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XNÉIO 0 1 ° XNÉCT 0 1E²13 ° XCÉFC 1 6 .,*0_² ° XNÉRL 0 16807 ° XCÉPR 1 1 ° XCÉLX 1 5 TEACH ° *(1996 4 6 16 4 50 384) ° FBIND ÉFX 'BIND' 'Σ Binding rules of APL2' ° ''' 1. Brackets bind to the left''' ° ''' 2. Left arrow binds to the left''' ° ''' 3. Dyadic operator binds to the right''' ° ''' 4. Strand notation binding''' ° ''' 5. Operator binds to its left''' ° ''' 6. Function binds to its left''' ° ''' 7. Function binds to its right''' ° X ''' 8. Left arrow binds to its right'',r' ° *(1997 9 14 12 30 44 504) ° XFDISCLAIMER ÉFX 'DISCLAIMER' 'Σ Copyright statement' 'disclaimer' ° *(1996 4 6 16 5 21 272) ° FDISPLAY ÉFX 'D╜S DISPLAY A;ÉIO;R;C;HL;HC;HT;HB;VL;VB;V;W;N;B' ° 'Σ DISPLAY A GENERAL ARRAY IN PICTORIAL FORM' ° 'Σ NORMAL CALL IS MONADIC. DYADIC CALL USED ONLY IN' ° 'Σ RECURSION TO SPECIFY DISPLAY RANK, SHAPE, AND DEPTH.' 'ÉIO╜0' ° '»(0=ÉNC ''S'')/''S╜µA''' 'R╜╞µ,S Σ PSEUDO RANK.' ° 'C╜''┐┌└┘'' Σ UR, UL, LL, AND LR CORNERS.' ° 'HL╜''─'' Σ HORIZONTAL LINE.' ° 'HC╜HL,''Θ╕'',HL,''~+ε'' Σ HORIZONTAL BORDERS.' ° 'HT╜HC[(0<R)⌡1+0<╞²1╞,S]' 'ΣW╜,0╧■╞0µΓ(1⌐µA)╞A' ° 'HB╜HC[3+3╛(''2⌡~A╧«A'' ÉEA ''1+╞ε0⌡(1⌐⌡/µA)╞,A'')+3⌡1<µµS]' ° 'VL╜''│'' Σ VERTICAL LINE.' ° 'VB╜VL,''Φ╟'' Σ VERTICAL BORDER.' ° 'V╜VB[(1<R)⌡1+0<²1╞²1╟,S]' ° '»(0εµA)/''A╜(1⌐µA)µΓ╞A'' Σ SHOW PROTOTYPE OF EMPTIES.' ° '╕(1<╧A)/GEN' '╕(2<µµA)/D3' ° 'D╜«A Σ SIMPLE ARRAYS.' 'W╜1╞µD╜(²2╞1 1,µD)µD' ° 'N╜²1+1╟µD' '╕(0=µµA)/SS' ° 'D╜(C[1],V,((W-1)µVL),C[2]),((HT,NµHL),[0]D,[0]HB,NµHL),C[0],(WµVL),C[ ° 3]' '╕0' 'SS:HB╜((0 '' '')=╞0µΓA)/'' -''' ° 'D╜'' '',('' '',[0]D,[0]HB,Nµ'' ''),'' ''' '╕0' ° 'GEN:D╜«DISPLAY■A Σ ENCLOSED ...' 'N╜Dδ.⌠'' ''' ° 'D╜(Nδ~1ΦN)≡D' 'D╜(δ≡~'' ''╤D)/D' 'D╜((1,µS)µS)DISPLAY D' ° '╕(2≥µ,S)╟D3E,0' 'D3:D╜0 ²1╟0 1╟«ΓA Σ MULT-DIMENSIONAL ...' ° 'W╜1╞µD' 'N╜²1+1╟µD' ° 'D╜(C[1],V,((W-1)µVL),C[2]),((HT,NµHL),[0]D,[0]HB,NµHL),C[0],(WµVL),C[ ° 3]' 'D3E:N╜²2+µ,S' ° X 'V╜C[Nµ1],[0]VB[1+0<²2╟,S],[0](((²3+╞µD),N)µVL),[0]C[Nµ2]' 'D╜V,D' ° *(1996 4 6 16 5 21 272) ° FEXIT ÉFX 'EXIT' 'Σ Exit from function' '''To log off type: )OFF''' ° X '╕' ° *(1996 4 6 16 5 21 272) ° FGO ÉFX 'GO;T;E;B' 'Σ Expression driver' 'L0:B╜E╜''''' 'æ╜'' ''' ° 'T╜æ' '╕(^/'' ''=T)/L0' '╕((^/'')OFF ''=5╞6╟T)doif ''EXIT'')/0' ° '╕(('':''εT)doif ''B╜evaldd (+/^\'''' ''''=T)╟T'')/L0' ° '''E╜ÉEM'' ÉEA T' '╕(0=µ,E)/L0' '╕B/L0' ° '''This is not a valid APL2 expression''' 'æ╜''*''' ° X '╕(''?''⌠╞1╟æ)/L0' 'E' '╕L0' ° *(1997 8 22 12 51 22 528) ° FHELP ÉFX 'HELP;N;I;T' 'Σ Help to student' '''WHAT TO DO'',r' ° ''' ° To get out of the lesson''' ''' ENTER: EXIT''' ° ''' ° To log off APL2''' ° ''' FIRST, ENTER: EXIT THEN ENTER: )OFF''' ° ''' ° To get help''' ''' ENTER: HELP''' ° ''' ° When you see the prompt on a blank line''' ° ''' ENTER AN APL2 EXPRESSION - OR JUST PRESS: ENTER''' 'do' ° ''' ° If you get this line'',r' ° '''This is not a valid APL2 expression'',r,''*'',r' ° ''' YOU CAN EITHER''' ''' A. PRESS: ENTER''' ° ''' B. PRESS: ? and then ENTER to see what was incorrect''' ° ''' in your expression causing that response'',r' 'do' ° '''HINTS'',r' ° '''This lesson is made up of '',(«N╜9),'' components named TEACHx, whe ° re''' '''the x stands for a digit:'',r' 'I╜0' ° 'L0:T╜''TEACH'',(«I╜I+1)' 'T,'' '',1╟notb(ÉCR T)[2;]' '╕(N>I)/L0' ° 'do' ° '''You may review either of these components separately. To do that,'' ° ' ° '''first enter EXIT (and RETURN), then enter the name of the lesson.'' ° ' '''component (e.g. TEACH4).'',r' ° '''To re-start the lesson, just enter TEACH'',r' ° '''When the screen fills up, it is a good idea to move the cursor to'' ° ' '''the start of a convenient paragraph, and press ENTER'',r' ° '''You may also wish to press PAGE UP to review the prevous pages.''' ° 'do' '''RESOURCES'',r' ° '''You may also enter ONE of the following words at a time'',r' ° X '''REVIEW To review the previous lesson''' 'endd' ° *(1996 4 6 16 5 21 272) ° FREVIEW ÉFX 'REVIEW' 'Σ Review of inner product' ° '''The inner product operator (also known as the DOT product) applies' ° '' ° '''two functions to a dyadic argument. The operator requires a left''' ° '''and a right function, as well as a left and a right argument.'',r' ° '''Although it will produce a result when the arguments are scalar''' ° '''or vectors, inner product is desidgned primarily to be used with''' ° '''arrays of rank 2 or greater.''' 'do' ° 'show ''5+.⌡3'' ''1 2 3+.⌡3 2 1'' ''(2 3µ∞6)+.⌡3 2µ∞6''' ° '''In the first example above, only the left function is applied to''' ° '''the two scalars. The last two examples illustrate the principal''' ° '''characteristic of the inner product. Just as the reduction operator ° ''' ° '''reduces one dimension, the inner product reduces two dimensions,''' ° '''namely the trailing one fron the left argument, and the leading one ° ''' '''from the right argument.'',r' ° '''Although many primitive functions can be used in the inner product, ° ''' '''the most common ones are ^.= and +.⌡'',r' ° 'show ''(π''''ONE'''' ''''TWO'''' ''''SIX'''')^.=φπ''''SIX'''' ''''ONE ° ''''''' 'show ''(3 3µ∞9)+.⌡3 2µΦ∞6''' ° '''The first example illustrates the usage to find matching rows and'' ° ' ° '''columns. The second example illustrates matrix multiplication. We'' ° ' ° '''will study this numeric method in more detail in subsequent lessons ° .''' 'do' ° '''The following examples illustrate some more unconventional usage''' ° '''of the inner product operator'',r' ° 'show ''(3 2µ(1 2) (3 4) (5 6))δ.ε2 2µ(1 2) (3 4)'' ''(∞4)+.,4 2µ∞8''' ° X 'endd' ° *(1997 7 4 12 17 58 460) ° FTEACH ÉFX 'TEACH' 'Σ Start lesson 11: APL2 by Zdenek V JIZBA' ° 'exit ''TEACH''' 'initialize' 'TEACH1 Σ User defined functions' ° 'TEACH2 Σ Using QUAD FIX and Canonical representation' ° 'TEACH3 Σ Defining function ROMAN' 'TEACH4 Σ The line editor' ° 'TEACH5 Σ Editorial on programming styles' ° 'TEACH6 Σ Re-entering function definition' ° 'TEACH7 Σ The session manager editor' 'TEACH8 Σ Headers' ° X 'TEACH9 Σ Local and global objects' 'problems' ° *(1997 6 17 12 44 35 524) ° FTEACH1 ÉFX 'TEACH1' 'Σ Introduction to defined functions' ° 'exit ''TEACH1''' ° '''In the previous lesson we learned a lot about an APL2 operator''' ° '''called the ARRAY PRODUCT. There is more to that operator, but''' ° '''we will postpone that, and take a look in this lesson at user''' ° '''defined functions. To review the previous lesson, enter REVIEW.'',r ° ' ° '''Before you continue, you may also wish to review lesson 5 first.''' ° ''' [T0 do that, enter EXIT to leave this lesson and then )LOAD TEACH ° 5]''' 'do' ° '''In lessons 3 4 and 5 we learned about DIRECT DEFINITION, but we als ° o''' ° '''found that this way of defining new APL2 functions is not supported ° by''' ° '''APL2. In this lesson we will study three ways to define a function. ° ''' ° ''' (APL2 is available on mainframes as well as on the PC. Mainframe ° ''' ° ''' versions support editors not currently available on the PC. Her ° e''' ''' we describe only the techniques available on the PC.)''' ° 'do' ° '''One way to define an APL2 function is to use the DEL MODE (╖). A se ° cond way''' ° '''is to apply a SYSTEM FUNCTION called QUAD FIX (ÉFX). A third way is ° to use''' '''the APL2 editor.''' 'do' ° '''The ╖ mode form invokes a special APL2 editor that prompts for''' ° '''expressions to be enterd at the keyboard. While in the ╖ mode,''' ° '''it is not possible to evaluate APL2 expressions. Conversely, during ° ''' ° '''execution of APL2 expressions, it is not possible to switch to the' ° '' ° '''╖ mode. It is because of this, that you will not be able to test''' ° '''╖ function editing until after the completion of this lesson.'',r' ° '''The second way to define new APL2 functions is with the ÉFX System' ° '' ° '''function. This approach allows you to specify the function as a''' ° '''character array first. The ÉFX function then converts the character ° ''' '''array to a user defined function.'',r' ° '''In the third approach, you can access the EDIT pull down menu and'' ° ' ° '''select the "Open Object" option. (If the function you wish to defin ° e''' ° '''already exists, there is a faster method: place the cursor on the'' ° ' '''name of the function and click twice).''' ° '''We will describe these techniques in more detail in this lesson. We ° will''' ° '''also introduce the supporting SYSTEM FUNCTIONS ÉCR, ÉEX and ÉNC.''' ° X 'endd' ° *(1997 6 16 12 48 15 456) ° FTEACH2 ÉFX 'TEACH2;R;T;FN;AVERAGE' 'Σ Quad fix' 'exit ''TEACH2''' ° '''Suppose we desire to define function AVERAGE. The objective of this ° ''' ° '''function is to add the elements of an array by reducing its last''' ° '''dimension, and dividing the sum by the number of elements added'',r ° ' 'show ''(+/∞5)÷5'' ''(+/2 3µ∞6)÷3''' ° '''The function AVERAGE is monadic, and will produce a result. Therefo ° re''' ° '''the first thing we have to define is this structural information'', ° r' 'show ''FN╜''''U╜AVERAGE R''''''' ° '''We have generated a character string named FN. The contents of FN i ° s''' ° '''called the HEADER. It describes to APL2 the fact that we are about ° to''' ° '''define a function called AVERAGE, which is monadic, and returns a v ° alue.''' ° '''Next we enter a comment to describe the nature of this function.'', ° r' 'show ''FN╜FN ''''Σ Average of last dimension''''''' ° '''A comment like this is not required, but it is an excellent practic ° e''' '''and is highly recommended'',r' 'show ''FN╜FN,Γ''''U╜+/R''''''' ° '''Can you see why we had to use the idiom ,Γ to catenate the string'' ° ' ° '''''''U╜+/R'''' to the nested vector FN? (If you have problems with t ° his,''' ° '''try the expressions DISPLAY FN string, DISPLAY FN,string and''' ° '''DISPLAY FN,Γstring.)'',r' 'show ''DISPLAY FN''' ° '''This first expression generates U by reducing R. To find the averag ° e,''' '''we divide U by the scalar 0¥µR'',r' ° 'show ''FN╜FN,Γ''''U╜U÷0¥µR''''''' ° '''Why the expression 0¥µR? This insures that the array +/R is divided ° ''' ° '''by a scalar no matter what its rank. (Look at lesson 5 to see why t ° he''' ° '''idiom 0¥ returns the last element of a vector as a scalar.)''' ° 'do' 'show ''FN'' ''DISPLAY πFN''' ° '''Either of the two versions of FN, a vector of simple character vect ° ors''' ° '''or a simple character array, can be then used as a right argument t ° o''' '''the APL2 System function ÉFX'',r' ° 'show ''ÉFX FN'' ''AVERAGE ∞5'' ''R╜AVERAGE 2 3µ∞6'' ''R''' ° '''To see how the defined function AVERAGE looks, there is another Sys ° tem''' ° '''Function called ÉCR (the CR stands for CANONICAL REPRESENTATION).'' ° ,r' 'show ''ÉCR ''''AVERAGE''''''' ° '''Why did we separate the expression (+/R)÷0¥µR into two expressions? ° ''' ° '''Actually a combined expression would have worked fine, but we do''' ° '''want to make a point. In a defined function, the evaluation proceed ° s''' ° '''from top to bottom, much the same as if we had written the individu ° al''' ° '''expressions one after the other. So when we enter AVERAGE ∞5, the'' ° ' ° '''function first assigns to R the result of evaluation of ∞5. Then it ° ''' ° '''finds the comment line which it ignores. The next line U╜+/R is''' ° '''evaluated, and then U╜U÷0¥µR completes the algorithm. The final val ° ue''' ° '''of U is then returned. If this value is assigned to a variable as i ° n''' ° '''the second example, the assignment is made in the usual manner.''' ° 'do' ° '''What would happen if we were to try fixing a function with invalid' ° '' '''arguments?'',r' 'show ''ÉFX ''''U╜5TEST'''' ''''U╜1''''''' ° '''In the example we have tried to fix a function named 5TEST. Names i ° n''' ° '''APL2 are not allowed beginning with digits. The fixing process fail ° ed,''' ° '''and the return is an integer (actually the 1 means that the error'' ° ' '''was detected in the first character vector.)''' 'do' ° '''The ÉFX system function also accepts a four element boolean left''' ° '''argument. The values control execution and the ability to display t ° he''' '''defined function.''' 'do' ° '''It is not always possible to solve problems as in function AVERAGE. ° In''' ° '''some algorithm it may be necessary to make decisions, and to procee ° d''' ° '''according to such decisions. This means that we need a way to skip' ° '' ° '''certain expressions (essentially a GO TO branch). To see how APL2'' ° X' '''handles this problem, we will define another function.''' 'endd' ° *(1997 6 17 12 52 3 428) ° FTEACH3 ÉFX 'TEACH3;R;T;ROMAN;RO;RX;FN;AVERAGE' ° 'Σ Branching and labels' 'exit ''TEACH3''' ° '''In lesson 5 we solved the problem of converting an Arabic number''' ° '''to Roman notation. We defined function ROMAN, and two additional''' ° '''functions, RO and RX, to be used as subroutines.'',r' ° '1 show ''ROMAN:RO 10 10 10 10ÿ∙:∙>3999:''''This number is too large'' ° ''''' ° 'T╜''RO:(∙[1]µ''''M''''),(''''CDM''''RX ∙[2]),(''''XLC''''RX ∙[3]),''' ° 'IVX''''RX ∙[4]''' '1 show T' ° '1 show ''RX:((∙>4)µα[2]),(5|∙)µα[1]:4=5|∙:α[1,2+∙=9]''' ° 'show ''ROMAN 27''' ° '''Function ROMAN calls on function RO, and this function in turn call ° s on''' ° '''function RX. This is a reasonable way to solve problems with APL2. ° Let''' '''us now define this function using the ÉFX approach.'',r' ° '''As before, we begin with the header'',r' ° 'show ''FN╜''''U╜ROMAN ARABIC''''''' ° '''Note that we labelled the argument to ROMAN ''''ARABIC''''. This is ° ''' ° '''perfectly valid. APL2 will understand that U and ARABIC are variabl ° es.''' '''We can now continue defining function ROMAN.'',r' ° 'show ''FN╜FN ''''Σ To convert Arabic number to Roman notation''''''' ° '''As before we begin with a comment. Now let us consider the algorith ° m.''' ° '''Right away we see that we have a problem. We need to decide whether ° ''' ° '''the value of the right argument to ROMAN is greater than 3999. If i ° t is,''' '''then we merely return the string'',r' ° ''' ''''This number is too large'''''',r' ° '''If ARABIC is less than 4000, we apply expression RO 10 10 10 10ÿARA ° BIC''' 'do' 'show ''FN╜FN,Γ''''╕(ARABIC<4000)/L0''''''' ° '''The right arrow (╕) is a symbol understood by the portion of APL2'' ° ' ° '''that evaluates user defined functions. It has no meaning within''' ° '''stand alone APL2 expressions.''' 'do' ° '''Within user defined functions, it tells the APL2 INTERPRETER to''' ° '''ignore the normal sequence of expressions, but instead to find''' ° '''the expression that begins with the string ''''L0''''.'',r' ° '''This branch will take place only if the expression to the right of' ° '' '''the ╕ returns a value other than null.''' 'do' ° 'show ''FN╜FN,Γ''''U╜''''''''This number is too large.''''''''''''''' ° '''If ARABIC is greater than 3999, then the expression ARABIC<4000 wil ° l''' ° '''return a zero, and the reduction 0/L0 will produce a null vector.'' ° ' ° '''The APL2 interpreter ignores any branch to a null vector. Therefore ° ''' ° '''the next expression to be evaluated will be the assignment of the'' ° ' '''string ''''This number is too large'''' to U''' 'do' ° 'show ''FN╜FN,Γ''''╕0''''''' ° '''A branch to zero is interpreted by APL2 as a command to EXIT the''' ° '''user defined function.''' 'do' ° 'show ''FN╜FN,Γ''''L0:U╜RO 10 10 10 10ÿARABIC''''''' ° '''This expression is LABELLED. The label L0 is recognized by the''' ° '''presence of the colon (:). If the value of ARABIC is less than 4000 ° ''' ° '''this expression will be evaluated, and the function will return the ° ''' '''value of U.''' 'do' ° '''We now have completed the programming part. Let us take a look at'' ° ' '''the array FN that we have just generated'',r' 'show ''πFN''' ° '''Before we can apply ÉFX, we could make sure that there is no APL2'' ° ' ° '''object with that name. There is the System Function ÉNC for that''' ° '''purpose'',r' 'show ''ÉNC ''''ROMAN'''''' ''ÉNC ''''FN''''''' ° '''System Function ÉNC is called NAME CLASSIFICATION. It tells whether ° ''' ° '''the right argument exists as an APL2 object. The 3 for ROMAN means' ° '' ° '''that ROMAN already exists as a function. The 2 for FN means that''' ° '''there is a variable called FN'',r' 'show ''ÉEX ''''ROMAN''''''' ° '''System function ÉEX (for EXPUNGE) has been applied to erase functio ° n''' ° '''ROMAN. The value 1 returned by ÉEX acknowledges successful erasure. ° '',r' ° '''It is good programming practice to apply ÉNC to a label, and then t ° o''' ° '''use ÉEX just before using ÉFX. (In APL2 ÉFX will override a previou ° sly''' '''defined function with the same name.)'',r' ° 'show ''ÉNC ''''ROMAN''''''' ° '''The 0 returned by ÉNC ''''ROMAN'''' means that the label ROMAN is n ° ot in''' '''use.'',r' ° 'show ''ÉFX FN'' ''ÉNC ''''ROMAN'''''' '' ROMAN 27 ''' ° '''Function ROMAN has been re-defined with FN, and works properly.''' ° 'do' ''' DIAMOND SEPARATOR'',r' ° '''APL2 supports a notation called the "diamond separator". The symbol ° ╪''' ° '''allows entering two or more expressions to be placed on a single li ° ne.''' '''The expressions are evaluated from left to right'',r' ° 'show ''''''First line'''' ╪ ∞5 ╪ ''''Third line''''''' ° '''Using the diamond, we can re-define function ROMAN'',r' ° 'FN╜''U╜ROMAN ARABIC''' ° 'FN╜''U╜ROMAN ARABIC'' ''Σ To convert Arabic number to Roman notation' ° '' ° 'FN╜FN,Γ''╕(ARABIC<4000)/L0 ╪ U╜''''This number is too large.'''' ╪ ╕0 ° ''' 'FN╜πFN,Γ''L0:U╜RO 10 10 10 10ÿARABIC''' 'show ''FN'' ''ÉFX FN''' ° '''We have collapsed three lines into one. This technique is more than ° ''' ° '''a device to reduce the number of APL lines in a function definition ° .''' ° '''As we will see later, it can be used to provide an important elemen ° t''' ° '''of structural programming. But now let us verify that the new versi ° Xon''' '''of ROMAN works properly'',r' 'show ''ROMAN 1997''' 'endd' ° *(1997 8 30 11 35 44 580) ° FTEACH4 ÉFX 'TEACH4;R;T;FN;MOVAVG' 'Σ Del mode' 'exit ''TEACH4''' ° '''Let us now describe the process of defining functions with the ╖''' ° '''symbol.'',r' ° '''WARNING! You will not be able to try out the examples on your own'' ° ' ° ''' until AFTER the lesson is completed. You may, however,''' ° ''' use ÉFX to try out ideas of your own.''' 'do' ° '''We will try to define function MOVAVG. This function will evaluate' ° '' '''the moving average of a numeric vector or array. Here are two''' ° '''examples of the algorithm to be defined'',r' ° 'show ''(3+/∞6)÷3'' ''(2+/2 4µ∞8)÷2''' ° '''We begin with the header. There are two arguments to this function: ° ''' ° '''One is the data to be averaged, and the other is the averaging leng ° th.''' ° '''The function therefore should be dyadic. What we have to decide is' ° '' ° '''which should be the left argument, and which the right argument.''' ° 'do' ° '''There are no hard and fast rules for deciding where arguments shoul ° d''' ° '''be placed. On the basis of past experience, and for other practical ° ''' ° '''reasons, it is a good idea to place the data to be modified as the' ° '' '''right argument'',r' ''' ╖U╜L MOVAVG DATA''' '''[1]''' ° 'FN╜''U╜L MOVAVG DATA'' ''Σ Moving average of length L on data''' ° 'FN╜FN,''U╜L+/DATA'' ''U╜U÷L''' 'T╜ÉFX FN' 'do' ° '''The symbol ╖ preceeding the header expression is a toggle switch.'' ° ' ° '''It transfers control to the APL2 function editor. At this point''' ° '''anything you enter at the terminal becomes part of the function''' ° '''under definition. You can always tell when you are in the APL2''' ° '''edit mode, because you are prompted by a line count'',r' ° '''[1] Σ Moving average of length L on DATA''' '''[2]''' 'do' ° '''Pressing ENTER terminates the line entry. A new prompt is issued''' ° '''for the next line'',r' '''[2] U╜L+/DATA''' '''[3] U╜U÷L╖''' 'do' ° '''Entering the symbol ╖ at the end of line 3 ends the function''' ° '''definition mode, as well as the process of definimg MOVAVG'',r' ° X 'show ''3 MOVAVG ∞6''' 'endd' ° *(1997 8 30 11 44 26 544) ° FTEACH5 ÉFX 'TEACH5;FN;T;MOVAVG' 'Σ Programming style' ° 'exit ''TEACH5''' ° 'FN╜''U╜L MOVAVG DATA'' ''Σ Running average of length L on data''' ° 'FN╜FN,''U╜L+/DATA'' ''U╜U÷L''' 'T╜ÉFX FN' '''PROGRAMMING STYLES'',r' ° '''Before proceeding with further description of defined functions,''' ° '''it is apropriate at this point to make a few EDITORIAL remarks abou ° t''' ° '''programming style. Since programming is a highly personal effort''' ° '''there is always room for disagreement. Hence, in this and in later' ° '' ° '''sessions, my personal comments will be preceeded by the heading''' ° 'do' '''''''PROGRAMMING STYLES''''.''' 'do' ° '''First, it should be clear that function MOVAVG has been designed''' ° '''merely to illustrate concepts in function definition. In practice'' ° ' ° '''it does not make sense to write a special function, where a simple' ° '' ° '''line of code, namely (L+/DATA)÷L will suffice. One should therefore ° ''' '''ask, why and when should one define an APL2 function.'',r' ° '''In my opinion there are three fundamental reasons for APL2 user def ° ined''' '''functions:'',r,r,'' 1. General utility functions''' ° ''' 2. Problem solving functions'',r,'' 3. Subroutines'',r' ° '''Utility APL2 functions are those that one might want to use in many ° ''' ° '''different applications. Problem solving functions are those that''' ° '''solve specific problems. An example of these would be function ROMA ° N.''' ° '''ROMAN uses functions RO and RX as subroutines. Defining RO and RX'' ° ' ° '''as separate APL2 functions simplifies the code, and makes it easier ° ''' '''to understand and to maintain.''' 'do' ° '''When defining utility functions, there are several considerations t ° o''' ° '''keep in mind. A utility has EDGE EFFECTS, DEFAULTS, and ABORTS.'',r ° ' ° '''By edge effects, I mean special cases that one does not normally''' ° '''consider a solution to that particular utility. Let us assume that' ° '' '''we desire to treat function MOVAVG as a utility. Then'',r' ° 'show ''1 MOVAVG ∞6'' ''6 MOVAVG ∞6''' ° '''The first expression returns the original argument unchanged, while ° ''' '''the second expression returns the average.''' 'do' ° '''The main difference between the second expression, and AVERAGE ∞6'' ° ' '''is in the rank of the result'',r' ° 'show ''DISPLAY (+/∞6)÷6'' ''DISPLAY 6 MOVAVG ∞6''' ° '''These examples are not normally thought of as ''''moving averages'' ° '', but''' '''are acceptable.''' 'do' ° '''Consider now the following expressions'',r' ° 'show ''DISPLAY 7 MOVAVG ∞6'' ''²2 MOVAVG ∞6''' ° '''While one could argue that these two examples are valid, it is not' ° '' '''likely one would consider the results as reasonable. Function''' ° '''MOVAVG, therefore, has some EDGE EFECTS that one might want to remo ° ve.''' 'do' ° '''Another problem is one of DEFAULTS. Suppose for the sake of argumen ° t''' ° '''that whenever we talk about moving averages, we normally assume tha ° t''' ° '''we are dealing with a specific value of the left argument, say 2.'' ° ' ° '''Then it might be reasonable to request the omission of the left''' ° '''argument to signify a default value of 2. In other words whenever'' ° ' '''one enters'',r,r,'' MOVAVG ∞6'',r' ° '''the result should be'',r,r,''1.5 2.5 3.5 4.5 5.5''' 'do' ° '''Finally, there may be expressions that cause the execution to be''' ° '''interrupted with an error message'',r' ° 'show ''8 MOVAVG ∞6'' ''1.5 MOVAVG ∞6''' ° '''My personal approach in this situation is to avoid, or postpone''' ° '''the interrupt. For example, instead of the error message, the''' ° '''function prints on the screen a character string, such as'',r' ° ''' You have entered an illegal argument in function MOVAVG'',r' ° '''and then returns a value that is clearly invalid (e.g. ∞0).''' ° '''Any subseqent handling of the result can be identified by the calli ° ng''' ° '''function, and remedial action be taken without an interrupt.''' ° 'do' ° '''This is the end of my EDITORIAL COMMENT. I am well aware that this ° is''' ° '''NOT the approach taken by other APL users. Some feel strongly that' ° '' ° '''any improper invocation of a user defined function should cause an' ° '' ° '''interrupt and display an error message. Ultimately the decision on' ° '' ° '''how to deal with such edge effects, defaults and aborts will depend ° on''' '''who gets to use the final product.''' 'do' ° '''We will now see how these objectives can be achieved by refining th ° Xe''' '''function definition of MOVAVG.''' 'endd' ° *(1997 8 30 11 51 48 660) ° FTEACH6 ÉFX 'TEACH6;T;FN;MOVAVG' 'Σ Modifying a defined function' ° 'exit ''TEACH6''' ° 'FN╜''U╜L MOVAVG DATA'' ''Σ Moving average of length L on DATA''' ° 'FN╜FN,''U╜L+/DATA'' ''U╜U÷L''' 'T╜ÉFX FN' ° '''Once a function has been defined, it is possible to re-enter the''' ° '''function definition mode with ╖MOVAVG[É]. This will produce a listi ° ng''' ° '''of the function, followed by a prompt to enter a new line'',r' ° 'showfn ''MOVAVG''' '''[4]''' 'do' ° '''At this point additional lines can be added to the function. Since' ° '' ° '''we do not wish to add new lines following line [3], we can insert'' ° ' '''lines by entering fractional line numbers'',r' '''[4] [1.1]''' ° '''[1.1] ╕(Lε∞²1╞µDATA)/L0''' ° '''[1.2] ''''You have entered an illegal argument in function MOVAVG'' ° '' ╪ U╜∞0 ╪ ╕0''' '''[1.3][2]''' '''[2] L0:U╜L+/DATA╖'',r' ° 'T╜''''''You have entered an illegal argument in function MOVAVG'''' ╪ ° U╜∞0 ╪ ╕0''' 'FN╜(2╞FN),Γ''╕(Lε∞²1╞µDATA)/L0''' ° 'FN╜FN,T ''L0:U╜L+/DATA'' ''U╜U÷L''' 'T╜ÉEX ''MOVAVG''' 'T╜ÉFX FN' ° '''We can now look at the modified function with ╖RUNAVG[É]╖''' ° '1 showfn ''MOVAVG''' ° 'r,''The expression "╖MOVAVG[É]╖", beginning and ending with ╖ has the ° ''' ° '''effect of entering the function definition mode, listing the functi ° on,''' ° '''and exiting the function definition mode. It is more useful than th ° e''' ° '''simpler ÉCR ''''MOVAVG'''' System Function in that it also provides ° the''' '''line numbering.''' 'do' ° '''The modified function MOVAVG now filters out invalid left arguments ° '',r' 'show ''²2 MOVAVG ∞6'' ''1.5 MOVAVG ∞6''' ° '''The next step is to allow MOVAVG to also support a monadic form.''' ° '''Whenever a function has that property, it is called AMBIVALENT.''' ° '''On a defined function, this can be done by testing whether the''' ° '''left argument is defined on entry to the function. This is done''' ° '''with the ÉNC System Function''' 'showfn ''MOVAVG''' '''[8]''' 'do' ° '''We will insert a test to that effect'',r' '''[8] [1.1]''' ° '''[1.1] ╕(2=ÉNC ''''L'''')/L1 ╪ L╜2''' ° '''[2] L1:╕(Lε∞²1╞µDATA)/L0╖''' ° 'T╜(2╞FN),''╕(2=ÉNC ''''L'''')/L1 ╪ L╜2'' ''L1:╕(Lε∞²1╞µDATA)/L0''' ° 'FN╜T,3╟FN' 'T╜ÉEX ''MOVAVG''' 'T╜ÉFX FN' 'do' ° '''Let us look at this new version. Note the usage of the diamond to d ° eal''' '''with the missing left argument'',r' '1 showfn ''MOVAVG''' ° 'r,''Applying MOVAVG monadically, we get a default 2 for left argument ° X'',r' 'show ''2 MOVAVG ∞6'' ''MOVAVG ∞6''' 'endd' ° *(1997 6 17 13 4 55 448) ° FTEACH7 ÉFX 'TEACH7' 'Σ The session Manager editor' 'exit ''TEACH7''' ° ''' THE SESSION MANAGER EDITOR'',r' ° '''Historically, the DEL (╖) editor is the oldest method of defining'' ° ' '''APL functions. The Character Representation (ÉCR) was an early''' ° '''improvement that made it possible to store user defined functions'' ° ' ° '''as character arrays in object libraries (See later tutorials dealin ° g''' '''with Auxilliary Processors 210 and 211.)'',r' ° '''The most recent development is an editor that is based on OS2. It i ° s''' ° '''called the Session Manager Editor. To invoke it, you simply press o ° n''' ° '''the EDIT pull down menu, and select "Open Object". A window will ap ° pear''' ° '''that is set to a user defined function default. It sets the prompt' ° '' ° '''in a box where you are expected to enter the name of the function.' ° '' ° '''However, if the function is already defined, you can save yourself ° the''' ° '''effort of typing it by scrolling down on the "Objects" box and clic ° king''' ° '''on the desired function name (That name will appear on the top box) ° '',r' ° '''At that point you can either double click on the name, or press the ° "OK"''' ° '''button. The session manager editor allows you to insert new lines, ° to''' ° '''change existing lines and to move text (to and from the current''' ° '''document or any other document accessible from OS2.)''' 'do' ° '''Note also the three buttons under the label "Type of Object". You c ° an''' ° '''switch between a character array or a function. (We will defer the' ° '' ° '''"Operator" option until such time this feature is discussed in a la ° ter''' ° '''tutorial session.) There is only one constraint. If a function has ° been''' ° '''defined, a character array cannot have that same name. Note also th ° at''' ° '''the Session Manager Editor can be used to create non-APL documents ° by''' ° '''taking advantage of the "COPY" and "PASTE" options in the pull down ° X''' '''editor.''' 'endd' ° *(1997 9 7 12 55 44 576) ° FTEACH8 ÉFX 'TEACH8;AVERAGE;T' 'Σ Headers' 'exit ''TEACH7''' ° '''We have seen examples of monadic and dyadic defined functions.''' ° '''We have also seen how a dyadic function can be made to behave as''' ° '''if it were monadic by making it ambivalent. Since the nature of''' ° '''arguments to a defined function is specified in the header, it is'' ° ' '''only natural to ask what other headers are possible.''' 'do' ° '''There are two other variations to headers: First, headers need not' ° '' ° '''have any arguments. Function without arguments are called NILADIC.' ° ',r' ° '''Niladic functions are typically used to provide explanations, or''' ° '''as main entries to applications. We will give specific examples in' ° '' '''future lessons of niladic functions.''' 'do' ° '''The other feature of headers deals with results. So far, our sample ° ''' ° '''functions had a header of the form U╜... . Whenever a header contai ° ns''' ° '''such an assignment arrow, it is generally expected that the named'' ° ' '''variable be generated in the body of the function before exit.''' ° '''Failure to do so will cause an error condition whenever an attempt' ° '' ° '''is made to assign the nonexistent result. (Some APL2 users will''' ° '''intentionally leave the result undefined to force an error whenever ° ''' '''the function is used improperly.)'',r' ° 'T╜ÉFX ''U╜AVERAGE R'' ''Σ Average of last dimension'' ''U╜+/R'' ''U╜Y ° ÷0¥µR''' ''' ATTRIBUTES'',r' ° '''There is a System function that provides information about the''' ° '''ATTRIBUTES of a user defined function. ÉAT is dyadic. The left''' ° '''argument specifies the type of information to be retrieved. The''' ° '''right argument is the name (or array of names) to be searched.''' ° '''The attributes that can be obtained fall into 4 categories:'',r' ° ''' 1 Valences (the nature of the headers of the function)''' ° ''' 2 Time when the user defined function was last fixed''' ° ''' 3 Whether the function is locked, displayable ....''' ° ''' 4 Size of the character object (used with shared variables)'',r' ° '''Earlier we have defined function AVERAGE (it is re-defined here).'' ° ,r' 'show ''ÉCR '''' AVERAGE ''''''' ° '''Let us look at its attributes:'',r' ° 'show ''1 ÉAT ''''AVERAGE''''''' ° '''The vector 1 1 0 means the function produces a result (1), is monad ° ic''' '''(1) and is a function (0)'',r' ° 'show ''2 ÉAT ''''AVERAGE''''''' ° '''The result gives the date and time when this function was fixed.'', ° r' 'show ''3 ÉAT ''''AVERAGE''''''' ° '''the vector indicates that this function is displayable, suspendable ° ,''' ° '''interruptible, and displays non-resource errors. (These subjects wi ° ll''' ° '''not be extensively discussed in these introductory tutorials .)'',r ° ' 'show ''4 ÉAT ''''AVERAGE''''''' ° '''The resulting vector indicates the function is a user defined funct ° Xion''' 'endd' ° *(1997 6 20 12 52 7 456) ° FTEACH9 ÉFX 'TEACH9;FN;TEST;TESTA;TESTB;TESTC;U;LEFT;RIGHT;T;F;G;H;I' ° 'Σ Local variables' 'exit ''TEACH8''' ° '''LOCALIZATION OF VARIABLES'',r' ° '''In the header for function RUNAVG, there are four labels'',r' ° ''' U L RUNAVG and DATA'',r' ° '''The labels U L and DATA are reserved names of variables. All header ° ''' ° '''labels in a defined function have a SCOPE and a STATUS. The scope c ° an be''' ° '''LOCAL or GLOBAL, and the status can be DEFINED or UNDEFINED. Let us ° ''' '''now study these concepts.''' 'do' ° '''Let us investigate a defined function we shall call TESTA'',r' ° 'show ''FN╜''''LEFT TESTA RIGHT'''' ''''DISPLAY LEFT RIGHT G'''' ''''G ° ╜''''''''global''''''''''''''' 'show ''ÉFX FN''' ° '''Let us first assign values to LEFT RIGHT and G'',r' ° 'show ''(LEFT RIGHT G)╜''''SIX'''' ''''SEVEN'''' ''''GLOBAL'''''' ''DI ° SPLAY LEFT RIGHT G''' '1 showfn ''TESTA''' '''''' ° 'show ''6 TESTA 7'' ''DISPLAY LEFT RIGHT G''' ° '''Within function TESTA the "value" of LEFT and RIGHT is 6 and 7 resp ° ectively.''' ° '''The "value" of G remains ''''GLOBAL'''' because G is not listed in ° the header''' ° '''of TESTA. On exit from function TESTA the value of variables LEFT a ° nd''' ° '''RIGHT reverts to their global setting. By re-defining G within func ° tion''' '''TESTA, we changed its content in the global variable G.''' ° 'do' ° '''Any variables not specified in the header of a function are called ° global.''' ° '''Any global variable having the same name as a variable in a header ° of a''' '''function cannot be reached from within that function.'',r' ° '''Suppose now, we wish to define an additional label in a function, s ° o that''' ° '''it too is local. APL2 supports such a localization in the header'', ° r' ° 'FN╜''TESTB;F G H I'' ''I╜π,■''''FGHI'''''' ''DISPLAY I'' ''ÉNC I'' '' ° H╜4''' 'show ''πFN''' ° '''We have defined a NILADIC function named TESTB. The header includes ° a''' ° '''semicolon followed by a list of labels (F G H and I). These now def ° ine''' '''APL2 objects that are strictly local to TESTB.''' ° '''(Note that ÉNC accepts rank 2 character arrays of labels)'',r' ° 'do' 'FN╜FN,''G╜''''U╜F H'''' ''''U╜∞H'''''' ''ÉFX G'' ''F H''' ° 'show ''πFN''' ° '''We have added three more lines to function TESTB. Variable G become ° s a''' ° '''nested vector defining F as a monadic function with argument H. Nex ° t,''' ° '''G is fixed defining function F. F becomes a function local to TESTB ° .''' '''The final line of function TESTB evaluates function F.'',r' ° 'show ''ÉFX FN''' '1 showfn ''TESTB''' ° '''Before we proceed with the evaluation of TESTB, you want to study'' ° ' '''carefully the listing of function TESTB.''' 'do' ° '''Before we evaluate TESTB, we will also define GLOBAL variables F, G ° ,''' '''H and I'',r' ° 'show ''(F G H I)╜''''ONE'''' ''''TWO'''' ''''THREE'''' ''''FOUR'''''' ° ''DISPLAY F G H I''' 'show ''TESTB'' ''πF G H I''' ° '''In summary, the header can be used to define not only the nature of ° ''' ° '''the function (monadic, dyadic, niladic and with or without result), ° ''' ° '''but also any labels that are to be stricly local to that function.' ° '' ° '''These localized object names can be used to define any valid APL2'' ° ' '''objects.''' 'do' ° '''Before we leave the subject of headers, there is one other aspect'' ° ' ° '''of its use. When the APL2 interpreter reads the header in order to' ° '' ° '''allocate and match arguments to names, it does so from left to righ ° t'',r' ° 'show ''ÉFX ''''U╜U TESTC U'''' ''''U'''' ''''U╜0'''''' ''5 TESTC ∞4'' ° ' ° '''In the header, the label repeats 3 times. As the header is evaluate ° d,''' ° '''the leftmost argument, the asigned variable is left undefined. Then ° ''' ° '''the left argument of TESTC, if present is assigned to U. Finally th ° e''' ° '''right argument of TEST is assigned to U. Knowing this sequence allo ° ws''' '''definition of default results in some applications'',r' ° 'show ''ÉFX ''''R╜L TEST R'''' ''''╕(0=ÉNC ''''''''L'''''''')/0'''' '' ° ''R╜R+L''''''' 'show ''ÉCR ''''TEST'''''' ''3 TEST 4'' ''TEST 5''' ° X 'endd' ° *(1997 7 13 12 28 49 504) ° Faddquote ÉFX 'u╜addquote w' ° 'Σ Put quotes around a string, and double existing quotes' ° X 'u╜ÉAV[40],((1+w=ÉAV[40])/w),ÉAV[40]' ° *(1997 7 24 13 20 38 476) ° Fav ÉFX 'av;A;N;I;ÉIO' 'Σ Display characters in ÉAV' 'ÉIO╜0' ° 'A╜22 78µ'' ''' 'N╜3 0«φ12 22µ1+∞356' 'A[;,(6⌡∞12)°.+2 3 4]╜N' ° 'A[;6+6⌡∞12]╜φ12 22µÉAV' 'ΣA[8 10 13;6]╜'' ''' 'A[13;6]╜'' ''' ° X 'A[14+∞8;68 69 70 72]╜'' ''' 'A' ° *(1991 11 11 8 25 13 316) ° Fdate ÉFX 'u╜date w' 'Σ Format date and time of day' 'u╜«6╞w' ° X 'u╜('' ''⌠u)Γu' 'u╜εu,■''-- .. ''' ° XCdig 1 10 1234567890 ° *(1997 9 9 13 0 45 372) ° Fdisclaimer ÉFX 'disclaimer' 'Σ Copyright statement' ° '(10µ'' ''),''Copyright, Z. V. Jizba, 1995,1996,1997'',r' ° ''' This and subsequent workspaces labelled TEACHxx are made available ° ''' ° '''at no cost to anyone who desires to learn how to use effectively''' ° '''the IBM/OS2 version of APL2.'',r' ° '''This software is provided "AS IS" with no WARRANTY of any kind, eit ° her''' ° '''express or implied. Any risk in its use resides with you, the user ° of''' '''these tutorials.'',r' ''' ACKNOWLEDGEMENTS'',r' ° ''' In writing these tutorials, I am greatly indebted to Roy Sykes, wh ° ose''' ° '''excellent lectures increased my understanding of the language.''' ° '''Discussions with the late Harry Bertucelli clarified a number of''' ° '''concepts and caused me to change some improper terminology that was ° ''' ° '''used in previous versions of these tutorials. Mr. Benjamin Archer'' ° ' ° '''kindly checked out a nearly final version, bringing to my attention ° ''' '''some ommisions, misspellings, and invalid terminology.'',r' ° X '''(PRESS ENTER to continue)''' ° *(1997 7 13 12 28 50 508) ° Fdo ÉFX 'do;T;E' 'Σ Expression driver' 'E╜''''' 'æ╜'' ''' 'T╜æ' ° '╕(^/'' ''=T)/0' ° '╕(('':''εT)doif ''B╜evaldd (+/^\'''' ''''=T)╟T'')/2' ° '''E╜ÉEM'' ÉEA T' '╕(0=µ,E)/2' ° '''This is not a valid APL2 expression''' 'æ╜''*''' '╕(''?''⌠╞1╟æ)/2' ° X 'E' '╕2' ° *(1997 7 13 12 28 50 508) ° Fdoif ÉFX 'U╢╜V╢ doif W╢;t╢' 'Σ Rule' '╕(^/~U╢╜V╢)/0' ° X '''U╢╜V╢ doif■ W╢'' ÉEA ''»V╢/W╢''' ° *(1997 9 9 12 50 14 444) ° Fendd ÉFX 'endd' 'Σ end of special feature' '20µ''²'' ╪ ╕(4<µÉLC)/0' ° X 'do' ° *(1997 8 16 12 11 1 260) ° Ferase ÉFX 'erase;t;EXIT;GO;HELP;BIND;DISPLAY;REVIEW;RULE;DISCLAIMER' ° 'Σ Erase all global functions and variables' 't╜ÉNL 3' ° 't╜(~t^.εlc,'' '')≡t' 't╜ÉEX(~t[;∞5]^.=''TEACH'')≡t' 't╜ÉNL 2' ° X 't╜ÉEX(~t^.εlc,'' '')≡t' ° *(1997 7 27 13 47 41 608) ° Fevaldd ÉFX 'u╜evaldd w;c;n' 'Σ Evaluate direct definition' 'u╜0' ° 'n╜(w∞''Σ'')-1' 'c╜(((n╞w)⌠'':'')Γn╞w),Γ''ΣDD '',(n+1)╟w' ° '╕((1 label╞c)doif ''''''Invalid label'''''')/0' ° '╕((2=µc)doif ''u╜showdd 1╙c'')/0' ° '╕((3=ÉNC╞c)doif ''u╜⌡µÉ╜(╞c),'''' is already defined.'''''')/0' ° '╕((3=µc)doif ''u╜simdd c'')/0' 'c╜(Γ''α∙ aw'')replace■c' ° 'u╜ε''u╜'',((''a''εεc[2 3 4])/''a ''),(╞c),'' w;t;b''' ° 'u╜u(5πc)(''b╜(t╜'',(3πc),'')/'',addquote ''u╜'',4πc)' ° X 'u╜u,''╕(t doif b)/0''(''u╜'',2πc)' 'u╜╧ÉFX u' ° *(1997 7 25 13 27 52 564) ° Fexit ÉFX 'V exit W;T' 'Σ Exit if too many suspended functions' ° '╕(0⌠ÉNC ''V'')/L0 ╪ V╜10' 'L0:╕(V>µÉLC)/0' ° '''There are too many suspended functions''' '''Please enter '',W' ° X '╕' ° *(1997 7 26 12 33 39 536) ° Fget ÉFX 'U╜V get W;t;T;ÉPR' 'Σ Prompt for response from keyboard' ° 'ÉPR╜T╜ÉAV[ÉIO+255] ╪ ╕(0⌠ÉNC ''V'')/L0 ╪ V╜1' 'L0:V╜V╧1' 'æ╜W ╪ t╜æ' ° 'U╜(+/^\t=T)╟t' '╕(''╕''⌠╞U)/L1 ╪ ╕' 'L1:╕V/0' 't╜(U⌠'' '')ΓU' ° X 'U╜(µt),(ΓU),t' ° *(1997 7 28 13 33 8 424) ° Fglobals ÉFX 'globals' 'Σ Initialize useful global variables' ° 'uc╜''ABCDEFGHIJKLMNOPQRSTUVWXYZ''' ° 'lc╜''abcdefghijklmnopqrstuvwxyz''' 'dig╜''1234567890''' ° X 'r╜ÉAV[13+ÉIO]' 'q╜''''''''' ° *(1997 7 3 12 47 6 368) ° Finitialize ÉFX 'initialize;T' 'Σ Initialize workspace' ° '''AT ALL TIMES, TO CONTINUE, PRESS RETURN!'',r' ° '''To see disclaimers enter:'',r,'' disclaimer''' 'do' 'erase' ° 'globals' ° '''Make sure the CAP LOCK light on your keyboard (upper right) is ON!' ° X'' 'endd' ° *(1997 7 27 13 14 33 444) ° Flabel ÉFX 'u╜v label w' ° 'Σ Return 1 if label w does not begin with a cap' ° '╕(0⌠ÉNC ''v'')/L0 ╪ v╜0' 'L0:v╜v╧1 ╪ w╜εw ╪ ╕v/L1 ╪ ╕(u╜0⌠ÉNC w)/0' ° X 'L1:╕(u╜~^/wεlc,uc,dig)/0' 'u╜w[1]εlc,dig' ° XClc 1 26 abcdefghijklmnopqrstuvwxyz ° *(1997 7 13 12 28 55 528) ° Fnon ÉFX 'non;T;RC;ET;R' 'Σ Ignore keyboard entry' 'æ╜'' ''' 'T╜æ' ° '╕(0=µ(T⌠'' '')/T)/0' '(RC ET R)╜ÉEC T' '╕(0=RC)/2' ° X '╕((1=RC)doif ''R'')/2' '╕2' ° *(1997 7 13 12 28 55 528) ° Fnotb ÉFX 'u╜notb w' 'Σ Remove trailing blanks' ° '╕((1<╧w)doif ''u╜notb■ w'')/0' '╕((1<µµw)doif ''u╜πnotb Γ[2]w'')/0' ° X 'u╜(1-(,'' ''⌠Φw)∞1)╟w' ° *(1997 7 27 12 55 6 496) ° Fproblems ÉFX 'problems' 'Σ Problems' ° '''That is all for this lesson. Remember, if you want to practice,''' ° '''and plan to use direct definitions, be sure to first enter GO.''' ° '''Direct definitions will then be accepted. To exit GO, enter EXIT.'' ° ,r' ° '''To erase a previously defined DIRECT DEFINITION FUNCTION, enter'',r ° ' ''' )ERASE functionname'',r' ° X '''WARNING! do not use )ERASE on other labels.'',r' ° XCq 0 ' ° XCr 0 ° *(1997 7 13 12 28 56 532) ° Freplace ÉFX 'u╜v replace u;i;r;s' 'Σ Replace elements in v in u' ° 'i╜Γ∞µu' 's╜2πv╜(v⌠'' '')Γv' 'i╜⌡r╜i⌡■Γ[1]u°.=╞v' ° X 'u[(εi)/εr]╜s[(εi)/εi⌡■∞µs]' ° *(1997 7 13 12 28 56 532) ° Fround ÉFX 'U╜V round W' 'Σ Half adjust to V th decimal' ° X 'U╜(╛0.5+W⌡10*V)÷10*V' ° *(1997 7 13 12 28 57 536) ° Fshow ÉFX '╢V show ╢W;╢T;╢B' 'Σ Display and execute ╢W' ° '╢T╜(0=ÉNC ''╢V'')doif ''╢V╜0''' ° '╕((0=╧╢W)doif ''show ╢W,'''' '''''')/0' ° '╕((1<╧╢W)doif ''╢V show ■╢W'')/0' ''' '',╢W' ° X '╕((╢V^'':''ε╢W)doif ''╢T╜evaldd ╢W'')/L0' '''ÉEM'' ÉEA ╢W' 'L0:do' ° *(1997 7 13 12 28 57 536) ° Fshowdd ÉFX 'u╜showdd w;a;b;c;r' ° 'Σ Display a direct definition function' ° '╕((1=╧w)doif ''u╜showdd Γw'')/u╜0' ° '╕((3⌠ÉNC╞w)doif ''(ε╞w),'''' is not a function'''''')/0' ° 'c╜Γ[2]ÉCR╞w' 'c╜notb(2╞c),(Γ''aw α∙'')replace■2╟c' ° '╕((~''ΣDD''╧3╞2πc)doif ''''''Not a direct definition function'''''')/ ° 0' 'u╜1' 'b╜('' ''⌠╞c)Γ╞c' 'a╜'' ''' 'r╜2╟3πc' ° '╕((3=µc)doif ''a,(╞w),'''':'''',r,(3<µ2πc)/'''' Σ'''',3╟2πc'')/0' ° 'a╜a,(╞w),'':'',(2╟5πc),'':''' 'b╜(+\r=''('')-+\r='')''' 'b╜b∞0' ° X 'a╜a,(²3╟(b-1)╞3╟r),'':'',2╟»(b+2)╟r' 'a,(3<µ2πc)/'' Σ'',3╟2πc' ° *(1997 7 13 12 28 57 536) ° Fshowfn ÉFX 'U╜V showfn W;F;N;T;ÉIO' 'Σ Simulate ╖W[É]' ° 'T╜(0=ÉNC ''V'')doif ''V╜0''' 'ÉIO╜0' ° 'U╜r,'' '',''╖'',W,''[É]'',(╞V)╞''╖''' 'N╜1╞µF╜ÉCR W' 'N╜«∞N' ° 'N╜(N⌠'' '')ΓN' 'F╜(π''['',■N,■Γ''] ''),F' ° 'T╜(1<µ,V)doif ''F╜F[1╟V;]'' ''U╜''''''''''' 'U╜²1╟U,r,,F,r' ° X 'U╜((-+/^\'' ''=ΦU)╟U),('' ╖'')[╞V],r' ° *(1997 7 13 12 28 58 540) ° Fsimdd ÉFX 'u╜simdd w;e' 'Σ Direct definition mode' 'u╜0' ° '╕((0⌠ÉNC╞w)doif ''''''Already defined'''''')/0' 'e╜''α''ε2πw' ° 'w[2]╜Γ''u╜'',''α∙ aw'' replace 2πw' 'w╜w[1 3 2]' ° X 'w[1]╜Γε''u╜'',(e/''a ''),w[1],'' w''' 'u╜╧ÉFX w' ° *(1992 6 3 9 59 17 424) ° Ftab ÉFX 'U╜V tab W;T;A;B;C;D;E;F;G;M;ÉPW' 'Σ Tabulate list W' ° 'T╜(0=ÉNC ''V'')doif ''V╜0''' 'M╜''Invalid data for tabulation''' ° 'V╜4╞V' 'ÉPW╜130╛30⌐G╜V[2]+79⌡V[2]=0' ° 'L1:╕((1<╧W)doif ''''''W╜∞0'''' ÉEA ''''W╜πW'''''')/L1' ° '╕(((0=µεW)δ2<µµW)doif ''U╜(~V╧4╞0)/M'')/0' ° 'T╜(1≥µµU╜«W)doif ''U╜πW╜(U⌠'''' '''')ΓU''' ° 'T╜(0<V[1])doif ''U╜(«(Φ1,╞µW)µ(V[3]µ'''' ''''),∞(╞µW)-V[3]),'''' '''' ° ,U''' '╕(G<30)/0' 'T╜(F╜µεV[4])+C╜1╟B╜µA╜(V[3],0)╟U' ° 'T╜⌐(1╞B)÷1⌐╛(ÉPW+F)÷T' 'U╜(E╜(V[3],C)╞U),[1](B╜T,1╟B)╞A' ° '''D╜εV[4]'' ÉEA ''D╜ÉAV[εV[4]+33⌡V[4]=0]''' 'L0:A╜(T,0)╟A' ° X '╕(0=1╞µA)/0' 'U╜U,(((T+V[3]),µD)µD),E,[1]B╞A' '╕L0' ° *(1997 7 13 12 28 59 544) ° Ftest ÉFX 'U╜V test W;P' ° 'Σ Describe problem in W, (correct answer in V)' 'U╜2' 'L1:W' ° 'É╜'' ''' 'P╜æ' '''╕L0'' ÉEA ''P╜»P''' '╕(V╧P)/0' ° X 'L0:╕(0=U╜U-1)/0' '''Incorrect. Try again''' '╕L1' ° XCuc 1 26 ABCDEFGHIJKLMNOPQRSTUVWXYZ ° *(1996 4 6 16 5 22 276) ° Fvec ÉFX 'U╜vec' 'Σ Draw 2d vector in plane' ° 'U╜r,r,''2- +'',r '': °'',r,''1- °'',r' ° X 'U╜U,'' : °'',r,''0|....|....|'',r,'' 0 1 2'',r' °