# Introduction to Functional Programming

Size: px
Start display at page:

Transcription

1 Introduction to Functional Programming Xiao Jia Summer 2013

2 Scheme Appeared in 1975 Designed by Guy L. Steele Gerald Jay Sussman Influenced by Lisp, ALGOL Influenced Common Lisp, Haskell, JavaScript, Lua, Racket, Ruby, Usual filename extensions.scm.ss 2

3 Expressions and lists Arithmetic expressions Defining names Procedures Special forms: if, cond Applicative order versus normal order Example: square roots by Newton s method Lists: cons, car, cdr 3

4 Arithmetic expressions 486 è 486 ( ) è 486 ( ) è 666 (* 5 99) è 495 (/ 10 5) è 2 ( ) è 12.7 ( ) è 75 (+ (* 3 (+ (* 2 4) (+ 3 5))) (+ (- 10 7) 6)) (* ) è

5 Defining names (define size 2) size è 2 (* 5 size) è 10 (define pi ) (define radius 10) (* pi (* radius radius)) è (define circumference (* 2 pi radius)) 5

6 Defining procedures (define (square x) (* x x)) (square 21) è 441 (square (+ 2 5)) è 49 (square (square 3)) è 81 (define (sum-of-squares x y) (+ (square x) (square y)) (sum-of-squares 3 4) è 25 (define (<name> <formal parameters>) <body>) 6

7 if (define (abs x) (if (< x 0) (- x) x)) (if <predicate> <consequent> <alternative>) 7

8 cond (define (abs x) (cond ((> x 0) x) ((= x 0) 0) (define (abs x) ((< x 0) (- x)))) (cond (<p 1 > <e 1 >) (<p 2 > <e 2 >) (<p n > <e n >)) (cond ((< x 0) (- x)) (else x))) 8

9 Applicative-order evaluation (sum-of-squares (+ 5 1) (* 5 2)) (sum-of-squares 6 10) (+ (square 6) (square 10)) (+ (* 6 6) (* 10 10)) ( ) 136 Evaluate the arguments and then apply 9

10 Normal-order evaluation (sum-of-squares (+ 5 1) (* 5 2)) (+ (square (+ 5 1)) (square (* 5 2)) ) (+ (* (+ 5 1) (+ 5 1)) (* (* 5 2) (* 5 2))) (+ (* 6 6) (* 10 10)) ( ) 136 Do not evaluate the operands until necessary 10

11 Square roots by Newton s method sqrt(x) is the y such that y 0 and y 2 = x Newton s method: given a guess y, average y and x/y to get a better guess Guess Quotient Average 1 (2/1) = 2 ((2 + 1)/2) = (2/1.5) = (( )/2) = (2/1.4167) = (( )/2) =

12 (define (sqrt-iter guess x) (if (good-enough? guess x) guess (sqrt-iter (improve guess x) x))) (define (good-enough? guess x) (< (abs (- (square guess) x)) 0.001)) (define (improve guess x) (average guess (/ x guess))) (define (sqrt x) (sqrt-iter 1.0 x)) 12

13 Lists (cons x y) è (x. y) (car (cons x y)) è x head (cdr (cons x y)) è y tail A sequence 1, 2, 3, 4 ó (cons 1 (cons 2 (cons 3 (cons 4 ())))) where () is pronounced as unit Shorter version: (list ) (cdr (list )) è (2 3 4) 13

14 14

15 (define (sum items) (+ (car items) (sum (cdr items)))) (sum (list 1 2 3)) (sum (1 2 3)) (+ (car (1 2 3)) (sum (cdr (1 2 3)))) (+ 1 (sum (2 3))) (+ 1 (+ (car (2 3)) (sum (cdr (2 3))))) (+ 1 (+ 2 (sum (3)))) (+ 1 (+ 2 (+ (car (3)) (sum (cdr (3)))))) (+ 1 (+ 2 (+ 3 (sum ())))) (+ 1 (+ 2 (+ 3 (+ (car ()) (sum (cdr ())))))) Error: Cannot apply car/cdr on the unit () 15

16 (define (sum items) (+ (car items) (sum (cdr items)))) (define (sum items) (if (null? items) 0 (+ (car items) (sum (cdr items))))) (sum (list 1 2 3)) è 6 16

17 Recursive style: (define (length items) (if (null? items) 0 (+ 1 (length (cdr items))))) Iterative style: (define (length items) (define (length-iter a count) (if (null? a) count (length-iter (cdr a) (+ 1 count)))) (length-iter items 0)) 17

18 How to represent a tree? A binary tree An arbitrary tree Define some utility functions height leaves 18

19 Functions and streams Linear recursion Tree recursion Higher-order functions Anonymous functions Local names Infinite streams 19

20 Linear recursion (define (factorial n) recursive style è linear space (if (= n 1) 1 (* n (factorial (- n 1))))) 20

21 Linear recursion (define (factorial n) iterative style è constant space (fact-iter 1 1 n)) (define (fact-iter product counter max-count) (if (> counter max-count) product (fact-iter (* counter product) (+ counter 1) max-count))) 21

22 Tree recursion (define (fib n) (cond ((= n 0) 0) ((= n 1) 1) (else (+ (fib (- n 1)) (fib (- n 2)))))) How to compute it with a linear iteration? 22

23 Higher-order functions (define (square x) (* x x)) (define (map f a) (if (null? a) () Treat a function as a value (cons (f (car a)) (map f (cdr a))))) (map square (list 1 2 3)) è (1 4 9) 23

24 Anonymous functions (define (square x) (* x x)) and functions are values (define square (lambda (x) (* x x))) closures (map (lambda (x) (+ x 10)) (list 1 2 3)) è ( ) 24

25 Local names (define (f x y) ((lambda (a b) (+ (* x (square a)) (* y b) (* a b))) (+ 1 (* x y)) (- 1 y))) (define (f x y) (let ((a (+ 1 (* x y)) ) (b (- 1 y) )) (+ (* x (square a)) (* y b) (* a b)))) 25

26 Infinite streams (define (numbers-from n) (cons n (numbers-from (+ n 1)))) (numbers-from 10) (cons 10 (numbers-from (+ 10 1))) (cons 10 (numbers-from 11)) (cons 10 (cons 11 (numbers-from (+ 11 1)))) 26

27 Infinite streams (define (numbers-from n) (cons n (lambda () delay evaluation (numbers-from (+ n 1))))) (numbers-from 10) è (10. #<Closure>) We need to define a tail function for infinite streams 27

28 Infinite streams (define (tail stream) ((cdr stream))) closure value closure stream car (head) cdr (tail) closure application (numbers-from 10) è (10. #<Closure>) (tail (numbers-from 10)) è (11. #<Closure>) 28

29 Infinite streams (define (nth stream n) (if (= n 1) (car stream) (nth (tail stream) (- n 1)))) (nth (numbers-from 10) 1) è 10 (nth (numbers-from 10) 2) è 11 (nth (numbers-from 10) 100) è

30 Infinite streams (define (make-stream a) (if (null? a) () (cons (car a) (lambda () (make-stream (cdr a)))))) (make-stream (list 1 2 3)) è (1. #<Closure>) 30

31 Infinite streams (define (append x y) (if (null? x) y (cons (car x) (lambda () (append (tail x) y))))) (nth (append (make-stream (list 1 2 3)) (numbers-from 10)) 4) è 10 31

32 Infinite streams (define (interleave x y) (if (null? x) y (cons (car x) (lambda () (interleave y (tail x)))))) (nth (interleave (numbers-from 1) (numbers-from 10)) 5) è 3 32

33 Infinite streams (define (map f stream) (if (null? stream) () (cons (f (car stream)) (lambda () (map f (tail stream)))))) (map square (numbers-from 10)) è (100. #<Closure>) 33

34 Infinite streams (define (filter p stream) (if (null? stream) () (if (p (car stream)) (cons (car stream) (lambda () (filter p (tail stream)))) (filter p (tail stream))))) (filter (lambda (x) (> x 100)) (numbers-from 10)) è (101. #<Closure>) 34

35 How to represent an infinite tree? 35

36 Search strategies and infinite lists (define (depth-first next x) (define (dfs y) (if (null? y) () (cons (car y) (lambda appends two finite lists next t is the list of the sub-trees of t (dfs (list x))) (dfs (next (car y)) (cdr y))))))) 36

37 Search strategies and infinite lists (define (breadth-first next x) (define (bfs y) (if (null? y) () (cons (car y) (lambda appends two finite lists next t is the list of the sub-trees of t (bfs (list x))) (bfs (cdr y) (next (car y)))))))) 37

38 Search strategies and infinite lists Write versions of depth-first and breadth-first with an additional argument: a predicate to recognize solutions. Solve the Eight Queens problem. 38

39 Standard ML tutorial 39

### An introduction to Scheme

An introduction to Scheme Introduction A powerful programming language is more than just a means for instructing a computer to perform tasks. The language also serves as a framework within which we organize

### Chapter 1. Fundamentals of Higher Order Programming

Chapter 1 Fundamentals of Higher Order Programming 1 The Elements of Programming Any powerful language features: so does Scheme primitive data procedures combinations abstraction We will see that Scheme

### SCHEME 10 COMPUTER SCIENCE 61A. July 26, Warm Up: Conditional Expressions. 1. What does Scheme print? scm> (if (or #t (/ 1 0)) 1 (/ 1 0))

SCHEME 0 COMPUTER SCIENCE 6A July 26, 206 0. Warm Up: Conditional Expressions. What does Scheme print? scm> (if (or #t (/ 0 (/ 0 scm> (if (> 4 3 (+ 2 3 4 (+ 3 4 (* 3 2 scm> ((if (< 4 3 + - 4 00 scm> (if

### Organization of Programming Languages CS3200/5200N. Lecture 11

Organization of Programming Languages CS3200/5200N Razvan C. Bunescu School of Electrical Engineering and Computer Science bunescu@ohio.edu Functional vs. Imperative The design of the imperative languages

### Streams and Evalutation Strategies

Data and Program Structure Streams and Evalutation Strategies Lecture V Ahmed Rezine Linköpings Universitet TDDA69, VT 2014 Lecture 2: Class descriptions - message passing ( define ( make-account balance

### CS 61A Interpreters, Tail Calls, Macros, Streams, Iterators. Spring 2019 Guerrilla Section 5: April 20, Interpreters.

CS 61A Spring 2019 Guerrilla Section 5: April 20, 2019 1 Interpreters 1.1 Determine the number of calls to scheme eval and the number of calls to scheme apply for the following expressions. > (+ 1 2) 3

### Functional Programming. Pure Functional Languages

Functional Programming Pure functional PLs S-expressions cons, car, cdr Defining functions read-eval-print loop of Lisp interpreter Examples of recursive functions Shallow, deep Equality testing 1 Pure

### Functional Programming. Pure Functional Programming

Functional Programming Pure Functional Programming Computation is largely performed by applying functions to values. The value of an expression depends only on the values of its sub-expressions (if any).

### Streams, Delayed Evaluation and a Normal Order Interpreter. CS 550 Programming Languages Jeremy Johnson

Streams, Delayed Evaluation and a Normal Order Interpreter CS 550 Programming Languages Jeremy Johnson 1 Theme This lecture discusses the stream model of computation and an efficient method of implementation

### Scheme Tutorial. Introduction. The Structure of Scheme Programs. Syntax

Scheme Tutorial Introduction Scheme is an imperative language with a functional core. The functional core is based on the lambda calculus. In this chapter only the functional core and some simple I/O is

### Chapter 15 Functional Programming Languages

Chapter 15 Functional Programming Languages Fundamentals of Functional Programming Languages Introduction to Scheme A programming paradigm treats computation as the evaluation of mathematical functions.

### Fall 2018 Discussion 8: October 24, 2018 Solutions. 1 Introduction. 2 Primitives

CS 6A Scheme Fall 208 Discussion 8: October 24, 208 Solutions Introduction In the next part of the course, we will be working with the Scheme programming language. In addition to learning how to write

### Functional Programming. Pure Functional Languages

Functional Programming Pure functional PLs S-expressions cons, car, cdr Defining functions read-eval-print loop of Lisp interpreter Examples of recursive functions Shallow, deep Equality testing 1 Pure

### Summer 2017 Discussion 10: July 25, Introduction. 2 Primitives and Define

CS 6A Scheme Summer 207 Discussion 0: July 25, 207 Introduction In the next part of the course, we will be working with the Scheme programming language. In addition to learning how to write Scheme programs,

### CS450 - Structure of Higher Level Languages

Spring 2018 Streams February 24, 2018 Introduction Streams are abstract sequences. They are potentially infinite we will see that their most interesting and powerful uses come in handling infinite sequences.

### Procedural abstraction SICP Data abstractions. The universe of procedures forsqrt. Procedural abstraction example: sqrt

Data abstractions Abstractions and their variations Basic data abstractions Why data abstractions are useful Procedural abstraction Process of procedural abstraction Define formal parameters, capture process

### 11/6/17. Functional programming. FP Foundations, Scheme (2) LISP Data Types. LISP Data Types. LISP Data Types. Scheme. LISP: John McCarthy 1958 MIT

Functional programming FP Foundations, Scheme (2 In Text: Chapter 15 LISP: John McCarthy 1958 MIT List Processing => Symbolic Manipulation First functional programming language Every version after the

### Streams. CS21b: Structure and Interpretation of Computer Programs Spring Term, 2004

Streams CS21b: Structure and Interpretation of Computer Programs Spring Term, 2004 We ve already seen how evaluation order can change behavior when we program with state. Now we want to investigate how

### Deferred operations. Continuations Structure and Interpretation of Computer Programs. Tail recursion in action.

Deferred operations Continuations 6.037 - Structure and Interpretation of Computer Programs Mike Phillips (define the-cons (cons 1 #f)) (set-cdr! the-cons the-cons) (define (run-in-circles l) (+

### Scheme: Expressions & Procedures

Scheme: Expressions & Procedures CS F331 Programming Languages CSCE A331 Programming Language Concepts Lecture Slides Friday, March 31, 2017 Glenn G. Chappell Department of Computer Science University

### Func%onal Programming in Scheme and Lisp

Func%onal Programming in Scheme and Lisp http://www.lisperati.com/landoflisp/ Overview In a func(onal programming language, func(ons are first class objects You can create them, put them in data structures,

### CPS 506 Comparative Programming Languages. Programming Language Paradigm

CPS 506 Comparative Programming Languages Functional Programming Language Paradigm Topics Introduction Mathematical Functions Fundamentals of Functional Programming Languages The First Functional Programming

### Func%onal Programming in Scheme and Lisp

Func%onal Programming in Scheme and Lisp http://www.lisperati.com/landoflisp/ Overview In a func(onal programming language, func(ons are first class objects You can create them, put them in data structures,

### CS 314 Principles of Programming Languages

CS 314 Principles of Programming Languages Lecture 16: Functional Programming Zheng (Eddy Zhang Rutgers University April 2, 2018 Review: Computation Paradigms Functional: Composition of operations on data.

### LECTURE 16. Functional Programming

LECTURE 16 Functional Programming WHAT IS FUNCTIONAL PROGRAMMING? Functional programming defines the outputs of a program as a mathematical function of the inputs. Functional programming is a declarative

### Chapter 15. Functional Programming Languages

Chapter 15 Functional Programming Languages Chapter 15 Topics Introduction Mathematical Functions Fundamentals of Functional Programming Languages The First Functional Programming Language: Lisp Introduction

### Functional Programming. Big Picture. Design of Programming Languages

Functional Programming Big Picture What we ve learned so far: Imperative Programming Languages Variables, binding, scoping, reference environment, etc What s next: Functional Programming Languages Semantics

### Functional Programming Languages (FPL)

Functional Programming Languages (FPL) 1. Definitions... 2 2. Applications... 2 3. Examples... 3 4. FPL Characteristics:... 3 5. Lambda calculus (LC)... 4 6. Functions in FPLs... 7 7. Modern functional

### COP4020 Programming Languages. Functional Programming Prof. Robert van Engelen

COP4020 Programming Languages Functional Programming Prof. Robert van Engelen Overview What is functional programming? Historical origins of functional programming Functional programming today Concepts

### 1.3. Conditional expressions To express case distinctions like

Introduction Much of the theory developed in the underlying course Logic II can be implemented in a proof assistant. In the present setting this is interesting, since we can then machine extract from a

https://lambda.mines.edu 1 Recursion is a beautiful way to express many algorithms, as it typically makes our algorithm easier to prove. 2 Calling a function requires space on the call stack for the variables,

### Principles of Programming Languages Topic: Functional Programming Professor L. Thorne McCarty Spring 2003

Principles of Programming Languages Topic: Functional Programming Professor L. Thorne McCarty Spring 2003 CS 314, LS, LTM: Functional Programming 1 Scheme A program is an expression to be evaluated (in

### HIERARCHICAL DATA What is a Tree? How is it different from a Deep List? When would you use one over the other?

HIERARCHICAL DATA 5 COMPUTER SCIENCE 61AS Concepts and Definitions 1. What is a Tree? How is it different from a Deep List? When would you use one over the other? A Tree is an Abstract Data Type composed

### Principles of Programming Languages

Principles of Programming Languages www.cs.bgu.ac.il/~ppl172 Lesson 6 - Defining a Programming Language Bottom Up Collaboration and Management - Elements of Programming Dana Fisman 1 What we accomplished

### Functional Programming Languages (FPL)

Functional Programming Languages (FPL) 1. Definitions... 3 2. Applications... 3 3. Examples... 4 4. FPL Characteristics:... 5 5. Lambda calculus (LC)... 6 5.1. LC expressions forms... 6 5.2. Semantic of

### Lecture #24: Programming Languages and Programs

Lecture #24: Programming Languages and Programs A programming language is a notation for describing computations or processes. These range from low-level notations, such as machine language or simple hardware

### COSE212: Programming Languages. Lecture 3 Functional Programming in OCaml

COSE212: Programming Languages Lecture 3 Functional Programming in OCaml Hakjoo Oh 2017 Fall Hakjoo Oh COSE212 2017 Fall, Lecture 3 September 18, 2017 1 / 44 Why learn ML? Learning ML is a good way of

### CSE341 Autumn 2017, Final Examination December 12, 2017

CSE341 Autumn 2017, Final Examination December 12, 2017 Please do not turn the page until 2:30. Rules: The exam is closed-book, closed-note, etc. except for both sides of one 8.5x11in piece of paper. Please

### Functional programming with Common Lisp

Functional programming with Common Lisp Dr. C. Constantinides Department of Computer Science and Software Engineering Concordia University Montreal, Canada August 11, 2016 1 / 81 Expressions and functions

### Interpreters and Tail Calls Fall 2017 Discussion 8: November 1, 2017 Solutions. 1 Calculator. calc> (+ 2 2) 4

CS 61A Interpreters and Tail Calls Fall 2017 Discussion 8: November 1, 2017 Solutions 1 Calculator We are beginning to dive into the realm of interpreting computer programs that is, writing programs that

### Tail Recursion and Accumulators

Tail Recursion and Accumulators Recursion Should now be comfortable with recursion: No harder than using a loop (Maybe?) OAen much easier than a loop When processing a tree (e.g., evaluate an arithmefc

### Introduction to Scheme

How do you describe them Introduction to Scheme Gul Agha CS 421 Fall 2006 A language is described by specifying its syntax and semantics Syntax: The rules for writing programs. We will use Context Free

### CS 342 Lecture 6 Scheme Procedures and Closures By: Hridesh Rajan

CS 342 Lecture 6 Scheme Procedures and Closures By: Hridesh Rajan 1 Reading Little Schemer Chapter 8 SICP 1, 3.2 2 Lecture Overview In this lecture, we will cover scheme procedures in a bit more detail

### Functional Programming

Functional Programming CS 1025 Computer Science Fundamentals I Stephen M. Watt University of Western Ontario When the Function is the Thing In O-O programming, you typically know where an action is needed,

### Introduction to Typed Racket. The plan: Racket Crash Course Typed Racket and PL Racket Differences with the text Some PL Racket Examples

Introduction to Typed Racket The plan: Racket Crash Course Typed Racket and PL Racket Differences with the text Some PL Racket Examples Getting started Find a machine with DrRacket installed (e.g. the

### User-defined Functions. Conditional Expressions in Scheme

User-defined Functions The list (lambda (args (body s to a function with (args as its argument list and (body as the function body. No quotes are needed for (args or (body. (lambda (x (+ x 1 s to the increment

### ITERATORS AND STREAMS 9

ITERATORS AND STREAMS 9 COMPUTER SCIENCE 61A November 12, 2015 1 Iterators An iterator is an object that tracks the position in a sequence of values. It can return an element at a time, and it is only

### Box-and-arrow Diagrams

Box-and-arrow Diagrams 1. Draw box-and-arrow diagrams for each of the following statements. What needs to be copied, and what can be referenced with a pointer? (define a ((squid octopus) jelly sandwich))

### Functional Programming Lecture 1: Introduction

Functional Programming Lecture 1: Introduction Viliam Lisý Artificial Intelligence Center Department of Computer Science FEE, Czech Technical University in Prague viliam.lisy@fel.cvut.cz Acknowledgements

### Functional Programming

Functional Programming CS331 Chapter 14 Functional Programming Original functional language is LISP LISt Processing The list is the fundamental data structure Developed by John McCarthy in the 60 s Used

### Delayed Expressions Fall 2017 Discussion 9: November 8, Iterables and Iterators. For Loops. Other Iterable Uses

CS 6A Delayed Expressions Fall 07 Discussion 9: November 8, 07 Iterables and Iterators An iterable is any container that can be processed sequentially. Examples include lists, tuples, strings, and dictionaries.

### CSC 533: Programming Languages. Spring 2015

CSC 533: Programming Languages Spring 2015 Functional programming LISP & Scheme S-expressions: atoms, lists functional expressions, evaluation, define primitive functions: arithmetic, predicate, symbolic,

### Heap storage. Dynamic allocation and stacks are generally incompatible.

Heap storage Dynamic allocation and stacks are generally incompatible. 1 Stack and heap location Pointer X points to stack storage in procedure Q's activation record that no longer is live (exists) when

### Problem Set 4: Streams and Lazy Evaluation

Due Friday, March 24 Computer Science (1)21b (Spring Term, 2017) Structure and Interpretation of Computer Programs Problem Set 4: Streams and Lazy Evaluation Reading Assignment: Chapter 3, Section 3.5.

### Programming Systems in Artificial Intelligence Functional Programming

Click to add Text Programming Systems in Artificial Intelligence Functional Programming Siegfried Nijssen 8/03/16 Discover thediscover world at the Leiden world University at Leiden University Overview

### SOFTWARE ARCHITECTURE 6. LISP

1 SOFTWARE ARCHITECTURE 6. LISP Tatsuya Hagino hagino@sfc.keio.ac.jp slides URL https://vu5.sfc.keio.ac.jp/sa/ 2 Compiler vs Interpreter Compiler Translate programs into machine languages Compilers are

### Scheme in Scheme: The Metacircular Evaluator Eval and Apply

Scheme in Scheme: The Metacircular Evaluator Eval and Apply CS21b: Structure and Interpretation of Computer Programs Brandeis University Spring Term, 2015 The metacircular evaluator is A rendition of Scheme,

### Class Structure. Prerequisites

Class Structure Procedural abstraction and recursion 6.037 - Structure and Interpretation of Computer Programs Mike Phillips, Benjamin Barenblat, Leon Shen, Ben Vandiver, Alex Vandiver, Arthur Migdal Massachusetts

### LISP. Everything in a computer is a string of binary digits, ones and zeros, which everyone calls bits.

LISP Everything in a computer is a string of binary digits, ones and zeros, which everyone calls bits. From one perspective, sequences of bits can be interpreted as a code for ordinary decimal digits,

### 4/19/2018. Chapter 11 :: Functional Languages

Chapter 11 :: Functional Languages Programming Language Pragmatics Michael L. Scott Historical Origins The imperative and functional models grew out of work undertaken by Alan Turing, Alonzo Church, Stephen

### 4.2 Variations on a Scheme -- Lazy Evaluation

[Go to first, previous, next page; contents; index] 4.2 Variations on a Scheme -- Lazy Evaluation Now that we have an evaluator expressed as a Lisp program, we can experiment with alternative choices in

### Scheme Basics > (butfirst '(help!)) ()

Scheme Basics > (butfirst '(help!)) () [The butfirst of a *sentence* containing one word is all but that word, i.e., the empty sentence. (BUTFIRST 'HELP!) without the inner parentheses would be butfirst

### Lisp Basic Example Test Questions

2009 November 30 Lisp Basic Example Test Questions 1. Assume the following forms have been typed into the interpreter and evaluated in the given sequence. ( defun a ( y ) ( reverse y ) ) ( setq a (1 2

### CS 314 Principles of Programming Languages

CS 314 Principles of Programming Languages Lecture 17: Functional Programming Zheng (Eddy Zhang Rutgers University April 4, 2018 Class Information Homework 6 will be posted later today. All test cases

### STREAMS 10. Basics of Streams. Practice with Streams COMPUTER SCIENCE 61AS. 1. What is a stream? 2. How does memoization work?

STREAMS 10 COMPUTER SCIENCE 61AS Basics of Streams 1. What is a stream? 2. How does memoization work? 3. Is a cons-stream a special form? Practice with Streams 1. Define a procedure (ones) that, when run

### COP4020 Programming Assignment 1 - Spring 2011

COP4020 Programming Assignment 1 - Spring 2011 In this programming assignment we design and implement a small imperative programming language Micro-PL. To execute Mirco-PL code we translate the code to

### Fall 2017 December 4, Scheme. Instructions

CS 61A Final Review Fall 2017 December 4, 2017 Instructions Form a small group. Start on the first problem. Check off with a helper or discuss your solution process with another group once everyone understands

### The purpose of this lesson is to familiarize you with the basics of Racket (a dialect of Scheme). You will learn about

Lesson 0.4 Introduction to Racket Preliminaries The purpose of this lesson is to familiarize you with the basics of Racket (a dialect of Scheme). You will learn about Expressions Numbers, Booleans, and

### Lisp: Question 1. Dr. Zoran Duric () Midterm Review 1 1/ 13 September 23, / 13

Lisp: Question 1 Write a recursive lisp function that takes a list as an argument and returns the number of atoms on any level of the list. For instance, list (A B (C D E) ()) contains six atoms (A, B,

### Functional Programming - 2. Higher Order Functions

Functional Programming - 2 Higher Order Functions Map on a list Apply Reductions: foldr, foldl Lexical scoping with let s Functional-11, CS5314, Sp16 BGRyder 1 Higher Order Functions Functions as 1st class

### SCHEME 7. 1 Introduction. 2 Primitives COMPUTER SCIENCE 61A. October 29, 2015

SCHEME 7 COMPUTER SCIENCE 61A October 29, 2015 1 Introduction In the next part of the course, we will be working with the Scheme programming language. In addition to learning how to write Scheme programs,

Administrivia Lists, higher order procedures, and symbols 6.037 - Structure and Interpretation of Computer Programs Mike Phillips (mpp) Massachusetts Institute of Technology Project 0 was due today Reminder:

### Scheme Quick Reference

Scheme Quick Reference COSC 18 Fall 2003 This document is a quick reference guide to common features of the Scheme language. It is not intended to be a complete language reference, but it gives terse summaries

### CS61A Notes 02b Fake Plastic Trees. 2. (cons ((1 a) (2 o)) (3 g)) 3. (list ((1 a) (2 o)) (3 g)) 4. (append ((1 a) (2 o)) (3 g))

CS61A Notes 02b Fake Plastic Trees Box and Pointer Diagrams QUESTIONS: Evaluate the following, and draw a box-and-pointer diagram for each. (Hint: It may be easier to draw the box-and-pointer diagram first.)

### UMBC CMSC 331 Final Exam

UMBC CMSC 331 Final Exam Name: UMBC Username: You have two hours to complete this closed book exam. We reserve the right to assign partial credit, and to deduct points for answers that are needlessly wordy

### Notes on Higher Order Programming in Scheme. by Alexander Stepanov

by Alexander Stepanov August 1986 INTRODUCTION Why Scheme? Because it allows us to deal with: 1. Data Abstraction - it allows us to implement ADT (abstact data types) in a very special way. The issue of

### (Func&onal (Programming (in (Scheme)))) Jianguo Lu

(Func&onal (Programming (in (Scheme)))) Jianguo Lu 1 Programming paradigms Func&onal No assignment statement No side effect Use recursion Logic OOP AOP 2 What is func&onal programming It is NOT what you

### CS61A Notes Disc 11: Streams Streaming Along

CS61A Notes Disc 11: Streams Streaming Along syntax in lecture and in the book, so I will not dwell on that. Suffice it to say, streams is one of the most mysterious topics in CS61A, trust than whatever

### Test 1 Summer 2014 Multiple Choice. Write your answer to the LEFT of each problem. 5 points each 1. Preprocessor macros are associated with: A. C B.

CSE 3302 Test 1 1. Preprocessor macros are associated with: A. C B. Java C. JavaScript D. Pascal 2. (define x (lambda (y z) (+ y z))) is an example of: A. Applying an anonymous function B. Defining a function

### Lecture Notes on Lisp A Brief Introduction

Why Lisp? Lecture Notes on Lisp A Brief Introduction Because it s the most widely used AI programming language Because Prof Peng likes using it Because it s good for writing production software (Graham

### Programming Languages

Programming Languages Tevfik Koşar Lecture - XIII March 2 nd, 2006 1 Roadmap Functional Languages Lambda Calculus Intro to Scheme Basics Functions Bindings Equality Testing Searching 2 1 Functional Languages

### 61A LECTURE 18 SCHEME. Steven Tang and Eric Tzeng July 24, 2013

61A LECTURE 18 SCHEME Steven Tang and Eric Tzeng July 24, 2013 What s happening today? We re learning a new language! After you know one language (Python), learning your second (Scheme) is much faster

### Programming Languages. Thunks, Laziness, Streams, Memoization. Adapted from Dan Grossman s PL class, U. of Washington

Programming Languages Thunks, Laziness, Streams, Memoization Adapted from Dan Grossman s PL class, U. of Washington You ve been lied to Everything that looks like a function call in Racket is not necessarily

### Lazy Evaluation and Parameter Transfer

Cristian Giumale / Lecture Notes Lazy Evaluation and Parameter Transfer Scheme comes with two interesting predefined functions: delay and force. The basic purpose of delay is to postpone the evaluation

### Scheme Quick Reference

Scheme Quick Reference COSC 18 Winter 2003 February 10, 2003 1 Introduction This document is a quick reference guide to common features of the Scheme language. It is by no means intended to be a complete

### Principles of Programming Languages 2017W, Functional Programming

Principles of Programming Languages 2017W, Functional Programming Assignment 3: Lisp Machine (16 points) Lisp is a language based on the lambda calculus with strict execution semantics and dynamic typing.

### Functional Programming in Scala. Raj Sunderraman

Functional Programming in Scala Raj Sunderraman Programming Paradigms imperative programming modifying mutable variables, using assignments, and control structures such as if-then-else, loops, continue,

### CS 360 Programming Languages Interpreters

CS 360 Programming Languages Interpreters Implementing PLs Most of the course is learning fundamental concepts for using and understanding PLs. Syntax vs. semantics vs. idioms. Powerful constructs like

### Scheme as implemented by Racket

Scheme as implemented by Racket (Simple view:) Racket is a version of Scheme. (Full view:) Racket is a platform for implementing and using many languages, and Scheme is one of those that come out of the

### Introduction to Logic Programming. Ambrose

Introduction to Logic Programming Ambrose Bonnaire-Sergeant @ambrosebs abonnairesergeant@gmail.com Introduction to Logic Programming Fundamental Logic Programming concepts Related to FP General implementation

### Modern Programming Languages. Lecture LISP Programming Language An Introduction

Modern Programming Languages Lecture 18-21 LISP Programming Language An Introduction 72 Functional Programming Paradigm and LISP Functional programming is a style of programming that emphasizes the evaluation

### An Introduction to Scheme

An Introduction to Scheme Stéphane Ducasse stephane.ducasse@inria.fr http://stephane.ducasse.free.fr/ Stéphane Ducasse 1 Scheme Minimal Statically scoped Functional Imperative Stack manipulation Specification

### Scheme: Data. CS F331 Programming Languages CSCE A331 Programming Language Concepts Lecture Slides Monday, April 3, Glenn G.

Scheme: Data CS F331 Programming Languages CSCE A331 Programming Language Concepts Lecture Slides Monday, April 3, 2017 Glenn G. Chappell Department of Computer Science University of Alaska Fairbanks ggchappell@alaska.edu

### Building a system for symbolic differentiation

Computer Science 21b Structure and Interpretation of Computer Programs Building a system for symbolic differentiation Selectors, constructors and predicates: (constant? e) Is e a constant? (variable? e)

### 6.001 SICP. Types. Types compound data. Types simple data. Types. Types procedures

Today s topics Types of objects and procedures Procedural abstractions Capturing patterns across procedures Higher Order Procedures Types (+ 5 1) ==> 15 (+ "hi 5) ;The object "hi", passed as the first

### CS 314 Principles of Programming Languages. Lecture 16

CS 314 Principles of Programming Languages Lecture 16 Zheng Zhang Department of Computer Science Rutgers University Friday 28 th October, 2016 Zheng Zhang 1 CS@Rutgers University Class Information Reminder:

### Scheme. Functional Programming. Lambda Calculus. CSC 4101: Programming Languages 1. Textbook, Sections , 13.7

Scheme Textbook, Sections 13.1 13.3, 13.7 1 Functional Programming Based on mathematical functions Take argument, return value Only function call, no assignment Functions are first-class values E.g., functions