TweetFollow Us on Twitter

Volume Number:2
Issue Number:1
Column Tag:Lisp Listener

First Class Citizens in MacScheme

By Andy Cohen, Hughes Aircraft, MacTutor Contributing Editor

This month the Lisp Listener will feature an in depth description of MacScheme. This description comes from William Clinger of Semantic Microsystems, the developers of MacScheme.

Imagine a programming language in which every number must be given before it can be used in an expression. For example, you could not print the circumference of a unit circle by saying "write (2 * 3.14159)"; you would instead have to say something like

let   two = 2 
let   pi  = 3.14159 
 two_pi = two * pi
 foo (two_pi)

Of course, such a language would be very clumsy. Nobody would want to use it. A student of programming languages would say that the problem with the language is that it treats numbers as second class citizens.

First class citizens have the right to remain anonymous. They have an identity that is independent of any names by which they may be known. Further more they have the right to participate in any activity sponsored by the language. If the language has arrays, then any first class citizen can be an element; if the language has assignments, any first class citizen can be stored in a variable. If the language can pass arguments to procedures, any first class citizen can be passed; if procedures can return results, any first class citizen can be returned.

Numbers are so important that they are first class citizens of nearly all programming languages. In some languages numbers are the only first class citizens. In many languages the only first class citizens are those that are easy to fit into a machine register.

Arrays are important and have been around a long time, but how many programming languages really treat arrays as first class citizens? Also, how many languages allow you to create a new array without giving it a name? Do they allow you to return an array (not just a pointer to the array) as the result of a procedure call? Do they allow arrays to appear on the right hand side of an assignment statement? First class arrays as in APL have a radical impact on programming style.

Procedures have been around a long time also, and most programming languages allow procedures to be passed as arguments to other procedures. Do they allow you to create a new procedure without giving it a name? Can you return a procedure as the result of a procedure call? Can a procedure appear on the right hand side of an assignment?

The most accessible of the languages with first class procedures are the two modern dialects of Lisp known as Scheme and Common Lisp. The following contains samples of First Class procedures using MacScheme.

An anonymous procedure is written as a lambda expression beginning with the keyword lambda, followed by a list of arguments, followed by the procedure body. The lambda expression evaluates to a procedure.

>>> (lambda (x) (+ X 12))

What can you do with an anonymous procedure? Anything you can do with a named procedure. For example, the second argument to the sort procedure that defines an ordering on the objects to be sorted. If you already have a procedure that defines the ordering you want, you can refer to it by one of its names:

>>>(sort '(1 3 5 7 9 8 6 4 2 0) >?)
(9 8 7 6 5 4 3 2 1 0)
>>>(sort '(1 3 5 7 9 8 6 4 2 0) >)
(9 8 7 6 5 4 3 2 1 0)

If you don't already have the procedure you want, you can create one with a lambda expression. There's no reason why you should have to think up a name for it:

>>> (sort '("Even" "mathematicians"    "are" "accustomed" "to" "treating" 
"functions" "as" underprivileged" "objects") 
  (lambda (x y)
       (or (<? (string-length x) (string-length y))
("as"  "to"  "are"  "Even"  "objects"  "treating"  "functions"  "accustomed" 
"mathematicians"  "underprivileged")

Names come in handy when you want to write a recursive procedure, however. The rec expression is convenient for that purpose. In the example below, the (rec fact ...) syntax introduces a new variable named fact whose value is the value of the lambda expression.

>>> (rec fact
             (lambda (n)
                  (if  (zero? n)
                         (* n (fact  (- n 1))))))


The variable named fact is visible only within the lambda expression, however. If we were now to ask for the value of fact, Scheme would say that fact is an undefined variable. Thus the result of the rec expression is just as anonymous as the result of a lambda expression. Admittedly its printed representation includes a name, but that name is nothing more than a comment generated by the Scheme system as it attempts to be helpful.

We can use the recursively defined anonymous procedure as the first argument to the map procedure, which will call the procedure on every element of its second argument and return a list of the results:

>>> (map  (rec fact  (lambda (n)  (if  (zero? n)  1 (* n (fact (- n 1))))))
          '(0 1 2 3 4 5 6 7 8 9 10 11 12))
(1 1 2 6 24 120 720 5040 40320 3629880 3628800 39916800 479001600)

In MacScheme, the map procedure is also called by its traditional name mapcar. The define expression below creates a new global variable named call-on-every whose initial value is the contents of the old variable map -- that is, the map procedure.

>>> (define call-on-every map)

If we want to create a procedure and a variable to hold it, we create the procedure using lambda expression and we create the variable using a define expression:

>>> (define cube (lambda) (x) (expt x 3)))
>>> cube
>>> (map cube '(o 1 2 3 4 5 6 7 8 9 10))
(0 1 9 27 64 125 216 343 512 729 1000)

If you don't like writing (define cube (lambda (x) (expt x 3))) when other dialects of Lisp will let you suppress the lambda by writing (define (cube x) (expt x 3)), don't despair. Scheme also allows the alternative syntax. I am avoiding the alternative syntax because it obscures the distinction between the anonymous procedure and the name of the variable in which it is stored.

Since procedures are first class citizens, they can be returned as the results of calls to other procedures. The power procedure defined below takes an argument y and returns an anonymous new procedure. The new procedure takes an argument x and returns x raised to the y-th power.

>>> (define power
          (lambda (y)
               (lambda (x)
                    (expt x y ))))
>>> (power 3)
>>> (map  (power 3)  '(0 1 2 3 4 5 6 7 8 9 10))
(0 1 8 27 64 125 216 343 512 729 1000)
>>> (map (power .5)  '(0 1 2 3 4 5 6 7 8 9 10))
(0.0 1.0 1.41421 1.73205 2.0 2.23607 3.44949 2.64575 3.82843 3.0 3.16228)

The cube procedure could have been defined using power.

>>> (define square (power 2))
>>> (map square ' (0 1 2  3 4 5 6 7 8 9 10)(0 1 444 9 16 25 36 49 64 
81 100)

Since procedures are first class citizens, we can create a list of anonymous procedures that will raise their argument to one of the powers 0 through 10:

>>> (map power '(0 1 2 3 4 5   6 7 8 9 10)

We can apply every procedure in that list to the integer 2:

>>> (map (lambda (f)  (f 2))
                 (map power ' (0 1 2 3 4 5 6 7 8 9 10)))
(1 2 4 8 16 32 64 128 256 512 1024)

I hope that this extremely simple and artificial example has suggested the new programming styles that become possible when a language treats procedures as first class citizens. The possibilities are both liberating and dizzying. There is no reason to be fancy for the sake of fanciness, but it is often true that intelligent use of first class procedures will simplify an otherwise intimidating program.

So far none of the examples have used any assignment statements. Assignments are used far less often in Scheme and Lisp than in mainstream programming languages like Pascal. It is quite practical to write major programs in Scheme without using a single assignment statement. Such programs are said to be written in the functional style. When a program is written in the functional style, every procedure can be specified entirely by the relationship between its arguments and its results. In the absence of assignments (and other side effects such as I/O), that relationship is a simple mathematical function -- it never changes.

Object-oriented programming, as epitomized by Smalltalk, relies heavily on assignments to change the internal state of objects. Scheme currently provides no special support for object-oriented programming, but first class procedures can serve as objects with internal state.

Consider the problem of implementing a counter in Pascal as part of a simulation program. We could use a global variable as the counter, but that would make it hard to add new behavior to the counter later on. (For example, we might want to animate the counter in some way, so the counter should update the display every time it is incremented.) It would be better to implement the counter as a procedure. In Pascal, unfortunately, the state of the procedure must still be a global variable, as in the following Scheme code.

>>> (define n 0)
>>> (define counter
               (lambda ()
                     (set! n (+ n 1))
>>> (counter)
>>> (counter)
>>> n

One problem with using a global variable to hold the state of the counter is that we are likely to forget about it and then try to use a global variable with the same name for some other purpose. If we are lucky the compiler will complain. If unlucky, we will also forget to declare the other variable and will have a hard time finding out why the program won't work.

One reason we might forget to declare the other variable is that in Pascal the declaration, initialization, and use of a global variable are so widely separated. Ideally the state of the counter procedure should be a variable that is visible only within the procedure, is declared near the procedure, and is initialized near the procedure. We would like to have a syntax very much like:

>>> (define counter
           (let ((n 0))
                 (lambda  ()
                       (set! n (+ n 1))

This actually works in Scheme. The (let ((n 0)) ...) syntax introduces a new variable n whose initial value is 0. The new variable is visible only within the lambda expression, and the value of that lambda expression -- an anonymous procedure -- is the value of the let expression. There's nothing special about the let expression; though Pascal has no equivalent, the let expression is roughly the same as block in Algol 60 or some of the newer C compilers. What's special is the lambda expression, because it evaluates to a first class procedure and first class procedures remember their non-local variables:

>>> (counter)
>>> (counter)
>>> (set! n 837)
>>> (counter)
>>> (counter)

As the assignment to n shows, the local state of the new counter procedure has nothing to do with the global variable n.

Suppose our simulation requires hundreds of counters. We could write hundreds of counter procedures, but then any change in the behavior of a counter would require us to change hundreds of lines of code. Why not write one procedure that creates new counter procedures? While we're at it, we'll make the initial state of the counter be a parameter to the procedure that creates counters.

>>> (define make-counter
             (lambda ()
                    (lambda ()
                         (set! n (+ n 1))
>>> (define c1 (make-counter 100))
>>> (define c2 (make-counter  -5000))

The local states of c1 and c2 are independent, because a new variable named n is created every time make-counter is called.

>>> (c1)
>>> (c1)
>>> (c1)
>>> (c1)
>>> (c2)
>>> (c2)
>>> (c2)
>>> (c1)

We have seen how to use first class procedures to implement objects with local state. The object we've been using as our example has a very simple behavior, however. What if there were several distinct operations on the object? One way to implement distinct operations is through message passing, which is similar to the way Smalltalk does it.

The code below introduces some new syntax. The case expression should be understandable. The (lambda (operation . args) ...) syntax is used to create a procedure that takes one or more arguments. The value of operation will be the first argument to the procedure, and the value of args will be a list of any remaining arguments. The car procedure extracts the first element of a list.

>>> (define make-counter
           (lambda (n)
              (rec self
                    (lambda (operation . args)
                         (case operation
                             ((count)  (set! n (+ n1) n)
                             ((report) n)
                             ((reset) (set! n (car args)) n)
                            (else (error "Bad operation on counter" self 

>>> (define c3 (make-counter 40))
>>> (c3 'count)
>>> (c3 'count)
>>> (c3 'report)
>>> (c3 'count)
>>> (c3 'reset 1000)
>>> (c3 'report)
>>> (c3 'count)
>>> (c3 'count)

Message-passing isn't the only way to implement objects with complex behaviors. It is sometimes more efficient to create a new procedure for each operation on an object. The make-counter procedure shown below returns a vector of three procedures.

>>> (define make-counter
           (lambda (n)
                 (rec count-method
                    (lambda  ()  (set! n (+ n 1)) n ))
                 (rec report-method)
                    (lambda () n))
                 (rec reset-method
                    (lambda (new-value)  (set! n new-value)   n)))))

>>> (define c4  (make-counter 0)
>>> c4
#(#<PROCEDURE count-method>   #<PROCEDURE report-method>  #<PROCEDURE 

Scheme vectors are accessed using zero-origin addressing, so element 0 of the vector is the procedure corresponding to the count operation.

>>> (vector-ref c4 0)
#<PROCEDURE count-method>

The count operation takes no arguments. In Scheme we call a procedure of no arguments by enclosing it in parentheses:

>>> ((vector-ref c4 0))
>>> ((vector-ref c4 0)
>>> ((vector-ref c4 0)
>>> ((vector-ref c4 0)

Element 2 of the vector corresponds to the reset operation. It takes one argument:

>>> (vector-ref c4 2)
#<PROCEDURE reset-method>
>>> ((vector-ref c4 2) -100)
>>> ((vector-ref c4 0))
>>> ((vector-ref c4 0))

The counter examples have shown that two features of object-oriented programming -- local state and message passing -- are provided for in Scheme without any special machinery, simply because procedures are first class citizens. Two other features of Smalltalk, namely inheritance and dynamic redefinition, can also be programmed in Scheme, but they are complicated enough to justify special machinery as in Smalltalk.

Numbers and procedures are not the only first class citizens of Scheme. Every Scheme value is first class. This is the ideal. Very few current programming languages achieve it.


Harold Abelson and Gerald Jay Sussman with Julie Sussman, Structure and Interpretation of Computer Programs, MIT Press and McGraw-Hill, 1985.

Abelson et al, "The Revised Revised Report on Scheme; or An Uncommon Lisp", MIT Artificial Intelligence Memo 848, August 1985.

Joseph Storey, Denstational Semantics; MIT Press, 1977.

Guy Steele Jr., Common Lisp, Digital Press, 1984.


A couple of months ago we reported the capacity of cons cells the MacScheme environment can produce. Those numbers were slightly incorrect. Using a 512K Mac one may get 10,000 cons cells. With a 2 megabyte mac one can get over 100,000 cons cells.

MacScheme comes with a small spiral bound book containing the reference manual, while it is not intended to be a major reference for the language, it is very informative. Macsheme contains a debugger which allows the user to gain specific access to the "heap". When a procedure cannot be evaluated due to a mistake or typo, MacScheme goes to the debugger automatically. The user then analyzes the code using the debugger commands which are displayed after the debugger is entered. The user can turn this feature off if they want to. Parenthesis matching is done when entering the right side parenthesis. The corresponding left side blinks in inverted video once. There are lots of other nifty features in the editor and compiler and we hope to discuss them more in the near future.

MacScheme, we are told, has already been chosen as the standard Macintosh Lisp environment for the Computer Science departments of at least two major universities. The users at these schools have logged thousands of hours of use with only one (!) intentional bomb.

It is very ironic situation. MacScheme has what ExperLisp seems to be lacking, a somewhat object oriented environment, usable debugging facilities, a comparatively easy to get used to style of operation and best of all, extreme reliability. While ExperLisp allows the programmer to build windows, bunny and Quickdraw graphics, menu bars and all the other Mac (or Lisp Machine) like stuff into the programmers' product. These two environments will more than likely gravitate toward each other until they are complete. [When will one product combine both features?? -Ed. ]

ExperTelligence has been telling us since the release of ExperLisp that a developer's version will be released shortly (frankly, they should finish the current version first!!!). So far that hasn't happened and there seems to be no indication that it will. ExperTelligence seems more concerned with adding gimicks like Macintalk to ExperLisp. In the mean time Semantic Microsystems has told us that an add-on to MacScheme which will give access to Quickdraw is under developement. For the moment, I'd bet on MacScheme. [What about the rest of the toolbox? -Ed.]

In coming months... ExperOps5, NEXPERT (!) and more on Common Lisp procedures.

From Volume 2 Number 6:


A couple of typos from the last column on MacScheme were identified by the author. The first was in one of the code samples using sort. The following is the correct code:

>>> (sort '("Even" "mathematicians" "are" "accustomed" "to" "treating" 
"functions" "as" "underprivileged" "objects")
 (lambda (x y)
 (or (<? (string-length x) (string-length y))
 (string<? x y))))

("as ...)

The second error was in the code defining the procedure make-counter. The code should have included the argument n as follows:

(define make-counter
 (lambda (n)
 (lambda ()
 (set! n (+ n 1))

There was also an error in the third reference. The reference was supposed to read Joseph Stoy's Denotational Semantics of Programming Languages. Our thanks to Will Clinger of the Tektronix Computer Research Laboratory (and also of Semantic Microsystems).


Community Search:
MacTech Search:

Software Updates via MacUpdate

Posterino 3.3.5 - Create posters, collag...
Posterino offers enhanced customization and flexibility including a variety of new, stylish templates featuring grids of identical or odd-sized image boxes. You can customize the size and shape of... Read more
Kodi 17.1. - Powerful media center tool...
Kodi (was XBMC) is an award-winning free and open-source (GPL) software media player and entertainment hub that can be installed on Linux, OS X, Windows, iOS, and Android, featuring a 10-foot user... Read more
Kodi 17.1. - Powerful media center tool...
Kodi (was XBMC) is an award-winning free and open-source (GPL) software media player and entertainment hub that can be installed on Linux, OS X, Windows, iOS, and Android, featuring a 10-foot user... Read more
Bookends 12.8 - Reference management and...
Bookends is a full-featured bibliography/reference and information-management system for students and professionals. Bookends uses the cloud to sync reference libraries on all the Macs you use.... Read more
Apple iTunes 12.6 - Play Apple Music and...
Apple iTunes lets you organize and stream Apple Music, download and watch video and listen to Podcasts. It can automatically download new music, app, and book purchases across all your devices and... Read more
Default Folder X 5.1.4 - Enhances Open a...
Default Folder X attaches a toolbar to the right side of the Open and Save dialogs in any OS X-native application. The toolbar gives you fast access to various folders and commands. You just click on... Read more
Amazon Chime 4.1.5587 - Amazon-based com...
Amazon Chime is a communications service that transforms online meetings with a secure, easy-to-use application that you can trust. Amazon Chime works seamlessly across your devices so that you can... Read more
CrossOver 16.2 - Run Windows apps on you...
CrossOver can get your Windows productivity applications and PC games up and running on your Mac quickly and easily. CrossOver runs the Windows software that you need on Mac at home, in the office,... Read more
Adobe Creative Cloud - Access...
Adobe Creative Cloud costs $19.99/month for a single app, or $49.99/month for the entire suite. Introducing Adobe Creative Cloud desktop applications, including Adobe Photoshop CC and Illustrator CC... Read more
MegaSeg 6.0.2 - Professional DJ and radi...
MegaSeg is a complete solution for pro audio/video DJ mixing, radio automation, and music scheduling with rock-solid performance and an easy-to-use design. Mix with visual waveforms and Magic... Read more

The best deals on the App Store this wee...
Deals, deals, deals. We're all about a good bargain here on 148Apps, and luckily this was another fine week in App Store discounts. There's a big board game sale happening right now, and a few fine indies are still discounted through the weekend.... | Read more »
The best new games we played this week
It's been quite the week, but now that all of that business is out of the way, it's time to hunker down with some of the excellent games that were released over the past few days. There's a fair few to help you relax in your down time or if you're... | Read more »
Orphan Black: The Game (Games)
Orphan Black: The Game 1.0 Device: iOS Universal Category: Games Price: $4.99, Version: 1.0 (iTunes) Description: Dive into a dark and twisted puzzle-adventure that retells the pivotal events of Orphan Black. | Read more »
The Elder Scrolls: Legends is now availa...
| Read more »
Ticket to Earth beginner's guide: H...
Robot Circus launched Ticket to Earth as part of the App Store's indie games event last week. If you're not quite digging the space operatics Mass Effect: Andromeda is serving up, you'll be pleased to know that there's a surprising alternative on... | Read more »
Leap to victory in Nexx Studios new plat...
You’re always a hop, skip, and a jump away from a fiery death in Temple Jump, a new platformer-cum-endless runner from Nexx Studio. It’s out now on both iOS and Android if you’re an adventurer seeking treasure in a crumbling, pixel-laden temple. | Read more »
Failbetter Games details changes coming...
Sunless Sea, Failbetter Games' dark and gloomy sea explorer, sets sail for the iPad tomorrow. Ahead of the game's launch, Failbetter took to Twitter to discuss what will be different in the mobile version of the game. Many of the changes make... | Read more »
Splish, splash! The Pokémon GO Water Fes...
Niantic is back with a new festival for dedicated Pokémon GO collectors. The Water Festival officially kicks off today at 1 P.M. PDT and runs through March 29. Magikarp, Squirtle, Totodile, and their assorted evolved forms will be appearing at... | Read more »
Death Road to Canada (Games)
Death Road to Canada 1.0 Device: iOS Universal Category: Games Price: $7.99, Version: 1.0 (iTunes) Description: Get it now at the low launch price! Price will go up a dollar every major update. Update news at the bottom of this... | Read more »
Bean's Quest Beginner's Guide:...
Bean's Quest is a new take on both the classic platformer and the endless runner, and it's free on the App Store for the time being. Instead of running constantly, you can't stop jumping. That adds a surprising new level of challenge to the game... | Read more »

Price Scanner via

Updated iPad Price Trackers
Scan our Apple iPad (and iPod touch) Price Trackers for the latest information on sales, bundles, and availability on systems from Apple’s authorized internet/catalog resellers. We update the... Read more
12-inch 32GB Space Gray iPad Pro on sale for...
B&H Photo has 12″ Space Gray 32GB WiFi Apple iPad Pros on sale for $50 off MSRP including free shipping. B&H charges sales tax in NY only: - 12″ Space Gray 32GB WiFi iPad Pro: $749 $50 off... Read more
2.6GHz Mac mini on sale for $559, $140 off MS...
Guitar Center has the 2.6GHz Mac mini (MGEN2LL/A) on sale for $559 including free shipping. Their price is $140 off MSRP, and it’s the lowest price available for this model. Read more
SSD Speeder RAM Disk SSD Life Extender App Fo...
Fehraltorf, Switzerland based B-Eng has announced they are making their SSD Speeder app for macOS publicly available for purchase on their website. SSD Speeder is a RAM disk utility that prevents... Read more
iPhone Scores Highest Overall in Smartphone D...
Customer satisfaction is much higher among smartphone owners who use their device to operate other connected home services such as smart thermostats and smart appliances, according to the J.D. Power... Read more
Swipe CRM Free Photo-Centric CRM Sales DEal C...
Swipe CRM LLC has introduced Swipe CRM: Visual Sales 1.0 for iPad, an app for creating, managing, and sharing visually stunning sales deals. Swipe CRM is targeted to small-and-medium creative... Read more
13-inch 2.0GHz Apple MacBook Pros on sale for...
B&H has the non-Touch Bar 13″ 2.0GHz MacBook Pros in stock today and on sale for $150 off MSRP. Shipping is free, and B&H charges NY sales tax only: - 13″ 2.0GHz MacBook Pro Space Gray (... Read more
15-inch Touch Bar MacBook Pros on sale for up...
B&H Photo has the new 2016 15″ Apple Touch Bar MacBook Pros in stock today and on sale for up to $150 off MSRP. Shipping is free, and B&H charges NY sales tax only: - 15″ 2.7GHz Touch Bar... Read more
Apple’s iPhone 6s Tops Best-Selling Smartphon...
In terms of shipments, the iPhone 6s from Apple bested all competitors for sales in 2016, according to new analysis from IHS Markit, a world leader in critical information, analytics and solutions.... Read more
Logitech Rugged Combo Protective iPad Case an...
Logitech has announced its Logitech Rugged Combo, Logitech Rugged Case, and Logitech Add-on Keyboard for Rugged Case for Apple’s new, more affordable $329 9.7-inch iPad, a complete solution designed... Read more

Jobs Board

*Apple* Mobile Master - Best Buy (United Sta...
**492889BR** **Job Title:** Apple Mobile Master **Location Number:** 000886-Norwalk-Store **Job Description:** **What does a Best Buy Apple Mobile Master do?** Read more
*Apple* Mobile Master - Best Buy (United Sta...
**492472BR** **Job Title:** Apple Mobile Master **Location Number:** 000470-Seattle-Store **Job Description:** **What does a Best Buy Apple Mobile Master do?** Read more
*Apple* Mobile Master - Best Buy (United Sta...
**492562BR** **Job Title:** Apple Mobile Master **Location Number:** 000853-Jackson-Store **Job Description:** **What does a Best Buy Apple Mobile Master do?** Read more
*Apple* Retail - Multiple Positions - Apple,...
Job Description: Sales Specialist - Retail Customer Service and Sales Transform Apple Store visitors into loyal Apple customers. When customers enter the store, Read more
Fulltime aan de slag als shopmanager in een h...
Ben jij helemaal gek van Apple -producten en vind je het helemaal super om fulltime shopmanager te zijn in een jonge en hippe elektronicazaak? Wil jij werken in Read more
All contents are Copyright 1984-2011 by Xplain Corporation. All rights reserved. Theme designed by Icreon.