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Introduction. Logo is a computer programming language which was designed to be both simple to use and extremely powerful. It was designed by a group of computer scientists at MIT and at Bolt, Beranek, and Newman. Its structure is based largely on the LISP language, which is widely used in Artificial Intelligence research, but the notation has been changed to make Logo far easier for a beginner than LISP. The power of Logo comes primarily from the idea of the procedure. A procedure is simply something the computer "knows" how to do; some pro- cedures are built into Logo itself (these are called primitive procedures), while others are defined by the programmer in terms of these simple pro- cedures. Defined procedures can be used as part of the definition of other procedures, so that a complicated program can be built in "layers" of com- plexity. This layered structure is analogous to the description of a com- plex machine in terms of building blocks: an automobile is made of a chassis, a drive train, an electrical system, and so on. The drive train contains an engine, a transmission, a clutch, an axle, and so on. The transmission contains a housing, gears, and levers. A lever may include connecting joints at the ends and at a pivot point. Eventually the description of the automobile reaches the level of bolts and washers; these correspond to the primitive procedures in Logo. Starting_Logo. Start the Logo interpreter from WorkBench or from the CLI. When Logo is running it will print a question mark (?) at the be- ginning of a line to indicate that it is ready for you to type in a Logo instruction. The instruction may print something on the terminal, or draw a line on a graphics display screen. Then another question mark is typed and you may give another instruction. (If Logo prints a "greater than" sign (>) instead of a question mark, it is in list input mode, which will be described later. Type your system quit character (control-G) to return to normal mode.) Syntax. Unlike most computer languages, Logo has an almost entirely uniform syntax. That is, all of the different commands Logo understands are represented using the same notation: the name of a procedure is fol- lowed by its inputs, which may be constants (like numbers) or else may be the results of using other procedures. Here is a simple example: print "hello In this Logo instruction, the primitive procedure print is used with a con- stant input, the word hello. The quotation mark indicates that hello is being used to represent the word itself; without the quotation mark it would have been interpreted as the name of a procedure, just as print is the name of a procedure. In Logo, the print procedure requires at least one input, which is the thing to print. The input can be a word, as in this example, or a list, which will be explained later. (A number is a special case of a word, and a sentence is a special case of a list.) Here is another example: print first "hello Here, the primitive procedure first is being used, also. It has one input, a word, and has an output which is the first letter of the word. The out- put from first is used as the input to print, so what is printed is the letter h rather than the word hello as in the earlier example. Don't confuse the output from a procedure with what is printed by the print command. In Logo, the word "output" is not used to refer to what is printed by a program, just as the word "input" does not mean something you type into the program. Instead, these words refer to objects (words or lists) which are given to a procedure (inputs) or produced by a procedure (outputs). A particular procedure will have a fixed number (possibly zero) of required inputs, and may have optional inputs. It may or may not pro- duce an output. A procedure with an output (like first) is called an oper- ation; one without an output (like print) is called a command. Some operations only have two possible outputs: the word TRUE and the word FALSE. Such a procedure is called a predicate. Predicates are used to allow a program to carry out some instruction only if a particular con- dition is met. By convention, predicates generally have names ending with the letter "p". Multiple_inputs_to_operations. Several Logo primitive procedures are operations with two inputs. The arithmetic operations, like sum, are exam- ples of this. A special extension to Logo syntax allows such an operation to have more than two inputs by enclosing the operation and its inputs in parentheses: ( sum 2 5 13 8.5 ) Multi-instruction_lines. It is possible to put more than one instruc- tion on the same line when you are typing to Logo. For example, print "hello print "goodbye Later in this manual, the phrase "instruction line" will mean one or more instructions on a line. Multi-line_instructions. It is possible to continue an instruction on a second line. At the end of the first line, close with a tilde (~) to let Logo know you want to continue: repeat 5 [ print ~ "Greetings! ] Here, Greetings! will be printed five times. Comments. It is possible to include comments in an instruction line which are meant for human readers of your program (including yourself, next week), and which are not Logo instructions. To do this, begin the comment with an semi-colon ";". Everything after the semi-colon on the line will be ignored by Logo. For example: print [ Hi, there. ] ; A friendly greeting. However, the semi-colon does not begin a comment if it is part of a word or list (see below). You must type a space before the semi-colon (if it is not at the beginning of a line) and after it, as in the example above, to make sure it will be interpreted as the beginning of a comment. Words. Every computer language deals with particular kinds of ob- jects. Most languages, like FORTRAN or BASIC or Pascal, are best at deal- ing with numbers. Logo is a list processing language, which is at its best with more complicated data structures. The two main categories of object are the word and the list. A word is a string of characters. A character is a letter, digit, space, or punctuation mark. A word can be any length, including zero. The way to indicate a word as part of a Logo program is to use the quotation mark (") before the word. The word begins with the character after the quotation mark and continues until a space, or the end of the line occurs. A quotation mark immediately followed by a space or RETURN indicates the empty word, which is a word of length zero. Please notice that, unlike most programming languages, Logo does not use quotation marks in pairs to delimit strings of characters. The follow- ing instruction is incorrect: print "aardvark" It will print `aardvark"'; not `aardvark'. In order to include a space in a word, you must precede it with a backslash (\). Do not confuse backslash with the regular slash (/) char- acter. For example, this instruction: print "Hello\ there will print `Hello there' as its result. To include a backslash in a word, precede it with another backslash (\\). Numbers. A number is a special case of a word, in which the charac- ters are all digits. (That definition isn't quite complete, and will be expanded in the next paragraph.) A number need not be preceded with a quo- tation mark. (This rule is possible because normally Logo interprets words without quotation marks as the names of procedures, but there are no pro- cedures whose names are all digits.) Actually, numbers may be written in scientific notation. That is, they can include signs, decimal points, and a power of 10 by which the number is multiplied. This exponent is indicated by the letter e followed by the integer power of 10. The following numbers have the same value: 1000 "1000 1000.00 1e3 10.0E+2 "+1.0e3 10000E-1 A number which contains only digits (no decimal point or exponent) is called an integer. Since a number is a word, the usual character-manipulating procedures may be applied to it. For example, print first 1024 prints the digit 1 which is the first character of the number. In addi- tion, there are arithmetic procedures which apply specifically to numbers: print sum 3 2 prints the number 5. These procedures will be listed later. Lists. A word can be thought of as a list of characters; for example, the word hello is a list of five letters. In Logo it is possible to mani- pulate not only lists of characters but also lists of words, lists of lists of words, and so on. This is a very powerful capability which allows very complicated data structures to be manipulated easily. To indicate a list in a program, you put square brackets ([ and ]) around the list, and separate the list elements with spaces. For example: print [ This is a list of seven words. ] A list all of whose elements are words is called a sentence. Here is an example of a list which is not a sentence: print [ [ This is a list ] [ of two sentences. ] ] Within a bracketed list, square brackets delimit sub-lists (lists which are elements of the main list). The quotation mark, parentheses, and braces are not considered special within a bracketed list, unlike the rules for quoted words. A list may extend over more than one line; that is, if you have typed an open square bracket ([) and have not yet typed the match- ing close square bracket, the Logo instruction is not ended by typing the RETURN key. Variables. A variable is an entity which has a name, which is a word, and a thing (also called a value), which can be any Logo object. Variables are used to "remember" a computed object for repeated or delayed use in a program. In Logo, the most common way that a variable acquires a value is that it is associated with an input to a user-written procedure. In the following example, don't worry about the details of the format of the pro- cedure, which will be explained later: to pff :in.sentence print first first :in.sentence end This is the definition of a command with one input. The name of the com- mand is pff. It has one input following the procedure name (For more about multiple and optional inputs, check "usermanual.doc".) The variable whose name is in.sentence is associated with the first (and only, in this case) input to pff. In the line starting with the word print, the notation :in.sentence means "the value of the variable whose name is in.sentence". (To refer to the name itself, quote it as you would any word.) If this procedure is used in a Logo instruction like this: pff [ This is the poop. ] then the variable in-sentence has the value [ This is the poop. ]. It is also possible to assign a value to a variable by an explicit Logo instruction. There is a primitive procedure to do this: make - Command, two inputs. The first input is the name of a variable (that is, it must be a word); the second is any Logo object. The effect of the command is to assign the second input as the value of the variable named by the first input. Ifyou are accustomed to programming in a non-procedural language like BASIC, you should strenuously avoid the temptation to overuse make; expli- cit assignment is almost always the wrong thing to do in Logo. Total abstention is the best policy for a Logo beginner. In Logo, variables are dynamically scoped. That means that a variable can "belong to" a particular procedure; such a variable can be used by that procedure and by any procedure which is used by an instruction within the procedure, but is not available to the procedure which invoked the owning procedure. In other words, such a local variable comes into being when the owning procedure starts running, and disappears when that procedure is fin- ished. It is possible for a procedure with a local variable to use another procedure with a local variable of the same name. In that case, the vari- able belonging to the "inner" procedure is the one which is associated with the name as long as it exists; when the inner procedure is finished, the "hidden" variable belonging to the outer procedure is again available. A variable which is associated with inputs to a procedure is local to that procedure. Other variables are global: they are "permanent" and do not disappear when the procedure in which they get their values finish. See "userman.doc" for details concerning inputs and local variables. The virtue of local variables is that they make procedures more inde- pendent of one another than they would be if global variables were used. In other words, if you use local variables consistently, then nothing that happens in one procedure will change the values of variables used in another procedure. This makes it very much easier to find program errors. Primitive_procedures_to_define_user_procedures. Procedures can be typed into the Logo interpreter at the question mark prompt, or loaded in from a file. In either case, the make command is used to construct the procedure definitions. to This command accepts the name of a procedure to be defined, followed by the names of inputs. Then follows one or more lines of the Logo instructions to be performed when the procedure is executed. The procedure ends with the word "end". printout The input to this command is a word or a list of words that are proce- dure or variable names. The command prints out a `to command' def- inition for that name. erase The input to this command is a word or a list of words that are proce- dure or variable names. The command removes the bindings of the input names. Primitive_procedures_to_manipulate_words_and_lists. There are primi- tive procedures to print text objects on the terminal, to read them from the terminal, to combine them into larger objects, to split them into smaller objects, and to determine their size and nature: print The input, which may be a word or a list, is printed on the terminal, followed by a new line character. (That is, the terminal is posi- tioned at the beginning of a new line after printing the object.) If the object is a list, any sub-lists are delimited by square brackets, but the entire object is not delimited by brackets. type The input, which may be a word or a list, is printed on the terminal, without a new line character. (That is, the terminal remains posi- tioned at the end of the object after printing it.) Brackets are used as with the print command. show The input is printed as by the print command, except that if it is a list (as opposed to a word) it is enclosed in square brackets. readlist Logo waits for a line to be typed by the user. The contents of the line are made into a list, as though typed within square brackets as part of a Logo instruction. (The user should not actually type brack- ets around the line, unless s/he desires a list of one element, which is a list itself.) That list is the output from the operation. word The two inputs must be words. The output is a word which is the con- catenation of the two inputs. There is no space or other separation of the two inputs in the output. sentence The two inputs may be words or lists. The output is a list formed from the two inputs in this way: if either input is a word, that word becomes a member of the output list; if either input is a list, the members of that input become members of the output. Here are some ex- amples: first input second input output "hello "test [ hello test ] "goodbye [ cruel world ] [ goodbye cruel world ] [ a b ] [ c d ] [ a b c d ] [ ] "garply [ garply ] If an input is the empty list, as in the last example above, it con- tributes nothing to the output. list The output is a list of two elements, namely, the two inputs. The in- puts may be words or lists. fput The first input may be any Logo object; if the first input is a list, the second must also be a list. The output is an object which is identical to the second input except with the first input at the beginning. lput The first input may be any Logo object; if the first input is a list, the second must also be a list. The output is an object which is identical to the second input except with the first input at the end. first The input may be any non-empty Logo object. If the input is a list, the output is its first member. If the input is a word, the output is a single-letter word, namely the first letter of the input. If the input is empty (a word or list of length zero) an error results. last The input may be any non-empty Logo object. If the input is a list, the output is its last member. If the input is a word, the output is a single-letter word, namely the last letter of the input. If the in- put is empty (a word or list of length zero) an error results. butfirst The input may be any non-empty Logo object. If the input is a list, the output is a list equal to the input list with the first member re- moved. (If the input list has only one member, the output is the emp- ty list, a list of zero members.) If the input is a word, the output is a word equal to the input word with the first letter removed. (If the input is a single-letter word, the output is the empty word.) If the input is empty, an error results. butlast The input may be any non-empty Logo object. If the input is a list, the output is a list equal to the input list with the last member re- moved. (If the input list has only one member, the output is the emp- ty list, a list of zero members.) If the input is a word, the output is a word equal to the input word with the last letter removed. (If the input is a single-letter word, the output is the empty word.) If the input is empty, an error results. count The input may be any Logo object. If the input is a list, the output is a number indicating the number of members in the list. (Note: only top-level members are counted, not members of members. The count of the list [ [ This is ] [ a list ] ] is 2, not 4.) If the input is a word, the output is the number of letters (or other characters) in the word. Remember that in Logo a number is just a particular kind of word, so the output from count can be manipulated like any other Logo word. emptyp The input can be any Logo object. The output is the word true if the input is of length zero (i.e., it is the empty word or the empty list). The output is the word false otherwise. equalp The inputs can be any Logo objects. The output is the word true if the two inputs are identical. That is, they must be of the same type (both words or both lists), they must have the same count, and their members (if lists) or their characters (if words) must be identical. The output is the word false otherwise. wordp The input can be any Logo object. The output is the word true if the input is a word. The output is the word false if the input is a list. memberp If the second input is a word, the first input must be a word (and only the first letter is used), and the output is true if and only if the first input is contained in the second as a character. If the second input is a list, the first input can be any Logo object, and the output is true if and only if the first input is a member of the second input. (Note that this is member, not subset.) item The first input must be a positive integer less than or equal to the count of the second input. If the second input is a word, the output is a word of length one containing the selected character from the word. (Items are numbered from 1, not 0.) If the second input is a list, the output is the selected member of the list. Primitive_procedures_for_turtles_and_graphics. An important part of the Logo environment is a rich set of applications to which the computer can be directed. The most important of these is turtle geometry, a way of describing paths of motion in a plane which is well-suited to computer pro- gramming. forward The input is a number, the distance you would like the turtle to move. The turtle moves in whatever direction it is pointing when you use the command. Negative inputs make the turtle go backwards. back The input is a number, a distance to move, as in the forward command. The difference is that the turtle moves backward, i.e., in the direc- tion exactly opposite to the way it's pointing. Negative inputs make the turtle go forward. left The input is a number, the number of degrees of angle through which the turtle should turn counterclockwise. This command does not change the position of the turtle, but merely its heading (the direction in which it points). Negative inputs make the turtle turn right. right The input is a number; the turtle turns through the specified number of degrees clockwise. Negative inputs make the turtle turn left. pu This command tells the turtle to raise its pen from the paper, so that it does not leave a trace when it moves. The effect is that any for- ward or back commands after this point will not draw a line. The tur- tle starts with its pen down. pd This command tells the turtle to lower its pen, so that later commands will draw lines when the turtle moves. clean It erases everything in the turtle display window, but does not affect the turtle. seth The turtle's heading is set to the input. toward The inputs are the x and y coordinates of a point. The output is a number which is the heading to which the turtle must be set, in order to point towards that point from its current position. Note: this operation does not actually move or turn the turtle. You must use it as the input to seth if that is what you want. heading The output is the turtle's current heading. Primitive_procedures_for_arithmetic. Several procedures are available for arithmetic operations on numbers. In all cases, the inputs to these procedures must be numbers, except as otherwise indicated in the individual descriptions. In general, procedures are used in Logo by typing first the name of the procedure, then its inputs. This is true of arithmetic procedures also, e.g., sum 3 2 quotient 4 2 Logo also supports infix operators, which are placed between the two numbers to be operated upon: 3 + 2 4 / 2 sum, + The output of this procedure is the sum of the two inputs. difference, - The output of this procedure is the difference of the two inputs. product, * The output of this procedure is the product of the two inputs. quotient, / The output of this procedure is the quotient of the two inputs. remainder The output is the remainder of dividing the first input by the second. > The output of this procedure is the word true if the first input is numerically strictly greater than the second input. Otherwise the output is the word false. < The output of this procedure is the word true if the first input is numerically strictly less than the second input. Otherwise the output is the word false. equalp, = The two inputs to this procedure may be any Logo objects. If they are numbers, then the output is the word true if they are numerically equal, false if they are numerically unequal. If either input is not a number, then the output is the same as for the procedure: it is true if the two inputs are identical, false if not. numberp The input may be any Logo object. The output is the word true if the input is a number, false if not. =0 The input must be a number. The output is the word true if the input is numerically equal to zero, false otherwise. random The output is a randomly selected integer between 0 and one less than the input. sqrt The input must be a nonnegative number. The output is its square root. power The inputs must be numbers. If the first is negative, the second must be an integer. The output is the first number raised to the power of the second input. sin The input must be numeric. The output is the sine of the input. cos The input must be numeric. The output is the cosine of the input. atan The input must be numeric. The output is the arctangent of the input. Primitive_procedures_for_conditional_execution. The predicates (like wordp) which we've mentioned above can be used to carry out some command only if a condition is met. The basic command for the purpose is if: if The first input to the if procedure must be either the word true or the word false. Typically, it is the output from a predicate. The second and third inputs are lists containing instruction lines. The second input is executed if the first input is true. The third input is executed if the first input is false: and The two inputs must both be either true or false. The output is true if both inputs are true; otherwise the output is false. or The two inputs must be either true or false. The output is true if at least one of the inputs is true; otherwise the output is false. not The input must be either true or false. The output is true if the in- put is false, and vice versa. Primitive_procedures_for_procedure_exit. A procedure written by a user, in Logo, can be a command or an operation. If it is an operation, you must, in the procedure, say what its output should be. If it is a com- mand, it can simply stop at the end of the procedure, or you can explicitly make it stop before the end. output This command is used in a user procedure which is meant to be an operation. The input to this command becomes the output from the user procedure. Please don't be confused by the fact that the user pro- cedure is an operation, while the output primitive procedure is a com- mand used in that procedure. Example: to nickname :person if equalp :person [ Peter Parker ] [ output "Spiderman ] if equalp :person [ Lamont Cranston ] [ output "Shadow ] output first :person end stop This command is used in user procedures which are meant to be com- mands. It stops the user procedure. (Note that it does not stop all running procedures. If user procedure A runs user procedure B, a stop command in procedure B returns to procedure A, which continues after the point where procedure B was invoked.) toplevel This command stops all running procedures. The user at the terminal is prompted to type another command. This can be used when a user procedure discovers some error condition and wants to abort the entire program, for example. Property_lists. It is possible to associate with any name a list of "properties". A property list contains property names and property values. For example: putprop "bh "firstname "Brian putprop "bh "lastname "Harvey The form of a property list is [ name1 val1 name2 val2 name3 val3 ] Although this data structure could be created using other Logo primitives, special property list primitives are provided because they are faster. The following primitives manipulate property lists. putprop The first input, which must be a word, is a name with which a property list is associated. The second input, which must be a word, is the name of a property. The third input can be any Logo object. It be- comes the value of the specified property of the specified name. getprop Both inputs must be words. The first is a name, and the second is a property name. The output is the value of the indicated property of the indicated object. It is not an error if there is no such proper- ty; the output in that case is the empty list. remprop - Command, two inputs. The inputs must be words, as for gprop. The specified property is re- moved from the specified name. Pausing. When you are debugging a complicated Logo program, it is very helpful to be able to stop in the middle of a procedure, so that you can give interactive commands to examine its inputs and other local vari- ables. This is different from stopping a procedure, which destroys its lo- cal environment. There are two ways a procedure can pause: (1) You can use the interrupt command (found in the Utilities file) in the procedure defin- ition, to make the procedure pause at a particular place you choose in ad- vance; or (2) you can decide to pause a procedure while it is running by using the interrupt menu item in the Utilities menu of the command window. Note that when you type the system "quit" character (control-G) Logo does not pause, but returns to toplevel. All information about the local state of your active procedures is lost. When you are paused, Logo accepts instructions from your terminal as it does at toplevel, but local variables can be examined or modified. To let you know that you are paused, Logo prompts with the characters "-->" instead of just "?" as usual. To get out of a pause, you can give the command toplevel, which stops all pending procedures and returns to interactive top level, or you can give the command 'stop', which will resume the procedure at the point where you paused. interrupt This command is meaningful only within a procedure. It causes a pause. Miscellaneous_primitives. The remaining primitives are one of a kind, or very obscure, or both. bye This command is used to leave Logo. It is the only way out, unless there is a bug somewhere. thing The input must be a word that is a variable or procedure name. The output is the value of the variable. These are equivalent: :foo thing "foo namep The input must be a word. The output is true if that word is the name of a variable which has a value assigned to it, false otherwise. wait The input must be a positive integer. Logo waits that many seconds before continuing. doscommand The input is a list containing a valid CLI command to be executed. run The input must be a list containing Logo instructions. The list is run as if you typed it directly to Logo. The run procedure can be used as an operation, if its input is a Logo expression which produces a value, instead of a complete instruction: print run [ sum 2 3 ] repeat The first input must be a positive number. The second is an instruc- tion list, as for the run command. The list is run repeatedly, the number of times specified by the first input: repeat 5 [ print "hello ]