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Text File | 1997-09-19 | 71KB | 866 lines

XNÉIO 0 1 ° XNÉCT 0 1E²13 ° XCÉFC 1 6 .,*0_² ° XNÉRL 0 1847012583 ° XCÉPR 1 1 ° XCÉLX 1 5 TEACH ° AANTE╜('1')('21=ISIN R╜EVAL P')('21<ISIN R╜EVAL P')('14 22<ISIN R')('1' ° X) ° *(1996 4 6 16 7 36 340) ° 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 8 17 11 44 17 456) ° FBLACKJACK ÉFX 'BLACKJACK;D;DECK;T;S;R' ° 'Σ Command for game of Blackjack' 'DECK╜∞52 ╪ DECK╜DECK[52?52]' ° 'D╜''Player'' ''I win'' ''I fold'' ''Hit me'' ''I stand'' ''BLACKJACK' ° '' '╕(INFEN D)/0 ╪ T╜æ ╪ ╕(21<S╜R)/0' ° 'D╜(5╞''Dealer'' ''You lose'' ''You win''),5╟D ╪ ╕(INFEN D)/0' ° X '╕(S≥R)/L0 ╪ D[2] ╪ ╕0' 'L0:D[3]' ° *(1997 8 17 11 44 21 472) ° FBLACKJACK2 ÉFX 'BLACKJACK2;D;DECK;T;S;R' ° 'Σ Command for game of Blackjack' ° 'DECK╜∞52 ╪ DECK╜DECK[52?52] ╪ P╜DEAL 2' ° 'D╜''Player'' ''I win'' ''I fold'' ''Hit me'' ''I stand'' ''BLACKJACK' ° '' 'INFEN2 RULES ╪ T╜æ ╪ ╕(21<S╜R)/0' ° 'D╜(5╞''Dealer'' ''You lose'' ''You win''),5╟D ╪ INFEN2 RULES' ° X '╕(S≥R)/L0 ╪ D[2] ╪ ╕0' 'L0:D[3]' ° ACONS╜('D[1] ''gets'' 2 ''cards:'' ╪ SHOW P╜DEAL 2 ╪ T╜æ')('D[6 2] ╪ N╜ ° ²1')('D[3] ╪ N╜²1')('D[5] ╪ N╜²1')('D[4] ╪ SHOW P╜P,DEAL 1 ╪ T╜æ ╪ N╜2' ° X) ° *(1997 8 17 11 43 58 616) ° XFDEAL ÉFX 'U╜DEAL W' 'Σ Deal W cards' 'U╜W╞DECK' 'DECK╜W╟DECK' ° NDECK 1 50 13 47 6 26 21 16 2 41 29 38 52 10 40 22 4 51 33 23 30 49 3 ° 14 50 45 18 37 28 8 12 36 42 11 19 44 7 31 27 24 39 1 35 17 48 25 15 ° X 20 5 32 9 43 ° *(1997 9 14 12 30 44 504) ° XFDISCLAIMER ÉFX 'DISCLAIMER' 'Σ Copyright statement' 'disclaimer' ° *(1996 4 6 16 7 36 340) ° 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' ° *(1997 8 17 11 44 1 392) ° FEVAL ÉFX 'U╜EVAL W;R' 'Σ Evaluate a blackjack hand' ° X 'U╜+/((∞10),3µ10)[1+R╜13|W]' '╕(~0εR)/0 ╪ U╜0¥U,(22>U+10)/U+10' ° *(1996 4 6 16 7 36 340) ° FEXIT ÉFX 'EXIT' 'Σ Exit from function' '''To log off type: )OFF''' ° X '╕' ° *(1997 8 17 11 42 34 516) ° FGETNO ÉFX 'U╜V GETNO W;E' 'Σ Prompt for numeric data' ° 'W ╪ U╜É ╪ ╕(0=ÉNC ''V'')/0' 'L0:╕((╞V)≤µ,U)/L1 ╪ U╜U,É ╪ ╕L0' ° 'L1:U╜(╞V)╞U ╪ ╕(1=µ,V)/0 ╪ U╜(╛0.5+U⌡10*V[2])÷10*V[2]' ° '╕(2=µV)/0 ╪ V╜(4⌐µV)╞V' 'E╜(U>V[3])-U<V[4] ╪ ╕(^/E=0)/0' ° X 'V╜6╞V,V[3 4] ╪ U[(E=1)/∞µE]╜V[5] ╪ U[(E=²1)/∞µE]╜V[6]' ° *(1996 4 6 16 7 36 340) ° 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 17 11 40 13 424) ° 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╜7),'' 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' ° '''BIND List binding rules''' ° '''BLACKJACK Sample blackjack game''' ° X '''REVIEW Review the contents of the previous lesson''' '' 'endd' ° *(1997 8 17 11 44 14 444) ° FINFEN ÉFX 'U╜INFEN W;P;T' 'Σ Blackjack rules and logic' 'U╜0' ° 'W[1],''gets'' 2 ''cards:'' ╪ SHOW P╜DEAL 2' ° 'L0:╕(21⌠ISIN R╜EVAL P)/L1 ╪ W[6 2] ╪ U╜1 ╪ ╕0' ° 'L1:╕(21>ISIN R)/L2 ╪ U╜1 ╪ W[3] ╪ ╕0' ° 'L2:╕(~14 21<ISIN R)/L3 ╪ ΓW[5] ╪ ╕0' ° X 'L3:W[4] ╪ T╜æ ╪ SHOW P╜P,DEAL 1 ╪ ╕L0' ° *(1997 8 17 11 44 21 472) ° FINFEN2 ÉFX 'INFEN2 W;N;ANTE;CONS' 'Σ A simple Inference Engine' ° '(ANTE CONS)╜W ╪ N╜0' ° X 'L0:╕(²1=N)/0 ╪ N╜N+1 ╪ ╕(~U╜0¥»NπANTE)/L0 ╪ »NπCONS ╪ ╕L0' ° *(1997 8 17 11 44 3 400) ° FISIN ÉFX 'U╜V(f ISIN)W' 'Σ Do cards W add up to range V' 'U╜(0¥ΦV)f W' ° X '╕(1=µ,V)/0' 'U╜U^W f V[2]' ° XNNO 0 97 ° XNR 0 17 ° *(1996 4 6 16 7 36 340) ° FREVIEW ÉFX 'REVIEW;OP' 'Σ Review outer product and defined operator' ° '''In lesson 12 we inroduced a one function version of the dot operato ° r''' '''called the outer product'',r' ° 'show ''(∞5)°.-∞5'' ''(∞3)°.Φ''''ABC'''' ''''CDE'''' ''''EFG''''''' ° '''When the left operand of the dot is the symbol JOT (°), the result' ° '' ° '''is an array with dimensions equal to the sum of dimensions of its'' ° ' '''arguments. The elements of this result include all possible''' ° '''compositions of the two arguments'',r' ° 'show ''µ(2 3µ∞6)°.⌡4 5µ∞20''' ° '''We also studied the user defined operator. This object is distingui ° shed''' ° '''from a user defined function by the presence of parentheses in the' ° '' '''header'',r' ° 'show ''ÉFX ''''(f OP) W'''' ''''W°.f W'''''' ''⌡OP ∞4''' ° '''A defined operator is useful in situations where the algorithm is'' ° ' ° '''independent of the function to be used. The assignment of the funct ° ion''' ° '''to be used (called binding) can be made just prior to the execution ° ''' ° '''of the function. The operand(s) in a user defined operator can be'' ° ' '''user defined function(s).'',r' ° 'show ''ÉFX ''''U╜ODDS W'''' ''''U╜²1+2⌡∞W'''''' ''⌡OP ODDS 4''' ° X 'endd' ° ARULES╜(('1')('21=ISIN R╜EVAL P')('21<ISIN R╜EVAL P')('14 22<ISIN R')(' ° 1'))(('D[1] ''gets'' 2 ''cards:'' ╪ SHOW P╜DEAL 2 ╪ T╜æ')('D[6 2] ╪ N╜² ° 1')('D[3] ╪ N╜²1')('D[5] ╪ N╜²1')('D[4] ╪ SHOW P╜P,DEAL 1 ╪ T╜æ ╪ N╜2') ° X) ° *(1997 8 17 11 43 56 608) ° FSHOW ÉFX 'U╜SHOW C' 'Σ Display cards C' ° X 'U╜(3Φ''JQKA23456789'',Γ''10'')[1+13|C]' 'U╜U,■(ÉAV[6 5 4 7])[⌐C÷13]' ° *(1997 6 30 20 58 36 668) ° FTEACH ÉFX 'TEACH' 'Σ Start lesson #13: APL2 by Zdenek V JIZBA' ° 'exit ''TEACH''' 'initialize' 'TEACH1 Σ The quad and the quote quad' ° 'TEACH2 Σ Prompting; the function GETNO' ° 'TEACH3 Σ The execute primitive and the monadic format' ° 'TEACH4 Σ Rndom link and time stamp' ° 'TEACH5 Σ Shuffling, displaying and dealing cards' ° 'TEACH6 Σ Blackjack as a production system' ° X 'TEACH7 Σ Blackjack as a rule based system' 'problems' ° *(1997 6 22 12 33 7 388) ° FTEACH1 ÉFX 'TEACH1;NO;CH;FOO;T;ÉPR' 'Σ Quad and quote quad input' ° 'ÉPR╜'' ''' ° '''To refresh your memory about the previous lesson, enter REVIEW.''' ° 'do' ° '''In this lessons we will study new primitive functions related to''' ° '''the process of interfacing a workspace with external devices. We wi ° ll''' '''also discuss utilities and programming strategies.''' 'do' ° '''When you enter an expression at the keyboard, you type a string of' ° '' ° '''characters. APL2 recognizes the presence or absence of leading and' ° '' ° '''trailing quotes in this string. If the quotes are present, the stri ° ng''' ° '''is returned to the screen without the quotes. If the quotes are abs ° ent,''' ° '''APL2 EVALUATES the string, and if it is a valid APL2 expression, it ° ''' '''will complete the evaluation.''' 'do' ° ''' THE QUAD AND THE QUOTE QUAD'',r' ° '''When APL2 is requested to display data on the screen, these are alw ° ays''' ° '''converted to a visual character representation. (Numeric data are N ° OT''' ° '''stored internally as decimal symbols.) We will now study APL2 primi ° tive''' ° '''functions that support communication between the workspace memory, ° the''' ° '''keyboard, the screen and other I/O (Input/Output) devices. We will ° also''' ° '''study APL2 primitive functions to translate between character strin ° gs''' '''and numeric arrays.''' 'do' ° '''The contents of character strings can be data or APL2 expressions.' ° '' ° '''Data can be character or numeric. We must be able to specify to APL ° 2''' ° '''The nature of data that we enter at the keyboard. Here is an exampl ° e.'',r' ° '''We know how to generate numeric or character data strings'',r' ° 'show ''NO╜1 (2 3) (3 3µ∞9)'' ''CH╜''''(∞4)°.⌡∞5''''''' ° '''The first expression generates a numeric nested vector. The second' ° '' ° '''expression generates a character string that also happens to be a'' ° ' ° '''valid APL2 expression. Suppose now, that the contents of NO and CH' ° '' ° '''is to be determined at the keyboard by the user. APL2 has two basic ° ''' ° '''keyboard entry primitive functions called QUAD and QUOTE QUAD. The' ° '' ° '''quad (É) generates a special prompt (É:) indicating that only numer ° ic''' ° '''data is to be entered. (This includes any APL2 expression that''' ° '''evaluates to a numeric array). In the following example you MUST''' ° '''enter some numbers'',r' 'show ''NO╜É'' ''2⌡NO''' ° '''The quote quad places the cursor at the beginning of the line, but' ° '' ° '''does not display a prompt. Anything you enter on that line prior to ° ''' ° '''ENTER becomes part of the string. In the next example, when you see ° ''' ° '''the prompt, first enter some blanks, then some characters and a few ° ''' '''more blanks before pressing ENTER:'',r' 'CH╜''''' ° 'show ''CH╜æ'' ''DISPLAY CH''' ° '''If you did as instructed, you will see that all blanks have been st ° ored''' '''in CH.'',r' 'do' ° '''The quad and quote quad have yet another function. When a complex'' ° ' ° '''APL2 expression contains intermediate results, we can display these ° ''' '''by assigning them to the quad'',r' 'show ''+/É╜3 3µ∞9''' ° '''Without the É╜ we would see only the final result. The 3 by 3 array ° ''' '''is displayed in a distinct color, but not stored.'',r' 'do' ° '''Assignment to the quote quad is best illustrated with an example'', ° r' 'T╜ÉFX ''U╜FOO W'' ''æ╜W'' ''U╜æ''' '1 showfn ''FOO''' ° '''Note that ÉPR is local to function FOO.'',r' ° 'show ''CH╜FOO ''''Enter anything: '''''' ''DISPLAY CH''' ° '''In function FOO, the right argument is the prompt. On line [2] this ° ''' ° '''prompt is assigned to the quote quad. This causes the prompt to be' ° '' ° '''displayed on the screen and to place the cursor at the end of the p ° rompt.''' ° '''Any text entered there is returned by FOO together with a string of ° ''' ° '''blanks of the same length as the prompt. In other words, the assign ° ment''' ° '''to the quote quad permits entering of character data from the keybo ° ard''' ° '''on the same line as the prompt. To work properly, the two expressio ° ns''' '''containing æ must follow immediately each other.''' 'do' ° ''' PROMPT REPLACEMENT'',r' ° '''Normally, the leading prompt blanks are not desired in the result.' ° '' '''Here is one way to remove them'',r' ° 'T╜ÉFX ''U╜FOO W'' ''æ╜W'' ''U╜(µW)╟æ''' '1 showfn ''FOO''' ° 'show ''CH╜FOO ''''Enter anything'''''' ''DISPLAY CH''' ° '''There is a System variable called PROMPT REPLACEMENT that can be us ° ed''' ° '''to specify how to deal with the prompt. This variable is stored in ° ÉPR,''' ° '''and contains a blank as a default. ÉPR can be assigned any SINGLE'' ° ' ° '''special character, or a null string. Here is an example of function ° ''' ° '''FOO taking as a left argument the character to be used as a prompt' ° '' '''replacement''' ° 'T╜ÉFX ''U╜V FOO W;ÉPR'' ''ÉPR╜V'' ''æ╜W'' ''U╜æ''' ° '1 showfn ''FOO''' ° 'show ''CH╜''''*'''' FOO ''''Enter anything'''''' ''DISPLAY CH''' ° 'show ''CH╜'''''''' FOO ''''Enter anything'''''' ''DISPLAY CH''' ° X '''A null string will retain the prompt string''' 'endd' ° *(1997 6 23 12 34 47 556) ° FTEACH2 ÉFX 'TEACH2;NAME;FN;N;T' 'Σ Quad utility' ° '''As you begin to develop APL2 applications, you will find the need t ° o''' ° '''use both the quad and the quote quad. Typically, just before asking ° ''' ° '''for user input, there has to be some sort of a text statement defin ° ing''' '''the nature of data to be entered (ENTER AS REQUESTED)'',r' ° ''' Enter two numbers in the range 1 to 100''' ° 'show ''NO╜É'' ''2⌡NO''' ''' What is your name?''' ° 'show ''NAME╜æ'' ''ΦNAME''' ° '''The need for a prompting phrase is so common that it makes sense to ° ''' ° '''have a special APL2 defined utility for that purpose. Let us call'' ° ' '''a utility function to prompt for numeric values GETNO'',r' ° 'show ''ÉFX ''''U╜GETNO W'''' ''''Σ Prompt for numeric data'''' ''''W ° ╪ U╜É''''''' '1 showfn ''GETNO''' ° '''Function GETNO prints the prompt first, and then applies the quad'' ° ,r' ° 'show ''N╜GETNO ''''Enter your age in years'''''' ''T╜''''You are'''', ° N,''''years old''''''' 'show ''DISPLAY T''' ° '''Since we desire to make function GETNO a useful utility, let us con ° sider''' ° '''what additional features it should have. Let us agree that GETNO sh ° ould''' ° '''prompt for a numeric scalar or vector entry. Beyond that we may wis ° h to''' '''specify the following:'',r' ° ''' a. If a vector, the number of elements in the vector''' ° ''' b. Whether the values are to be integers. If fractions, then spec ° ify''' ''' the number of decimal digits.''' ° ''' c. The largest allowed values''' ° ''' d. The smallest allowed values''' ° ''' e. What to do if some entries are outside permitted range'',r' ° '''To support options (a to d) we should add a left argument to GETNO' ° ',r' ° 'FN╜''U╜V GETNO W;E'' ''Σ Prompt for numeric data'' ''W ╪ U╜É ╪ ╕(0=ÉN ° C ''''V'''')/0''' 'show ''πFN''' ° '''If the left argument is absent (i.e. GETNO is used monadically) the ° n''' '''no further processing will be done'',r' ° 'show ''FN╜FN,Γ''''L0:╕((╞V)≤µ,U)/L1 ╪ U╜U,É ╪ ╕L0''''''' ° '''If the number of entries is less than the specified value in the fi ° rst''' ° '''element of the left argument, then request additional values''' ° 'do' ° 'show ''FN╜FN,Γ''''L1:U╜(╞V)╞U ╪ ╕(1=µ,V)/0 ╪ U╜(╛.5+U⌡10*V[2])÷10*V[2 ° ]''''''' ° '''Save only as many values as specified in the left argument. Then, i ° f the''' ° '''left argument has only one element, exit. Else do a half-adjust in ° the''' '''last decimal position.''' 'do' ° 'show ''FN╜FN,Γ''''╕(2=µV)/0 ╪ V╜(4⌐µV)╞V''''''' ° '''If the left argument has only two elements, exit. Else make sure th ° at''' ° '''the left argument has at least four elements (This provides a defau ° lt''' '''of zero for the smallest permissible value.)'',r' ° 'show ''FN╜FN,Γ''''E╜(U>V[3])-U<V[4] ╪ ╕(^/E=0)/0''''''' ° '''If the values of the vector are all within range, exit. Else contin ° ue'',r' ° 'show ''FN╜FN,Γ''''V╜6╞V,V[3 4] ╪ U[(E=1)/∞µE]╜V[5] ╪ U[(E=²1)/∞µE]╜V[ ° 6]''''''' ° '''If the left argument has only four elements, use the values of V[3 ° 4]''' ° '''as replacement defaults. Replace values outside range by upper and' ° '' '''lower bounds.'',r' 'show ''ÉFX FN''' '1 showfn ''GETNO''' ° 'show ''5 GETNO ''''Enter numbers two at a time''''''' ° '''The function requested new values until you entered 6. Then it save ° d only 5'',r' 'show ''2 4 GETNO ''''Enter: *2 3 4''''''' ° '''The function returned results to 4 decimal points'',r' ° 'show ''10 0 20 10 ²2 ²1 GETNO ''''Enter: 3⌡∞10''''''' ° '''If you entered the requested expression, function GETNO returns a'' ° ' ° '''vector of length 10 with negative values in positions where the''' ° '''expression generates values outside the desired range (10 to 20).'' ° X' 'endd' ° *(1997 6 23 12 50 19 508) ° FTEACH3 ÉFX 'TEACH3;N;C;FN' 'Σ Format, Execute and the DOIF utility' ° ''' THE EXECUTE AND FORMAT FUNCTIONS'',r' ° '''The EXECUTE primitive (») provides the means of converting valid AP ° L2''' '''character string expressions into evaluated results.'',r' ° 'show ''C╜''''1.56 2 34'''''' ''µC'' ''DISPLAY C'' ''N╜»C'' ''µN'' ''D ° ISPLAY 2⌡N''' ° '''In the example we converted the character string C representing a'' ° ' ° '''numeric vector to the numeric vector N. In commercial applications' ° '' ° '''this is very useful, since numeric data is commonly stored in files ° ''' ° '''as character strings. To store numeric arrays in files we also need ° ''' ° '''the converse function. In APL2 this process is done with the FORMAT ° ''' ° '''primitive function. The monadic version of format is given by the s ° ymbol''' ° '''«, also called the thorn. (We will study the dyadic version of form ° at''' '''in a later session.)'',r' 'show ''µÉ╜«N'' ''DISPLAY «N''' ° '''These two functions are dual for vectors only if we begin with the' ° '' '''format of a numeric vector. Here is why'',r' ° 'show ''µC╜''''1 2 3'''''' ''µ«»C''' ° '''The starting character string need not comply with the strict rules ° ''' ° '''for conversion of a numeric vector to a string using the « function ° .''' 'do' ° '''For that matter, the character expression need not even be a symbol ° ''' '''representation of a numeric vector. It can be ANY valid APL2''' ° '''expression'',r' ° 'show ''C╜''''+/5 4µ6+∞15'''''' ''N╜»C'' ''DISPLAY N''' ° '''Some APL2 theoreticians are uneasy with the execute command, becaus ° e''' ° '''it tends to be misused. In some studies of user defined functions i ° t''' ° '''was found that the execute can frequently be avoided by a more care ° fully''' '''thought out algorithm.'',r' ° '''There are times, however, when the execute can be a very powerful t ° ool.''' ° '''Here is an example of a utility function that uses the execute. (No ° te''' ° '''that in this workspace, utility functions have been defined in lowe ° r''' '''case.)'',r' '1 showfn ''doif''' ° '''NOTE: Actually this function has become obsolescent with the''' ° ''' introduction of the DIAMOND (╪) separator. (We will study''' ° ''' the System function ÉEA in later sessions, but for the time'' ° ' ° ''' being, the left argument of ÉEA is evaluated only if the righ ° t''' ''' argument fails.)''' 'do' ° '''Function ''''doif'''' is dyadic. It tests the left argument which m ° ust''' ° '''return a boolean scalar or vector. If the result of the test is 1'' ° ' ° '''then the right argument is executed. The function returns the boole ° an''' '''result'',r' 'show ''N╜2'' ''C╜(N<10) doif ''''∞N'''''' ''C''' ° '''The right argument must be valid APL2 expression as a character str ° ing.''' '''It may even be a vector of APL2 expressions'',r' ° 'show ''N╜2 12 3'' ''C╜(N<10) doif ''''∞2'''' ''''∞3'''' ''''∞4'''''' ° X''C''' 'endd' ° *(1997 6 24 11 41 32 524) ° FTEACH4 ÉFX 'TEACH4;RL' 'Σ Random link and Time stamp' 'RL╜?100' ° ''' RANDOM LINK AND TIME STAMP'',r' ° '''We have previously studied the functions ROLL and DEAL, but we have ° ''' ° '''not discussed how these functions generate random values. Ignoring ° the''' ° '''actual algorithm, there is a SYSTEM variable called RANDOM LINK tha ° t''' '''determines the actual sequence of random numbers.'',r' ° '''Random link is stored in ÉRL. It will accept integer values and wil ° l''' ° '''return its current value which changes each time the roll or deal'' ° ' '''function is invoked'',r' ° 'show ''RL╜É╜ÉRL'' ''?5µ100'' ''ÉRL'' ''ÉRL╜RL'' ''?3µ100'' ''?2µ100'' ° ''ÉRL''' ° '''One consequence of this is that the "random results" in a workspac ° e''' ° '''may ALWAYS return the same sequence, each time that workspace is lo ° aded.''' ° '''This is because the value of ÉRL is stored with the workspace.''' ° 'do' ° '''In some applications this may not be desired. How can the random li ° nk''' ° '''be INITIALIZED when the workspace is loaded? One way of doing it is ° to''' ° '''use another SYSTEM function called the TIME STAMP. The time stamp'' ° ' ° '''(ÉTS) generates a numeric vector of length 7. The values represent ° the''' ° '''YEAR, MONTH, DAY, HOUR(24), MINUTE, SECOND, and MILISECOND of the i ° nstant''' '''the time stamp was invoked'',r' 'show ''ÉTS'' ''ÉTS''' ° '''Since the time when a workspace is loaded is unpredictable, it is a ° ''' ° '''convenient way of extracting a random link. To do that, simply ente ° r''' ° '''an expression such as the following in the appropriate function'',r ° X' 'show ''RL╜ÉRL╜+/²3╞ÉTS''' 'endd' ° *(1997 6 24 12 41 26 504) ° FTEACH5 ÉFX 'TEACH5;DECK;T;FN' 'Σ The game of BLACKJACK' ° '''We will now illustrate the usage of random link and the time stamp' ° '' '''by developing an application of the game of blackjack.''' 'do' ° ''' SHUFFLING, DISPLAYING AND DEALING CARDS'',r' ° '''As in any card game, cards have to be shuffled and then dealt to th ° e''' ° '''players. We must, therefore, begin by defining a card deck, definin ° g''' ° '''the process of shuffling cards, and the process of dealing cards.'' ° ,r' ° '''NOTE: You may wish to use the font... option in the options pull do ° wn''' ° ''' menu to increase the size of your font (12 or 14 should do it ° ).''' 'do' ° '''Since a card deck contains 52 cards, it makes sense to associate''' ° '''each card with an integer in the interval (1,52). We will use the'' ° ' ° '''following scheme: For integers 1-13 we will associate CLUBS, for''' ° '''14-26 DIAMONDS, for 27-39 HEARTS, and for 40-52 SPADES. Within each ° ''' ° '''suit, the sequence will be 2,3,4,5,6,7,8,9,10,J,Q,K,A. In this way' ° '' ° '''the integer 10, for example will represent the JACK of CLUBS, and'' ° ' '''the integer 28 will represent the 3 of HEARTS.''' 'do' ° '''We define a variable called DECK to contain all cards in a deck'',r ° ' 'show ''DECK╜∞52''' '''We next shuffle this deck'',r' ° 'show ''ÉRL╜+/²3╞ÉTS'' ''DECK╜DECK[52?52]'' ''4 13µDECK''' ° '''We have shuffled the deck of cards, but it is difficult to see what ° ''' ° '''these integers stand for. What we need is a display function'',r' ° 'FN╜''U╜SHOW C'' ''Σ Display cards C''' ° 'FN╜FN,Γ''U╜(3Φ''''JQKA23456789'''',Γ''''10'''')[1+13|C]''' ° 'FN╜FN,Γ''U╜U,■(ÉAV[6 5 4 7])[⌐C÷13]'' ╪ πFN ╪ T╜ÉFX FN' 'do' ° '''We can now display cards from this deck'',r' ° 'show ''2╞DECK'' ''SHOW 2╞DECK''' ° '''Next we need a function to deal cards from this deck'',r' ° 'FN╜''U╜DEAL W'' ''Σ Deal W cards'' ''U╜W╞DECK'' ''DECK╜W╟DECK'' ╪ πFN ° ╪ T╜ÉFX FN' 'r' 'show ''SHOW 4 5µDEAL 20'' ''µDECK''' ° 'r,''(Function DEAL does not handle the case when the deck contains fe ° wer''' ° '''cards than requested. This would be needed in the game of poker.)'' ° ,r' 'do' ''' THE GAME OF BLACKJACK'',r' ° '''Let us now look at the basic rules of BLACKJACK. For simplicity, we ° ''' ° '''will assume there are only two players: Dealer and Player. We will' ° '' '''also ignore betting in this sample game.'',r' ° ''' A. Dealer shuffles the deck, and deals two cards each. (We will sh ° ow''' ° ''' all cards as dealt, and deal to Player first which is not the w ° ay''' ''' the actual game is played.)'',r' ° ''' B. The value of cards is that of their pip (number on the card)''' ° ''' Face cards count 10, and the Ace can be counted as 1 OR 11'',r' ° ''' DECISION RULES'',r' ° ''' 1. If player sees a 10 value card and an ACE, player says''' ° ''' BLACKJACK and wins.''' ° ''' 2. If cards ad up to 15 or more, but less than 22, player says' ° '' ° ''' I hold. Action then passes to the next player (Dealer).''' ° ''' 3. If cards in players hand add up to 22 or more player LOSES.' ° '' ° ''' 4. Else player says HIT ME, gets another card, and goes to rule ° 2'',r' ° ''' C. After Player stops, Dealer''''s cards are evaluated under the'' ° ' ''' same rules. EXCEPTION: in case of draw, Dealer wins.''' 'do' ° ''' TWO MORE UTILITIES'',r' ° '''Before we define function BLACKJACK, we need two more defined objec ° ts.''' ° '''We need a function to evaluate a blackjack hand, and we need an''' ° '''operator that can be used to determine what to do with a given hand ° .'',r' '''Let us call the function to evaluate a hand EVAL'',r' ° 'FN╜''U╜ EVAL W;R'' ''Σ Evaluate a blackjack hand''' ° 'FN╜FN,Γ''U╜+/((∞10),3µ10)[1+R╜13|W]''' ° 'FN╜FN,Γ''╕(~0εR)/0 ╪ U╜0¥U,(22>U+10)/U+10'' ╪ πFN ╪ T╜ÉFX FN' ° 'r,''The last expression in EVAL takes care of a hand containing aces' ° ',r' 'show ''SHOW 13 26 39'' ''EVAL 13 26 39''' ° '''Finally, we define the operator ISIN. This operator returns a boole ° an''' '''scalar in response to a range inquiry'',r' ° 'FN╜''U╜V (f ISIN) W'' ''Σ Do cards W add up to range V''' ° 'FN╜FN,''U╜(0¥ΦV) f W'' ''╕(1=µ,V)/0'' ''U╜U^W f V[2]'' ╪ πFN ╪ T╜ÉFX ° FN' ° 'r,''Notice that in the last line the W preceeds V[2] in the compariso ° n.''' '''Let us see how ISIN works'',r' ° 'show ''21 =ISIN 21'' ''14 21 <ISIN É╜13+∞9'' ''15 >ISIN É╜12+∞4''' ° X 'endd' ° *(1997 6 27 13 43 42 592) ° FTEACH6 ÉFX 'TEACH6;T;FN' ° 'Σ Using utility ''doif'' in function BLACKJACK' ° ''' A PROGRAMMING STYLE EDITORIAL'',r' ° '''In what follows, we will illustrate a programming style. Since this ° ''' ° '''subject does not describe new APL2 primitives or its architecture,' ° '' '''this section is labelled as an editorial.''' 'do' ° '''The object of this exercise is to display one possible programming' ° '' ° '''style that one might use in solving a particular problem. We could' ° '' ° '''define function BLACKJACK "conventionally" by writing code that''' ° '''makes no distinction between the game, the logic and the rules of'' ° ' ° '''the game. Indeed as an exercise, you should try to define such a''' ° '''function at the end of this lesson. (Such conventional version of'' ° ' '''blackjack, written by Harry Bertucelli is available.)''' 'do' ° ''' A SAMPLE EXPERT SYSTEM'',r' ° '''An early version of an Expert System, was first introduced by''' ° '''Post in 1943. It is called a PRODUCTION SYSTEM. We will design the' ° '' ° '''card game of BLACKJACK using this Production System approach.'',r' ° 'do' ° '''We begin by defining function INFEN (for INFerence ENgine). This''' ° '''function will will combine the rules of the game AND its logic'',r' ° 'show ''FN╜''''U╜INFEN W;P;T'''' ''''Σ Blackjack rules and logic'''' ' ° '''U╜0''''''' ° '''Initialization includes setting U to zero --to indicate continuatio ° n''' ° '''of the game. The right argument to INFEN is a nested string of word ° s''' ° '''that apply to a specific player. For the player, these would be:''' ° '''(Player, I win, I fold, Hit me, I stand, BLACKJACK).''' 'do' ° 'show ''FN╜FN,Γ'''' W[1],''''''''gets'''''''' 2 ''''''''cards:'''''''' ° ╪ SHOW P╜DEAL 2''''''' ° '''The game is initialized. Two cards are dealt and displayed.''' ° 'do' ° 'show ''FN╜FN,Γ''''L0:╕(21⌠ISIN R╜EVAL P)/L1 ╪ W[6 2] ╪ U╜1 ╪ ╕0'''''' ° ' ° '''If the cards add up to 21, the game is over. The value of U is set ° to''' ° '''one to indicate that fact. Else if R<21, more tests have to be made ° .''' ° '''Variable R which contains the value of the hand is GLOBAL to functi ° on''' '''INFEN. (This is called a "side effect".)''' 'do' ° 'show ''FN╜FN,Γ''''L1:╕(21>ISIN R)/L2 ╪ U╜1 ╪ W[3] ╪ ╕0''''''' ° '''If R is greater than 21, player loses. The value of U is also set t ° o''' '''one to indicate the end of the game.''' 'do' ° 'show ''FN╜FN,Γ''''L2:╕(~14 21<ISIN R)/L3 ╪ ΓW[5] ╪ ╕0''''''' ° '''If the value is greater than 14 but less than 21, Player says "I st ° and"''' 'do' ° 'show ''FN╜FN,Γ''''L3:W[4] ╪ T╜æ ╪ SHOW P╜P,DEAL 1 ╪ ╕L0''''''' ° '''If the value is less than 15, player says "hit me", and pauses. The ° n a''' ° '''new card is shown to the player and evaluation is repeated.''' ° 'T╜ÉFX FN' 'do' '''Here is a listing of this function''' ° '1 showfn ''INFEN''' 'do' ° '''Before we can try out this function, we must define DECK'',r' ° 'show ''DECK╜52?52''' ° 'show ''INFEN ''''Player'''' ''''I win'''' ''''fold'''' ''''Hit me'''' ° ''''I stand'''' ''''BJ''''''' ° '''Function INFEN works. Now we can define the niladic function BLACKJ ° ACK.''' ° '''In my teminology a niladic function is called a COMMAND. It serves ° as''' '''an entry to an application.'',r' ° 'FN╜''BLACKJACK ;D;DECK;T;S;R'' ''Σ Command for game of Blackjack''' ° 'FN╜FN,Γ''DECK╜∞52 ╪ DECK╜DECK[52?52]''' ° 'FN╜FN,Γ''D╜''''Player'''' ''''I win'''' ''''I fold'''' ''''Hit me'''' ° ''''I stand'''' ''''BLACKJACK''''''' ° 'FN╜FN,Γ''╕(INFEN D)/0 ╪ T╜æ ╪ ╕(21<S╜R)/0''' ° 'FN╜FN,Γ''D╜(5╞''''Dealer'''' ''''You lose'''' ''''You win''''),5╟D ╪ ° ╕(INFEN D)/0''' 'FN╜FN,''╕(S≥R)/L0 ╪ D[2] ╪ ╕0'' ''L0:D[3]'' ╪ ÉFX FN' ° '1 showfn ''BLACKJACK''' ° '''Function BLACKJACK first defines a card deck and shuffles it. Then ° a''' ° '''dictionary of terms used by the player is stored in local variable ° D.''' ° '''If Player does not end the game (by getting a BLACKJACK or by losin ° g),''' ° '''then the game continues. The player''''s score is saved in S (recal ° l that''' ° '''R is a "side effect" of function INFEN). A pause is produced by ass ° igning''' ° '''a quote quad to T. The dictionary is updated to that of the dealer, ° and''' '''function INFEN is invoked for the dealer.'',r' 'do' ° '''Here is a sample run of function BLACKJACK'',r' ° X 'show ''BLACKJACK''' 'endd' ° *(1997 6 30 20 48 20 564) ° FTEACH7 ÉFX 'TEACH7;F;FN;T' 'Σ Another version of BLACKJACK' ° ''' A RULE BASED APPROACH'',r' ° '''Function BLACKJACK works fine, but the decision making is hardwired ° ''' ° '''in function INFEN. There is yet another way to solve this game. The ° ''' ° '''idea is to write a UTILITY function called INFEN2, and to store the ° ''' '''rules of the game in nested arrays.''' 'do' ° 'FN╜''INFEN2 W;N;ANTE ;CONS'' ''Σ A simple Inference Engine'' ''(ANTE ° CONS)╜W ╪ N╜0''' ° 'T╜ÉFX FN,Γ''L0:╕(²1=N)/0 ╪ N╜N+1 ╪ ╕(~U╜0¥»NπANTE)/L0 ╪ »NπCONS ╪ ╕L0 ° ''' '''We now illustrate this approach''' '1 showfn ''INFEN2''' ° '''The right argument W is a nested array. Its two components are the' ° '' ° '''antecedents and the consequents of a set of rules. The two local''' ° '''variables ANTE and CONS are initialized, as well as the rule counte ° r N.'',r' ° '''The first rule to be looked at is rule 1. The function evaluates th ° e''' ° '''first element of the nested string ANTE (for Antecedent). If this r ° eturns''' ° '''a 1 (TRUE), then the first element of nested string CONS (for Conse ° quent)''' ° '''will be evaluated next. Note that if NπCONS contains an expression ° of''' '''the form''' ''' N╜²1 or (...,N)╜...,²1''' ° '''then on branchimg back to L0, there will be an exit from INFEN2. Th ° e''' ° '''number of rules evaluated by INFEN2, will depend entirely on the''' ° '''contents of arrays ANTE and CONS. The elements of ANTE must return ° a''' ° '''boolean value, but the elements of CONS may produce arbitrary side' ° '' '''effects.'',r' ° '''Note that function INFEN2 is perfectly general. It could be used fo ° r''' ° '''any other "rule based" application. Indeed, The consequents of a ru ° le''' ° '''set may invoke INFEN2 recursively using additional rule sets.''' ° 'do' '''Let us now see how we must re-design function BLACKJACK.''' ° 'FN╜''BLACKJACK2 ;D;DECK;T;S;R'' ''Σ Command for game of Blackjack''' ° 'FN╜FN,Γ''DECK╜∞52 ╪ DECK╜DECK[52?52] ╪ P╜DEAL 2''' ° 'FN╜FN,Γ''D╜''''Player'''' ''''I win'''' ''''I fold'''' ''''Hit me'''' ° ''''I stand'''' ''''BLACKJACK''''''' ° 'FN╜FN,Γ''INFEN2 RULES ╪ T╜æ ╪ ╕(21<S╜R)/0''' ° 'FN╜FN,Γ''D╜(5╞''''Dealer'''' ''''You lose'''' ''''You win''''),5╟D ╪ ° INFEN2 RULES''' ° 'FN╜FN,''╕(S≥R)/L0 ╪ D[2] ╪ ╕0'' ''L0:D[3]'' ╪ T╜ÉFX FN' ° '1 showfn ''BLACKJACK2''' ° '''This function is essentially the same as BLACKJACK. The only differ ° ence''' ° '''is in function INFEN2. Its right argument now is the array of rules ° .''' 'do' '''Here are the simple rules of blackjack'',r' ° '''RULE ANTECEDENT CONSEQUENT'',r' ° ''' 1 1 D[1] ╪ ''''gets'''' 2 ''''cards:'''' ╪ SHOW P╜D ° EAL 2 ╪ T╜æ''' ''' 2 21=ISIN R╜EVAL P D[6 2] ╪ N╜²1''' ° ''' 3 21<ISIN R╜EVAL P D[3] ╪ N╜²1''' ° ''' 4 14 22<ISIN R D[5] ╪ N╜²1''' ° ''' 5 1 D[4] ╪ SHOW P╜P,DEAL 1 ╪ N╜1 ╪ T╜æ'',r' 'do' ° 'ANTE╜''1'' ''21=ISIN R╜EVAL P'' ''21<ISIN R╜EVAL P'' ''14 22<ISIN R'' ° ''1''' ° 'CONS╜Γ''D[1] ''''gets'''' 2 ''''cards:'''' ╪ SHOW P╜DEAL 2 ╪ T╜æ''' ° 'CONS╜CONS,''D[6 2] ╪ N╜²1'' ''D[3] ╪ N╜²1'' ''D[5] ╪ N╜²1''' ° 'CONS╜CONS,Γ''D[4] ╪ SHOW P╜P,DEAL 1 ╪ T╜æ ╪ N╜2''' 'RULES╜ANTE CONS' ° X 'show ''DISPLAY π1πRULES'' ''DISPLAY π2πRULES'' ''BLACKJACK''' '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 17 11 35 51 556) ° Ferase ÉFX ° 'erase;t;EXIT;GO;HELP;DISPLAY;BIND;REVIEW;RULE;SHOW;DEAL;EVAL;ISIN;INF ° EN;BLACKJACK;DISCLAIMER' 'Σ Erase all global functions and variables' ° 't╜ÉNL 3' 't╜(~t^.εlc,'' '')≡t' 't╜ÉEX(~t[;∞5]^.=''TEACH'')≡t' ° X 't╜ÉNL 2' 't╜ÉEX(~t^.εlc,'' '')≡t' 't╜ÉNL 4' '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 7 37 344) ° 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' °