https://ocw.cs.pub.ro/ppcarte/ 2026-04-24T18:40:13+03:00 https://ocw.cs.pub.ro/ppcarte/ https://ocw.cs.pub.ro/ppcarte/lib/tpl/bootstrap3/images/favicon.ico text/html 2021-05-06T17:32:28+03:00 https://ocw.cs.pub.ro/ppcarte/doku.php?id=fp:assig-01&rev=1620311548&do=diff Deadline: May 7th, 23:55 Introduction For this assignment, we will work with images and implement some basic image manipulations. We will work with two types of images: greyscale and RGB. Image representation Internally, images are modeled as two-dimensional matrices of pixels; in Haskell we will model this by using lists of lists. text/html 2021-05-28T11:05:31+03:00 https://ocw.cs.pub.ro/ppcarte/doku.php?id=fp:assig-02&rev=1622189131&do=diff Deadline: May 31th, 23:55 Introduction Similar to the first assignment, we will perform some image manipulations. You do not need to have worked on the first assignment in order to work on this one, but you should read its statement to understand the basic ideas behind the image formats used.$ f = \frac{259\cdot(c + 255)}{255\cdot(259 - c)}$$ f\cdot(oldValue - 128) + 128$ text/html 2022-03-16T12:41:14+03:00 https://ocw.cs.pub.ro/ppcarte/doku.php?id=fp:assignment-rules&rev=1647427274&do=diff Submission guidelines Project format * You should not change any other files of the project, except for the template-file. For this homework, the template-file is FSets.scala. Warning: if a submission has changes in other files, it may not be graded text/html 2021-05-27T15:37:24+03:00 https://ocw.cs.pub.ro/ppcarte/doku.php?id=fp:exam2021-rules&rev=1622119044&do=diff FP Exam (june 2021) The exam will take place online (via MS Teams) and it will consist of four questions: * (Q1) a simple Haskell programming task - 2 points * (Q2) a list processing task in Haskell - 2 points * (Q3) an algebraic datatype task - text/html 2022-05-31T18:03:13+03:00 https://ocw.cs.pub.ro/ppcarte/doku.php?id=fp:exam2022&rev=1654009393&do=diff Exam FP 2022 * The exam will take place on the 9th of June, at 14:00, in room Pr001 from the Precis building. * It is advisable that you should be present with at least 10 minutes in advance. * Having a laptop is a prerequisite for taking the exam. text/html 2023-03-22T08:44:40+03:00 https://ocw.cs.pub.ro/ppcarte/doku.php?id=fp:homework01&rev=1679467480&do=diff Homework 1. Sets as functions Problem statement Sets are unordered collections of unique elements. There are several ways to store sets. One of them relies on characteristic functions. Such functional sets are especially useful if we expect many insert/retrieve$ A \subseteq U$$ f: U \rightarrow \{0,1\}$$ f(x) = 1$$ x \in A$$ f(x) = 0$$ x \not\in A$$ U$$ \{1,2,3\}$$ \{start, start+1, \ldots, stop\}$$ \exists x. P(X) \iff \lnot \forall x.\lnot P(X)$ text/html 2022-03-31T13:38:50+03:00 https://ocw.cs.pub.ro/ppcarte/doku.php?id=fp:homework02-draft&rev=1648723130&do=diff H02. Tree Sets Problem statement In this homework, you will implement a binary search tree, that you will use to gather stats about words from a particular text. Generally, in a binary search tree: * each non-empty node contains exactly one value and two children$ f \circ g$ text/html 2022-04-11T16:34:56+03:00 https://ocw.cs.pub.ro/ppcarte/doku.php?id=fp:homework02-filteraux&rev=1649684096&do=diff Suppose pred = x => x % 3 == 0 We abstract away the predicate, to make the example clearer. 3 / \ 1 5 .filterAux( Empty ) \ / \ 2 4 6 5 1 / \ .filterAux( \ .filterAux(Empty)) 4 6 2 5 / \ .filterAux(Empty.filterAux((2.filterAux(Empty)).ins(1))) 4 6 5 … text/html 2022-04-01T09:53:33+03:00 https://ocw.cs.pub.ro/ppcarte/doku.php?id=fp:homework02&rev=1648796013&do=diff H02. Tree Sets Problem statement In this homework, you will implement a binary search tree, that you will use to gather stats about words from a particular text. Generally, in a binary search tree: * each non-empty node contains exactly one value and two children$ f \circ g$ text/html 2022-04-11T15:55:58+03:00 https://ocw.cs.pub.ro/ppcarte/doku.php?id=fp:homework03-draft&rev=1649681758&do=diff Homework 3 - Tic Tac Toe In this homework, you will implement some functionality which will allow you to design a completely functional tic-tac-toe AI. The latter will be part of homework 4. About Tic Tac Toe Tic Tac Toe is usually played on a 3 by 3 board, marking positions by each player in rounds. Our game is slightly different: text/html 2022-04-19T12:08:17+03:00 https://ocw.cs.pub.ro/ppcarte/doku.php?id=fp:homework03&rev=1650359297&do=diff Homework 3 - Tic Tac Toe In this homework, you will implement some functionality which will allow you to design a completely functional tic-tac-toe AI. The latter will be part of homework 4. About Tic Tac Toe Tic Tac Toe is usually played on a 3 by 3 board, marking positions by each player in rounds. Our game is slightly different: text/html 2023-05-09T15:27:22+03:00 https://ocw.cs.pub.ro/ppcarte/doku.php?id=fp:homework04&rev=1683635242&do=diff Homework 4. Five in a row AI Homework 4 consists in developing a complete five-in-a-row game, together with an AI and a very basic interface. * For this stage, you will decide on the structure of your project, as well as write tests to guide your implementation. text/html 2021-03-11T14:50:35+03:00 https://ocw.cs.pub.ro/ppcarte/doku.php?id=fp:lab01-java-intro&rev=1615467035&do=diff Introduction to Functional Programming (in Java!) 1. A single function to implement all of them 1.1. Write a method that takes a list of integers and returns a new list with all elements multiplied by two. 1.2. Write a method that takes a list of $ f : A \rightarrow B$$ A$$ B$ text/html 2022-02-24T11:47:08+03:00 https://ocw.cs.pub.ro/ppcarte/doku.php?id=fp:lab01&rev=1645696028&do=diff Introduction to Scala Scala setup Installation Scala can be downloaded and installed on either a Windows or NIX platform (e.g. Linux, OS-X) here. For this lecture you must install Scala 3, and we recommend installing it using Coursier (see the previous link) text/html 2022-02-24T11:06:16+03:00 https://ocw.cs.pub.ro/ppcarte/doku.php?id=fp:lab02-old&rev=1645693576&do=diff 2. Introduction to Haskell 2.1. Functions in Haskell In mathematics, functions have a domain an codomain. In Haskell, functions have types or signatures. They often can be omitted in Haskell, but can also be explicitly written as in: f :: Integer -> Integer -> Integer f x y = x + y $ e_1$$ e_2$$ e_1$$ e_2$ text/html 2023-03-10T10:16:40+03:00 https://ocw.cs.pub.ro/ppcarte/doku.php?id=fp:lab02&rev=1678436200&do=diff 2. Scala syntax and function definition Objectives: * get yourself familiar with Scala syntax basics * practice writing tail-recursive functions as an alternative to imperative loops * keep your code clean and well-structured. Create a new Scala worksheet to write your solutions $ n$$ 1 + 2^2 + 3^2 + \ldots + (n-1)^2 + n^2$$ \sqrt{a}$$ x_0 = 1$$ x_{n+1} = \displaystyle\frac{1}{2}(x_n+\frac{a}{x_n})$$ x_n$$ \sqrt{a}$$ x_{n+1}$$ x_0 = 1$$ x_n$$ \sqrt{a}$$ a$$ n$$ (x_n)_n$$ \sqrt{a}$$ … text/html 2022-03-18T15:31:02+03:00 https://ocw.cs.pub.ro/ppcarte/doku.php?id=fp:lab03&rev=1647610262&do=diff 3. Higher-order functions Objectives: * implement and use higher-order functions. A higher-order function takes other functions as parameter or returns them * implement curry and uncurry functions, and how they should be properly used (review lecture).$ count_k(n) = k + 2k + 3k + \ldots x*k$$ x*k \leq n$$ k$$ count_1(n) + count_2(n) + \ldots + count_k(n)$$ a_1, a_2, \ldots, a_k$$ f(a_1)\;op\;f(a_2)\;op\;\ldots f(a_k)$$ 1 + 2^2 + 3^2 + \ldots + (n-1)^2 + n^2$$ (f(a) + f(b))(b-a)/2$ text/html 2022-05-15T23:54:27+03:00 https://ocw.cs.pub.ro/ppcarte/doku.php?id=fp:lab04&rev=1652648067&do=diff 4. Lists in Scala Objectives: * get familiar with pattern matching lists, as well as common list operations from Scala and how they work * get familiar with common higher-order functions over lists (partition, map, foldRight, foldLeft, filter) text/html 2022-03-31T08:53:41+03:00 https://ocw.cs.pub.ro/ppcarte/doku.php?id=fp:lab05&rev=1648706021&do=diff 5. Functional data representation 5.1. Nats Consider the following toy implementation of the type Nat which encodes natural numbers. trait Nat {} case object Zero extends Nat {} case class Succ(n: Nat) extends Nat {} For instance, 3 will be encoded as the value: text/html 2022-04-08T12:45:26+03:00 https://ocw.cs.pub.ro/ppcarte/doku.php?id=fp:lab06&rev=1649411126&do=diff Lab 06. Polymorphism in Scala This lab will start with the implementations discussed during lecture. Please find the polymorphic trait FList[A] below: trait FList[A]{ // list with elements of type A def length: Int def head: A def tail: FList[A] def map[B](f: A => B): FList[B] // a op (b op (c op acc)) def foldRight[B](acc: B)(op: (A,B) => B): B // ((acc op a) op b) op c def foldLeft[B](acc: B)(op: (B,A) => B): B def contains(e: A):Boolean = this.foldRight(false)(_ ==… text/html 2022-05-03T17:25:26+03:00 https://ocw.cs.pub.ro/ppcarte/doku.php?id=fp:lab07&rev=1651587926&do=diff L07. For expressions In this lab, we will use matrices to encode Bitmap images. The format is called BPM, and more details are available here. Our format will be grayscale only. Each pixel of the matrix is encoded as an integer, with values from 0 to 255. Some examples are shown below: text/html 2022-04-27T17:32:43+03:00 https://ocw.cs.pub.ro/ppcarte/doku.php?id=fp:lab08&rev=1651069963&do=diff L08. Maps in Scala 8.1. Gradebooks as maps We represent a gradebook as a map which holds, for each student (encoded as String), its grade (an Int). We implement a gradebook as a case class, as follows: case class Gradebook(book: Map[String,Int]) text/html 2021-05-13T17:39:33+03:00 https://ocw.cs.pub.ro/ppcarte/doku.php?id=fp:lab09&rev=1620916773&do=diff 9. Algebraic data-types (ADT) A simple definition of an ADT in Haskell is: data Shape = Rectangle Integer Integer | Circle Integer The part data Shape = ... of a definition introduces a new type called Shape in the program. Objects of any type (including text/html 2021-05-20T13:32:21+03:00 https://ocw.cs.pub.ro/ppcarte/doku.php?id=fp:lab10&rev=1621506741&do=diff 10. Trees File systems are one common application that uses a tree representation. We define the following data type to model a very simplistic file system: data FTree = Dir String [FTree] | File String deriving (Show, Eq) deriving (Show, Eq)Show text/html 2022-03-08T14:07:35+03:00 https://ocw.cs.pub.ro/ppcarte/doku.php?id=fp:lecture02&rev=1646741255&do=diff Introduction to Scala syntax A few basic examples def myAddition(x: Int, y: Int): Int = x + y myAddition(1,2) def inRange(start: Int, stop: Int, x: Int): Boolean = if (x <= stop && x >= start) true else false def inRange1(start: Int, stop: Int, x: Int): Boolean = x <= stop && x >= start def and(x: Boolean, y: Boolean): Boolean = if (x) y else false and(false, true) false && true text/html 2022-03-18T12:28:21+03:00 https://ocw.cs.pub.ro/ppcarte/doku.php?id=fp:lecture03&rev=1647599301&do=diff L03. Higher-order functions Functions that take other functions as parameter def sumWithf (f: Int => Int, start: Int, stop:Int): Int = { def aux(i: Int, acc: Int): Int = if (i>stop) acc else aux(i+1, f(i) + acc) aux(start,0) } sumWithf(x => x, 0, 10) text/html 2022-03-22T12:12:39+03:00 https://ocw.cs.pub.ro/ppcarte/doku.php?id=fp:lecture04&rev=1647943959&do=diff L04. Lists and their higher-order functions /* how to construct lists */ val l0 = List(1,2,3) // the list [1,2,3] has type List[Int] List("apples","banannas") // List[String] List('c','h','a','r') // List[Char] List(Nil, List(3,4), List(5,6)) // List[List[Int]] /* * Lists are: homogeneous - THEY CONTAIN ELEMENTS OF THE * same type * */ /* how to construct lists (using cons, and Nil)*/ (1 :: (2 :: (3 :: Nil))).head //just the same as List(1,2,3) /* e :: l ^ current element … text/html 2022-03-29T12:26:21+03:00 https://ocw.cs.pub.ro/ppcarte/doku.php?id=fp:lecture05&rev=1648545981&do=diff 5. Functional data representation in Scala /* (Functional) Data representation in Scala A few syntax basics: */ // we define a class (called Point) // we define the constructor for the class: // Point(1,2) class Point(x: Int, y: Int){ def xVal:Int = x def yVal:Int = y // checks if a point is higher on the y axis than our current point // higher is method of the class Point def higher(p: Point): Boolean = p.yVal > y override def toString : String = s"({},{})" } val… text/html 2022-04-05T13:14:12+03:00 https://ocw.cs.pub.ro/ppcarte/doku.php?id=fp:lecture06&rev=1649153652&do=diff L06. Polymorphism /* (A) Subtype polymorphism: A type S is related to another type T (supertype) by some notion of substitutability, meaning that functions written to operate on elements of type T(supertype) can also operate on elements of type S (subtype) Example: */ class Animal { def scream: String = "An animal screams!" } class Wolf extends Animal { override def scream: String = "A wolf screams" } new Animal().scream /* (B) Ad-hoc polymorphism Is obtained w… text/html 2022-04-19T12:07:35+03:00 https://ocw.cs.pub.ro/ppcarte/doku.php?id=fp:lecture08&rev=1650359255&do=diff L08. For expressions A few motivational examples for using for expressions: val l = List("this", "is", "a", "list", "of", "strings") l.map(_.length) l.map(_.length).filter(_ > 2) // suppose we have another list of strings: val l1 = List("is", "s", "th", "list", "str", "ings", "i", "t", "") // suppose we have a dictionary (words which make sense in English) val dictionary = l /* We want to find ALL PAIRS of words from l1, which are valid English words */ // We start by constructing… text/html 2022-05-06T10:47:19+03:00 https://ocw.cs.pub.ro/ppcarte/doku.php?id=fp:lecture09&rev=1651823239&do=diff L09. Scala collections val letters = Vector("v", "m", "n", "i") /* the colon operator, allways indicates "associativity" * collection :@ element * * element #: collection * * */ letters :+ "z" "a" +: letters /* Ranges * (Int, Int) => Range * _.to(_) * * (Int, Int) => Range * _.until(_) * * (Range, Int) => Range * _.by(_) * * * */ 1.to(5) 1 to 5 1.until(5) 1 until 5 1 to 5 by 2 /* shorthand a b c for: a.b(c) */ /* In Scala you can define functions that are not named only wi… text/html 2022-03-09T20:13:24+03:00 https://ocw.cs.pub.ro/ppcarte/doku.php?id=fp:old-labs&rev=1646849604&do=diff 4. Higher order functions 4.1. Map, foldl, foldr, filter, zipWith Map The function map has signature: (a->b) -> [a] -> [b]. It takes as parameter: * a transformer function f :: a->b * a list of objects of type a It returns: * a list of transformed objects of type text/html 2021-03-05T09:07:31+03:00 https://ocw.cs.pub.ro/ppcarte/doku.php?id=fp:plagiarism&rev=1614928051&do=diff Plagiarism and academic integrity Acording to UPB rules for diploma studies (article 51. points d. and i.), students are required to uphold the rules for academic integrity described in The UPB charter. Of these we explicitly mention article 45, point 13) a. which states that plagiarism is a severe misconduct text/html 2022-03-01T15:45:53+03:00 https://ocw.cs.pub.ro/ppcarte/doku.php?id=fp:rules&rev=1646142353&do=diff Rules Points * Semester: 5.5p * Exam: 5p * For exam admission, a minimum of: * 2.5p semester points are required * 1.5p homework points are required * a minimum of 2.5p are required to pass the exam Semester points * Lab: 1p (lab attendance) text/html 2022-02-22T11:55:06+03:00 https://ocw.cs.pub.ro/ppcarte/doku.php?id=fp:team&rev=1645523706&do=diff Functional Programming 2021 Team members * Matei Popovici Lecture * weekly: Fridays 10:00-12:00 MS Teams Labs * 1231A: Fridays 12:00-14:00 MS Teams * 1231B: Thursdays 16:00-18:00 MS Teams