MiniLogo (based on BYOB) User Manual This miniLogo
Contents
1. The second input is an instructionlist The effect of FOR is to run that instructionlist repeatedly assigning a new value to the control variable the one named by the first member of the forcontrol list each time First the starting value is assigned to the control variable Then the value is compared to the limit value FOR is complete when the sign of current limit is the same as the sign of the step size If no explicit step size is provided the instructionlist is always run at least once An explicit step size can lead to a zero trip FOR e g FOR I 101 Otherwise the instructionlist is run then the step is added to the current value of the control variable and FOR returns to the comparison step for i 2 7 1 5 print i 2 3 9 5 vO oO command Repeatedly evaluates the instructionlist as long as the evaluated tfexpression remains TRUE Evaluates the first input first so the instructionlist is always run at least once The tfexpression must be an expressionlist whose value when evaluated is TRUE or FALSE command Repeatedly evaluates the instructionlist as long as the evaluated tfexpression remains TRUE Evaluates the first input first so the instructionlist may never be run at all The tfexpression must be an expressionlist whose value when evaluated is TRUE or FALSE command Repeatedly evaluates the instructionlist as long as2. AND tfl tf2 tf3 outputs TRUE if all inputs are TRUE otherwise FALSE All inputs must be TRUE or FALSE Comparison is case insensitive regardless of the value of CASEIGNOREDP hat is true or True or TRUE are all the same An input can be a list in which case it is taken as an expression to run that expression must produce a TRUE or FALSE value List expressions are evaluated from left to right as soon as a FALSE value is found the remaining inputs are not examined Example MAKE RESULT AND NOT X 0 1 X gt 5 to avoid the division by zero if the first part is false OR tll CE2 CES asa outputs TRUE if any input is TRUE otherwise FALSE All inputs must be TRUE or FALSE Comparison is case insensitive regardless of the value of CASEIGNOREDP That is true or True or TRUE are all the same An input can be a list in which case it is taken as an expression to run that expression must produce a TRUE or FALSE value List expressions are evaluated from left to right as soon as a TRUE value is found the remaining inputs are not examined Example IF OR X 0 some long computation to avoid the long computation if the first condition is met outputs TRUE if the input is FALSE and vice versa The input can be a list in which case it is taken as an expression to run that expression must produce a TRUE or FALSE value G
3. command Removes the property named propname from the property list named plistname outputs a list whose odd numbered members are the names and whose even numbered members are the values of the properties in the property list named plistname The output is a copy of the actual property list changing properties later will not magically change a list output earlier by PLIST PREDICATES PROCEDUREP name outputs TRUE if the input is the name of a procedure PRIMITIVEP name PRIMITIVE name outputs TRUE if the input is the name of a primitive procedure one built into Logo Note that some of the procedures described in this document are library procedures not primitives DEFINEDP name outputs TRUE if the input is the name of a user defined procedure including a library procedure NAMEP name outputs TRUE if the input is the name of a variable PLISTP name outputs TRUE if the input is the name of a nonempty property list In principle every word is the name of a property list if you haven t put any properties in it PLIST of that name outputs an empty list rather than giving an error message CONTROL STRUCTURES X command or operation Runs the Logo instructions in the input list outputs if the list contains an expression that outputs runs the instructions in the input outputs an empty list if those instructions produce no output or a list whose only member is the ou
4. inputname default value expression When the procedure is invoked if actual inputs are not supplied for these optional inputs the default value expressions are evaluated to set values for the corresponding input names The inputs are processed from left to right so a default value expression can be based on earlier inputs Example EE IN F to proc inlist startvalue first inlist If the procedure is invoked by saying proc a b c then the variable INLIST will have the value A B C and the variable STARTVALUE will have the value A If the procedure is invoked by saying proc a b c x then INLIST will have the value A B C and STARTVALUE will have the value X After all the required and optional input can come a single rest input represented by the following notation inputname This is a rest input rather than an optional input because there is no default value expression There can be at most one rest input When the procedure is invoked the value of this inputname will be a list containing all of the actual inputs provided that were not used for required or optional inputs Example to proc sint PianZ VEGOJ Frins baz ean If this procedure is invoked by saying proc x then IN1 has the value X IN2 has the value FOO IN3 has the value BAZ and IN4 has the value the empty list If it s invoked by saying proc We b Le qd e then IN1 has the value A IN2 h
5. result of evaluating the second template in the previous round If the total number of inputs including the first endtest input is odd then the output from CASCADE is the final value of the first template If the total number of inputs is even then the last input is a template that is evaluated once after th nd test is satisfied to determine the output from CASCADE Fl to fibonacci n output cascade n 1 2 1 1 0 end to piglatin word output cascade vowelp first word bf first sword word ay end CASCADE 2 endtest templ startvall temp2 startval2 library procedure outputs the result of invoking CASCADE with the same inputs The only difference is that the default number of inputs is five instead of three TRANSFER endtest template inbasket library procedure outputs the result of repeated evaluation of the template The template is evaluated once for each member of the list inbasket TRANSFER maintains an outbasket that is initially the empty list After each evaluation of the template the resulting value becomes the new outbasket In the template the symbol IN represents the current member from the inbasket the symbol OUT represents the entire current outbasket Other slot symbols should not be used If the first endtest input is an empty list evaluation continues until all inbasket members have been used If not the first inpu
6. The second input if present must be a single integer that applies to every dimension of the array Ex MDARRAY 3 5 0 outputs a two dimensional array whose members range from 0 0 to 2 4 LISTTOARRAY list outputs an array of the same size as the input list whose members are the members of the input list outputs a list whose members are the members of the input array The first member of the output is the first member of the array regardless of the array s origin if thing2 is a word outputs WORD thingl thing2 If thing2 is a list outputs FPUT thingl thing2 outputs a list whose members are the members of the input list in reverse order GENSYM library procedure outputs a unique word each time it s invoked The words are of the form Gl G2 etc if the input is a word outputs the first character of the word If the input is a list outputs the first member of the list If the input is an array outputs the origin of the array that is the INDEX OF the first member of the array outputs a list containing the FIRST of each member of the input list It is an error if any member of the input list is empty The input itself may be empty in which case the output is also empty This could be written as to firsts 1ist output map first list end but is provided as a primitive in order to speed up the iteration tools MAP MAP SE and FOREACH to transpose matrix if emptyp first matrix
7. op op fput firsts matrix transpose bfs matrix end if the input is a word outputs the last character of the word If the input is a list outputs the last member of the list BF wordorlist if the input is a word outputs a word containing all but the first character of the input If the input is a list outputs a list containing all but the first member of the input BFS list outputs a list containing the BUTFIRST of each member of the input list It is an error if any member of the input list is empty or an array The input itself may be empty in which case the output is also empty This could be written as to butfirsts list output map butfirst list end but is provided as a primitive in order to speed up the iteration tools MAP MAP SE and FOREACH BL wordorlist if the input is a word outputs a word containing all but the last character of the input If the input is a list outputs a list containing all but the last member of the input if the thing is a word outputs the index th character of the word If the thing is a list outputs the index th member of the list If the thing is an array outputs the index th member of the array Index starts at 1 for words and lists the starting index of an array is specified when the array is created outputs the member of the multidimensional array selected by the list of numbers indexlist outputs a randomly chosen member of the input lis
8. an expression whose value is TRUE or FALSE or the word ELSE and whose butfirst is a Logo expression or instruction COND examines the clauses in order If a clause begins with the word ELSE upper or lower case then the butfirst of that clause is evaluated and CASE outputs its value if any Otherwise the first element of the clause is evaluated th resulting value must be TRUE or FALSE If it s TRUE then the butfirst of that clause is evaluated and COND outputs its value if any If the value is FALSE then COND goes on to the next clause If no clause is satisfied COND does nothing Example to evens numbers select even numbers from a list op cond emptyp numbers evenp first numbers assuming EVENP is defined fput first numbers evens butfirst numbers else evens butfirst numbers end EMPLATE BASED ITERATION The procedures in this section are iteration tools based on the idea of a template This is a generalization of an instruction list or an expression list in which slots are provided for the tool to insert varying data Four different forms of template can be used question mark form Example show map 2 3 4 5 4 9 16 25 In this example the MAP tool evaluated the template repeatedly with each of the members of the data list 2 3 4 5 substituted in turn for the question mark
9. are initial assignments for the first 16 colors 0 black 1 blue 2 green 3 cyan 4 red 5 magenta 6 yellow 7 white 8 brown 9 tan 10 forest 11 aqua 12 salmon 13 purple 14 orange 15 grey but other colors can be assigned to numbers by the PALETTE command Alternatively sets the pen color to the given RGB values a list of three nonnegative numbers less than 100 specifying the percent saturation of red green and blue in the desired color sets the thickness of the pen The input is either a single positive integer or a list of two positive integers for horizontal and vertical thickness Some versions pay no attention to the second number but always have a square pen sets the pen s position mode thickness and hardware dependent characteristics according to the information in the input list which should be taken from an earlier invocation of PEN wn ETBG colornumber or rgblist set the screen background color by slot number or RGB values See SETPENCOLOR for details PEN QUERIES PENDOWNP outputs TRUE if the pen is down FALSE if it s up outputs one of the words PAINT ERASE or REVERSE according to the current pen mode outputs a color number a nonnegative integer that is associated with a particular color or a list of RGB values if such a list was used as the most recent input to SETPENCOLOR There are initial assignments for the first 16 colors 0 black 1 blue 2 green 3 cy
10. on subsequent evaluations the slot is filled with the result of the previous evaluation The number of evaluations is determined by the first input This can be either a nonnegative integer in which case the template is evaluated that many times or a predicate expression template in which case it is evaluated with the same slot filler that will be used for the evaluation of the second input repeatedly and the CASCADE evaluation continues as long as the predicate value is FALSE In other words the predicate template indicates the condition for stopping If the template is evaluated zero times the output from CASCADI is the third startvalue input Otherwise the output is the value produced by the last template evaluation Fl CASCADE templates may include the symbol to represent the number of times the template has been evaluated This slot is filled with 1 for the first evaluation 2 for the second and so on show cascade 5 lput 1 2 3 4 5 show cascade vowelp first bf spring ing show cascade 5 1 120 7 Several cascaded results can be computed in parallel by providing additional template startvalue pairs as inputs to CASCADE In this case all templates including th ndtest template if used are multi slot with the number of slots equal to the number of pairs of inputs In each round of evaluations 2 for example represents the
11. template the symbol represents the position in the data input of the member currently being used as the slot filler That is if the data input is A B C D E and the template is being evaluated with replaced by B then would be replaced by 2 outputs the result of applying the template to accumulate the members of the data input The template must be a two slot function Typically it is an associative function name like SUM If the data input has only one constituent member in a list or character in a word the output is that consituent Otherwise the template is first applied with 1 filled with the next to last consitient and 2 with the last constituent Then if there are more constituents the template is applied with 1 filled with the next constituent to the left and 2 with the result from the previous evaluation This process continues until all constituents have been used The data input may not be empty Note If the template is like SUM the name of a procedure that is capable of accepting arbitrarily many inputs it is more efficient to use APPLY instead of REDUCE The latter is good for associative procedures that have been written to accept exactly two inputs to max a b output ifelse a gt b a b end print reduce max Alternatively REDUCE can be used to write MAX as a procedure that accepts any number of inputs as SUM does to max inputs 2 if emptyp inputs
12. the evaluated tfexpression remains FALSE Evaluates the first input first so the instructionlist is always run at least once The tfexpression must be an expressionlist whose value when evaluated is TRUE or FALSE command Repeatedly evaluates the instructionlist as long as the evaluated tfexpression remains FALSE Evaluates the first input first so the instructionlist may never be run at all The tfexpression must be an expressionlist whose value when evaluated is TRUE or FALSE command or operation The second input is a list of lists clauses each clause is a list whose first element is either a list of values or the word ELSE and whose butfirst is a Logo expression or instruction CASE examines the clauses in order If a clause begins with the word ELSE upper or lower case then the butfirst of that clause is evaluated and CASE outputs its value if any If the first input to CASE is a member of the first element of a clause then the butfirst of that clause is evaluated and CASE outputs its value if any If neither of these conditions is met then CASE goes on to the next clause If no clause is satisfied CASE does nothing Example F a rH a to vowelp letter output case letter a e i o u true else false end COND clauses library procedure command or operation The input is a list of lists clauses each clause is a list whose first element is either
13. EADLIST processes backslash vertical bar and tilde characters in the read stream the output list will not contain these characters but they will have had their usual effect READLIST does not however treat semicolon as a comment character READWORD R reads a line from the read stream and outputs that line as a word The output is a single word even if the line contains spaces brackets etc If the read stream is a file and the end of file is reached READWORD outputs the empty list not the empty word READWORD processes backslash vertical bar and tilde characters in the read stream In the case of a tilde used for line continuation the output word DOES include the tilde and the newline characters so that the user program can tell exactly what the user entered Vertical bars in the line are also preserved in the output Backslash characters are not preserved in the output reads a line from the read stream and outputs that line as a word The output is a single word even if the line contains spaces brackets etc If the read stream is a file and the end of file is reached READRAWLINE outputs the empty list not the empty word READRAWLINE outputs the exact string of characters as they appear in the line with no special meaning for backslash vertical bar tilde or any other formatting characters RC reads a single character from the read stream and outputs that character as a word If the read str
14. MiniLogo based on BYOB User Manual This miniLogo implementation of the Logo programming language has been modelled on Berkeley Logo UCBlogo http www cs berkeley edu bh logo html Harvey Only parts of UCBlogo have been implemented namely e data structure primitives constructors fo selectors mutators predicates fe queries e communication fe transmitters fe receivers fe terminal access arithmetic fe numeric operations fe predicates e logical operations e graphics fe turtle motion turtle motion queries fe turtle and window control fo turtle and window queries fe pen and background control fe pen queries mouse queries e workspace management fe procedure definition variable definition fe property lists predicates 0 Control structures fe template based iteration e special variables Substantial parts of UCBlogo are some forever missing namely e file access e terminal access e print formatting bitwise operations e saving and loading pictures queries e inspection e workspace control e macros e error processing Still the miniLogo programming language is widely usable What follows is an extract of the UCBlogo http www cs berkeley edu bh usermanual thanks Brian in which that have been implemented in miniLogo are highlighted in green by Brian manual the parts Note that shortcuts given the block nature of miniLogo have not been imp
15. RAPHICS Logo begins with a black background and white pen TURTLE MOTION moves the turtle forward in the direction that it s facing by the specified distance measured in turtle steps BK dist moves the turtle backward i e exactly opposite to the direction that it s facing by the specified distance The heading of the turtle does not change LT degrees turns the turtle counterclockwise by the specified angle measured in degrees 1 360 of a circle RT degrees turns the turtle clockwise by the specified angle measured in degrees 1 360 of a circle moves the turtle to an absolute position in the graphics window The input is a list of two numbers the X and Y coordinates moves the turtle to an absolute position in the graphics window The two inputs are numbers the X and Y coordinates moves the turtle horizontally from its old position to a new absolute horizontal coordinate The input is the new X coordinate moves the turtle vertically from its old position to a new absolute vertical coordinate The input is the new Y coordinate wn ETH degrees turns the turtle to a new absolute heading The input is a number the heading in degrees clockwise from the positive Y axis moves the turtle to the center of the screen Equivalent to SETPOS 0 0 SETHEADING 0 draws an arc of a circle with the turtle at the center with the specified radius starting at the turtle s heading and extending cl
16. Widgets only outputs a list of two positive integers the width and height of characters displayed by LABEL measured in turtle steps which will be different from screen pixels if SETSCRUNCH has been used There is no SETLABELSIZE because the width and height of a font are not separately controllable so the inverse of this operation is SETLABELHEIGHT which takes just one number for the desired height az EN AND BACKGROUND CONTROL The turtle carries a pen that can draw pictures At any time the pen can be UP in which case moving the turtle does not change what s on the graphics screen or DOWN in which case the turtle leaves a trace If the pen is down it can operate in one of three modes PAINT so that it draws lines when the turtle moves ERASE so that it erases any lines that might have been drawn on or through that path earlier or REVERSE so that it inverts the status of each point along the turtle s path sets the pen s position to DOWN without changing its mode sets the pen s position to UP without changing its mode av PT sets the pen s position to DOWN and mode to PAINT Y kal sets the pen s position to DOWN and mode to ERASE sets the pen s position to DOWN and mode to REVERSE This may interact in system dependent ways with use of color wn ETPC colornumber or rgblist sets the pen color to the given number which must be a nonnegative integer There
17. ake buttonact button action to button action buttonact whatever you want the button to do end KEYACT variable if nonempty should be an instruction list that will be evaluated whenever a key is pressed on the keyboard The instruction list can use READCHAR to find out what key was pressed Note that only keys that produce characters qualify pressing SHIFT or CONTROL alone will not cause KEYACT to be evaluated Note that it s possible for the user to press a key during the evaluation of the instruction list If this would confuse your program prevent it by temporarily setting KEYACT to the empty list One easy way to do that is the following make keyact key action to key action keyact whatever you want the key to do end
18. an 4 red 5 magenta 6 yellow 7 white 8 brown 9 tan 10 forest 11 aqua 12 salmon 13 purple 14 orange 15 grey but other colors can be assigned to numbers by the PALETTE command outputs a list of two positive integers specifying the horizontal and vertical thickness of the turtle pen In some implementations including wxWidgets the two numbers are always equal outputs a list containing the pen s position mode thickness and hardware specific characteristics for use by SETPEN BG outputs the graphics background color either as a slot number or as an RGB list whichever way it was set See PENCOLOR outputs the coordinates of the mouse provided that it s within the graphics window in turtle coordinates If the mouse is outside the graphics window then the last position within the window is returned Exception If a mouse button is pressed within the graphics window and held while the mouse is dragged outside the window the mouse s position is returned as if the window were big enough to include it outputs the coordinates that the mouse was at when a mouse button was most recently pushed provided that that position was within the graphics window in turtle coordinates wxWidgets only BUTTONP outputs TRUE if a mouse button is down and the mouse is over the graphics window Once the button is down BUTTONP remains true until the button is released even if the mouse is dragged out of the gra
19. as the value B IN3 has the value C and IN4 has the value D E The MAXIMUM number of inputs for a procedure is infinite if a rest input is given otherwise it is the number of required inputs plus the number of optional inputs The DEFAULT number of inputs for a procedure which is the number of inputs that it will accept if its invocation is not enclosed in parentheses is ordinarily equal to the minimum number If you want a different default number you can indicate that by putting the desired default number as the last thing on the TO line example to proc inl in2 foo in3 3 This procedure has a minimum of one input a default of three inputs and an infinite maximum Logo responds to the TO command by entering procedure definition mode The prompt character changes from to gt and whatever instructions you type become part of the definition until you type a line containing only the word END procname text command Defines a procedure with name procname and text text If there is already a procedure with the same name the new definition replaces the old one The text input must be a list whose members are lists The first member is a list of inputs it looks like a TO line but without the word TO without the procedure name and without the colons before input names In other words the members of this first sublist are words for the names of required inputs and lists for the names of optiona
20. at FOO means THING FOO GLOBAL varname GLOBAL varnamelist GLOBAL varnamel varname2 command Accepts as inputs one or more words or a list of words A global variable is created for each of these words with that word as its name The only reason this is necessary is that you might want to use the setter notation SETXYZ for a variable XYZ that does not already have a value GLOBAL XYZ makes that legal Note If there is currently a local variable of the same name this command does not make Logo use the global value instead of the local one PROPERTY LISTS Note Names of property lists are always case insensitive Names of individual properties are case sensitive or case insensitive depending on the value of CASEIGNOREDP which is TRUE by default In principle every possible name is the name of a property list which is initially empty So Logo never gives a no such property list error as it would for undefined procedure or variable names But the primitive procedures that deal with all property lists CONTENTS PLISTS etc list only nonempty ones To erase a property list see ERASE below means to make it empty removing all properties from it command Adds a property to the plistname property list with name propname and value value outputs the value of the propname property in the plistname property list or the empty list if there is no such property
21. eam is a file and the end of file is reached READCHAR outputs the empty list not the empty word If the read stream is the keyboard echoing is turned off when READCHAR is invoked and remains off until READLIST or READWORD is invoked or a Logo prompt is printed Backslash vertical bar and tilde characters have no special meaning in this context RCS num H reads num characters from the read stream and outputs those characters as a word If the read stream is a file and the end of file is reached READCHARS outputs the empty list not the empty word If the read stream is a terminal echoing is turned off when READCHARS is invoked and remains off until READLIST or READWORD is invoked or a Logo prompt is printed Backslash vertical bar and tilde characters have no special meaning in this context ERMINAL ACCESS w ti K tu x x K S predicate outputs TRUE if there are characters waiting to be read from the read stream If the read stream is a file this is equivalent to NOT EOFP If the read stream is the terminal then echoing is turned off and the terminal is set to CBREAK character at a time instead of line at a time mode It remains in this mode until some line mode reading is requested e g READLIST The Unix operating system forgets about any pending characters when it switches modes so the first KEYP invocation will always output FALSE CT com
22. et of the members for a list or characters for a word of the input The template is evaluated once for each member or character of the data and it must produce a TRUE or FALSE value If the value is TRUE then the corresponding input constituent is included in the output print filter vowelp elephant eea In a template the symbol REST represents the portion of the data input to the right of the member currently being used as the slot filler That is if the data input is A B C D E and the template is being evaluated with replaced by B then REST would be replaced by C D E In a template the symbol represents the position in the data input of the member currently being used as the slot filler That is if the data input is A B C D E and the template is being evaluated with replaced by B then would be replaced DY 2x outputs the first constituent of the data input the first member of a list or the first character of a word for which the value produced by evaluating the template with that consituent in its slot is TRUE If there is no such constituent the empty list is output In a template the symbol REST represents the portion of the data input to the right of the member currently being used as the slot filler That is if the data input is A B C D E and the template is being evaluated with replaced by B then REST would be replaced by C D E In a
23. g on one machine will probably not have the desired effect if printed on another type of machine In the Macintosh classic version the way that standout works is incompatible with the use of characters whose ASCII code is greater than 127 Therefore you have a choice to make The instruction CANINVERSE 0 disables standout but enables the display of ASCII codes above 127 and the instruction CANINVERSE 1 restores the default situation in which standout is enabled and the extra graphic characters cannot be printed word outputs the list that would result if the input word were entered in response to a READLIST operation That is PARSE READWORD has the same value as READLIST for the same characters read RUNPARSE wordorlist outputs the list that would result if the input word or list were entered as an instruction line characters such as infix operators and parentheses are separate members of the output Note that sublists of a runparsed list are not themselves runparsed COMMUNICATION TRANSMITTERS PRINT thing PR thing PR thingl thing2 command Prints the input or inputs to the current write stream initially the screen All the inputs are printed on a single line separated by spaces ending with a newline If an input is a list square brackets are not printed around it but brackets are printed around sublists Braces are always printed around arrays command Prints the input o
24. ged in these two examples print apply x output x 3 5 Can only use output inside a procedure print apply x x 3 5 You don t say what to do with 8 The named slot form can be used with STOP or OUTPUT inside a procedure to stop the enclosing procedure The following iteration tools are extended versions of the ones in Appendix B of the book _Computer_Science_Logo_Style _Volume_3 _Advanced_Topics_ by Brian Harvey MIT Press 1987 The extensions are primarily to allow for variable numbers of inputs command or operation Runs the template filling its slots with the members of inputlist must be an acceptable number illegal to apply the primitive TO as a template is okay APPLY outputs what INVOKE template input command or operation The number of members in inputlist of slots for template It is but anything else if anything template outputs library procedure Exactly like APPLY except that the inputs are provided as separate expressions rather than ina list FOREACH data template library procedure command Evaluates the template list repeatedly once for each member of the data list If more than one data list are given each of them must be the same length The data inputs can be words in which case the template is evaluated once for each character In a template the symbol REST represents the portion of the data input to the right of the member c
25. he number of available data This form is needed primarily when one iteration tool must be used within the template list of another and the notation would be ambiguous in the inner templat Example to matmul ml m2 tm2 transpose m2 multiply two matrices output map row map col dotprod row col tm2 ml end The fourth form is procedure text form a variant of lambda form In this form the template list contains at least two members all of which are lists This is the form used by the DEFINE and TEXT primitives and APPLY accepts it so that the text of a defined procedure can be used as a template Note The fourth form of template is interpreted differently from the others in that Logo considers it to be an independent defined procedure for the purposes of OUTPUT and STOP For example the following two instructions are identical x x 3 5 print apply print apply x output x 3 5 although the first instruction is in named slot form and the second is in procedure text form The named slot form can be understood as telling Logo to evaluate the expression x 3 in place of the entire invocation of apply with the variable x temporarily given the value 5 The procedure text form can be understood as invoking the procedure to foo x output x 3 end but without actually giving the procedure a name If we d get errors with input 5 the use of OUTPUT were interchan
26. herwise EMPTYP thing outputs TRUE if the input is the empty word or the empty list FALSE otherwise EQUALP thingl thing2 EQUAL thingl thing2 outputs TRUE if the inputs are equal FALSE otherwise Two numbers are equal if they have the same numeric value Two non numeric words are equal if they contain the same characters in the same order If there is a variable named CASEIGNOREDP whose value is TRUE then an upper case letter is considered the same as the corresponding lower case letter This is the case by default Two lists are equal if their members are equal An array is only equal to itself two separately created arrays are never equal even if their members are equal It is important to be able to know if two expressions have the same array as their value because arrays are mutable if for example two variables have the same array as their values then performing SETITEM on one of them will also change the other NOTEQUALP thingl thing2 NOTEQUAL thingl thing2 outputs FALSE if the inputs are equal TRUE otherwise See EQUALP for the meaning of equality for different data types BEFOREP wordl word2 outputs TRUE if wordl comes before word2 in ASCII collating sequence for words of letters in alphabetical order Case sensitivity is determined by the value of CASEIGNOREDP Note that if the inputs are numbers the result may not be the same as with LESSP for example BEFOREP 3 12 is false because 3 c
27. l or rest inputs The remaining sublists of the text input make up the body of the procedure with one sublist for each instruction line of the body There is no END line in the text input It is an error to redefine a primitive procedure unless the variable REDEFP has the value TRUE TEXT procname outputs the text of the procedure named procname in the form expected by DEFINE a list of lists the first of which describes the inputs to the procedure and the rest of which are the lines of its body The text does not reflect formatting information used when the procedure was defined such as continuation lines and extra spaces FULLTEXT procname outputs a representation of the procedure procname in which formatting information is preserved If the procedure was defined with TO EDIT or LOAD then the output is a list of words Each word represents one entire line of the definition in the form output by READWORD including extra spaces and continuation lines The last member of the output represents the END line If the procedure was defined with DEFINE then the output is a list of lists If these lists are printed one per line the result will look like a definition using TO Note the output from FULLTEXT is not suitable for use as input to DEFINE command Makes newname a procedure identical to oldname The latter may be a primitive If newname was already defined its pre
28. lemented DATA STRUCTURE PRIMITIVES CONSTRUCTORS WORD wordl word2 outputs a word formed by concatenating its inputs LIST thingl thing2 outputs a list whose members are its inputs which can be any Logo datum word list or array SENTENCE thingl thing2 SE thingl thing2 SE thingl thing2 thing3 outputs a list whose members are its inputs if those inputs are not lists or the members of its inputs if those inputs are lists outputs a list equal to its second input with one extra member the first input at the beginning If the second input is a word then the first input must be a one letter word and FPUT is equivalent to WORD outputs a list equal to its second input with one extra member the first input at the end If the second input is a word then the first input must be a one letter word and LPUT is equivalent to WORD with its inputs in the other order ARRAY size outputs an array of size members must be a positive integer each of which initially is an empty list Array members can be selected with ITEM and changed with SETITEM The first member of the array is member number 1 unless an origin input must be an integer is given in which case the first member of the array has that number as its index Typically 0 is used as the origin if MDARRAY sizelist library procedure outputs a multi dimensional array The first input must be a list of one or more positive integers
29. mand Clears the text window NUMERIC OPERATIONS SUM numl num2 SUM numl num2 num3 outputs the sum of its inputs DIFFERENCE numl num2 outputs the difference of its inputs Minus sign means infix difference in ambiguous contexts when preceded by a complete expression unless it is preceded by a space and followed by a nonspace See also MINUS MINUS num outputs the negative of its input Minus sign means unary minus if the previous token is an infix operator or open parenthesis or it is preceded by a space and followed by a nonspace There is a difference in binding strength between the two forms MINUS 3 4 means 3 4 3 4 means 3 4 PRODUCT num1 num2 PRODUCT numi num2 num3 outputs the product of its inputs QUOTIENT numl num2 QUOTIENT num outputs the quotient of its inputs The quotient of two integers is an integer if and only if the dividend is a multiple of the divisor In other words QUOTIENT 5 2 is 2 5 not 2 but QUOTIENT 4 2 is 2 not 2 0 it does the right thing With a single input QUOTIENT outputs the reciprocal of the input outputs the remainder on dividing numl by num2 both must be integers and the result is an integer with the same sign as numl MODULO numl num2 outputs the remainder on dividing numl by num2 both must be integers and the result is an integer with the same sign as num2 outputs its input with fractional part re
30. moved i e an integer with the same sign as the input whose absolute value is the largest integer less than or equal to the absolute value of the input outputs the nearest integer to the input outputs the square root of the input which must be nonnegative outputs numl to the num2 power If numl is negative then num2 must be an integer outputs e 2 718281828 to the input power outputs the common logarithm of the input outputs the natural logarithm of the input outputs the sine of its input which is taken in degrees outputs the sine of its input which is taken in radians outputs the cosine of its input which is taken in degrees outputs the cosine of its input which is taken in radians ARCTAN x y outputs the arctangent in degrees of its input With two inputs outputs the arctangent of y x if x is nonzero or 90 or 90 depending on the sign of y if x is zero RADARCTAN x y outputs the arctangent in radians of its input With two inputs outputs the arctangent of y x if x is nonzero or pi 2 or pi 2 depending on the sign of y if x is zero The expression 2 RADARCTAN 0 1 can be used to get the value of pi outputs a list of the integers from FROM to TO inclusive show iseq 3 7 3 45 6 7 show iseq 7 3 7 6 5 4 3 outputs a list of COUNT equally spaced rational numbers between FROM and TO inclusive show rseq 3 5 9 3 3 29 325 3 79 4 4 25 4 5 4 75 5 sho
31. ockwise through the specified angle The turtle does not move TURTLE MOTION QUERIES outputs the turtle s current position as a list of two numbers the X and Y coordinates outputs a number the turtle s X coordinate outputs a number the turtle s Y coordinate outputs a number the turtle s heading in degrees outputs a number the heading at which the turtle should be facing so that it would point from its current position to the position given as the input TURTLE AND WINDOW CONTROL n H makes the turtle visible H makes the turtle invisible It s a good idea to do this while you re in the middle of a complicated drawing because hiding the turtle speeds up the drawing substantially erases all lines that the turtle has drawn on the graphics window The turtle s state position heading pen mode etc is not changed n erases the graphics window and sends the turtle to its initial position and heading Like HOME and CLEAN together tells the turtle to enter wrap mode From now on if the turtle is asked to move past the boundary of the graphics window it will wrap around and reappear at the opposite edge of the window The top edge wraps to the bottom edge while the left edge wraps to the right edge So the window is topologically equivalent to a torus This is the turtle s initial mode Compare WINDOW and FENCE tells the turtle to enter window mode From now on if the tur
32. ollates after 1 outputs TRUE if its two inputs are the same datum so that applying a mutator to one will change the other as well Outputs FALSE otherwise even if the inputs are equal in value WARNING Primitives whose names start with a period are DANGEROUS Their use by non experts is not recommended The use of mutators can lead to circular data structures infinite loops or Logo crashes MEMBERP thingl thing2 if thing2 is a list or an array outputs TRUE if thingl is EQUALP to a member of thing2 FALSE otherwise If thing2 is a word outputs TRUE if thingl is a one character word EQUALP to a character of thing2 FALSE otherwise SUBSTRINGP thingl thing2 if thingl or thing2 is a list or an array outputs FALSE If thing2 is a word outputs TRUE if thingl is EQUALP to a substring of thing2 FALSE otherwise NUMBERP thing outputs TRUE if the input is a number FALSE otherwise QUERIES outputs the number of characters in the input if the input is a word outputs the number of members in the input if it is a list or an array For an array this may or may not be the index of the last member depending on the array s origin outputs the integer between 0 and 255 that represents the input character in the ASCII code Interprets control characters as representing vbarred punctuation and returns the character code for the corresponding punctuation character wi
33. phics window outputs 0 if no mouse button has been pushed inside the Logo window since the last call to BUTTON Otherwise it outputs an integer between 1 and 3 indicating which button was most recently pressed Ordinarily 1 means left 2 means right and 3 means center but operating systems may reconfigure these WORKSPACE MANAGEMENT PROC EDUR EFINITION command Prepares Logo to accept a procedure definition The procedure will be named procname and there must not already be a procedure by that name The inputs will be called input1 etc Any number of inputs are allowed including none Names of procedures and inputs are case insensitive Unlike every other Logo procedure TO takes as its inputs the actual words typed in the instruction line as if they were all quoted rather than the results of evaluating expressions to provide the inputs That s what special form means This version of Logo allows variable numbers of inputs to a procedure After the procedure name come four kinds of things in this order Every procedure has a MINIMUM DEFAULT and MAXIMUM number of inputs The latter can be infinite The MINIMUM number of inputs is the number of required inputs which must come first A required input is indicated by the inputname notation After all the required inputs can be zero or more optional inputs each of which is represented by the following notation
34. r inputs like PRINT except that no newline character is printed at the end and multiple inputs are not separated by spaces Note printing to the terminal is ordinarily line buffered that is the characters you print using TYPE will not actually appear on the screen until either a newline character is printed for example by PRINT or SHOW or Logo tries to read from the keyboard either at the request of your program or after an instruction prompt This buffering makes the program much faster than it would be if each character appeared immediately and in most cases the effect is not disconcerting To accommodate programs that do a lot of positioned text display using TYPE Logo will force printing whenever SETCURSOR is invoked This solves most buffering problems Still on occasion you may find it necessary to force the buffered characters to be printed explicitly this can be done using the WAIT command WAIT 0 will force printing without actually waiting SHOW thing command Prints the input or inputs like PRINT except that if an input is a list it is printed inside square brackets RECEIVERS READLIST RL reads a line from the read stream initially the keyboard and outputs that line as a list The line is separated into members as though it were typed in square brackets in an instruction If the read stream is a file and the end of file is reached READLIST outputs the empty word not the empty list R
35. represents the position in the data input of the member currently being used as the slot filler That is if the data input is A B C D E and the template is being evaluated with replaced by B then would be replaced by 2 MAP SE template data library procedure MAP SE template datal data2 outputs a list formed by evaluating the template list repeatedly and concatenating the results using SENTENCE That is the members of the output are the members of the results of the evaluations The output list might therefore be of a different length from that of the data input s If the result of an evaluation is the empty list it contributes nothing to the final output The data inputs may be words or lists In a template the symbol REST represents the portion of the data input to the right of the member currently being used as the slot filler That is if the data input is A BCD E and the template is being evaluated with replaced by B then REST would be replaced by C D E If multiple parallel slots are used then REST 1 goes with 1 etc In a template the symbol represents the position in the data input of the member currently being used as the slot filler That is if the data input is A B C D E and the template is being evaluated with replaced by B then would be replaced by 2 outputs a word or list depending on the type of the data input containing a subs
36. s The same value was used for every question mark in a given evaluation Some tools allow for more than one datum to be substituted in parallel in these cases the slots are indicated by 1 for the first datum 2 for the second and so on show map word 1 2 1 a b c d e f ada beb cfc If the template wishes to compute the datum number the form 1 is equivalent to 1 so 1 means the datum whose number is given in datum number 1 Some tools allow additional slot designations as shown in the individual descriptions The second form of template is the named procedure form If the template is a word rather than a list it is taken as the name of a procedure That procedure must accept a number of inputs equal to the number of parallel data slots provided by the tool the procedure is applied to all of the available data in order That is if data 1 through 3 are available the template PROC is equivalent to PROC 1 2 3 show map word a b c de f ad be cf to dotprod a b vector dot product op apply sum map product a b end The third form of template is named slot or lambda form This form is indicated by a template list containing more than one member whose first member is itself a list The first member is taken as a list of names local variables are created with those names and given the available data in order as their values The number of names must equal t
37. st that outputs a list when run The members of that list replace the and the instructionlist Example show foo baz bf a b c garply bf a b c will print foo baz b c garply b c A word starting with or is treated as if the rest of the word were a one word list e g FOO is equivalent to FOO A word starting with quote comma or colon comma becomes a word starting with or but with the result of running the substitution or its first word if the result is a list replacing what comes after the comma Backquotes can be nested Substitution is done only for commas at the same depth as the backquote in which they are found show a b 1 2 foo 1 3 d e f a gt b 1 2 foo 4 da el f make namel x make name2 y show a b namel name2 d e fa b x y d e command The first input must be a list containing three or four members 1 a word which will be used as the name of a local variable 2 a word or list that will be evaluated as by RUN to determine a number the starting value of the variable 3 a word or list that will be evaluated to determine a number the limit value of the variable 4 an optional word or list that will be evaluated to determine the step size If the fourth member is missing the step size will be 1 or 1 depending on whether the limit value is greater than or less than the starting value respectively
38. st time the procedure is invoked in each Logo session command or operation If the first input has the value TRUE then IFELSE runs the second input If the first input has the value FALSE then IFELSE runs the third input IFELSE outputs a value if the instructionlist contains an expression that outputs a value command Remembers its input which must be TRUE or FALSE for use by later IFTRUE or IFFALSE instructions The effect of TEST is local to the procedure in which it is used any corresponding IFTRUE or IFFALSE must be in the same procedure or a subprocedure IFT instructionlist command Runs its input if the most recent TEST instruction had a TRUE input The TEST must have been in the same procedure or a superprocedure IFF instructionlist command Runs its input if the most recent TEST instruction had a FALSE input The TEST must have been in the same procedure or a superprocedure command Ends the running of the procedure in which it appears Control is returned to the context in which that procedure was invoked The stopped procedure does not output a value OP value command Ends the running of the procedure in which it appears That procedure outputs the value value to the context in which it was invoked Don t be confused OUTPUT itself is a command but the procedure that invokes OUTPUT is an operation command Delays further execution for time 60ths of a second Also ca
39. t outputs a copy of list with every member equal to thing removed outputs a copy of list with duplicate members removed If two or more members of the input are equal the rightmost of those members is the one that remains in the output outputs its input if a list outputs its input with a quotation mark prepended if a word MUTATORS command Replaces the index th member of array with the new value Ensures that the resulting array is not circular i e value may not be a list or array that contains array command Replaces the member of array chosen by indexlist with the new value SETFIRST list value command Changes the first member of list to be value WARNING Primitives whose names start with a period are DANGEROUS Their use by non experts is not recommended The use of SETFIRST can lead to circular list structures which will get some Logo primitives into infinite loops and to unexpected changes to other data structures that share storage with the list being modified SETBF list value SETIT command Changes the butfirst of list to be value WARNING Primitives whose names start with a period are DANGEROUS Their use by non experts is not recommended The use of SETBF can lead to circular list structures which will get some Logo primitives into infinite loops unexpected changes to other data structures that share storage with the list being modified or
40. t must be a predicate expression template and evaluation continues until either that template s value is TRUE or the inbasket is used up SPECIAL VARIABLES Logo takes special action if any of the following variable names exists They follow the normal scoping rules so a procedure can locally set one of them to limit the scope of its effect Initially no variables exist except for ALLOWGETSET CASEIGNOREDP and UNBURYONEDIT which are TRUE and buried ALLOWGETSET variable if TRUE indicates that an attempt to use a procedure that doesn t exist should be taken as an implicit getter or setter procedure setter if the first three letters of the name are SET for a variable of the same name without the SET if appropriate if nonempty should be an instruction list that will be evaluated whenever a mouse button is pressed Note that the user may have released the button before the instructions are evaluated BUTTON will still output which button was most recently pressed CLICKPOS will output the position of the mouse cursor at the moment the button was pressed this may be different from MOUSEPOS if the user moves the mouse after clicking Note that it s possible for the user to press a button during the evaluation of the instruction list If this would confuse your program prevent it by temporarily setting BUTTONACT to the empty list One easy way to do that is the following m
41. thout vertical bars Compare RAWASCII RAWASCII char outputs the integer between 0 and 255 that represents the input character in the ASCII code Interprets control characters as representing themselves To find out the ASCII code of an arbitrary keystroke use RAWASCII RC outputs the character represented in the ASCII code by the input which must be an integer between 0 and 255 if thing2 is a word or list and if MEMBERP with these inputs would output TRUE outputs the portion of thing2 from the first instance of thingl to the end If MEMBERP would output FALSE outputs the empty word or list according to the type of thing2 It is an error for thing2 to be an array outputs a copy of the input word but with all uppercase letters changed to the corresponding lowercase letter outputs a copy of the input word but with all lowercase letters changed to the corresponding uppercase letter STANDOUT thing PARSE outputs a word that when printed will appear like the input but displayed in standout mode boldface reverse video or whatever your version does for standout The word contains machine specific magic characters at the beginning and end in between is the printed form as if displayed using TYPE of the input The output is always a word even if the input is of some other type but it may include spaces and other formatting characters Note a word output by STANDOUT while Logo is runnin
42. throw error not enough inputs to max output reduce ifelse 1 gt 2 1 2 inputs end CROSSMAP template datal data2 outputs a list containing the results of template evaluations Each data list contributes to a slot in the template the number of slots is equal to the number of data list inputs As a special case if only one data list input is given that list is taken as a list of data lists and each of its members contributes values to a slot CROSSMAP differs from MAP in that instead of taking members from the data inputs in parallel it takes all possible combinations of members of data inputs which need not be the same length show crossmap word 1 2 a b c 1 2 3 4 al a2 a3 a4 bl b2 b3 b4 cl c2 c3 c4 2 For compatibility with the version in the first edition of CSLS CROSSMAP templates may use the notation 1 instead of 1 to indicate slots CASCADE endtest tmpl svl tmp2 sv2 CASCADE endtest tmpl svl tmp2 sv2 finaltemplate outputs the result of applying a template or several templates as explained below repeatedly with a given value filling the slot the first time and the result of each application filling the slot for the following application In the simplest case CASCADE has three inputs The second input is a one slot expression template That template is evaluated some number of times perhaps zero On the first evaluation the slot is filled with the third input
43. tle is asked to move past the boundary of the graphics window it will move offscreen The visible graphics window is considered as just part of an infinite graphics plane the turtle can be anywhere on the plane If you lose the turtle HOME will bring it back to the center of the window Compare WRAP and FENCE tells the turtle to enter fence mode From now on if the turtle is asked to move past the boundary of the graphics window it will move as far as it can and then stop at the edge with an out of bounds error message Compare WRAP and WINDOW takes a word or list as input and prints the input on the graphics window starting at the turtle s position command wxWidgets only Takes a positive integer argument and tries to set the font size so that the character height including descenders is that many turtle steps This will be different from the number of screen pixels if SETSCRUNCH has been used Also note that SETSCRUNCH changes the font size to try to preserve this height in turtle steps Note that the query operation corresponding to this command is LABELSIZE not LABELHEIGHT because it tells you the width as well as the height of characters in the current font TURTLE AND WINDOW QUERIES SHOWNP T outputs TRUE if the turtle is shown visible FALSE if the turtle is hidden See SHOWTURTLE and HIDETURTLE outputs the word WRAP FENCE or WINDOW depending on the current turtle mode wx
44. to Logo crashes and coredumps if the butfirst of a list is not itself a list EM index array value command Changes the index th member of array to be value like SETITEM but without checking for circularity WARNING Primitives whose names start with a period are DANGEROUS Their use by non experts is not recommended The use of SETITEM can lead to circular arrays which will get some Logo primitives into infinite loops command Adds the thing to the stack that is the value of the variable whose name is stackname This variable must have a list as its value the initial value should be the empty list New members are added at the front of the list outputs the most recently PUSHed member of the stack that is the value of the variable whose name is stackname and removes that member from the stack command Adds the thing to the queue that is the value of the variable whose name is queuename This variable must have a list as its value the initial value should be the empty list New members are added at the back of the list outputs the least recently QUEUEd member of the queue that is the value of the variable whose name is queuename and removes that member from the queue PREDICATES WORDP thing outputs TRUE if the input is a word FALSE otherwise LISTP thing outputs TRUE if the input is a list FALSE otherwise ARRAYP thing outputs TRUE if the input is an array FALSE ot
45. tput from running the input instructionlist Useful for inventing command or operation control structures local result make result runresult something if emptyp result stop output first result command Runs the instructionlist repeatedly num times command Runs the instructionlist repeatedly until something inside the instructionlist such as STOP or THROW makes it stop outputs the repetition count of the innermost current REPEAT or FOREVER starting from 1 If no REPEAT or FOREVER is active outputs The abbreviation can be used for REPCOUNT unless the REPEAT is inside the template input to a higher order procedure such as FOREACH in which case has a different meaning IF tf instructionlistl instructionlist2 command If the first input has the value TRUE then IF runs the second input If the first input has the value FALSE then IF does nothing If given a third input IF acts like IFELSE as described below It is an error if the first input is not either TRUE or FALSE For compatibility with earlier versions of Logo if an IF instruction is not enclosed in parentheses but the first thing on the instruction line after the second input expression is a literal list i e a list in square brackets the IF is treated as if it were IFELSE but a warning message is given If this aberrant IF appears in a procedure body the warning is given only the fir
46. urrently being used as the slot filler That is if the data input is A BCD E and the template is being evaluated with replaced by B then REST would be replaced by C D E If multiple parallel slots are used then REST 1 goes with 1 etc In a template the symbol represents the position in the data input of the member currently being used as the slot filler That is if the data input is A B C D E and the template is being evaluated with replaced by B then would be replaced by 2 MAP template datal data2 outputs a word or list depending on the type of the data input of the same length as that data input If more than one data input are given the output is of the same type as datal Each member of the output is the result of evaluating the template list filling the slots with the corresponding member s of the data input s All data inputs must be the same length In the case of a word output the results of the template evaluation must be words and they are concatenated with WORD In a template the symbol REST represents the portion of the data input to the right of the member currently being used as the slot filler That is if the data input is ABCD E and the template is being evaluated with replaced by B then REST would be replaced by C D E If multiple parallel slots are used then REST 1 goes with 1 etc In a template the symbol
47. uses any buffered characters destined for the terminal to be printed immediately WAIT 0 can be used to achieve this buffer flushing without actually waiting command Exits from Logo returns to the operating system MAYBEOUTPUT value special form works like OUTPUT except that the expression that provides the input value might not in fact output a value in which case the effect is like STOP This is intended for use in control structure definitions for cases in which you don t know whether or not some expression produces a value Example to invoke function inputs 2 maybeoutput apply function inputs end invoke print a b c abc print invoke word a b c abc This is an alternative to RUNRESULT It s fast and easy to use at the cost of being an exception to Logo s evaluation rules Ordinarily it should be an error if the expression that s supposed to provide an input to something doesn t have a value command Does nothing Used when an expression is evaluated for a side effect and its actual value is unimportant outputs a list equal to its input but with certain substitutions If a member of the input list is the word comma then the following member should be an instructionlist that produces an output when run That output value replaces the comma and the instructionlist If a member of the input list is the word comma atsign then the following member should be an instructionli
48. vious definition is lost If newname was already a primitive the redefinition is not permitted unless the variable REDEFP has the value TRUE ie Ry Note dialects of Logo differ as to the order of inputs to COPYD This dialect uses MAKE order not NAME order VARIABLE DEFINITION command Assigns the value value to the variable named varname which must be a word Variable names are case insensitive Ifa variable with the same name already exists the value of that variable is changed If not a new global variable is created XOCAL varname OCAL varnamelist command Accepts as inputs one or more words or a list of words A variable is created for each of these words with that word as its name The variables are local to the currently running procedure Logo variables follow dynamic scope rules a variable that is local to a procedure is available to any subprocedure invoked by that procedure The variables created by LOCAL have no initial value they must be assigned a value e g with MAKE before the procedure attempts to read their value command Makes the named variable local like LOCAL and assigns it the given value like MAKE outputs the value of the variable whose name is the input If there is more than one such variable the innermost local variable of that name is chosen The colon notation is an abbreviation not for THING but for the combination thing so th
49. w rseq 3 5 5 3 355 4 4 5 5 PREDICATES ESSP numl num2 ESS numi num2 outputs TRUE if its first input is strictly less than its second GREATERP numl num2 GREATER numl num2 outputs TRUE if its first input is strictly greater than its second ESSEQUALP numl num2 ESSEQUAL numl num2 outputs TRUE if its first input is less than or equal to its second GREATEREQUALP numl num2 GREATEREQUAL numl num2 outputs TRUE if its first input is greater than or equal to its second RANDOM NUMBERS RANDOM num with one input outputs a random nonnegative integer less than its input which must be a positive integer With two inputs RANDOM outputs a random integer greater than or equal to the first input and less than or equal to the second input Both inputs must be integers and the first must be less than the second RANDOM 0 9 is equivalent to RANDOM 10 RANDOM 3 8 is equivalent to RANDOM 6 3 ERANDOM RERANDOM seed v command Makes the results of RANDOM reproducible Ordinarily the sequence of random numbers is different each time Logo is used If you need the same sequence of pseudo random numbers repeatedly e g to debug a program say RERANDOM before the first invocation of RANDOM If you need more than one repeatable sequence you can give RERANDOM an integer input each possible input selects a unique sequence of numbers LOGICAL OPERATIONS
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