# Functional Programming Languages (FPL)

Size: px
Start display at page:

Transcription

1 Functional Programming Languages (FPL) 1. Definitions Applications Examples FPL Characteristics: Lambda calculus (LC) Functions in FPLs Modern functional languages Scheme overview Get your own Scheme from MIT General overview Data Typing Comments Recursion Instead of Iteration Evaluation Storing and using Scheme code Variables Data types Arithmetic functions Selection functions Iteration Defining functions ML Haskell A. Bellaachia Page: 1

2 1. Definitions Functional programming languages were originally developed specifically to handle symbolic computation and listprocessing applications. In FPLs the programmer is concerned only with functionality, not with memory-related variable storage and assignment sequences. FPL can be categorized into two types; PURE functional languages, which support only the functional paradigm (Haskell), and Impure functional languages that can also be used for writing imperative-style programs (LISP). 2. Applications AI is the main application domain for functional programming, covering topics such as: expert systems knowledge representation machine learning natural language processing modelling speech and vision A. Bellaachia Page: 2

3 o In terms of symbolic computation, functional programming languages have also proven useful in some editing environments (EMACS) and some mathematical software (particularly calculus) Lisp and its derivatives are still the dominant functional languages (we will consider one of the simpler derivatives, Scheme, in some detail). 3. Examples Lisp, Scheme, Miranda, Sisal, Haskell, APL, ML 4. FPL Characteristics: Functional programming languages are modeled on the concept of mathematical functions, and use only conditional expressions and recursion to effect computation. In the purest form they use neither variables nor assignment statements, although this is relaxed somewhat in most applied functional languages. The concept of side effects is also alien to purely functional programming: a function is given values and returns a value, there are no variables to manipulate and hence no possibility for side effects. A. Bellaachia Page: 3

4 Programs are constructed by composing function applications - the values produced by one or more functions become the parameters to another. For reasons of efficiency (because the underlying machine is, in fact, imperative) most functional languages provide some imperative-style capabilities, including variables with assignment, sequences of statements, and imperative style loop structures. Note that the functional paradigm can also be used with some imperative languages - e.g. C has both a conditional expression and support for recursion - so the factorial function code be coded in functional style in C (or C++ or Java) as follows: int fact(int x){ return (x == 0)? 1 : x * fact(x - 1); } Three primary components: A set of data object: A single, high-level data structure like a list A set of built-in functions for object manipulation: Building, deconstructing, and accessing lists A set of functional forms for building new functions: Composition, reduction, etc. 5. Lambda calculus (LC) A method of modeling the computational aspects of functions A. Bellaachia Page: 4

5 It helps us understand the elements and semantics of functional programming languages independent of syntax LC expressions are of three forms: e1: A single identifier (such as x, or 3) e2: A function definition of the form (λx.e):the expression e, with x being a bound variable e is the body of the function, x is a parameter e may be any of the three types of expressions square( x ) would be written as (λx.x*x) e3: A function application of the form e1 e2 Meaning e1 applied e2 square applied to 2 would be ((λx.x*x) 2) Free and Bound Variables: A variable appearing in a function F is said to be free if it is not bound in F Bound variables are like formal parameters, and act like local variables Free variables are like non-local variables that will be bound at an outer level: In the function λx.xk, x is bound and k is free A. Bellaachia Page: 5

6 Substitution: Applying a function o To apply a function, we rewrite the function, substituting all occurrences of the bound variable by the argument o We use substitution to replace all occurrences of an identifier with an expression: [e/x]y means "substitute e for all occurrences of x in expression y" Semantic of Functional Computations: o We define the result of a function application in terms of the following: Rewriting the definition Replacing bound variables with the corresponding arguments o Rewrite rules: r1: Renaming λxi.e λxj.[xj/xi]e, where xj is not free in e We can replace all occurrences of the name of a bound variable with another name without changing the meaning r2: Application A. Bellaachia Page: 6

7 (λx.e1)e2 [e2/x]e1 Replace the bound variable with the argument to the application r3: Redundant function elimination λx.(e x) e, if x is not free in e An expression that can no longer be reduced is said to be in normal form: (λx.( λy.x + y) 5)(( λy.y * y) 6) = (λx.x + 5)(( λy.y * y) 6) = (λx.x + 5)(6 * 6) = ((6 * 6) + 5) 6. Functions in FPLs In a functional language, the basic unit of computation is the FUNCTION. The function definitions typically include a name for the function, its associated parameter list, and the expressions used to carry out the computation. A function computes a single value based on 0 or more parameters. Though the parameters of a function look like variables in an imperative language, they are different in that they are not subject to having A. Bellaachia Page: 7

8 their value changed by assignment - i.e. they retain their initial value throughout the computation of the function. Pure functional languages don't need an assignment statement. Function construction: given one or more functions as parameters, as well as a list of other parameters, construction essentially calls each function and passes it the list of "other" parameters. Function composition: applying one function to the result of another. E.g. square_root(absolute_value(-3)) Apply-to-all functions: takes a single function as a parameter along with list of operand values. It then applies the function to each parameter, and returns a list containing the results of each call. Example: suppose applyall carried this out with the function square and the data list (1 2 3). The result would be a list with the values from square(1), square(2), and square(3), i.e. (1 4 9) Example: A LISP factorial function, illustrating use of conditional expressions and recursion for iteration A. Bellaachia Page: 8

9 7. Modern functional languages (DEFUN FACT (X) (IF (= X 0) 1 ( * X (FACT (- 1 X)) ) ) ) In a functional language like Miranda named parameters have been re-introduced. They do not denote updatable storage, but rather are used as a convenient way of defining expressions. Example: factorial :: num->num factorial 0 = 1 factorial n = n * factorial (n-1) A. Bellaachia Page: 9

10 IPL vs. FPL Note that in imperative programming we concern ourselves with both the computation sequence and maintaining the program state (i.e. the collection of current data values). Unlike IPLs, purely functional languages (no variables and hence no assignments) have no equivalent concept of state: the programmer focuses strictly on defining the desired functionality. Iteration is not accomplished by loop statements, but rather by conditional recursion. Functional programmers are concerned only with functionality. This comes at a direct cost in terms of efficiency, since the code is still translated into something running on Von Neuman architecture. A. Bellaachia Page: 10

11 8. Scheme overview 8.1. Get your own Scheme from MIT swissnet.ai.mit.edu/projects/scheme/index.html 8.2. General overview Scheme is a functional programming language Scheme is a small derivative of LISP: LISt Processing Dynamic typing and dynamic scooping Scheme introduced static scooping Data Objects An expression is either an atom or a list An atom is a string of characters A Austria A. Bellaachia Page: 11

12 As in Lisp, a Scheme program is a set of expressions written in prefix notation: to add 2 and 3, the expression is (+ 2 3) to subtract 2 from 3, the expression is (- 3 2) to use the built-in function max to determine the maximum value from 2, 3, and 17, the expression is (max ) 8.3. Data Typing Scheme uses dynamic typing (data types are associated with values rather than with variables) and uses static scoping for determining the visibility of non-local variables Comments Comments begin with a semi-colon Example: For instance, showing > as the prompt for user input, a session might look like: >; First some commentary, which won't get evaluated ; below we will provide the postfix for ; 2+3, and then for (2+3)+6 A. Bellaachia Page: 12

13 ; and finally for (2+3)-(2*2) ; we'll start the statements to be evaluated ; on the next line (+ 2 3) ; Value: 5 >(+ (+ 2 3) 6) ; Value: 11 >(- (+ 2 3) (* 2 2)) ; Value: Recursion Instead of Iteration Since we are expressing the entire computation as a composition of functions into a single function, recursion is usually used rather than iteration Example: >; the first line is the header for the Fibonacci function: (define Fibonacci (lambda (n) ; next is the termination case ( if (< n 3) 1 ; and the recursive cal (+ (Fibonacci (- n 1)) (Fibonacci (- n 2)))))) > (Fibonacci 6) ; Value: 8 A. Bellaachia Page: 13

14 8.6. Evaluation The functional approach sometimes requires us to take a "bottom-up" view of the problem: creating functions to compute the lowest layer of values, then other functions taking those as operands. Example: Design a code to compute (a + b + c) / (x + y + z) Compute the numerator and denominator separately, ; for the numerator (+ a b c) ; for the denominator (+ x y z) and then decide how to apply division with those two functions as operands, i.e.: (/ (+ a b c) (+ x y z)) 8.7. Storing and using Scheme code The load function is available to load a Scheme program stores in a an text file, e.g.: > (load "myfile.txt") ; Loading "myfile.txt" -- done A. Bellaachia Page: 14

15 8.8. Variables Variables are always bound to values To declare and initialize a variable, we use the built in define command, giving it the variable name and the value it is to be initialized with (the value may be an expression) Examples: > (define x 3) ; Value:x > (define foo (+ 4 7)) ; Value: foo Check the content of a variable: >x ; Value: 3 >foo ; Value: 11 A. Bellaachia Page: 15

16 8.9. Data types Literals are described as self-evaluating, in that evaluating the literal returns the value they represent. (E.g. evaluating 3 returns the integer value 3.) The primitive types are: characters strings (in double-quotes) Booleans: True: #t False: The empty set for false or #f (see example below). Integers rational numbers real numbers complex numbers. List: There is also a composite data type, called the list, which is a fundamental part of Scheme. Lists are considered in detail in a later section. Numbers There are integers, rationals, reals, and complex numbers. In general, Scheme will return as exact an answer as it can (i.e. it will give an exact integer or rational over a real approximation). Examples: Let's see the results of some basic arithmetic: >(/ ) A. Bellaachia Page: 16

17 ; Value: 2. >(/ 16 10) ; Value: 8/5 Suppose we were to try some comparisons: >(< 2 3) ; Value: #t >(< 4 3) ; Value: () Arithmetic functions There are many built-in arithmetic functions. Some of the commonly used ones include: max, min +, *, -, / quotient, modulo, remainder ceiling, floor, abs, magnitude, round, truncate gcd, lcm exp, log, sqrt sin, cos, tan There are also a number of comparison operators returning Boolean values A. Bellaachia Page: 17

18 <, >, =, <=, >= real?, number?, complex?, rational?, integer? Example: (complex? 4+3i) ;Value: #t zero?, positive?, negative?, odd?, even?, exact? Examples: >; does 7 divided by 3 produce an integer result? (integer? (/ 7 3)) ; Value: () >; does 7 divided by 3 produce an exact result? (exact? (/ 7 3)) ; Value: #t (Note that rational values are considered exact.) Boolean functions and, or, not equal?, Boolean? Selection functions E.g., check to see if three is less than seven and two is not equal to four >(and (< 3 7) (not (= 2 4))) ; Value: #t A. Bellaachia Page: 18

19 Selection in a functional language still controls the choice between different computations, but is expressed by returning the results of functions representing the different computations. The two major Boolean control operations are: IF COND. IF: For example, suppose if x is less than 0 we want to return y - x: (if (< x 0) (- y x)) Now suppose that if x is less than 0 we want to return 0, otherwise we want to return the value x - 1: (if (< x 0) 0 (- x 1)) COND statement is somewhat like the C switch statement, allowing a series of conditions to test for (with corresponding functions to evaluate and return) and a default case: (cond ((= x y) 0) ((> x y) 1) (else -1) ) A. Bellaachia Page: 19

20 Lists Lists are the main composite data type in Scheme. Lists are composed of a series of elements, enclosed in brackets. Implementation note: the typical implementation format for lists is to represent each element in a list using two pointers: Example: One points to the actual implementation of the element (hence allowing us to use anything we like as a list element, the pointer can refer to a primitive data element, a list, a string, etc) The other points to the next element in the list (a b c d) has the four elements a, b, c, and d. The empty list is denoted () Examples of lists include '(a) ; a list with a single element '(a b c) ; a list with three elements '() ; an empty, or null, list '((a b)) ; a list with a single element, which happens to be another list A. Bellaachia Page: 20

21 List functions '("blah" 3.7 () (a b) c) ; a list with 5 elements of a variety of types Head: The front element of the list It is always an element Tail: The list of the remaining elements. It is always a list Single quote: It is used to denote elements which are actually lists (see the examples in list functions below) Constructing lists: (list a b c d): creates a list of the given elements (a b c d) (append '(a b) '(c d)): joins the two lists to create list (a b c d) (cons a '(b c d)): adds the first operand at the head of the other list to create a new list (a b c d) Note that (cons '(a) '(b c d)) would add the list (a) as the head element, giving ((a) b c d) CAR function returns the head element of a list, i.e. (car '(a b c d)) gives a CDR function returns the tail of a list, i.e. (car '(a b c d)) gives (b c d) Examples: A. Bellaachia Page: 21

22 >(define mylist (list )) ; Value: mylist >mylist ; Value: ( ) >(length mylist) ; Value: 5 >(reverse mylist) ; Value: ( ) >mylist ; Value: ( ) >(reverse (cdr mylist)) ; Value: ( ) Observe that the functions applied to mylist are NOT altering the list itself - they are returning manipulated copies of the list. A. Bellaachia Page: 22

23 8.12.Iteration Scheme do expression is similar to a C for loop. (do ) (( variable init step)...) ( test test-expression...) body-expression... Example: (do ) ; for(i=1;i<10;i++) ( (i 1 (+ i 1))) ((> i 10)) (write i) (write-char #\newline) step part may be omitted (do ) ( ; for(i=10,sum=0;i!=0;i--) (i 10 (- i 1)) (sum 0) ) ((= i 0) (write-char #\newline) (write "The sum is:") (write sum) ) (set! sum (+ sum i)) A. Bellaachia Page: 23

24 8.13. Defining functions User-defined functions can be created through the use of the lambda operator as follows: (define functionname (lambda (functionparameters) (expression) (expression)... (expression) )) NOTE: The value returned by the function is the value of the last expression in the list Example: For example, the function below calculates factorials: >(define factorial (lambda (n) ( if (< n 3) n (* n (factorial (- n 1)))) )) ; Value: factorial >(factorial 3) ; Value: 6 A. Bellaachia Page: 24

25 9. ML A static-scoped functional language with syntax that is closer to Pascal than to LISP Uses type declarations, but also does type inferencing to determine the types of undeclared variables (See Chapter 4) It is strongly typed (whereas Scheme is essentially typeless) and has no type coercions Includes exception handling and a module facility for implementing abstract data types Includes lists and list operations The val statement binds a name to a value (similar to DEFINE in Scheme) Function declaration form: fun function_name (formal_parameters) = function_body_expression; e.g., fun cube (x : int) = x * x * x; A. Bellaachia Page: 25

26 10. Haskell Similar to ML (syntax, static scoped, strongly typed) Different from ML (and most other functional languages) in that it is PURELY functional (e.g., no variables, no assignment statements, and no side effects of any kind) Most Important Features: Uses lazy evaluation (evaluate no subexpression until the value is needed) Has list comprehensions, which allow it to deal with infinite lists Examples 1. Fibonacci numbers (illustrates function definitions with different parameter forms) fib 0 = 1 fib 1 = 1 fib (n + 2) = fib (n + 1) + fib n 2. Factorial (illustrates guards) fact n n == 0 = 1 n > 0 = n * fact (n - 1) A. Bellaachia Page: 26

27 3. List operations - List notation: Put elements in brackets e.g., directions = [north, south, east, west] - Length: # e.g., #directions is 4 - Arithmetic series with the.. operator e.g., [2, 4..10] is [2, 4, 6, 8, 10] - Catenation is with ++ e.g., [1, 3] ++ [5, 7] results in [1, 3, 5, 7] - CAR and CDR via the colon operator (as in Prolog) e.g., 1:[3, 5, 7] results in [1, 3, 5, 7] A. Bellaachia Page: 27

### 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

### 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

### 15. Functional Programming

15. Functional Programming 15.1 Introduction The design of the imperative languages is based directly on the von Neumann architecture Efficiency is the primary concern, rather than the suitability of the

### Example Scheme Function: equal

ICOM 4036 Programming Languages Functional Programming Languages Mathematical Functions Fundamentals of Functional Programming Languages The First Functional Programming Language: LISP Introduction to

### 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

### 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

### 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

### 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,

### 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

### 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

### 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

### Chapter 15. Functional Programming Languages ISBN

Chapter 15 Functional Programming Languages ISBN 0-321-49362-1 Chapter 15 Topics Introduction Mathematical Functions Fundamentals of Functional Programming Languages The First Functional Programming Language:

### 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

### 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.

### 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

### 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

### 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).

### 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

### Functional Languages. Hwansoo Han

Functional Languages Hwansoo Han Historical Origins Imperative and functional models Alan Turing, Alonzo Church, Stephen Kleene, Emil Post, etc. ~1930s Different formalizations of the notion of an algorithm

### 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

### Concepts of Programming Languages

Concepts of Programming Languages Lecture 15 - Functional Programming Patrick Donnelly Montana State University Spring 2014 Patrick Donnelly (Montana State University) Concepts of Programming Languages

### CSC312 Principles of Programming Languages : Functional Programming Language. Copyright 2006 The McGraw-Hill Companies, Inc.

CSC312 Principles of Programming Languages : Functional Programming Language Overview of Functional Languages They emerged in the 1960 s with Lisp Functional programming mirrors mathematical functions:

### 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,

### CSE 341 Section Handout #6 Cheat Sheet

Cheat Sheet Types numbers: integers (3, 802), reals (3.4), rationals (3/4), complex (2+3.4i) symbols: x, y, hello, r2d2 booleans: #t, #f strings: "hello", "how are you?" lists: (list 3 4 5) (list 98.5

### FP Foundations, Scheme

FP Foundations, Scheme In Text: Chapter 15 1 Functional Programming -- Prelude We have been discussing imperative languages C/C++, Java, Fortran, Pascal etc. are imperative languages Imperative languages

### 11/6/17. Outline. FP Foundations, Scheme. Imperative Languages. Functional Programming. Mathematical Foundations. Mathematical Foundations

Outline FP Foundations, Scheme In Text: Chapter 15 Mathematical foundations Functional programming λ-calculus LISP Scheme 2 Imperative Languages We have been discussing imperative languages C/C++, Java,

### Documentation for LISP in BASIC

Documentation for LISP in BASIC The software and the documentation are both Copyright 2008 Arthur Nunes-Harwitt LISP in BASIC is a LISP interpreter for a Scheme-like dialect of LISP, which happens to have

### Fundamentals of Artificial Intelligence COMP221: Functional Programming in Scheme (and LISP)

Fundamentals of Artificial Intelligence COMP221: Functional Programming in Scheme (and LISP) Prof. Dekai Wu Department of Computer Science and Engineering The Hong Kong University of Science and Technology

### 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

### 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

### 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

### It is better to have 100 functions operate one one data structure, than 10 functions on 10 data structures. A. Perlis

Chapter 14 Functional Programming Programming Languages 2nd edition Tucker and Noonan It is better to have 100 functions operate one one data structure, than 10 functions on 10 data structures. A. Perlis

### Principles of Programming Languages COMP251: Functional Programming in Scheme (and LISP)

Principles of Programming Languages COMP251: Functional Programming in Scheme (and LISP) Prof. Dekai Wu Department of Computer Science and Engineering The Hong Kong University of Science and Technology

### 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.

### 6.034 Artificial Intelligence February 9, 2007 Recitation # 1. (b) Draw the tree structure corresponding to the following list.

6.034 Artificial Intelligence February 9, 2007 Recitation # 1 1 Lists and Trees (a) You are given two lists: (define x (list 1 2 3)) (define y (list 4 5 6)) What would the following evaluate to: (append

### 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

### 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

### 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

### 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

### 1 Lexical Considerations

Massachusetts Institute of Technology Department of Electrical Engineering and Computer Science 6.035, Spring 2013 Handout Decaf Language Thursday, Feb 7 The project for the course is to write a compiler

### 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

### SCHEME 8. 1 Introduction. 2 Primitives COMPUTER SCIENCE 61A. March 23, 2017

SCHEME 8 COMPUTER SCIENCE 61A March 2, 2017 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,

### Lexical Considerations

Massachusetts Institute of Technology Department of Electrical Engineering and Computer Science 6.035, Spring 2010 Handout Decaf Language Tuesday, Feb 2 The project for the course is to write a compiler

### 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

### 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

### Chapter 11 :: Functional Languages

Chapter 11 :: Functional Languages Programming Language Pragmatics Michael L. Scott Copyright 2016 Elsevier 1 Chapter11_Functional_Languages_4e - Tue November 21, 2017 Historical Origins The imperative

### Processadors de Llenguatge II. Functional Paradigm. Pratt A.7 Robert Harper s SML tutorial (Sec II)

Processadors de Llenguatge II Functional Paradigm Pratt A.7 Robert Harper s SML tutorial (Sec II) Rafael Ramirez Dep Tecnologia Universitat Pompeu Fabra Paradigm Shift Imperative Paradigm State Machine

### Programming Languages

Programming Languages Lambda Calculus and Scheme CSCI-GA.2110-003 Fall 2011 λ-calculus invented by Alonzo Church in 1932 as a model of computation basis for functional languages (e.g., Lisp, Scheme, ML,

### Lexical Considerations

Massachusetts Institute of Technology Department of Electrical Engineering and Computer Science 6.035, Fall 2005 Handout 6 Decaf Language Wednesday, September 7 The project for the course is to write a

### A First Look at ML. Chapter Five Modern Programming Languages, 2nd ed. 1

A First Look at ML Chapter Five Modern Programming Languages, 2nd ed. 1 ML Meta Language One of the more popular functional languages (which, admittedly, isn t saying much) Edinburgh, 1974, Robin Milner

### Imperative languages

Imperative languages Von Neumann model: store with addressable locations machine code: effect achieved by changing contents of store locations instructions executed in sequence, flow of control altered

### (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

### Functional Languages. CSE 307 Principles of Programming Languages Stony Brook University

Functional Languages CSE 307 Principles of Programming Languages Stony Brook University http://www.cs.stonybrook.edu/~cse307 1 Historical Origins 2 The imperative and functional models grew out of work

### CS 314 Principles of Programming Languages

CS 314 Principles of Programming Languages Lecture 15: Review and Functional Programming Zheng (Eddy) Zhang Rutgers University March 19, 2018 Class Information Midterm exam forum open in Sakai. HW4 and

### 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

### How to Design Programs Languages

How to Design Programs Languages Version 4.1 August 12, 2008 The languages documented in this manual are provided by DrScheme to be used with the How to Design Programs book. 1 Contents 1 Beginning Student

### CMSC 330: Organization of Programming Languages

CMSC 330: Organization of Programming Languages Lambda Calculus CMSC 330 1 Programming Language Features Many features exist simply for convenience Multi-argument functions foo ( a, b, c ) Use currying

### 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

### 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

### LECTURE 17. Expressions and Assignment

LECTURE 17 Expressions and Assignment EXPRESSION SYNTAX An expression consists of An atomic object, e.g. number or variable. An operator (or function) applied to a collection of operands (or arguments)

### 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

### Harvard School of Engineering and Applied Sciences CS 152: Programming Languages. Lambda calculus

Harvard School of Engineering and Applied Sciences CS 152: Programming Languages Tuesday, February 19, 2013 The lambda calculus (or λ-calculus) was introduced by Alonzo Church and Stephen Cole Kleene in

### A Brief Introduction to Scheme (I)

A Brief Introduction to Scheme (I) Philip W. L. Fong pwlfong@cs.uregina.ca Department of Computer Science University of Regina Regina, Saskatchewan, Canada Scheme Scheme I p.1/44 Scheme: Feature Set A

### 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

### Lisp. Versions of LISP

Lisp Versions of LISP Lisp is an old language with many variants Lisp is alive and well today Most modern versions are based on Common Lisp LispWorks is based on Common Lisp Scheme is one of the major

### Lambda Calculus and Lambda notation in Lisp II. Based on Prof. Gotshalks notes on Lambda Calculus and Chapter 9 in Wilensky.

λ Calculus Basis Lambda Calculus and Lambda notation in Lisp II Based on Prof. Gotshalks notes on Lambda Calculus and Chapter 9 in Wilensky Mathematical theory for anonymous functions» functions that have

### 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

### 5. Introduction to the Lambda Calculus. Oscar Nierstrasz

5. Introduction to the Lambda Calculus Oscar Nierstrasz Roadmap > What is Computability? Church s Thesis > Lambda Calculus operational semantics > The Church-Rosser Property > Modelling basic programming

### CSc 372. Comparative Programming Languages. 2 : Functional Programming. Department of Computer Science University of Arizona

1/37 CSc 372 Comparative Programming Languages 2 : Functional Programming Department of Computer Science University of Arizona collberg@gmail.com Copyright c 2013 Christian Collberg 2/37 Programming Paradigms

### Lambda Calculus see notes on Lambda Calculus

Lambda Calculus see notes on Lambda Calculus Shakil M. Khan adapted from Gunnar Gotshalks recap so far: Lisp data structures basic Lisp programming bound/free variables, scope of variables Lisp symbols,

### 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

### Introduction to Functional Programming

Introduction to Functional Programming Xiao Jia xjia@cs.sjtu.edu.cn Summer 2013 Scheme Appeared in 1975 Designed by Guy L. Steele Gerald Jay Sussman Influenced by Lisp, ALGOL Influenced Common Lisp, Haskell,

### G Programming Languages - Fall 2012

G22.2110-003 Programming Languages - Fall 2012 Lecture 3 Thomas Wies New York University Review Last week Names and Bindings Lifetimes and Allocation Garbage Collection Scope Outline Control Flow Sequencing

### Haskell 98 in short! CPSC 449 Principles of Programming Languages

Haskell 98 in short! n Syntax and type inferencing similar to ML! n Strongly typed! n Allows for pattern matching in definitions! n Uses lazy evaluation" F definition of infinite lists possible! n Has

### CMSC330. Objects, Functional Programming, and lambda calculus

CMSC330 Objects, Functional Programming, and lambda calculus 1 OOP vs. FP Object-oriented programming (OOP) Computation as interactions between objects Objects encapsulate mutable data (state) Accessed

### 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

### Functional Programming. Functional Programming

2014-06-27 Functional Programming Functional Programming 2014-06-27 Functional Programming 1 Imperative versus Functional Languages attributes of imperative languages: variables, destructive assignment,

### Fall 2017 Discussion 7: October 25, 2017 Solutions. 1 Introduction. 2 Primitives

CS 6A Scheme Fall 207 Discussion 7: October 25, 207 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

### Introduction to the Lambda Calculus

Introduction to the Lambda Calculus Overview: What is Computability? Church s Thesis The Lambda Calculus Scope and lexical address The Church-Rosser Property Recursion References: Daniel P. Friedman et

### A Small Interpreted Language

A Small Interpreted Language What would you need to build a small computing language based on mathematical principles? The language should be simple, Turing equivalent (i.e.: it can compute anything that

### Essentials of Programming Languages Language

Essentials of Programming Languages Language Version 5.3 August 6, 2012 The Essentials of Programming Languages language in DrRacket provides a subset of functions and syntactic forms of racket mostly

### Essentials of Programming Languages Language

Essentials of Programming Languages Language Version 6.90.0.26 April 20, 2018 The Essentials of Programming Languages language in DrRacket provides a subset of functions and syntactic forms of racket mostly

Functional Programming and Haskell Tim Dawborn University of Sydney, Australia School of Information Technologies Tim Dawborn Functional Programming and Haskell 1/22 What are Programming Paradigms? A programming

### Programming Language Features. CMSC 330: Organization of Programming Languages. Turing Completeness. Turing Machine.

CMSC 330: Organization of Programming Languages Lambda Calculus Programming Language Features Many features exist simply for convenience Multi-argument functions foo ( a, b, c ) Ø Use currying or tuples

### CMSC 330: Organization of Programming Languages

CMSC 330: Organization of Programming Languages Lambda Calculus CMSC 330 1 Programming Language Features Many features exist simply for convenience Multi-argument functions foo ( a, b, c ) Ø Use currying

### CIS24 Project #3. Student Name: Chun Chung Cheung Course Section: SA Date: 4/28/2003 Professor: Kopec. Subject: Functional Programming Language (ML)

CIS24 Project #3 Student Name: Chun Chung Cheung Course Section: SA Date: 4/28/2003 Professor: Kopec Subject: Functional Programming Language (ML) 1 Introduction ML Programming Language Functional programming

### The PCAT Programming Language Reference Manual

The PCAT Programming Language Reference Manual Andrew Tolmach and Jingke Li Dept. of Computer Science Portland State University September 27, 1995 (revised October 15, 2002) 1 Introduction The PCAT language

### Lecture 5: Lazy Evaluation and Infinite Data Structures

Lecture 5: Lazy Evaluation and Infinite Data Structures Søren Haagerup Department of Mathematics and Computer Science University of Southern Denmark, Odense October 3, 2017 How does Haskell evaluate a

### 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

### CS61A Discussion Notes: Week 11: The Metacircular Evaluator By Greg Krimer, with slight modifications by Phoebus Chen (using notes from Todd Segal)

CS61A Discussion Notes: Week 11: The Metacircular Evaluator By Greg Krimer, with slight modifications by Phoebus Chen (using notes from Todd Segal) What is the Metacircular Evaluator? It is the best part

### 6.184 Lecture 4. Interpretation. Tweaked by Ben Vandiver Compiled by Mike Phillips Original material by Eric Grimson

6.184 Lecture 4 Interpretation Tweaked by Ben Vandiver Compiled by Mike Phillips Original material by Eric Grimson 1 Interpretation Parts of an interpreter Arithmetic calculator

### Topic 1: Introduction

Recommended Exercises and Readings Topic 1: Introduction From Haskell: The craft of functional programming (3 rd Ed.) Readings: Chapter 1 Chapter 2 1 2 What is a Programming Paradigm? Programming Paradigm:

### 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

### SML A F unctional Functional Language Language Lecture 19

SML A Functional Language Lecture 19 Introduction to SML SML is a functional programming language and acronym for Standard d Meta Language. SML has basic data objects as expressions, functions and list

### 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,

### Data Types The ML Type System

7 Data Types 7.2.4 The ML Type System The following is an ML version of the tail-recursive Fibonacci function introduced Fibonacci function in ML in Section 6.6.1: EXAMPLE 7.96 1. fun fib (n) = 2. let

### 15 Unification and Embedded Languages in Lisp

15 Unification and Embedded Languages in Lisp Chapter Objectives Chapter Contents Pattern matching in Lisp: Database examples Full unification as required for Predicate Calculus problem solving Needed