(download for better quality)
Introducing Assignment invalidates the Substitution Model of Evaluation and violates Referential Transparency
- as explained in SICP (the Wizard Book)
The Functional Programming Triad of fold, scan and iteratePhilip Schwarz
In the functional programming paradigm, the programmer does not need to write any loops or use array indices. Instead, functional programers deal with iterative calculations by translating mathematical induction directly into code, so that they can reason about sequences as mathematical values. The implement mathematical induction by folding, scanning and iterating.
Ouch - a couple of occurrences of 'mathematical' are misspelled (missing h) :-(
Folding Unfolded - Polyglot FP for Fun and Profit - Haskell and Scala - Part 2Philip Schwarz
(download for perfect quality) See aggregation functions defined inductively and implemented using recursion.
Learn how in many cases, tail-recursion and the accumulator trick can be used to avoid stack-overflow errors.
Watch as general aggregation is implemented and see duality theorems capturing the relationship between left folds and right folds.
Through the work of Sergei Winitzki and Richard Bird.
The Functional Programming Triad of Folding, Scanning and Iteration - a first...Philip Schwarz
This slide deck can work both as an aide mémoire (memory jogger), or as a first (not completely trivial) example of using left folds, left scans and iteration, to implement mathematical induction.
Errata: on almost half of the slides there is some minor typo or imperfection or in some cases a minor error and in one case, an omission. See a later version for corrections and some improvements.
(for best quality images, either download or view here: https://philipschwarz.dev/fpilluminated/?page_id=455)
Scala code for latest version: https://github.com/philipschwarz/fp-fold-scan-iterate-triad-a-first-example-scala
Folding Unfolded - Polyglot FP for Fun and Profit - Haskell and Scala Part 2 ...Philip Schwarz
(download for perfect quality) See aggregation functions defined inductively and implemented using recursion.
Learn how in many cases, tail-recursion and the accumulator trick can be used to avoid stack-overflow errors.
Watch as general aggregation is implemented and see duality theorems capturing the relationship between left folds and right folds.
Through the work of Sergei Winitzki and Richard Bird.
This version corrects the following issues:
slide 32: = reverse --> reverse =
Slide 33: 100_000 -> 1_000_000
It also adds slides 36, 37 and 38
The Functional Programming Triad of Folding, Scanning and Iteration - a first...Philip Schwarz
This slide deck can work both as an aide mémoire (memory jogger), or as a first (not completely trivial) example of using left folds, left scans and iteration, to implement mathematical induction.
This is just an updated version of the original slide deck which makes minor improvements and minor corrections in almost half of the slides.
(for best quality images, either download or view here: https://philipschwarz.dev/fpilluminated/?page_id=455)
You can see the Scala code here: https://github.com/philipschwarz/fp-fold-scan-iterate-triad-a-first-example-scala
Download for flawless quality (slides viewed online look a bit grainy and out of focus). A monad is an implementation of one of the minimal sets of monadic combinators, satisfying the laws of associativity and identity - see how compositional responsibilities are distributed in each combinator set
Game of Life - Polyglot FP - Haskell - Scala - Unison - Part 3Philip Schwarz
(download for picture-perfect quality) Follow along as Trampolining is used to overcome Stack Overflow issues with the simple IO monad, deepening you understanding of the IO monad in the process. See Game of Life IO actions migrated to the Cats Effect IO monad, which is trampolined in its flatMap evaluation.
Errata:
slide 33: "impure factorial function" should be "initial factorial function"
slide 34: there is a pointless short vertical bar inside a speech bubble
slide 39: "it is till annoying" should be "it is still annoying"
slide 44: "values that we are interested" should be "values that we are interested in"
The Functional Programming Triad of fold, scan and iteratePhilip Schwarz
In the functional programming paradigm, the programmer does not need to write any loops or use array indices. Instead, functional programers deal with iterative calculations by translating mathematical induction directly into code, so that they can reason about sequences as mathematical values. The implement mathematical induction by folding, scanning and iterating.
Ouch - a couple of occurrences of 'mathematical' are misspelled (missing h) :-(
Folding Unfolded - Polyglot FP for Fun and Profit - Haskell and Scala - Part 2Philip Schwarz
(download for perfect quality) See aggregation functions defined inductively and implemented using recursion.
Learn how in many cases, tail-recursion and the accumulator trick can be used to avoid stack-overflow errors.
Watch as general aggregation is implemented and see duality theorems capturing the relationship between left folds and right folds.
Through the work of Sergei Winitzki and Richard Bird.
The Functional Programming Triad of Folding, Scanning and Iteration - a first...Philip Schwarz
This slide deck can work both as an aide mémoire (memory jogger), or as a first (not completely trivial) example of using left folds, left scans and iteration, to implement mathematical induction.
Errata: on almost half of the slides there is some minor typo or imperfection or in some cases a minor error and in one case, an omission. See a later version for corrections and some improvements.
(for best quality images, either download or view here: https://philipschwarz.dev/fpilluminated/?page_id=455)
Scala code for latest version: https://github.com/philipschwarz/fp-fold-scan-iterate-triad-a-first-example-scala
Folding Unfolded - Polyglot FP for Fun and Profit - Haskell and Scala Part 2 ...Philip Schwarz
(download for perfect quality) See aggregation functions defined inductively and implemented using recursion.
Learn how in many cases, tail-recursion and the accumulator trick can be used to avoid stack-overflow errors.
Watch as general aggregation is implemented and see duality theorems capturing the relationship between left folds and right folds.
Through the work of Sergei Winitzki and Richard Bird.
This version corrects the following issues:
slide 32: = reverse --> reverse =
Slide 33: 100_000 -> 1_000_000
It also adds slides 36, 37 and 38
The Functional Programming Triad of Folding, Scanning and Iteration - a first...Philip Schwarz
This slide deck can work both as an aide mémoire (memory jogger), or as a first (not completely trivial) example of using left folds, left scans and iteration, to implement mathematical induction.
This is just an updated version of the original slide deck which makes minor improvements and minor corrections in almost half of the slides.
(for best quality images, either download or view here: https://philipschwarz.dev/fpilluminated/?page_id=455)
You can see the Scala code here: https://github.com/philipschwarz/fp-fold-scan-iterate-triad-a-first-example-scala
Download for flawless quality (slides viewed online look a bit grainy and out of focus). A monad is an implementation of one of the minimal sets of monadic combinators, satisfying the laws of associativity and identity - see how compositional responsibilities are distributed in each combinator set
Game of Life - Polyglot FP - Haskell - Scala - Unison - Part 3Philip Schwarz
(download for picture-perfect quality) Follow along as Trampolining is used to overcome Stack Overflow issues with the simple IO monad, deepening you understanding of the IO monad in the process. See Game of Life IO actions migrated to the Cats Effect IO monad, which is trampolined in its flatMap evaluation.
Errata:
slide 33: "impure factorial function" should be "initial factorial function"
slide 34: there is a pointless short vertical bar inside a speech bubble
slide 39: "it is till annoying" should be "it is still annoying"
slide 44: "values that we are interested" should be "values that we are interested in"
Folding Unfolded - Polyglot FP for Fun and Profit - Haskell and ScalaPhilip Schwarz
(download for perfect quality) - See how recursive functions and structural induction relate to recursive datatypes.
Follow along as the fold abstraction is introduced and explained.
Watch as folding is used to simplify the definition of recursive functions over recursive datatypes
Part 1 - through the work of Richard Bird and Graham Hutton.
Errata:
slide 7, 11 fib(0) is 0,rather than 1
slide 23: was supposed to be followed by 2-3 slides recapitulating definitions of factorial and fibonacci with and without foldr, plus translation to scala
slide 36: concat not invoked in concat example
slides 48 and 49: unwanted 'm' in definition of sum
throughout: a couple of typographical errors
throughout: several aesthetic imperfections (wrong font, wrong font colour)
Sierpinski Triangle - Polyglot FP for Fun and Profit - Haskell and ScalaPhilip Schwarz
Take the very first baby steps on the path to doing graphics in Haskell and Scala.
Learn about a simple yet educational recursive algorithm producing images that are pleasing to the eye.
Learn how functional programs deal with the side effects required to draw images.
See how libraries like Gloss and Doodle make drawing Sierpinski’s triangle a doddle.
Code for this slide deck:
https://github.com/philipschwarz/sierpinski-triangle-haskell-gloss
https://github.com/philipschwarz/sierpinski-triangle-scala-cats-io
https://github.com/philipschwarz/sierpinski-triangle-scala-awt-and-doodle
Errata:
1. the title 'Sierpinski Triangle' on the front slide could be improved by replacing it with 'Sierpinski's Triangle'.
2. a couple of typos on two slides
3. the triangles drawn using Doodle are not equilateral, as intended but isosceles.
(UPDATE 2021-06-15 I opened PR https://github.com/creativescala/doodle/pull/99 and as a result, an equilateral triangle has now been added to Doodle: https://github.com/creativescala/doodle/commit/30d20efebcc2016942e9cdbae85fefca5b95fa3c).
Here is a corrected version of the deck: https://www.slideshare.net/pjschwarz/sierpinski-triangle-polyglot-fp-for-fun-and-profit-haskell-and-scala-with-minor-corrections
N-Queens Combinatorial Problem - Polyglot FP for Fun and Profit – Haskell and...Philip Schwarz
See how the guard function has migrated from MonadPlus to Alternative and learn something about the latter.
Learn how to write a Scala program that draws an N-Queens solution board using the Doodle graphics library.
See how to write the equivalent Haskell program using the Gloss graphics library.
Learn how to use Monoid and Foldable to compose images both in Haskell and in Scala.
Link to part 1: https://www.slideshare.net/pjschwarz/nqueens-combinatorial-problem-polyglot-fp-for-fun-and-profit-haskell-and-scala-part-1
Errata:
On slide 22, the last line of the showQueens function should of course be show(solution).draw(frame) rather than show(solution).draw
On slide 43, it would be better if the definitions of the beside, above and on Monoids were also shown.
Function Applicative for Great Good of Palindrome Checker Function - Polyglot...Philip Schwarz
Embark on an informative and fun journey through everything you need to know to understand how the Applicative instance for functions makes for a terse palindrome checker function definition in point-free style.
(download for flawless quality) State Monad - Learn how it works - Follow Alvin Alexander’s example-driven build up to the State Monad and then branch off into a detailed look at its inner workings.
Functional Core and Imperative Shell - Game of Life Example - Haskell and ScalaPhilip Schwarz
See a program structure flowchart used to highlight how an FP program breaks down into a functional core and imperative shell
View a program structure flowchart for the Game of Life
See the code for Game of Life’s functional core and imperative shell, both in Haskell and in Scala.
Code:
https://github.com/philipschwarz/functional-core-imperative-shell-scala
https://github.com/philipschwarz/functional-core-imperative-shell-haskell
Folding Unfolded - Polyglot FP for Fun and Profit - Haskell and Scala - with ...Philip Schwarz
(download for perfect quality) - See how recursive functions and structural induction relate to recursive datatypes.
Follow along as the fold abstraction is introduced and explained.
Watch as folding is used to simplify the definition of recursive functions over recursive datatypes
Part 1 - through the work of Richard Bird and Graham Hutton.
This version corrects the following issues:
slide 7, 11 fib(0) is 0,rather than 1
slide 23: was supposed to be followed by 2-3 slides recapitulating definitions of factorial and fibonacci with and without foldr, plus translation to scala
slide 36: concat not invoked in concat example
slides 48 and 49: unwanted 'm' in definition of sum
throughout: a couple of typographical errors
throughout: several aesthetic imperfections (wrong font, wrong font colour)
Game of Life - Polyglot FP - Haskell, Scala, Unison - Part 2 - with minor cor...Philip Schwarz
(download for picture-perfect quality) Follow along as the impure functions in the Game of Life are translated from Haskell into Scala, deepening you understanding of the IO monad in the process.
This is simply a copy of the original with an error corrected on slides 3 and 52, which were supposed to show Scala code and instead showed the Haskell equivalent! Plus removal of a few minor aesthetic imperfections.
Original: https://www.slideshare.net/pjschwarz/game-of-life-polyglot-fp-haskell-scala-unison-part-2
Folding Unfolded - Polyglot FP for Fun and Profit - Haskell and Scala - Part 4Philip Schwarz
(download for flawless image quality) Can a left fold ever work over an infinite list? What about a right fold? Find out.
Learn about the other two functions used by functional programmers to implement mathematical induction: iterating and scanning.
Learn about the limitations of the accumulator technique and about tupling, a technique that is the dual of the accumulator trick.
Download for flawless quality (slides viewed online look a bit grainy and out of focus).
Equivalence of nested flatMaps and chained flatMaps for Kleisli arrow composition.
Introduction to Functional Programming in JavaScripttmont
A presentation I did for work on functional programming. It's meant as an introduction to functional programming, and I implemented the fundamentals of functional programming (Church Numerals, Y-Combinator, etc.) in JavaScript.
Folding Unfolded - Polyglot FP for Fun and Profit - Haskell and Scala - Part 5Philip Schwarz
(download for best quality slides) Gain a deeper understanding of why right folds over very large and infinite lists are sometimes possible in Haskell.
See how lazy evaluation and function strictness affect left and right folds in Haskell.
Learn when an ordinary left fold results in a space leak and how to avoid it using a strict left fold.
Errata:
slide 15: "as sharing is required" should be "as sharing is not required"
slide 43: 𝑠𝑓𝑜𝑙𝑑𝑙 (⊕) 𝑎 should be 𝑠𝑓𝑜𝑙𝑑𝑙 (⊕) 𝑒
I am Samuel H. I am a Mechanical Engineering Assignment Expert at matlabassignmentexperts.com. I hold a Ph.D. Matlab, University of Alberta, Canada. I have been helping students with their homework for the past 12 years. I solve assignments related to Mechanical Engineering.
Visit matlabassignmentexperts.com or email info@matlabassignmentexperts.com.
You can also call on +1 678 648 4277 for any assistance with Mechanical Engineering Assignments.
Folding Unfolded - Polyglot FP for Fun and Profit - Haskell and ScalaPhilip Schwarz
(download for perfect quality) - See how recursive functions and structural induction relate to recursive datatypes.
Follow along as the fold abstraction is introduced and explained.
Watch as folding is used to simplify the definition of recursive functions over recursive datatypes
Part 1 - through the work of Richard Bird and Graham Hutton.
Errata:
slide 7, 11 fib(0) is 0,rather than 1
slide 23: was supposed to be followed by 2-3 slides recapitulating definitions of factorial and fibonacci with and without foldr, plus translation to scala
slide 36: concat not invoked in concat example
slides 48 and 49: unwanted 'm' in definition of sum
throughout: a couple of typographical errors
throughout: several aesthetic imperfections (wrong font, wrong font colour)
Sierpinski Triangle - Polyglot FP for Fun and Profit - Haskell and ScalaPhilip Schwarz
Take the very first baby steps on the path to doing graphics in Haskell and Scala.
Learn about a simple yet educational recursive algorithm producing images that are pleasing to the eye.
Learn how functional programs deal with the side effects required to draw images.
See how libraries like Gloss and Doodle make drawing Sierpinski’s triangle a doddle.
Code for this slide deck:
https://github.com/philipschwarz/sierpinski-triangle-haskell-gloss
https://github.com/philipschwarz/sierpinski-triangle-scala-cats-io
https://github.com/philipschwarz/sierpinski-triangle-scala-awt-and-doodle
Errata:
1. the title 'Sierpinski Triangle' on the front slide could be improved by replacing it with 'Sierpinski's Triangle'.
2. a couple of typos on two slides
3. the triangles drawn using Doodle are not equilateral, as intended but isosceles.
(UPDATE 2021-06-15 I opened PR https://github.com/creativescala/doodle/pull/99 and as a result, an equilateral triangle has now been added to Doodle: https://github.com/creativescala/doodle/commit/30d20efebcc2016942e9cdbae85fefca5b95fa3c).
Here is a corrected version of the deck: https://www.slideshare.net/pjschwarz/sierpinski-triangle-polyglot-fp-for-fun-and-profit-haskell-and-scala-with-minor-corrections
N-Queens Combinatorial Problem - Polyglot FP for Fun and Profit – Haskell and...Philip Schwarz
See how the guard function has migrated from MonadPlus to Alternative and learn something about the latter.
Learn how to write a Scala program that draws an N-Queens solution board using the Doodle graphics library.
See how to write the equivalent Haskell program using the Gloss graphics library.
Learn how to use Monoid and Foldable to compose images both in Haskell and in Scala.
Link to part 1: https://www.slideshare.net/pjschwarz/nqueens-combinatorial-problem-polyglot-fp-for-fun-and-profit-haskell-and-scala-part-1
Errata:
On slide 22, the last line of the showQueens function should of course be show(solution).draw(frame) rather than show(solution).draw
On slide 43, it would be better if the definitions of the beside, above and on Monoids were also shown.
Function Applicative for Great Good of Palindrome Checker Function - Polyglot...Philip Schwarz
Embark on an informative and fun journey through everything you need to know to understand how the Applicative instance for functions makes for a terse palindrome checker function definition in point-free style.
(download for flawless quality) State Monad - Learn how it works - Follow Alvin Alexander’s example-driven build up to the State Monad and then branch off into a detailed look at its inner workings.
Functional Core and Imperative Shell - Game of Life Example - Haskell and ScalaPhilip Schwarz
See a program structure flowchart used to highlight how an FP program breaks down into a functional core and imperative shell
View a program structure flowchart for the Game of Life
See the code for Game of Life’s functional core and imperative shell, both in Haskell and in Scala.
Code:
https://github.com/philipschwarz/functional-core-imperative-shell-scala
https://github.com/philipschwarz/functional-core-imperative-shell-haskell
Folding Unfolded - Polyglot FP for Fun and Profit - Haskell and Scala - with ...Philip Schwarz
(download for perfect quality) - See how recursive functions and structural induction relate to recursive datatypes.
Follow along as the fold abstraction is introduced and explained.
Watch as folding is used to simplify the definition of recursive functions over recursive datatypes
Part 1 - through the work of Richard Bird and Graham Hutton.
This version corrects the following issues:
slide 7, 11 fib(0) is 0,rather than 1
slide 23: was supposed to be followed by 2-3 slides recapitulating definitions of factorial and fibonacci with and without foldr, plus translation to scala
slide 36: concat not invoked in concat example
slides 48 and 49: unwanted 'm' in definition of sum
throughout: a couple of typographical errors
throughout: several aesthetic imperfections (wrong font, wrong font colour)
Game of Life - Polyglot FP - Haskell, Scala, Unison - Part 2 - with minor cor...Philip Schwarz
(download for picture-perfect quality) Follow along as the impure functions in the Game of Life are translated from Haskell into Scala, deepening you understanding of the IO monad in the process.
This is simply a copy of the original with an error corrected on slides 3 and 52, which were supposed to show Scala code and instead showed the Haskell equivalent! Plus removal of a few minor aesthetic imperfections.
Original: https://www.slideshare.net/pjschwarz/game-of-life-polyglot-fp-haskell-scala-unison-part-2
Folding Unfolded - Polyglot FP for Fun and Profit - Haskell and Scala - Part 4Philip Schwarz
(download for flawless image quality) Can a left fold ever work over an infinite list? What about a right fold? Find out.
Learn about the other two functions used by functional programmers to implement mathematical induction: iterating and scanning.
Learn about the limitations of the accumulator technique and about tupling, a technique that is the dual of the accumulator trick.
Download for flawless quality (slides viewed online look a bit grainy and out of focus).
Equivalence of nested flatMaps and chained flatMaps for Kleisli arrow composition.
Introduction to Functional Programming in JavaScripttmont
A presentation I did for work on functional programming. It's meant as an introduction to functional programming, and I implemented the fundamentals of functional programming (Church Numerals, Y-Combinator, etc.) in JavaScript.
Folding Unfolded - Polyglot FP for Fun and Profit - Haskell and Scala - Part 5Philip Schwarz
(download for best quality slides) Gain a deeper understanding of why right folds over very large and infinite lists are sometimes possible in Haskell.
See how lazy evaluation and function strictness affect left and right folds in Haskell.
Learn when an ordinary left fold results in a space leak and how to avoid it using a strict left fold.
Errata:
slide 15: "as sharing is required" should be "as sharing is not required"
slide 43: 𝑠𝑓𝑜𝑙𝑑𝑙 (⊕) 𝑎 should be 𝑠𝑓𝑜𝑙𝑑𝑙 (⊕) 𝑒
Similar to Introducing Assignment invalidates the Substitution Model of Evaluation and violates Referential Transparency - as explained in SICP (the Wizard Book)
I am Samuel H. I am a Mechanical Engineering Assignment Expert at matlabassignmentexperts.com. I hold a Ph.D. Matlab, University of Alberta, Canada. I have been helping students with their homework for the past 12 years. I solve assignments related to Mechanical Engineering.
Visit matlabassignmentexperts.com or email info@matlabassignmentexperts.com.
You can also call on +1 678 648 4277 for any assistance with Mechanical Engineering Assignments.
From Declarative to Imperative Operation Specifications (ER 2007)Jordi Cabot
Declarative specifications are better but have ambiguity problems. Here I present my common sense -based approach to interpret declarative postconditions in a non-ambiguos way
Full paper: http://jordicabot.com/papers/ER07.pdf
(presented in the ER'07 conference)
Programming in Java: Control Flow. Last delivered in 2016. All educational material listed or linked to on these pages in relation to King's College London may be provided for reference only, and therefore does not necessarily reflect the current course content.
I am Baddie K. I am a C++ Homework Expert at cpphomeworkhelp.com. I hold a Masters in Programming from The University of Queensland. I have been helping students with their homework for the past 9 years. I solve homework related to C++.
Visit cpphomeworkhelp.com or email info@cpphomeworkhelp.com. You can also call on +1 678 648 4277 for any assistance with C++ Homework.
CSCI 2033 Elementary Computational Linear Algebra(Spring 20.docxmydrynan
CSCI 2033: Elementary Computational Linear Algebra
(Spring 2020)
Assignment 1 (100 points)
Due date: February 21st, 2019 11:59pm
In this assignment, you will implement Matlab functions to perform row
operations, compute the RREF of a matrix, and use it to solve a real-world
problem that involves linear algebra, namely GPS localization.
For each function that you are asked to implement, you will need to complete
the corresponding .m file with the same name that is already provided to you in
the zip file. In the end, you will zip up all your complete .m files and upload the
zip file to the assignment submission page on Gradescope.
In this and future assignments, you may not use any of Matlab’s built-in
linear algebra functionality like rref, inv, or the linear solve function A\b,
except where explicitly permitted. However, you may use the high-level array
manipulation syntax like A(i,:) and [A,B]. See “Accessing Multiple Elements”
and “Concatenating Matrices” in the Matlab documentation for more informa-
tion. However, you are allowed to call a function you have implemented in this
assignment to use in the implementation of other functions for this assignment.
Note on plagiarism A submission with any indication of plagiarism will be
directly reported to University. Copying others’ solutions or letting another
person copy your solutions will be penalized equally. Protect your code!
1 Submission Guidelines
You will submit a zip file that contains the following .m files to Gradescope.
Your filename must be in this format: Firstname Lastname ID hw1 sol.zip
(please replace the name and ID accordingly). Failing to do so may result in
points lost.
• interchange.m
• scaling.m
• replacement.m
• my_rref.m
• gps2d.m
• gps3d.m
• solve.m
1
Ricardo
Ricardo
Ricardo
Ricardo
�
The code should be stand-alone. No credit will be given if the function does not
comply with the expected input and output.
Late submission policy: 25% o↵ up to 24 hours late; 50% o↵ up to 48 hours late;
No point for more than 48 hours late.
2 Elementary row operations (30 points)
As this may be your first experience with serious programming in Matlab,
we will ease into it by first writing some simple functions that perform the
elementary row operations on a matrix: interchange, scaling, and replacement.
In this exercise, complete the following files:
function B = interchange(A, i, j)
Input: a rectangular matrix A and two integers i and j.
Output: the matrix resulting from swapping rows i and j, i.e. performing the
row operation Ri $ Rj .
function B = scaling(A, i, s)
Input: a rectangular matrix A, an integer i, and a scalar s.
Output: the matrix resulting from multiplying all entries in row i by s, i.e. per-
forming the row operation Ri sRi.
function B = replacement(A, i, j, s)
Input: a rectangular matrix A, two integers i and j, and a scalar s.
Output: the matrix resulting from adding s times row j to row i, i.e. performing
the row operatio.
Mini-lab 1: Stochastic Gradient Descent classifier, Optimizing Logistic Regre...Yao Yao
https://github.com/yaowser/data_mining_group_project
https://www.kaggle.com/c/zillow-prize-1/data
From the Zillow real estate data set of properties in the southern California area, conduct the following data cleaning, data analysis, predictive analysis, and machine learning algorithms:
Mini-lab 1: Stochastic Gradient Descent classifier, Optimizing Logistic Regression Model Performance, Optimizing Support Vector Machine Classifier, Accuracy of results and efficiency, Logistic Regression Feature Importance, interpretation of support vectors, Density Graph
Exploring Support Vector Regression - Signals and Systems ProjectSurya Chandra
Our team competed in a Kaggle competition to predict the bike share use as a part of their capital bike share program in Washington DC using a powerful function approximation technique called support vector regression.
The purpose of this tutorial is to get started using Scilab as a basic calculator by discovering some predefined data types and functions.
Similar to Introducing Assignment invalidates the Substitution Model of Evaluation and violates Referential Transparency - as explained in SICP (the Wizard Book) (20)
Direct Style Effect Systems -The Print[A] Example- A Comprehension AidPhilip Schwarz
The subject of this deck is the small Print[A] program in the following blog post by Noel Welsh: https://www.inner-product.com/posts/direct-style-effects/.
Keywords: "direct-style", "context function", "context functions", "algebraic effect", "algebraic effects", "scala", "effect system", "effect systems", "effect", "side effect", "composition", "fp", "functional programming"
Folding Cheat Sheet #4 - fourth in a seriesPhilip Schwarz
For functions that can be defined both as an instance of a right fold and as an instance of a left fold, one may be more efficient than the other.
Let's look at the example of a function 'decimal' that converts a list of digits into the corresponding decimal number.
Erratum: it has been pointed out that it is possible to define the zip function using a right fold (see slide 5).
Tagless Final Encoding - Algebras and Interpreters and also ProgramsPhilip Schwarz
Tagless Final Encoding - Algebras and Interpreters and also Programs - An introduction, through the work of Gabriel Volpe.
Slide deck home: http://fpilluminated.com/assets/tagless-final-encoding-algebras-interpreters-and-programs.html
A sighting of traverseFilter and foldMap in Practical FP in ScalaPhilip Schwarz
Slide deck home: http://fpilluminated.com/assets/sighting-of-scala-cats-traverseFilter-and-foldMap-in-practical-fp-in-scala.html.
Download PDF for perfect image quality.
A sighting of sequence function in Practical FP in ScalaPhilip Schwarz
Slide deck home: http://fpilluminated.com/assets/sighting-of-scala-cats-sequence-function-in-practical-fp-in-scala.html.
Download PDF for perfect image quality.
This talk was presented on Aug 3rd 2023 during the Scala in the City event a ITV in London https://www.meetup.com/scala-in-the-city/events/292844968/
Visit the following for a description, slideshow, all slides with transcript, pdf, github repo, and eventually a video recording: http://fpilluminated.com/assets/n-queens-combinatorial-puzzle-meets-cats.html
At the centre of this talk is the N-Queens combinatorial puzzle. The reason why this puzzle features in the Scala book and functional programming course by Martin Odersky (the language’s creator), is that such puzzles are a particularly suitable application area of 'for comprehensions'.
We’ll start by (re)acquainting ourselves with the puzzle, and seeing the role played in it by permutations. Next, we’ll see how, when wanting to visualise candidate puzzle solutions, Cats’ monoidal functions fold and foldMap are a great fit for combining images.
While we are all very familiar with the triad providing the bread, butter and jam of functional programming, i.e. map, filter and fold, not everyone knows about the corresponding functions in Cats’ monadic variant of the triad, i.e. mapM, filterM and foldM, which we are going to learn about next.
As is often the case in functional programming, the traverse function makes an appearance, and we shall grab the opportunity to point out the symmetry that exists in the interrelation of flatMap / foldMap / traverse and flatten / fold / sequence.
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Nat, List and Option Monoids -from scratch -Combining and Folding -an examplePhilip Schwarz
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Download for better results.
Java 19 Code: https://github.com/philipschwarz/fruit-salad-and-fruit-snack-ADT-example-java
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The European Union Agency for Law Enforcement Cooperation (Europol) has suffered an alleged data breach after a notorious threat actor claimed to have exfiltrated data from its systems. Infamous data leaker IntelBroker posted on the even more infamous BreachForums hacking forum, saying that Europol suffered a data breach this month.
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2. (define (square x) (* x x))
To square something, multiply it by itself
(define (square x) (* x x))
(square 21)
441
(square (+ 2 5))
49
(square (square 3))
81
Now we will learn about procedure definitions, a much more powerful abstraction technique
by which a compound operation can be given a name and then referred to as a unit.
(define (square x) (* x x))
We can understand this in the following way:
We begin by examining how to express the idea of ''squaring.''
We might say, ''To square something, multiply it by itself.''
Compound Procedures
Having defined square, we can now use it:
(define (sum-of-squares x y)
(+ (square x) (square y)))
(sum-of-squares 3 4)
25
(define (f a)
(sum-of-squares (+ a 1) (* a 2)))
(f 5)
136
This is expressed in our language as
3. (f 5)
(sum-of-squares (+ 5 1) (* 5 2))
(+ (square 6) (square 10))
(+ (* 6 6) (* 10 10))
(+ 36 100)
136
(define (square x) (* x x))
(define (sum-of-squares x y)
(+ (square x) (square y)))
(define (f a)
(sum-of-squares (+ a 1) (* a 2)))
The process we have just described is called the substitution model for
procedure application. It can be taken as a model that determines the
''meaning'' of procedure application, insofar as the procedures in
this chapter are concerned.
Applying a procedure should be interpreted as evaluating the
body of the procedure with the formal parameters replaced by
their values.
The Substitution Model for Procedure Application
4. (define acc (make-account 100))
((acc 'withdraw) 25)
75
((acc 'withdraw) 25)
50
((acc 'withdraw) 60)
"Insufficient funds"
((acc 'deposit) 40)
90
((acc 'withdraw) 60)
30
Local State Variables
To illustrate what we mean by having a
computational object with time-varying state,
let us model a bank account. We should obtain
the following sequence of responses:
(define (make-account balance)
(define (withdraw amount)
(if (>= balance amount)
(begin (set! balance (- balance amount))
balance)
"Insufficient funds"))
(define (deposit amount)
(set! balance (+ balance amount))
balance)
(define (dispatch m)
(cond ((eq? m 'withdraw) withdraw)
((eq? m 'deposit) deposit)
(else (error "Unknown request -- MAKE-ACCOUNT"
m))))
dispatch)
Combining set! with local variables is the general programming technique we will use for constructing
computational objects with local state. Unfortunately, using this technique raises a serious problem:
When we first introduced procedures, we also introduced the substitution model of evaluation to
provide an interpretation of what procedure application means. We said that applying a procedure
should be interpreted as evaluating the body of the procedure with the formal parameters replaced
by their values. The trouble is that, as soon as we introduce assignment into our language,
substitution is no longer an adequate model of procedure application.
This uses the set! special form, whose
syntax is
(set! <name> <new-value>)
Here <name> is a symbol and <new-value> is
any expression. set! changes <name> so
that its value is the result obtained by
evaluating <new-value>.
In the case at hand, we are changing balance so
that its new value will be the result of
subtracting amount from the previous value
of balance.
Observe that the expression ((acc 'withdraw) 25) evaluated twice,
yields different values. This is a new kind of behavior for a procedure. Until
now, all our procedures could be viewed as specifications for computing
mathematical functions. A call to a procedure computed the value of the
function applied to the given arguments, and two calls to the same procedure
with the same arguments always produced the same result.
Actually, this is not quite true. One exception was the random-number
generator in section ... Another exception involved ... On the other hand, until
we introduce assignment, we have no way to create such procedures
ourselves.
Here is a procedure that returns a ''bank-account object'' with a
specified initial balance:
introducing assignment
5. As we have seen, the set! operation enables us to model objects that have local state. However, this advantage comes at a
price. Our programming language can no longer be interpreted in terms of the substitution model of procedure application
that we introduced in section 1.1.5. Moreover, no simple model with ''nice'' mathematical properties can be an adequate
framework for dealing with objects and assignment in programming languages.
So long as we do not use assignments, two evaluations of the same procedure with the same arguments will produce the
same result, so that procedures can be viewed as computing mathematical functions. Programming without any use of
assignments, as we did throughout the first two chapters of this book, is accordingly known as functional programming.
(define (create-account-decrementer! balance)
(lambda (amount)
(set! balance (- balance amount))
balance))
((create-account-decrementer 25) 20)
((lambda (amount) (- 25 amount)) 20)
(- 25 20)
5
If we adhered to the substitution model, we would have to say that the meaning of the procedure application is to first set! balance to 5 and then return 25 as the value of the
expression. This gets the wrong answer. In order to get the correct answer, we would have to somehow distinguish the first occurrence of balance (before the effect of the set!) from the
second occurrence of balance (after the effect of the set!), and the substitution model cannot do this.
The trouble here is that substitution is based ultimately on the notion that the symbols in our language are essentially names for values. But as soon as we introduce set! and the idea
that the value of a variable can change, a variable can no longer be simply a name. Now a variable somehow refers to a place where a value can be stored, and the value stored at this
place can change.
we can use the substitution model to explain
how create-account-decrementer works
(define (create-account-decrementer balance)
(lambda (amount)
(- balance amount)))
(define account-decrementer (create-account-decrementer 25))
(account-decrementer 20)
5
(account-decrementer 10)
15
(define account-decrementer! (create-account-decrementer! 25))
(account-decrementer! 20)
5
(account-decrementer! 10)
- 5
((create-account-decrementer! 25) 20)
((lambda (amount) (set! balance (- 25 amount)) 25) 20)
(set! balance (- 25 20)) 25
25
The Cost of Introducing Assignment
if we attempt a similar substitution analysis with create-
account-decrementer!, we get the wrong answer.
Does not use set! Uses set!
programming without assignments is Functional Programming
6. The issue surfacing here is more profound than the mere breakdown of a particular model of computation.
As soon as we introduce change into our computational models, many notions that were previously straightforward
become problematical. Consider the concept of two things being the "same."
Suppose we call create-account-decrementer twice with the same argument to create two procedures:
(define account-decrementer-1 (create-account-decrementer 25))
(define account-decrementer-2 (create-account-decrementer 25))
In fact, account-decrementer-1 could be substituted for account-decrementer-2 in any computation without changing the result.
(define account-decrementer-1!(create-account-decrementer! 25))
(define account-decrementer-2! create-account-decrementer! 25))
(account-decrementer-1! 20)
5
(account-decrementer-1! 20)
- 15
(account-decrementer-2! 20)
5
Even though account-decrementer-1! and account-decrementer-2! are ''equal'' in the sense that they are both created by
evaluating the same expression, (create-account-decrementer! 25), it is not true that account-decrementer-1! could be
substituted for account-decrementer-2! in any expression without changing the result of evaluating the expression.
A language that supports the concept that ''equals can be substituted for equals'' in an expression without changing the value of the expression is said to be referentially transparent.
Referential transparency is violated when we include set!in our computer language. This makes it tricky to determine when we can simplify expressions by substituting equivalent
expressions. Consequently, reasoning about programs that use assignment becomes drastically more difficult.
Are account-decrementer-1 and account-decrementer-2 the same?
Contrast this with making two calls to create-account-decrementer!:
Are account-decrementer-1! and account-decrementer-2! the same?
Surely not, because calls to account-decrementer-1! and account-decrementer-2! have distinct effects, as shown by the following sequence of interactions:
An acceptable answer is yes, because account-decrementer-1 and account-decrementer-2 have the same computational behavior -- each is a procedure that subtracts
its input from 25.
Sameness and Change introducing assignment violates Referential Transparency