Logo is a computer programming language first developed in the late 1960s, by a team at BBN led by Seymour Papert, Wallace Feurzeig, and Daniel Bobrow. Logo was originally about manipulating words and sentences, hence its name, derived from the Greek word "logos" meaning "word". Papert, a professor at MIT and the author of Mindstorms: Children, Computers, and Powerful Ideas, later added the turtle graphics for which Logo is now most famous.
Papert used LISP but changed the syntax so it is much easier to read. One could say that Logo is Lisp without the parentheses. Today, it is known principally for its "Turtle Graphics" but it has significant list handling facilities, file handling and I/O facilities and can be used to teach most computer science concepts, as Brian Harvey does in his "Computer Science Logo Style" trilogy. Equally it can be used to prepare microworlds for students to investigate,
There are over 130 implementations of Logo, each of which has its own strengths. A popular Linux implementation is UCBLogo. MSWLogo, its freeware Windows derivative, is commonly used in schools in the United Kingdom. Comenius Logo is available in Dutch, German, Czech etc. and is worth considering.
A modern derivative of Logo is a variation that allows thousands of "turtles", each moving independently. There are two popular implementations: MIT StarLogo and NetLogo. These derivatives allow for the exploration of emergent phenomena and come with many experiments in social studies, biology, physics, and many other sciences. Although the focus is on the interactions of a large number of independent agents, these variations still capture the original flavor of Logo.
The idea is that a turtle with a pen strapped to it can be instructed to do simple things like move forward 100 spaces or turn around. From these building blocks you can build more complex shapes like squares, triangles, circles--using these to draw houses or sail boats.
The turtle moves with commands that are relative to its own position, "LEFT 90" meant rotate left by 90 degrees. A student could understand (and predict and reason about) the turtle's motion by imagining what she would do if she were the turtle. Papert called this "body syntonic" reasoning.
The idea of turtle graphics is also useful for example in Lindenmayer system for generating fractals.
The following are examples of Turtle code. While seemingly very simple, titles can be given to groups of instructions, essentially creating libraries of more complex commands. In practice short forms are used "LEFT 90" is written "LT 90"
The turtle's pen could be lifted and lowered; drawing a dotted line was rudimentary. In this example we'll use the short form for
You could also use loop (repeat) commands. This would draw the exact same box in the first example:
If you are using the editor you must exit from it, and the new word is saved into the availabe vocabulary, but will be lost when LOGO is exited.
Now any time
CS CHAIR WAIT 200 ERASECHAIR
If you do need help. Type
Logo is an interpreted language. It is not case dependant , but retains the case used for formatting. It is written in lines . It is a compromise between a sequential programming language with block structures, and a functional programming language. There is no 'standard' LOGO, but UCBLogo is highly regarded. It is a teaching language but its list handling facilities make it remarkably useful for producing useful scripts.
Each line is made up of 'function calls'. There are two types
A special subset of operations called predicates, that just output the word
spiral 10
There are three datatypes in UCBLogo,
There is no strong typing. The interpreter detects the datatype by context.
There are two important symbols
Assignment in Pascal
Indirection (within a procedure) is possible with the form
Discussing lists comes as a surprise to a Pascal programmer, who has managed quite well without them, however this opens many new possibilities. Arrays are also provided for the timid.
show firstfive [1 2 3 4 5 6 7 8 9 ]
[1 2 3 4 5]
foreach firstfive [1 2 3 4 5 6 7 8 9 ] show 10 - ?
[9 8 7 6 5]
to firstfive :list
output firstn 5 :list
end
The standard Pascal controls are available, there is selection
The Pascal programmer will be surprised by a series of list based control structures. The basic idea is that you have two lists
RUN [ list of commands ] ;run a list of commands ( or programs ) from in a program.
The standard commands are
MSWLogo supports multiple turtles, and 3D Graphics. MSWLogo allows input from COM ports and LPT ports and also 'hardware' ports. MSWLogo also supports a windows interface thus I/O is available through this GUI- and keyboard and mouse events can trigger interrupts.
Logo is slow, it is not suitable for processsing vast amount of data- it is a learning language. If speed is not an issue anymore it is educationally more useful to watch a program cranking through a problem. The visual output allows this. It assists students understanding how the computer is working sequentially through the instructions.
Logo scores on graphics, and MSWLogo allows the use the Windows dll.. A crucial point for learning Pascal is that students must master 'pointers' before they can do any useful data structure theory. This excludes all except the most committed. In Logo, Lists, stacks and queues are trivial. Trees are more fun. All are recursive in nature.
UCBLogo and MSWLogo include a rudimentary Pascal intrepreter written in Logo as one of the examples.
Implementations of Logo
Logo programming
Turtle programming
Key words are usual written in UPPER CASE for beginners, but more advanced texts use lower case.Example 1: a square
FORWARD 100
LEFT 90
FORWARD 100
LEFT 90
FORWARD 100
LEFT 90
FORWARD 100
This would draw a square with sides 100 units long ( but the turtle still has to turn LT 90 to be in the starting position).Example 2: a triangle
The commands may be written on one line, or more
FORWARD 100 RIGHT 120
FORWARD 100 RIGHT 120 FORWARD 100
Would draw a triangle.Example 3: dotted line
FORWARD, which is FD. When teaching this say "FD space 10" is saves alot of frustration. Anything written after the ; (semicolon) is ignored so can be used as a comment.FD 10 ;(drawing a line and moving)
PENUP ;(now we've lifted the pen so it won't draw anything even if we do move)
FD 10 ;(not drawing but moving)
PENDOWN ;(now we've lowered the pen so it draws a line wherever the turtle moves)
FD 10 ;(drawing a line and moving)
PENUP
FD 10 ;(etc...)
PENDOWN
FD 10
Example 4: loops
Which would execute the command "
REPEAT 4 [FD 100 RIGHT 90]
FD 100 RIGHT 90" four times.
A simplistic circle consists of 360 individual rotations with a step forward, so "REPEAT 360 [FD 1 RIGHT 1]" would have the expected result.Example 5: new words
You can teach the turtle new words, i.e. groups of instructions,or procedures. These can to be done from Logo prompt or an Editor, that is invoked by EDALL in many logo dialects.
'TO CHAIR' must be on a separate line. 'END' must be on a separate line. Anything written after a ';' is ignored- so can be used as a comment.EDALL
TO CHAIR
REPEAT 4 [FD 100 RT 90] FD 200
END
CHAIR is entered, "REPEAT 4 [FD 100 LEFT 90] FD 30" will be executed. You could compound these by REPEAT 4 [CHAIR] if you wanted.Example 6: erasing (in the UCBLogo dialect)
The turtle can erase a line. PENERASE PE. You must then replace the 'pen' with the command PENPAINT PPT.
There were two new instructions- which are easier to use than explain. Thats the spirit of LOGO. EDALL ;(to enter the editor mode, then the actual procedure)
TO ERASECHAIR
PE
REPEAT 4 [FD 100 RT 90] FD 200
PPT
END
Example 7: parameters: giving the word changeable information
Logo can pass extra information to its words, and return information. We must tell the word to expect something and give it a name. Notice the use of the colon. We are passing 'by value' and the colon is pronounced as 'the value of'. When the procedure is run with a command like CHAIR 200, the size takes the value 200 so we go 'FD the value of 200'.
Try
EDALL (to enter the editor mode, then the actual procedure)
TO CHAIR :thesize
REPEAT 4 [FD :thesize RT 90] FD :thesize FD :thesize
END
CS REPEAT 9 [CHAIR 50 RT 20 CHAIR 100 WAIT 50 RT 20]
HELP, or HELP "HOME ( note the single quote mark.)The language
Functions and procedures
A command is similar to a Pascal procedure, and a operation is similar to a Pascal function."true or "false, these are conventionally written with a final ‘p’- like emptyp, wordp, listp.
Mathematics in Logo uses prefix notation, like: sum :x :y, product :x :y, difference :x :y, quotient :x :y. Infix is also available.help "keyword ;(will bring up a full description of the expression) .
A command can call itself, this is called recursionExample 8: A spiral drawn using recursion
to spiral :size
if :size > 30 [stop] ; a condition stop
fd :size rt 15 ; many lines of action
spiral :size *1.02 ; the tailend recursive call
end
Data
A number is a special case of word.
This is an extremely useful symbol that keeps reminding students that a variable is really some 'place' in memory.:- this means 'the contents of'
A number is a special case of self evaluation- it really could be written with a quote 2 is really "2x:= y +3 becomes in Logo
make "x sum :y 3
or
make "x sum :y "3
make takes 2 parameters, the second of which here is sum :y "3. Now sum takes two 'parameters' and is a 'operation', thus the calculation is possible. "3 evaluates to 3, and :y takes the contents of the thing called y, these are summed giving a number. The effect of make is to place the result into the first parameter.
An alternative way of looking at this, maybe, is that the second parameter is 'passed by value' while the first is 'passed by address.' make :x :x + 1.Scoping
Variables don’t have to be declared before use. Their scope is then global.
A variable may be declared local, thenits scope is limited to that procedure and its subprocedures. This is dynamic scoping. Calling a 'procedure' with 'inputs', creates 'local variables' which hold the contents of the parameters.Lists
Example 9: using list primitives to extract the first five members of a list
a: One way would be to use iteration.
to firstfive :alist
ifelse lessp count :alist 5 [ op :alist ][
make "olist []
repeat 5 [ make "olist lput first :alist :olist make "alist bf :alist ] output :olist ]
end
b: Another, more elegant way would be to firstn :num :list
if :num = 0 [output []]
output fput (first :list) (firstn :num-1 butfirst :list)
end
This method uses recursion, and is an example of a 'functional' rather than a 'sequential' programming approach.Control structure commands
* ifelse test [ do_if_true list ] [do_if_false list]
There are iteration commands * while condition [instruction list]
* until condition [instruction list ]
* repeat number [instruction list]
Recursion is Logo prefered processing paradigm.Template iteration
OPERATION [ a list of commands ] [ many data items ]
each of the commands is applied in turn to each of the data items. There are several of these template commands with names like MAP, APPLY, FILTER, FOREACH, REDUCE and CASCADE. They repesent four flavours of template iteration, known as explicit-slot, named-procedure, named-slot (or Lambda) and procedure-text.show map [? * ? ] [ 5 6 7 ]
[25 36 49 ]
show filter [ (count ? ) > 4 ] [ the quick brown fox jumps over the lazy dog ]
[quick brown jumps]
show foreach [1 2 3 4 5] [ ? * 10 ]
[10 20 30 40 50]
Property Lists
A property list is a special list where the odd number items are property name, and the even are property values. There are three commands to process property list.
pprop :listname :name :value ;to add a new pair to the list
remprop :listname :name :value ;to remove a pair to the list
show gprop :listname :name ;to get the matching value from the list
I/O Commands
Text may be written to the command window (output stream) using print, show and to the graphics window using label readlist readword readchar with the normal input stream being the keyboard. In Unix tradition the input stream can be changed, so input can come from a disk file. Similarly, output can be redirected. The technique will be familiar to Pascal Programmers- using a sequenceopenread [filename]
setread[filename]
setreadpos nn
readchar
setread[]
close [filename].
There are equivalent commands to change the output stream, openwrite, openappend, setwrite, setwritepos nn. dribble [filename]
Creates a transcript of everything that is typed in or outputted to the command window.
nodribble
This turns it off.Graphics
Turtle graphics is a powerful method of introducing thinking but LOGO also has a few useful Cartesian commands
home ;returns the turtle to (0,0)
setx xx
sety yy ; sends the turtle, still drawing to (xx,yy)
seth nn ; sets the turtle on a heading or compass bearing of (nn)
Example 10: calculating and drawing a sundial for a given latitude
This is a typical garden dial. The graphic can be printed and transfered to wood or brass to make an accurate garden timepiece.
to dial
cs show [Type in your latitude as a whole number]
make "latitude readword ;uses keyboad input
for [i 0 6 1][
make "ang arctan product sin :latitude tan product :i 15 ;the calculation
rt :ang fd 200 bk 200 lt :ang ;draw the morning line
lt :ang fd 200 bk 200 rt :ang ;use symmetry to draw the afternoon line
]
pu setx -300 sety -300 seth 90 pd ;send the turtle to the bottom
fd 300 seth 270 rt 90 - :latitude fd 300 ;draw the style or gnomon
pu home pd ;tidy it up
end
A sundial plate must be calculated for its latitude using the formula
x= arctan( sin(latitude)*tan(HourDiff * 15 ) )
The Gnomon Angle = 90 - latitude.
This dial is set for 38N, the latitude of Berkeley, California- the home of UCBLogo. A small correction should be made for Longitude. MSWLogo extensions
Comparisons between Logo and Pascal
Bibliography
External links
