the identity conditions (exercise)
17. Further Reading
Monoids - Used in Reduce operations in Map Reduce to parallelize operations
that cumulate a single value. E.g. + is a monoid.
Covariance and Contravariance - Used in Typing rules for type inference
18. Summary of Applications
1. Using Category Theoretic notions in code is a little like a formalization of
design patterns
2. When a reader sees a particular notion, they need to use less cognitive
resources to comprehend the code by familiarity
3. It’s easier to refactor code due to known equivalences, some of these
equivalences are even used by Intellij (and ReSharper for LINQ) for the auto-
refactor shortcuts
4. Sometimes APIs allow the user to write readable code, but the resulting
compiled code will be in it’s most computationally efficient representation.
5. Compilers use concepts in Category Theory
6. State hiding FP design