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

Size: px
Start display at page:

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

Transcription

1 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 not been bound to names Present a subset of full definition to present the flavour Notation and interpretation scheme identifies» functions and their application to operands > argument-parameter binding» Clearly indicates which variables are free and which are bound LC2-1 LC2-2 Bound and Free Variables Bound variables are similar to local variables in Java function (or any procedural language)» Changing the name of a bound variable (consistently) does not change the semantics (meaning) of a function Free variables are similar to global variables in Java function (or any procedural language)» Changing the name of a free variable normally changes the semantics (meaning) of a function. { λ u, w. ( u + 1 ) ( v 1 ) ( w + 2 ) } bound variables In the above λ expression:» u and w are bound» v is free λ functions defining form LC2-3 LC2-4

2 Work from the inside out Function application Work right to left so arguments are evaluated first λ function example { λ u, v. ( u * v) / ( u + 6 ) } [ { λ a. a ( a + 1 ) } [ 3 ], { λ b. ( b + 1 )**2 } [ 2 ] ] Build up longer definitions with auxiliary definitions { λ u, v. ( u * v) / ( u + 6 ) } [ 12, { λ b. ( b + 1 )**2 } [ 2 ] ] { λ u, v. ( u * v) / ( u + 6 ) } [ 12, 9 ] 108/18 6 LC2-5 LC2-6 λ function example { λ f. f * (f + 1) } [ { λ a, b. a ( b + 1 ) } [ x + 1, x - 1 ] ] { λ f. f * (f + 1)} [ (x+1) * x ] λ function example - 1 Example» Define f(u(a)) = u(a)**2+1 where u(a) = a ( a + 1 ) where a = z+1 where z = 1 (x+1)*x*((x+1)*x+1) x * (x+1) * (x**2+x+1) LC2-7 LC2-8

3 λ function example - 2 Example» Define f(u(a)) = u(a)**2+1 where u(a) = a ( a + 1 ) where a = z+1 where z = 1 λ function example - 3 Example» Define f(u(a)) = u(a)**2+1 where u(a) = a ( a + 1 ) where a = z+1 where z = 1 { λ z. z + 1 } [ 1 ] { λ a. a ( a + 1 ) } [ { λ z. z + 1 } [ 1 ] ] LC2-9 LC2-10 λ function example - 4 Example» Define f(u(a)) = u(a)**2+1 where u(a) = a ( a + 1 ) where a = z+1 where z = 1 λ function example - 5 Example» Define f(u(a)) = u(a)**2+1 where u(a) = a ( a + 1 ) where a = z+1 where z = 1 { λ f. f ** } [ { λ a. a ( a + 1 ) } [ { λ z. z + 1 } [ 1 ] ] ] { λ f. f ** } [ { λ a. a ( a + 1 ) } [ { λ z. z + 1 } [ 1 ] ] ] { λ f. f ** } [ { λ a. a ( a + 1 ) } [ 2 ] ] { λ f. f ** } [ 6 ] 37 LC2-11 LC2-12

4 Lambda functions in Lisp Lambda functions in Lisp are anonymous functions or functions without a name. Eliminate the need to allot a function storage space Use lambda functions when you don t expect to reuse the function Lambda functions can be found wherever Lisp expects to find a function All Lisp functions are stored as lambda functions Lamba notation in Lisp Lambda expressions are a direct analogue of λ-calculus expressions» They are the basis of Lisp functions a modified syntax to simplify the interpreter For example ( defun double ( x ) ( + x x ) ) > is the named version of the following unnamed lambda expression ( lambda ( x ) ( + x x ) ) { λ x. ( x + x ) } > Note the similar syntax with λ-calculus and the change to prefix, from infix, to permit a uniform syntax for functions of any number of arguments LC2-13 LC2-14 Lambda expression - 1 ( lambda ( list of symbols ) list of forms ) list of symbols: list of formal parameters Lambda expression - 2 We are used to seeing functions at the beginning of a list followed by arguments. Lambda functions can be used the same way. ( (lambda ( list of symbols ) list of forms ) arguments ) list of forms: body of the function list of symbols: list of formal parameters list of forms: body of the function arguments: arguments supplied to lambda function LC2-15 LC2-16

5 Lambda examples > ( ( lambda ( x ) (cons x nil ) ) y) (Y) > ( apply ( lambda ( x y ) ( list y x ) ) ( 1 2 ) ) ( 2 1 ) > ( mapcar ( lambda ( x ) ( / 1 ( sqrt x ) ) ) ( ) ) ( ) > ( ( lambda ( x ) ( setq x 5 ) ) ( setq x 4 ) ) 5 > x 4 More lambda examples > ( apply ( lambda ( x y ) ( list y x ) ) ( ( list ) car ) ) ( CAR ( LIST )) > ( funcall ( lambda ( x y ) ( list y x ) ) ( list ) car ) ( CAR ( LIST )) > ( eval ( ( lambda ( x y ) ( list y x ) ) (list ) car ) ) 1 > ( eval ( funcall ( lambda ( x y ) ( list y x ) ) ( list ) car ) ) 1 LC2-17 LC2-18 Even more lambda examples > ( mapcar ( lambda ( x ) ( list a x ) ) ( ) ) ( ( A 1 ) ( A 2 ) ( A 3 ) ) > ( mapc ( lambda ( x ) ( + x x ) ) ( ) ) ( ) > ( mapcar ( lambda ( x ) ( or ( atom x ) ( equal ( a b ) x ) ) ) ( a b ( a b ) ( ) x ( ( x ) ) ) ) Remember sumint sumint (defun sumint (func n) (cond ((equal n 0) 0) ( t ( + (funcall func n) (sumint func (1- n)))))) ( T T T T T NIL ) > ( maplist ( lambda (x) ( cons (car x) ( b ) ) ) (1 2 3 ) ) ( ( 1 B ) ( 2 B ) ( 3 B ) ) LC2-19 LC2-20

6 Anonymous functions - 1 Recall in the abstraction for sumint we defined support functions to handle each case (defun double (int) (+ int int)) (defun square (int) (* int int)) (defun identity (int) int) Then we called sumint with the desired function as an argument (sumint double 10 ) -- > 110 (sumint square 2 ) -- > 5 (sumint identity 5 ) -- > 15 Anonymous functions - 2 This adds additional symbols we may not want, especially if the function is to be used only once. Using lambda we get the same effect without adding symbols (sumint # (lambda (int) (+ int int)) 10) (sumint # (lambda (int) (* int int)) 10) (sumint # (lambda (int) int) 10) LC2-21 LC2-22 The function 'function' What is the meaning of # in the following (sumint # (lambda (int) (+ int int)) 10) It is a short hand» # (...) ==> (function (...)) One of its attributes is it works like quote, in that its argument is not evaluated, thus, in this simple context the following will also work (sumint (lambda (int) (+ int int)) 10) Later we will see another attribute of function that makes it different from quote. Another example - 1 Suppose we have a two step process we want to apply when iterating down a list. For example: we first want to take the absolute value of each number and then we want to take the square root. Applying these operations to the list ( ) would produce ( ). Whenever a function is to be quoted use # in place of LC2-23 LC2-24

7 Another example - 2 We could accomplish this by using functionals: Another example - 3 We could accomplish this by using functionals: (???? # sqrt (???? # abs ( ) ) ) (???? # sqrt (mapcar # abs ( ) ) ) LC2-25 LC2-26 Another example - 4 We could accomplish this by using functionals: Another example - 5 A different way to accomplish the same thing: ( mapcar # sqrt (mapcar # abs ( ) ) ) ( defun compose ( f g ) # ( lambda ( x ) ( funcall f (funcall g x ) ) ) ) NOTE: instead of passing a function into a function, here you are passing a function out of a function LC2-27 LC2-28

8 Another example - 6 A different way to accomplish the same thing: > ( mapcar # sqrt (mapcar # abs ( ) ) ) ( ) > ( funcall (compose # sqrt # abs ) -9 ) 3.0 > ( mapcar (compose # sqrt # abs ) ( ) ) ( ) Note: this gets rid of the nested mapcars Recursion Recursion with lambda functions uses labels to temporarily name a function The following is a general λ-calculus template. > The name is in scope within the entire body but is out of scope outside of the lambda expression. { label name ( lambda arguments. body_references_name ) } In Lisp can use labels to define a mutually recursive set of functions ( labels (list of named lambda expressions) sequence of forms using the temporarily named functions ) LC2-29 LC2-30 Example 1 of recursion A recursive multiply that uses only addition. > The temporary function is called mult (labels ((mult (k n) (cond ((zerop n) 0) (t (+ k (mult k (1- n)))) ))) (mult 2 3) ) Example 2 of recursion rectimes computes k * n by supplying the parameters to a unary function that is a variation of example 1. (defun rectimes (k n) )) (labels (( temp (n) ))) (temp n) (cond ((zerop n) 0) ( t (+ k (temp (1- n)))) LC2-31 LC2-32

9 A Lisp hackers puzzle A Lisp hackers puzzle Self replicating So t No good must be non-atomic Generate a self-reproducing non-atomic Lisp form??? It is considered cheating if your form involves any permanent side-effects. How about creating a function foo that returns foo Also no good - creating a function involves a permanent sideeffect. All known solutions involve using lambda! LC2-33 LC2-34 A Lisp hackers puzzle TEST 1 A solution: ( ( lambda ( x ) ( list ( list lambda ( x ) x ) ( list quote x ) ) ) ( list ( list lambda ( x ) x ) ( list quote x ) ) ) ) TEST 1 WILL COVER ALL MATERIAL UNTIL HERE!! LC2-35 LC2-36

10 TEST 1 What is on the test?» All my slides» Wilensky chapters 1, 2, 3, 15, 4, 6, 7, 8, 9 (not 9.6)» Notes on symbols, notes on functionals (no Backus notation), notes on lambda calculus > Notes are on the web site under resources LC2-37

### Lambda Calculus. Gunnar Gotshalks LC-1

Lambda Calculus LC-1 l- Calculus History Developed by Alonzo Church during 1930 s-40 s One fundamental goal was to describe what can be computed. Full definition of l-calculus is equivalent in power to

### Lambda Calculus LC-1

Lambda Calculus LC-1 λ- Calculus History-1 Developed by Alonzo Church during 1930 s-40 s One fundamental goal was to describe what can be computed. Full definition of λ-calculus is equivalent in power

### 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,

### 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

### 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

### 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

### History. Functional Programming. Based on Prof. Gotshalks notes on functionals. FP form. Meaningful Units of Work

History Functional Programming Based on Prof. Gotshalks notes on functionals 1977 Turing 1 Lecture John Backus described functional programming The problem with current languages is that they are word-at-a-time

### 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,

### 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. 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. 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

### Review of Functional Programming

Review of Functional Programming York University Department of Computer Science and Engineering 1 Function and # It is good programming practice to use function instead of quote when quoting functions.

### 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

### 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).

### 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,

### 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

### 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

### Imperative, OO and Functional Languages A C program is

Imperative, OO and Functional Languages A C program is a web of assignment statements, interconnected by control constructs which describe the time sequence in which they are to be executed. In Java programming,

### Functions, Conditionals & Predicates

Functions, Conditionals & Predicates York University Department of Computer Science and Engineering 1 Overview Functions as lambda terms Defining functions Variables (bound vs. free, local vs. global)

### 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

### 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

### 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

### 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

### Functional Programming. Contents

Functional Programming Gunnar Gotshalks 2003 September 27 Contents Introduction... 2 Example for Inner Product... 2 Basis Set for Functionals... 3 Example Function Definitions... 3 Lisp Builtin Functionals...

### CSCI337 Organisation of Programming Languages LISP

Organisation of Programming Languages LISP Getting Started Starting Common Lisp \$ clisp i i i i i i i ooooo o ooooooo ooooo ooooo I I I I I I I 8 8 8 8 8 o 8 8 I \ `+' / I 8 8 8 8 8 8 \ `-+-' / 8 8 8 ooooo

### 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

### CIS4/681 { Articial Intelligence 2 > (insert-sort '( )) ( ) 2 More Complicated Recursion So far everything we have dened requires

1 A couple of Functions 1 Let's take another example of a simple lisp function { one that does insertion sort. Let us assume that this sort function takes as input a list of numbers and sorts them in ascending

### Announcement. Overview. LISP: A Quick Overview. Outline of Writing and Running Lisp.

Overview Announcement Announcement Lisp Basics CMUCL to be available on sun.cs. You may use GNU Common List (GCL http://www.gnu.org/software/gcl/ which is available on most Linux platforms. There is also

### 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

### 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

### Midterm Examination (Sample Solutions), Cmput 325

Midterm Examination (Sample Solutions, Cmput 325 [15 marks] Consider the Lisp definitions below (defun test (L S (if (null L S (let ((New (add (cdar L S (test (cdr L New (defun add (A S (if (null S (cons

### 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.

### FUNKCIONÁLNÍ A LOGICKÉ PROGRAMOVÁNÍ 4. LISP: PROMĚNNÉ, DALŠÍ VLASTNOSTI FUNKCÍ, BLOKY, MAPOVACÍ FUNKCIONÁLY, ITERAČNÍ CYKLY,

FUNKCIONÁLNÍ A LOGICKÉ PROGRAMOVÁNÍ 4. LISP: PROMĚNNÉ, DALŠÍ VLASTNOSTI FUNKCÍ, BLOKY, MAPOVACÍ FUNKCIONÁLY, ITERAČNÍ CYKLY, 2011 Jan Janoušek MI-FLP Evropský sociální fond Praha & EU: Investujeme do vaší

### MIDTERM EXAMINATION - CS130 - Spring 2005

MIDTERM EAMINATION - CS130 - Spring 2005 Your full name: Your UCSD ID number: This exam is closed book and closed notes Total number of points in this exam: 231 + 25 extra credit This exam counts for 25%

### 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

### 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,

### 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

### Basics of Using Lisp! Gunnar Gotshalks! BLU-1

Basics of Using Lisp BLU-1 Entering Do Lisp work Exiting Getting into and out of Clisp % clisp (bye)» A function with no arguments» CTRL d can also be used Documentation files are in the directory» /cse/local/doc/clisp

### 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

### 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,

### 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

### 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

### 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

### John McCarthy IBM 704

How this course works SI 334: Principles of Programming Languages Lecture 2: Lisp Instructor: an arowy Lots of new languages Not enough class time to cover all features (e.g., Java over the course of 34-36:

### INF4820: Algorithms for Artificial Intelligence and Natural Language Processing. Common Lisp Fundamentals

INF4820: Algorithms for Artificial Intelligence and Natural Language Processing Common Lisp Fundamentals Stephan Oepen & Murhaf Fares Language Technology Group (LTG) August 30, 2017 Last Week: What is

### 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

### 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.

### Spring 2018 Discussion 7: March 21, Introduction. 2 Primitives

CS 61A Scheme Spring 2018 Discussion 7: March 21, 2018 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

### 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

### 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

### Recursion & Iteration

Recursion & Iteration York University Department of Computer Science and Engineering 1 Overview Recursion Examples Iteration Examples Iteration vs. Recursion Example [ref.: Chap 5,6 Wilensky] 2 Recursion

### 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

### 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

### 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,

### INF4820. Common Lisp: Closures and Macros

INF4820 Common Lisp: Closures and Macros Erik Velldal University of Oslo Oct. 19, 2010 Erik Velldal INF4820 1 / 22 Topics for Today More Common Lisp A quick reminder: Scope, binding and shadowing Closures

### SCHEME AND CALCULATOR 5b

SCHEME AND CALCULATOR 5b COMPUTER SCIENCE 6A July 25, 203 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,

### Department of Computer and information Science Norwegian University of Science and Technology

Department of Computer and information Science Norwegian University of Science and Technology http://www.idi.ntnu.no/ A Crash Course in LISP MNFIT272 2002 Anders Kofod-Petersen anderpe@idi.ntnu.no Introduction

### 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

### CSCC24 Functional Programming Scheme Part 2

CSCC24 Functional Programming Scheme Part 2 Carolyn MacLeod 1 winter 2012 1 Based on slides from Anya Tafliovich, and with many thanks to Gerald Penn and Prabhakar Ragde. 1 The Spirit of Lisp-like Languages

### Announcements. The current topic: Scheme. Review: BST functions. Review: Representing trees in Scheme. Reminder: Lab 2 is due on Monday at 10:30 am.

The current topic: Scheme! Introduction! Object-oriented programming: Python Functional programming: Scheme! Introduction! Numeric operators, REPL, quotes, functions, conditionals! Function examples, helper

### 19 Machine Learning in Lisp

19 Machine Learning in Lisp Chapter Objectives Chapter Contents ID3 algorithm and inducing decision trees from lists of examples. A basic Lisp implementation of ID3 Demonstration on a simple credit assessment

### Common LISP-Introduction

Common LISP-Introduction 1. The primary data structure in LISP is called the s-expression (symbolic expression). There are two basic types of s-expressions: atoms and lists. 2. The LISP language is normally

### 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

### 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

### Basic Scheme February 8, Compound expressions Rules of evaluation Creating procedures by capturing common patterns

Basic Scheme February 8, 2007 Compound expressions Rules of evaluation Creating procedures by capturing common patterns Previous lecture Basics of Scheme Expressions and associated values (or syntax and

### Symbolic Programming. Dr. Zoran Duric () Symbolic Programming 1/ 89 August 28, / 89

Symbolic Programming Symbols: +, -, 1, 2 etc. Symbolic expressions: (+ 1 2), (+ (* 3 4) 2) Symbolic programs are programs that manipulate symbolic expressions. Symbolic manipulation: you do it all the

### A Quick Introduction to Common Lisp

CSC 244/444 Notes last updated ug. 30, 2016 Quick Introduction to Common Lisp Lisp is a functional language well-suited to symbolic I, based on the λ-calculus and with list structures as a very flexible

### 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

### Common Lisp. Blake McBride

Contents Common Lisp Blake McBride (blake@mcbride.name) 1 Data Types 2 2 Numeric Hierarchy 3 3 Comments 3 4 List Operations 4 5 Evaluation and Quotes 5 6 String Operations 5 7 Predicates 6 8 Math Predicates

### Introduction to Functional Programming and basic Lisp

Introduction to Functional Programming and basic Lisp Based on Slides by Yves Lespérance & Peter Roosen-Runge 1 Functional vs Declarative Programming declarative programming uses logical statements to

### Putting the fun in functional programming

CM20167 Topic 4: Map, Lambda, Filter Guy McCusker 1W2.1 Outline 1 Introduction to higher-order functions 2 Map 3 Lambda 4 Filter Guy McCusker (1W2.1 CM20167 Topic 4 2 / 42 Putting the fun in functional

### 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

### Recursive Functions of Symbolic Expressions and Their Computation by Machine Part I

Recursive Functions of Symbolic Expressions and Their Computation by Machine Part I by John McCarthy Ik-Soon Kim Winter School 2005 Feb 18, 2005 Overview Interesting paper with By John Mitchell Interesting

### 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

### 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

### 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,

### 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)

### 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

### Comp 411 Principles of Programming Languages Lecture 7 Meta-interpreters. Corky Cartwright January 26, 2018

Comp 411 Principles of Programming Languages Lecture 7 Meta-interpreters Corky Cartwright January 26, 2018 Denotational Semantics The primary alternative to syntactic semantics is denotational semantics.

### Robot Programming with Lisp

4. Functional Programming: Higher-order Functions, Map/Reduce, Lexical Scope Institute for Artificial University of Bremen 9 of November, 2017 Functional Programming Pure functional programming concepts

### 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,

### 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

### CS115 - Module 9 - filter, map, and friends

Fall 2017 Reminder: if you have not already, ensure you: Read How to Design Programs, Intermezzo 3 (Section 18); Sections 19-23. Abstraction abstraction, n. 3a.... The process of isolating properties or

### FUNKCIONÁLNÍ A LOGICKÉ PROGRAMOVÁNÍ 2. ÚVOD DO LISPU: ATOMY, SEZNAMY, FUNKCE,

FUNKCIONÁLNÍ A LOGICKÉ PROGRAMOVÁNÍ 2. ÚVOD DO LISPU: ATOMY, SEZNAMY, FUNKCE, 2011 Jan Janoušek MI-FLP Evropský sociální fond Praha & EU: Investujeme do vaší budoucnosti L I S P - Introduction L I S P

### Recap: Functions as first-class values

Recap: Functions as first-class values Arguments, return values, bindings What are the benefits? Parameterized, similar functions (e.g. Testers) Creating, (Returning) Functions Iterator, Accumul, Reuse

### 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

### 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

### 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

### Lecture08: Scope and Lexical Address

Lecture08: Scope and Lexical Address Free and Bound Variables (EOPL 1.3.1) Given an expression E, does a particular variable reference x appear free or bound in that expression? Definition: A variable

### Concepts of programming languages

Concepts of programming languages Lecture 7 Wouter Swierstra 1 Last time Relating evaluation and types How to handle variable binding in embedded languages? 2 DSLs: approaches A stand-alone DSL typically

### 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

Announcements 1 Today s Menu Finish Introduction to ANNs (original material by Dr. Mike Nechyba) > Slides 58-60 > Adjusting the Learning Rate Loose Ends in > Lambda Expressions Review > I/O Functions >

### INF4820: Algorithms for Artificial Intelligence and Natural Language Processing. More Common Lisp

INF4820: Algorithms for Artificial Intelligence and Natural Language Processing More Common Lisp Stephan Oepen & Murhaf Fares Language Technology Group (LTG) September 6, 2017 Agenda 2 Previously Common

### 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

### Closures. Mooly Sagiv. Michael Clarkson, Cornell CS 3110 Data Structures and Functional Programming

Closures Mooly Sagiv Michael Clarkson, Cornell CS 3110 Data Structures and Functional Programming t ::= x x. t t t Call-by-value big-step Operational Semantics terms variable v ::= values abstraction x.

### Project 2: Scheme Interpreter

Project 2: Scheme Interpreter CSC 4101, Fall 2017 Due: 12 November 2017 For this project, you will implement a simple Scheme interpreter in C++ or Java. Your interpreter should be able to handle the same

### Evaluating Scheme Expressions

Evaluating Scheme Expressions How Scheme evaluates the expressions? (procedure arg 1... arg n ) Find the value of procedure Find the value of arg 1 Find the value of arg n Apply the value of procedure