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*	Fix getAddrInfo, add IPPROTO_ICMPV6 Closes #10198	Federico Ceratto	2019-01-06	1	-0/+36

<P> <P><A NAME="accountant"></A><CENTER><IMG SRC="../ss-pics/accountant.jpg" ALT="figure: accountant"></CENTER><P><CENTER>They did spreadsheets by hand in the old days. </CENTER><P> <HTML> <HEAD> <TITLE>Simply Scheme: Introducing Computer Science ch 25: Implementing the Spreadsheet Program</TITLE> </HEAD> <BODY> <HR> <CITE>Simply Scheme:</CITE> <CITE>Introducing Computer Science</CITE> 2/e Copyright (C) 1999 MIT <H2>Chapter 25</H2> <H1>Implementing the Spreadsheet Program</H1> <TABLE width="100%"><TR><TD> <IMG SRC="../simply.jpg" ALT="cover photo"> <TD><TABLE> <TR><TD align="right"><CITE><A HREF="http://www.cs.berkeley.edu/~bh/">Brian Harvey</A><BR>University of California, Berkeley</CITE> <TR><TD align="right"><CITE><A HREF="http://ccrma.stanford.edu/~matt">Matthew Wright</A><BR>University of California, Santa Barbara</CITE> <TR><TD align="right"><BR> <TR><TD align="right"><A HREF="../pdf/ssch25.pdf">Download PDF version</A> <TR><TD align="right"><A HREF="../ss-toc2.html">Back to Table of Contents</A> <TR><TD align="right"><A HREF="../ssch24/spread.html"><STRONG>BACK</STRONG></A> chapter thread <A HREF="database.html"><STRONG>NEXT</STRONG></A> <TR><TD align="right"><A HREF="http://mitpress.mit.edu/0262082810">MIT Press web page for <CITE>Simply Scheme</CITE></A> </TABLE></TABLE> <HR> <P>This is a big program and you can't keep it all in your head at once. In this chapter, we'll discuss different parts of the program separately. For example, while we're talking about the screen display procedures, we'll just take the rest of the program for granted. We'll assume that we can ask for the value in a cell, and some other part of the program will ensure that we can find it out. <P>Our division of the program includes these parts: <P><P><TABLE><TR><TH align="right" valign="top">•<TD>    <TD valign="top">The command processor, which reads user commands and oversees their execution. </TABLE><TABLE><TR><TH align="right" valign="top">•<TD>    <TD valign="top">The specific commands: cell selection commands, <CODE>load</CODE>, and <CODE>put</CODE>. </TABLE><TABLE><TR><TH align="right" valign="top">•<TD>    <TD valign="top">The formula translator, which turns a formula into an <EM>expression</EM> by translating relative cell positions to specific cells. </TABLE><TABLE><TR><TH align="right" valign="top">•<TD>    <TD valign="top">The dependency manager, which keeps track of which cells' expressions depend on which other cells. </TABLE><TABLE><TR><TH align="right" valign="top">•<TD>    <TD valign="top">The expression evaluator. </TABLE><TABLE><TR><TH align="right" valign="top">•<TD>    <TD valign="top">The screen printer. </TABLE><TABLE><TR><TH align="right" valign="top">•<TD>    <TD valign="top">The cell management procedures, which store and retrieve cell information for the rest of the program. </TABLE> <P> <P>The diagram below shows the interconnections among these seven parts of the program by showing what information they have to provide for each other. <P><CENTER><IMG SRC="../ss-pics/dataflow.jpg" ALT="figure: dataflow"></CENTER> <P>(The arrows that <EM>aren't</EM> in the diagram convey as much information as the ones that are. For example, since there is no arrow from the evaluator to the printer, we know that when the spreadsheet program redisplays the screen, the values printed are found directly in the data structure; no new computation of formulas is needed.) <P><H2>Cells, Cell Names, and Cell IDs</H2> <P>The spreadsheet program does its work by manipulating cells. In this section we introduce three abstract data types having to do with cells. Before we jump into the spreadsheet procedures themselves, we must introduce these three types, which are used throughout the program. <P>Each cell is a data structure that contains various pieces of information, including its value and other things that we'll talk about later. Just as these cells are arranged in a two-dimensional pattern on the screen, they are kept within the program in a two-dimensional data structure: a vector of vectors. <P>The elements of a vector are selected by number, using <CODE>vector-ref</CODE>. Therefore, if we're looking for a particular cell, such as <CODE>c5</CODE>, what the program really wants to know is that this cell is in column 3, row 5.<A NAME="text1" HREF="spread-implement#ft1">[1]</A> If the program refers to cells by name, then there will be several occasions for it to split the word <CODE>c5</CODE> into its pieces <CODE>c</CODE> and <CODE>5</CODE>, and to convert the letter <CODE>c</CODE> into the number 3. These operations are fairly slow. To avoid carrying them out repeatedly, the spreadsheet program identifies cells internally using a form that's invisible to the person using the program, called a "cell ID." <P><A NAME="g1"></A> <A NAME="g2"></A> Therefore, there are three different <A NAME="g3"></A><A NAME="g4"></A>abstract data types in the program that have to do with cells: cell names, such as <CODE>c5</CODE>; cell IDs; and cells themselves. We've chosen to represent cell IDs as three-element lists like this one: <P><PRE>(id 3 5) </PRE> <P>but you won't see much evidence of that fact within the program because we've implemented selectors and constructors for all of these three types. The representation includes the word <CODE>id</CODE> because one facility that the program needs is the ability to determine whether some datum is or is not a cell ID. The predicate <CODE>cell-id?</CODE> looks for a list whose first element is <CODE>id</CODE>. <P>The selectors for cell IDs are <CODE>id-row</CODE> and <CODE>id-col</CODE>; both take a cell ID as argument and return a number. The constructor, <CODE>make-id</CODE>, takes a column number (not a letter) and a row number as arguments. <P>When the program recognizes a cell name typed by the user, it calls <CODE>cell-name->id</CODE> to translate the name to an ID, and only the ID is stored for later use. <P>(These application-specific ADTs are similar to the database of known values in the pattern matcher, as opposed to more general-purpose ADTs like trees and sentences.) <P><H2>The Command Processor</H2> <P>Here's the core of the command processor: <P><PRE>(define (<A NAME="g5"></A>command-loop) (print-screen) (let ((command-or-formula (read))) (if (equal? command-or-formula 'exit) "Bye!" (begin (process-command command-or-formula) (command-loop))))) </PRE> <P>This short program runs until the user types <CODE>exit</CODE>, because it invokes itself as its last step. During each invocation, it prints the current spreadsheet display, uses <CODE>read</CODE> to read a command, and carries out whatever actions that command requires. Those actions probably change something in the spreadsheet data, so the next cycle has to redisplay the modified data before accepting another command. <P><CODE>Print-screen</CODE> is a large chunk of the program and will be discussed in its own section. <P>How does <CODE>process-command</CODE> work? It looks for the command name (a word such as <CODE>put</CODE>) in its list of known commands. The commands are kept in an association list, like this: <P><PRE>((p …) (n …) (b …) (f …) (select …) (put …) (load …)) </PRE> <P>Each of these sublists contains two elements: the name and the procedure that carries out the command. We'll see shortly how these procedures are invoked. <P>Looking for the command name is a little tricky because in the spreadsheet language a command can be invoked either by typing its name inside parentheses with arguments, as in Scheme, or by typing the name alone, without parentheses, which Scheme wouldn't interpret as a request to invoke a procedure. For example, the argument to <CODE>process-command</CODE> might be a list, such as <CODE>(f 3)</CODE>, or just a word, such as <CODE>f</CODE>. A third case is that the argument might not be one of these commands at all, but instead might be a formula, just like one that could be used to determine the value in a cell. <CODE>Process-command</CODE> must recognize these three cases: <P><PRE>(define (<A NAME="g6"></A>process-command command-or-formula) (cond ((and (list? command-or-formula) (command? (car command-or-formula))) (execute-command command-or-formula)) ((command? command-or-formula) (execute-command (list command-or-formula 1))) (else (exhibit (ss-eval (pin-down command-or-formula (selection-cell-id))))))) </PRE> <P>The <CODE>command?</CODE> predicate tells whether its argument is one of the command names in the list. As you can see, if a command name is used without parentheses, <CODE>process-command</CODE> pretends that it was given an argument of <CODE>1</CODE>. <P><CODE>Execute-command</CODE> looks up the command name in the list of commands, then applies the associated procedure to the arguments, if any: <P> <PRE>(define (<A NAME="g7"></A>execute-command command) (apply (get-command (car command)) (cdr command))) </PRE> <P>The <CODE>else</CODE> clause in <CODE>process-command</CODE>, which handles the case of a formula typed instead of a command, invokes several procedures that you haven't seen yet. We'll explain them when we get to the section of the program that manipulates formulas. The only one that's used just for command processing is <CODE>exhibit</CODE>: <P><PRE>(define (<A NAME="g8"></A>exhibit val) (show val) (show "Type RETURN to redraw screen") (read-line) (read-line)) </PRE> <P>This prints a value on the screen, gives the user a chance to read it, and then, when the user is ready, returns to processing commands. (This will entail redrawing the spreadsheet display; that's why we have to wait for the user to hit return.) The reason that we invoke <CODE>read-line</CODE> twice is that the call to <CODE>read</CODE> from <CODE>command-loop</CODE> reads the spreadsheet formula you typed but doesn't advance to the next line. Therefore, the first <CODE>read-line</CODE> invocation gobbles that empty line; the second call to <CODE>read-line</CODE> reads the (probably empty) line that the user typed in response to the prompting message.<A NAME="text2" HREF="spread-implement#ft2">[2]</A> <P><H2>Cell Selection Commands</H2> <P>Several commands have to do with selecting a cell. We'll show just one typical procedure, the one that carries out the <CODE>p</CODE> (previous row) command: <P><PRE>(define (<A NAME="g9"></A>prev-row delta) (let ((row (id-row (selection-cell-id)))) (if (< (- row delta) 1) (error "Already at top.") (set-selected-row! (- row delta))))) (define (<A NAME="g10"></A>set-selected-row! new-row) (select-id! (make-id (id-column (selection-cell-id)) new-row))) (define (<A NAME="g11"></A>select-id! id) (set-selection-cell-id! id) (adjust-screen-boundaries)) </PRE> <CODE>Prev-row</CODE> must ensure that the selected cell is within the legal boundaries. Since <CODE>prev-row</CODE> only moves upward, it has to check only that we don't go beyond row 1. (<CODE>Next-row</CODE> will instead check that we don't go beyond row 30 in the other direction.) <P><CODE>Adjust-screen-boundaries</CODE> checks for the situation in which the newly selected cell, although within the bounds of the spreadsheet, is not within the portion currently visible on the screen. In that case the visible portion is shifted to include the selected cell. (The procedure is straightforward and uninteresting, so we're not showing it here. You can see it in the complete listing of the spreadsheet program at the end of this chapter.) <P><CODE>Selection-cell-id</CODE> is a procedure that returns the cell ID of the cell that's currently selected. Similarly, <CODE>set-selection-cell-id!</CODE> sets the current selection. There are comparable procedures <CODE>screen-corner-cell-id</CODE> and <CODE>set-screen-corner-cell-id!</CODE> to keep track of which cell should be in the upper left corner of the screen display. There is a vector named <CODE>*special-cells*</CODE> that holds these two cell IDs; you can see the details in the complete program listing. <P> <H2>The <CODE><B>Load</B></CODE> Command</H2> <P>Loading commands from files is easy. The <CODE>command-loop</CODE> procedure, which carries out commands from the keyboard, repeatedly reads a command with <CODE>read</CODE> and invokes <CODE>process-command</CODE> to carry it out. To load commands from a file, we want to do exactly the same thing, except that we read from a file instead of from the keyboard: <P><PRE>(define (spreadsheet-load filename) (let ((port (open-input-file filename))) (sl-helper port) (close-input-port port))) (define (sl-helper port) (let ((command (read port))) (if (eof-object? command) 'done (begin (show command) (process-command command) (sl-helper port))))) </PRE> <P><H2>The <CODE><B>Put</B></CODE> Command</H2> <P>The <CODE>put</CODE> command takes two arguments, a formula and a place to put it. The second of these can specify either a single cell or an entire row or column. (If there is no second argument, then a single cell, namely the selected cell, is implied.) <CODE>Put</CODE> invokes <CODE>put-formula-in-cell</CODE> either once or several times, as needed. If only a single cell is involved, then <CODE>put</CODE> calls <CODE>put-formula-in-cell</CODE> directly. If a row or column is specified, then <CODE>put</CODE> uses the auxiliary procedure <CODE>put-all-cells-in-row</CODE> or <CODE>put-all-cells-in-col</CODE> as an intermediary. <P><PRE>(define (<A NAME="g12"></A>put formula . where) (cond ((null? where) (put-formula-in-cell formula (selection-cell-id))) ((cell-name? (car where)) (put-formula-in-cell formula (cell-name->id (car where)))) ((number? (car where)) (put-all-cells-in-row formula (car where))) ((letter? (car where)) (put-all-cells-in-col formula (letter->number (car where)))) (else (error "Put it where?")))) </PRE> <P>The only tricky part of this is the first line. <CODE>Put</CODE> can be invoked with either one or two arguments. Therefore, the dot notation is used to allow a variable number of arguments; the parameter <CODE>where</CODE> will have as its value not the second argument itself, but a list that either contains the second argument or is empty. Thus, if there is a second argument, <CODE>put</CODE> refers to it as <CODE>(car where)</CODE>. <P><PRE>(define (<A NAME="g13"></A>put-all-cells-in-row formula row) (put-all-helper formula (lambda (col) (make-id col row)) 1 26)) (define (<A NAME="g14"></A>put-all-cells-in-col formula col) (put-all-helper formula (lambda (row) (make-id col row)) 1 30)) (define (<A NAME="g15"></A>put-all-helper formula id-maker this max) (if (> this max) 'done (begin (try-putting formula (id-maker this)) (put-all-helper formula id-maker (+ 1 this) max)))) (define (<A NAME="g16"></A>try-putting formula id) (if (or (null? (cell-value id)) (null? formula)) (put-formula-in-cell formula id) 'do-nothing)) </PRE> <P><CODE>Put-all-cells-in-row</CODE> and <CODE>put-all-cells-in-col</CODE> invoke <CODE>put-all-helper</CODE>, which repeatedly puts the formula into a cell.<A NAME="text3" HREF="spread-implement#ft3">[3]</A> <CODE>Put-all-helper</CODE> is a typical sequential recursion: Do something for this element, and recur for the remaining elements. The difference is that "this element" means a cell ID that combines one constant index with one index that varies with each recursive call. How are those two indices combined? What differs between filling a row and filling a column is the <EM>function</EM> used to compute each cell ID. <P>The substitution model explains how the <CODE>lambda</CODE> expressions used as arguments to <CODE>put-all-helper</CODE> implement this idea. Suppose we are putting a formula into every cell in row 4. Then <CODE>put-all-cells-in-row</CODE> will be invoked with the value <CODE>4</CODE> substituted for the parameter <CODE>row</CODE>. After this substitution, the body is <P><PRE>(put-all-helper formula (lambda (col) (make-id col 4)) 1 26) </PRE> <P>The <CODE>lambda</CODE> expression creates a procedure that takes a column number as argument and returns a cell ID for the cell in row 4 and that column. This is just what <CODE>put-all-helper</CODE> needs. It invokes the procedure with the varying column number as its argument to get the proper cell ID. <P><CODE>Put-all-helper</CODE> doesn't directly invoke <CODE>put-formula-in-cell</CODE>. The reason is that if a particular cell already has a value, then the new formula isn't used for that particular cell, unless the formula is empty. That is, you can erase an entire row or column at once, but a non-empty formula affects only cells that were empty before this command. <CODE>Try-putting</CODE> decides whether or not to put the formula into each possible cell. (In <CODE>try-putting</CODE>, the third argument to <CODE>if</CODE> could be anything; we're interested only in what happens if the condition is true.) <P>All that's left is, finally, to put the formula into a cell: <P><PRE>(define (<A NAME="g17"></A>put-formula-in-cell formula id) (put-expr (pin-down formula id) id)) </PRE> <P>The two new procedures seen here, <CODE>pin-down</CODE> and <CODE>put-expr</CODE>, are both large sections of the program and are described in the next two sections of this chapter. <P><H2>The Formula Translator</H2> <P>Suppose the user has said <P><PRE>(put (* (cell b) (cell c)) d) </PRE> <P>The <CODE>put</CODE> procedure puts this formula into each cell of column <CODE>d</CODE> by repeatedly calling <CODE>put-formula-in-cell</CODE>; as an example, let's concentrate on cell <CODE>d4</CODE>. <P>The purpose of the formula is that later we're going to use it to compute a value for <CODE>d4</CODE>. For that purpose, we will need to multiply two particular numbers together: the ones in cells <CODE>b4</CODE> and <CODE>c4</CODE>. Although the same formula applies to cell <CODE>d5</CODE>, the particular numbers multiplied together will be found in different places. So instead of storing the same general formula in every <CODE>d</CODE> cell, what we'd really like to store in <CODE>d4</CODE> is something that refers specifically to <CODE>b4</CODE> and <CODE>c4</CODE>. <P>We'll use the term "expression" for a formula whose cell references have been replaced by specific cell IDs. We started with the idea that we wanted to put a formula into a cell; we've refined that idea so that we now want to put an expression into the cell. This goal has two parts: We must translate the formula (as given to us by the user in the <CODE>put</CODE> command) to an expression, and we must store that expression in the cell data structure. These two subtasks are handled by <CODE>pin-down</CODE>, discussed in this section, and by <CODE>put-expr</CODE>, discussed in the next section. <CODE>Pin-down</CODE> is entirely functional; the only modification to the spreadsheet program's state in this process is carried out by <CODE>put-expr</CODE>. <P>We'll refer to the process of translating a formula to an expression as "pinning down" the formula; the procedure <CODE>pin-down</CODE> carries out this process. It's called "pinning down" because we start with a <EM>general</EM> formula and end up with a <EM>specific</EM> expression. <CODE>Pin-down</CODE> takes two arguments: The first is, of course, a formula; the second is the ID of the cell that will be used as the reference point for relative cell positions. In the context of the <CODE>put</CODE> command, the reference point is the cell into which we'll put the expression. But <CODE>pin-down</CODE> doesn't think about putting anything anywhere; its job is to translate a formula (containing relative cell locations) into an expression (containing only absolute cell IDs).<A NAME="text4" HREF="spread-implement#ft4">[4]</A> <CODE>Pin-down</CODE> needs a reference point as a way to understand the notation <CODE><3</CODE>, which means "three cells before the reference point." <P>Let's go back to the specific example. <CODE>Put-formula-in-cell</CODE> will invoke <P><PRE>(pin-down '(* (cell b) (cell c)) 'd4) </PRE> <P>and <CODE>pin-down</CODE> will return the expression <P><PRE>(* (id 2 4) (id 3 4)) </PRE> <P>The overall structure of this problem is tree recursive. That's because a formula can be arbitrarily complicated, with sublists of sublists, just like a Scheme expression: <P><PRE>(put (+ (* (cell b) (cell c)) (- (cell 2< 3>) 6)) f) </PRE> <P>Here's <CODE>pin-down</CODE>: <P><PRE>(define (<A NAME="g18"></A>pin-down formula id) (cond ((cell-name? formula) (cell-name->id formula)) ((word? formula) formula) ((null? formula) '()) ((equal? (car formula) 'cell) (pin-down-cell (cdr formula) id)) (else (bound-check (map (lambda (subformula) (pin-down subformula id)) formula))))) </PRE> <P>The base cases of the tree recursion are specific cell names, such as <CODE>c3</CODE>; other words, such as numbers and procedure names, which are unaffected by <CODE>pin-down</CODE>; null formulas, which indicate that the user is erasing the contents of a cell; and sublists that start with the word <CODE>cell</CODE>. The first three of these are trivial; the fourth, which we will describe shortly, is the important case. If a formula is not one of these four base cases, then it's a compound expression. In that case, we have to pin down all of the subexpressions individually. (We basically <CODE>map</CODE> <CODE>pin-down</CODE> over the formula. That's what makes this process tree recursive.) <P>One complication is that the pinned-down formula might refer to nonexistent cells. For example, saying <P><PRE>(put (+ (cell 2< 3<) 1) d) </PRE> <P>refers to cells in column <CODE>b</CODE> (two to the left of <CODE>d</CODE>) three rows above the current row. That works for a cell such as <CODE>d7</CODE>, referring to cell <CODE>b4</CODE>, but not for <CODE>d2</CODE>, which has no row that's three above it. (There is no row <CODE>-1</CODE>.) So our program must refrain from pinning down this formula for cells <CODE>d1</CODE>, <CODE>d2</CODE>, and <CODE>d3</CODE>. <CODE>Pin-down</CODE> will instead return the word <CODE>out-of-bounds</CODE> to signal this situation. <P>The case of a nonexistent cell is discovered by <CODE>pin-down-cell</CODE> at the base of a tree recursion. The <CODE>out-of-bounds</CODE> signal must be returned not only by the base case but by the initial invocation of <CODE>pin-down</CODE>. That's why <CODE>bound-check</CODE> is used to ensure that if any part of a formula is out of bounds, the entire formula will also be considered out of bounds: <P><PRE>(define (<A NAME="g19"></A>bound-check form) (if (member 'out-of-bounds form) 'out-of-bounds form)) </PRE> <P>When a formula contains a <CODE>(cell …)</CODE> sublist, the procedure <CODE>pin-down-cell</CODE> is invoked to translate that notation into a cell ID. <P>The arguments to <CODE>pin-down-cell</CODE> are a list of the "arguments" of the <CODE>cell</CODE> sublist and the reference point's cell ID. (The word "arguments" is in quotation marks because the word <CODE>cell</CODE> doesn't represent a Scheme procedure, even though the parenthesized notation looks like an invocation. In a way, the special treatment of <CODE>cell</CODE> by <CODE>pin-down</CODE> is analogous to the treatment of special forms, such as <CODE>cond</CODE>, by the Scheme evaluator.) <P>There can be one or two of these "arguments" to <CODE>cell</CODE>. A single argument is either a number, indicating a row, or a letter, indicating a column. Two arguments specify both a column and a row, in that order: <P><PRE>(define (<A NAME="g20"></A>pin-down-cell args reference-id) (cond ((null? args) (error "Bad cell specification: (cell)")) ((null? (cdr args)) (cond ((number? (car args)) ; they chose a row (make-id (id-column reference-id) (car args))) ((letter? (car args)) ; they chose a column (make-id (letter->number (car args)) (id-row reference-id))) (else (error "Bad cell specification:" (cons 'cell args))))) (else (let ((col (pin-down-col (car args) (id-column reference-id))) (row (pin-down-row (cadr args) (id-row reference-id)))) (if (and (>= col 1) (<= col 26) (>= row 1) (<= row 30)) (make-id col row) 'out-of-bounds))))) </PRE> <P>In the two-argument case, the job of <CODE>pin-down-col</CODE> and <CODE>pin-down-row</CODE> is to understand notations like <CODE><3</CODE> for relative rows and columns: <P><PRE>(define (pin-down-col new old) (cond ((equal? new '*) old) ((equal? (first new) '>) (+ old (bf new))) ((equal? (first new) '<) (- old (bf new))) ((letter? new) (letter->number new)) (else (error "What column?")))) (define (pin-down-row new old) (cond ((number? new) new) ((equal? new '*) old) ((equal? (first new) '>) (+ old (bf new))) ((equal? (first new) '<) (- old (bf new))) (else (error "What row?")))) </PRE> <P><H2>The Dependency Manager</H2> <P>The remaining part of the <CODE>put</CODE> command is <CODE>put-expr</CODE>, which actually stores the translated expression in the cell data structure. You might imagine that putting an expression into a cell would require nothing more than invoking a mutator, like this: <P><PRE>(define (put-expr expr cell) ;; wrong (set-cell-expr! cell expr)) </PRE> <P>The trouble is that adding an expression to a cell might have many consequences beyond the mutation itself. For example, suppose we say <P><PRE>(put (+ a3 b2) c4) </PRE> <P>If cells <CODE>a3</CODE> and <CODE>b2</CODE> already have values, we can't just put the formula into <CODE>c4</CODE>; we must also compute its value and put that value into <CODE>c4</CODE>. <P>Also, once <CODE>c4</CODE> has a value, that could trigger the computation of some other cell's value. If we've previously said <P><PRE>(put (+ a3 c4) b5) </PRE> <P>then we're now able to compute a value for <CODE>b5</CODE> because both of the cells that it depends on have values. <P>All this implies that what's inside a cell is more than just an expression, or even an expression and a value. Each cell needs to know which other cells it depends on for its value, and also which other cells depend on it. <P><A NAME="g21"></A> <A NAME="g22"></A> Our program represents each cell as a four-element vector. Each cell includes a value, an expression, a list of <EM>parents</EM> (the cells that it depends on), and a list of <EM>children</EM> (the cells that depend on it). The latter two lists contain cell IDs. So our example cell <CODE>c4</CODE> might look like this: <P><PRE>#(12 (+ (id 1 3) (id 2 2)) ((id 1 3) (id 2 2)) ((id 2 5))) </PRE> <P>In a simpler case, suppose we put a value into a cell that nothing depends on, by saying, for example, <P><PRE>(put 6 a1) </PRE> <P>Then cell <CODE>a1</CODE> would contain <P><PRE>#(6 6 () ()) </PRE> <P>(Remember that a value is just a very simple formula.) <P>There are selectors <CODE>cell-value</CODE> and so on that take a cell ID as argument, and mutators <CODE>set-cell-value!</CODE> and so on that take a cell ID and a new value as arguments. There's also the constructor <CODE>make-cell</CODE>, but it's called only at the beginning of the program, when the 780 cells in the spreadsheet are created at once. <P>When a cell is given a new expression, several things change: <P><P><TABLE><TR><TH align="right" valign="top">•<TD>    <TD valign="top">The new expression becomes the cell's expression, of course. </TABLE><TABLE><TR><TH align="right" valign="top">•<TD>    <TD valign="top">The cells mentioned in the expression become the parents of this cell. </TABLE><TABLE><TR><TH align="right" valign="top">•<TD>    <TD valign="top">This cell becomes a child of the cells mentioned in the expression. </TABLE><TABLE><TR><TH align="right" valign="top">•<TD>    <TD valign="top">If all the parents have values, the value of this cell is computed. </TABLE><P> Some of these changes are simple, but others are complicated. For example, it's not enough to tell the cell's new parents that the cell is now their child (the third task). First we have to tell the cell's <EM>old</EM> parents that this cell <EM>isn't</EM> their child any more. That has to be done before we forget the cell's old parents. <P>Here is an example. (In the following tables, we represent the data structures as if cells were represented by their names, even though really their IDs are used. We've done this to make the example more readable.) Suppose that we have five cells set up like this: <P><TABLE><TR><TH>cell  <TH>expression  <TH>value   <TH>parents  <TH>children <TR><TD>  <TR><TD><CODE>a1</CODE><TD><CODE>20</CODE> <TD><CODE>20</CODE><TD><CODE>()</CODE><TD><CODE>(a2)</CODE> <TR><TD><CODE>b1</CODE><TD><CODE>5</CODE><TD><CODE>5</CODE><TD><CODE>()</CODE> <TD><CODE>(a2 b2)</CODE> <TR><TD><CODE>c1</CODE><TD><CODE>8</CODE><TD><CODE>8</CODE><TD><CODE>()</CODE> <TD><CODE>()</CODE> <TR><TD><CODE>a2</CODE><TD><CODE>(+ a1 b1)</CODE><TD><CODE>25</CODE> <TD><CODE>(a1 b1)</CODE><TD><CODE>(b2)</CODE> <TR><TD><CODE>b2</CODE><TD><CODE>(+ a2 b1)</CODE><TD><CODE>30</CODE> <TD><CODE>(a2 b1)</CODE><TD><CODE>()</CODE> </TABLE> <P>If we now enter the spreadsheet command <P><PRE>(put (+ b1 c1) a2) </PRE> <P>the program must first remove <CODE>a2</CODE> from the children of its old parents (changes are shown in boldface): <P><TABLE><TR><TH>cell  <TH>expression  <TH>value   <TH>parents  <TH>children <TR><TD>  <TR><TD><CODE>a1</CODE><TD><CODE>20</CODE> <TD><CODE>20</CODE><TD><CODE>()</CODE><TD><CODE><STRONG><BIG>()</BIG></STRONG></CODE> <TR><TD><CODE>b1</CODE><TD><CODE>5</CODE><TD><CODE>5</CODE><TD><CODE>()</CODE> <TD><CODE><STRONG><BIG>(b2)</BIG></STRONG></CODE> <TR><TD><CODE>c1</CODE><TD><CODE>8</CODE><TD><CODE>8</CODE><TD><CODE>()</CODE> <TD><CODE>()</CODE> <TR><TD><CODE>a2</CODE><TD><CODE>(+ a1 b1)</CODE><TD><CODE>25</CODE> <TD><CODE>(a1 b1)</CODE><TD><CODE>(b2)</CODE> <TR><TD><CODE>b2</CODE><TD><CODE>(+ a2 b1)</CODE><TD><CODE>30</CODE> <TD><CODE>(a2 b1)</CODE><TD><CODE>()</CODE> </TABLE> <P>Then the program can change the expression and compute a new list of parents: <P> <TABLE><TR><TH>cell  <TH>expression  <TH>value   <TH>parents  <TH>children <TR><TD>  <TR><TD><CODE>a1</CODE><TD><CODE>20</CODE> <TD><CODE>20</CODE><TD><CODE>()</CODE><TD><CODE>()</CODE> <TR><TD><CODE>b1</CODE><TD><CODE>5</CODE><TD><CODE>5</CODE><TD><CODE>()</CODE> <TD><CODE>(b2)</CODE> <TR><TD><CODE>c1</CODE><TD><CODE>8</CODE><TD><CODE>8</CODE><TD><CODE>()</CODE> <TD><CODE>()</CODE> <TR><TD><CODE>a2</CODE><TD><CODE><STRONG><BIG>(+ b1 c1)</BIG></STRONG></CODE> <TD><CODE>25</CODE><TD><CODE><STRONG><BIG>(b1 c1)</BIG></STRONG></CODE> <TD><CODE>(b2)</CODE> <TR><TD><CODE>b2</CODE><TD><CODE>(+ a2 b1)</CODE><TD><CODE>30</CODE> <TD><CODE>(a2 b1)</CODE><TD><CODE>()</CODE> </TABLE> <P>Next it can tell the new parents to add <CODE>a2</CODE> as a child, and can compute <CODE>a2</CODE>'s new value: <P><TABLE><TR><TH>cell  <TH>expression  <TH>value   <TH>parents  <TH>children <TR><TD>  <TR><TD><CODE>a1</CODE><TD><CODE>20</CODE> <TD><CODE>20</CODE><TD><CODE>()</CODE><TD><CODE>()</CODE> <TR><TD><CODE>b1</CODE><TD><CODE>5</CODE><TD><CODE>5</CODE><TD><CODE>()</CODE> <TD><CODE><STRONG><BIG>(a2 b2)</BIG></STRONG></CODE> <TR><TD><CODE>c1</CODE><TD><CODE>8</CODE><TD><CODE>8</CODE><TD><CODE>()</CODE> <TD><CODE><STRONG><BIG>(a2)</BIG></STRONG></CODE> <TR><TD><CODE>a2</CODE><TD><CODE>(+ b1 c1)</CODE> <TD><CODE><STRONG><BIG>13</BIG></STRONG></CODE><TD><CODE>(b1 c1)</CODE> <TD><CODE>(b2)</CODE> <TR><TD><CODE>b2</CODE><TD><CODE>(+ a2 b1)</CODE><TD><CODE>30</CODE> <TD><CODE>(a2 b1)</CODE><TD><CODE>()</CODE> </TABLE> <P>Changing <CODE>a2</CODE>'s value affects the values of all of its children, and also its grandchildren and so on (except that in this example there are no grandchildren): <P><TABLE><TR><TH>cell  <TH>expression  <TH>value   <TH>parents  <TH>children <TR><TD>  <TR><TD><CODE>a1</CODE><TD><CODE>20</CODE> <TD><CODE>20</CODE><TD><CODE>()</CODE><TD><CODE>()</CODE> <TR><TD><CODE>b1</CODE><TD><CODE>5</CODE><TD><CODE>5</CODE><TD><CODE>()</CODE> <TD><CODE>(a2 b2)</CODE> <TR><TD><CODE>c1</CODE><TD><CODE>8</CODE><TD><CODE>8</CODE><TD><CODE>()</CODE> <TD><CODE>(a2)</CODE> <TR><TD><CODE>a2</CODE><TD><CODE>(+ b1 c1)</CODE> <TD><CODE>13</CODE><TD><CODE>(b1 c1)</CODE> <TD><CODE>(b2)</CODE> <TR><TD><CODE>b2</CODE><TD><CODE>(+ a2 b1)</CODE> <TD><CODE><STRONG><BIG>18</BIG></STRONG></CODE><TD><CODE>(a2 b1)</CODE><TD><CODE>()</CODE> </TABLE> <P>Now that we've considered an example, here is the main procedure that oversees all these tasks: <P><PRE>(define (<A NAME="g23"></A>put-expr expr-or-out-of-bounds id) (let ((expr (if (equal? expr-or-out-of-bounds 'out-of-bounds) '() expr-or-out-of-bounds))) (for-each (lambda (old-parent) (set-cell-children! old-parent (remove id (cell-children old-parent)))) (cell-parents id)) (set-cell-expr! id expr) (set-cell-parents! id (remdup (extract-ids expr))) (for-each (lambda (new-parent) (set-cell-children! new-parent (cons id (cell-children new-parent)))) (cell-parents id)) (figure id))) </PRE> Remember that <CODE>put-expr</CODE>'s first argument is the return value from <CODE>pin-down</CODE>, so it might be the word <CODE>out-of-bounds</CODE> instead of an expression. In this case, we store an empty list as the expression, indicating that there is no active expression for this cell. <P>Within the body of the <CODE>let</CODE> there are five Scheme expressions, each of which carries out one of the tasks we've listed. The first expression tells the cell's former parents that the cell is no longer their child. The second expression stores the expression in the cell. <P>The third Scheme expression invokes <CODE>extract-ids</CODE> to find all the cell ids used in <CODE>expr</CODE>, removes any duplicates, and establishes those identified cells as the argument cell's parents. (You wrote <CODE>remdup</CODE> in Exercise <A HREF="../ssch14/recur-patterns.html#remdup">14.3</A>.) For example, if the <CODE>expr</CODE> is <P><PRE>(+ (id 4 2) (* (id 1 3) (id 1 3))) </PRE> <P>then <CODE>extract-ids</CODE> will return the list <P><PRE>((id 4 2) (id 1 3) (id 1 3)) </PRE> <P>and <CODE>remdup</CODE> of that will be <P><PRE>((id 4 2) (id 1 3)) </PRE> <P>The fourth expression in the <CODE>let</CODE> tells each of the new parents to consider the argument cell as its child. The fifth expression may or may not compute a new value for this cell. (As we'll see in a moment, that process is a little complicated.) <P>Two of these steps require closer examination. Here is the procedure used in the third step: <P><PRE>(define (<A NAME="g24"></A>extract-ids expr) (cond ((id? expr) (list expr)) ((word? expr) '()) ((null? expr) '()) (else (append (extract-ids (car expr)) (extract-ids (cdr expr)))))) </PRE> <P>This is a tree recursion. The first three <CODE>cond</CODE> clauses are base cases; cell IDs are included in the returned list, while other words are ignored. For compound expressions, we use the trick of making recursive calls on the <CODE>car</CODE> and <CODE>cdr</CODE> of the list. We combine the results with <CODE>append</CODE> because <CODE>extract-ids</CODE> must return a flat list of cell IDs, not a cheap tree. <P>The fifth step in <CODE>put-expr</CODE> is complicated because, as we saw in the example, changing the value of one cell may require us to recompute the value of other cells: <P><PRE>(define (<A NAME="g25"></A>figure id) (cond ((null? (cell-expr id)) (setvalue id '())) ((all-evaluated? (cell-parents id)) (setvalue id (ss-eval (cell-expr id)))) (else (setvalue id '())))) (define (<A NAME="g26"></A>all-evaluated? ids) (cond ((null? ids) #t) ((not (number? (cell-value (car ids)))) #f) (else (all-evaluated? (cdr ids))))) (define (<A NAME="g27"></A>setvalue id value) (let ((old (cell-value id))) (set-cell-value! id value) (if (not (equal? old value)) (for-each figure (cell-children id)) 'do-nothing))) </PRE> <P><CODE>Figure</CODE> is invoked for the cell whose expression we've just changed. If there is no expression (that is, if we've changed it to an empty expression or to an out-of-bounds one), then <CODE>figure</CODE> will remove any old value that might be left over from a previous expression. If there is an expression, then <CODE>figure</CODE> will compute and save a new value, but only if all of this cell's parents have numeric values. If any parent doesn't have a value, or if its value is a non-numeric label, then <CODE>figure</CODE> has to remove the value from this cell. <P><CODE>Setvalue</CODE> actually puts the new value in the cell. It first looks up the old value. If the new and old values are different, then all of the children of this cell must be re-<CODE>figure</CODE>d. This, too, is a tree recursion because there might be several children, and each of them might have several children. <P>We haven't yet explained how <CODE>ss-eval</CODE> actually computes the value from the expression. That's the subject of the next major part of the program. <P><H2>The Expression Evaluator</H2> <P><CODE>Figure</CODE> invokes <CODE>ss-eval</CODE> to convert a cell's expression into its value. Also, we've seen earlier that <CODE>process-command</CODE> uses <CODE>ss-eval</CODE> to evaluate an expression that the user types in response to a spreadsheet prompt. (That is, <CODE>ss-eval</CODE> is invoked if what the user types isn't one of the special commands recognized by <CODE>process-command</CODE> itself.) <P>The <CODE>ss</CODE> in <CODE>ss-eval</CODE> stands for "spreadsheet"; it distinguishes this procedure from <A NAME="g28"></A><CODE>eval</CODE>, a primitive procedure that evaluates Scheme expressions. As it turns out, <CODE>ss-eval</CODE>'s algorithm is similar in many ways to that of Scheme's <CODE>eval</CODE>, although <CODE>ss-eval</CODE> is much simpler in other ways. The experience you already have with Scheme's expression evaluation will help you understand the spreadsheet's. <P>Scheme's evaluator takes an expression and computes the corresponding value. The expressions look quite different from the values, but there are well-defined rules (the ones we studied in Chapter 3) to translate expressions to values. In the spreadsheet language, as in Scheme, an expression can be one of three things: <P><P><TABLE><TR><TH align="right" valign="top">•<TD>    <TD valign="top">a constant expression (a number or quoted word), whose value is itself. </TABLE><TABLE><TR><TH align="right" valign="top">•<TD>    <TD valign="top">a variable (a cell ID, in the case of the spreadsheet language). </TABLE><TABLE><TR><TH align="right" valign="top">•<TD>    <TD valign="top">a procedure invocation enclosed in parentheses. </TABLE><P> The spreadsheet language is simpler than Scheme for three main reasons. <P><P><TABLE><TR><TH align="right" valign="top">•<TD>    <TD valign="top">There are no special forms such as <CODE>if</CODE> or <CODE>define</CODE>.<A NAME="text5" HREF="spread-implement#ft5">[5]</A> </TABLE><TABLE><TR><TH align="right" valign="top">•<TD>    <TD valign="top">The only variables, the cell IDs, are global; in Scheme, much of the complexity of evaluation has to do with variables that are local to procedures (i.e., formal parameters). </TABLE><TABLE><TR><TH align="right" valign="top">•<TD>    <TD valign="top">The only procedures are primitives, so there is no need to evaluate procedure bodies. </TABLE><P> The structure of <CODE>ss-eval</CODE> is a <CODE>cond</CODE> whose clauses handle the three types of expressions. Constants and variables are easy; invocations require recursively evaluating the arguments before the procedure can be invoked. <P><PRE>(define (<A NAME="g29"></A>ss-eval expr) (cond ((number? expr) expr) ((quoted? expr) (quoted-value expr)) ((id? expr) (cell-value expr)) ((invocation? expr) (apply (get-function (car expr)) (map ss-eval (cdr expr)))) (else (error "Invalid expression:" expr)))) </PRE> <P>The value of a number is itself; the value of a quoted word is the word without the quotation mark. (Actually, by the time <CODE>ss-eval</CODE> sees a quoted word, Scheme has translated the <CODE>'abc</CODE> notation into <CODE>(quote abc)</CODE> and that's what we deal with here. Also, double-quoted strings look different to the program from single-quoted words.) <P><PRE>(define (<A NAME="g30"></A>quoted? expr) (or (string? expr) (and (list? expr) (equal? (car expr) 'quote)))) (define (<A NAME="g31"></A>quoted-value expr) (if (string? expr) expr (cadr expr))) </PRE> <P>The third clause checks for a cell ID; the value of such an expression is the value stored in the corresponding cell. <P>If an expression is none of those things, it had better be a function invocation, that is, a list. In that case, <CODE>ss-eval</CODE> has to do three things: It looks up the function name in a table (as we did earlier for spreadsheet commands); it recursively evaluates all the argument subexpressions; and then it can invoke <CODE>apply</CODE> to apply the procedure to the argument values. <P><CODE>Get-function</CODE> looks up a function name in the name-to-function association list and returns the corresponding Scheme procedure. Thus, only the functions included in the list can be used in spreadsheet formulas. <P>The entire expression evaluator, including <CODE>ss-eval</CODE> and its helper procedures, is functional. Like the formula translator, it doesn't change the state of the spreadsheet. <P><H2>The Screen Printer</H2> <P>The procedures that print the spreadsheet on the screen are straightforward but full of details. Much of the work here goes into those details. <P>As we mentioned earlier, a better spreadsheet program wouldn't redraw the entire screen for each command but would change only the parts of the screen that were affected by the previous command. However, Scheme does not include a standard way to control the positioning of text on the screen, so we're stuck with this approach. <P><PRE>(define (<A NAME="g32"></A>print-screen) (newline) (newline) (newline) (show-column-labels (id-column (screen-corner-cell-id))) (show-rows 20 (id-column (screen-corner-cell-id)) (id-row (screen-corner-cell-id))) (display-cell-name (selection-cell-id)) (show (cell-value (selection-cell-id))) (display-expression (cell-expr (selection-cell-id))) (newline) (display "?? ")) </PRE> <P><CODE>Screen-corner-cell-id</CODE> returns the ID of the cell that should be shown in the top left corner of the display; <CODE>selection-cell-id</CODE> returns the ID of the selected cell. <P><CODE>Show-column-labels</CODE> prints the first row of the display, the one with the column letters. <CODE>Show-rows</CODE> is a sequential recursion that prints the actual rows of the spreadsheet, starting with the row number of the <CODE>screen-corner</CODE> cell and continuing for 20 rows. (There are 30 rows in the entire spreadsheet, but they don't all fit on the screen at once.) The rest of the procedure displays the value and expression of the selected cell at the bottom of the screen and prompts for the next command. <P>Why isn't <CODE>display-expression</CODE> just <CODE>display</CODE>? Remember that the spreadsheet stores expressions in a form like <P><PRE>(+ (id 2 5) (id 6 3)) </PRE> <P>but the user wants to see <P><PRE>(+ b5 f3) </PRE> <P><CODE>Display-expression</CODE> is yet another tree recursion over expressions. Just as <CODE>pin-down</CODE> translates cell names into cell IDs, <CODE>display-expression</CODE> translates IDs back into names. (But <CODE>display-expression</CODE> prints as it goes along, instead of reconstructing and returning a list.) The definition of <CODE>display-expression</CODE>, along with the remaining details of printing, can be seen in the full program listing at the end of this chapter. <P>Just to give the flavor of those details, here is the part that displays the rectangular array of cell values. <CODE>Show-rows</CODE> is a sequential recursion in which each invocation prints an entire row. It does so by invoking <CODE>show-row</CODE>, another sequential recursion, in which each invocation prints a single cell value. <P><PRE>(define (show-rows to-go col row) (cond ((= to-go 0) 'done) (else (display (align row 2 0)) (display " ") (show-row 6 col row) (newline) (show-rows (- to-go 1) col (+ row 1))))) (define (show-row to-go col row) (cond ((= to-go 0) 'done) (else (display (if (selected-indices? col row) ">" " ")) (display-value (cell-value-from-indices col row)) (display (if (selected-indices? col row) "<" " ")) (show-row (- to-go 1) (+ 1 col) row)))) (define (selected-indices? col row) (and (= col (id-column (selection-cell-id))) (= row (id-row (selection-cell-id))))) </PRE> <P>Why didn't we write <CODE>show-row</CODE> in the following way? <P><PRE>(define (show-row to-go col row) ;; alternate version (cond ((= to-go 0) 'done) (else (let ((id (make-id col row))) (display (if (equal? id (selection-cell-id)) ">" " ")) (display-value (cell-value id)) (display (if (equal? id (selection-cell-id)) "<" " ")) (show-row (- to-go 1) (+ 1 col) row))))) </PRE> <P>That would have worked fine and would have been a little clearer. In fact, we did write <CODE>show-row</CODE> this way originally. But it's a little time-consuming to construct an ID, and <CODE>show-row</CODE> is called 120 times whenever <CODE>print-screen</CODE> is used. Since printing the screen was annoyingly slow, we sped things up as much as we could, even at the cost of this kludge. <P><H2>The Cell Manager</H2> <P>The program keeps information about the current status of the spreadsheet cells in a vector called <CODE>*the-spreadsheet-array*</CODE>. It contains all of the 780 cells that make up the spreadsheet (30 rows of 26 columns). It's not a vector of length 780; rather, it's a vector of length 30, each of whose elements is itself a vector of length 26. In other words, each element of the spreadsheet array is a vector representing one row of the spreadsheet. (Each element of <EM>those</EM> vectors is one cell, which, as you recall, is represented as a vector of length four. So the spreadsheet array is a vector of vectors of vectors!) <P>The selectors for the parts of a cell take the cell's ID as argument and return one of the four elements of the cell vector. Each must therefore be implemented as two steps: We must find the cell vector, given its ID; and we must then select an element from the cell vector. The first step is handled by the selector <CODE>cell-structure</CODE> that takes a cell ID as argument: <P><PRE>(define (<A NAME="g33"></A>cell-structure id) (global-array-lookup (id-column id) (id-row id))) (define (<A NAME="g34"></A>global-array-lookup col row) (if (and (<= row 30) (<= col 26)) (vector-ref (vector-ref *the-spreadsheet-array* (- row 1)) (- col 1)) (error "Out of bounds"))) </PRE> <P><CODE>Global-array-lookup</CODE> makes sure the desired cell exists. It also compensates for the fact that Scheme vectors begin with element number zero, while our spreadsheet begins with row and column number one. Two invocations of <CODE>vector-ref</CODE> are needed, one to select an entire row and the next to select a cell within that row. <P>Selectors and mutators for the parts of a cell are written using <CODE>cell-structure</CODE>: <P><PRE>(define (<A NAME="g35"></A>cell-value id) (vector-ref (cell-structure id) 0)) (define (<A NAME="g36"></A>set-cell-value! id val) (vector-set! (cell-structure id) 0 val)) (define (<A NAME="g37"></A>cell-expr id) (vector-ref (cell-structure id) 1)) (define (<A NAME="g38"></A>set-cell-expr! id val) (vector-set! (cell-structure id) 1 val)) (define (<A NAME="g39"></A>cell-parents id) (vector-ref (cell-structure id) 2)) (define (<A NAME="g40"></A>set-cell-parents! id val) (vector-set! (cell-structure id) 2 val)) (define (<A NAME="g41"></A>cell-children id) (vector-ref (cell-structure id) 3)) (define (<A NAME="g42"></A>set-cell-children! id val) (vector-set! (cell-structure id) 3 val)) </PRE> <P>The constructor is <P><PRE>(define (make-cell) (vector '() '() '() '())) </PRE> <P>The spreadsheet program begins by invoking <CODE>init-array</CODE> to set up this large array. (Also, it sets the initial values of the selected cell and the screen corner.) <P><PRE>(define (<A NAME="g43"></A>spreadsheet) (init-array) (set-selection-cell-id! (make-id 1 1)) (set-screen-corner-cell-id! (make-id 1 1)) (command-loop)) (define *the-spreadsheet-array* (make-vector 30)) (define (<A NAME="g44"></A>init-array) (fill-array-with-rows 29)) (define (<A NAME="g45"></A>fill-array-with-rows n) (if (< n 0) 'done (begin (vector-set! *the-spreadsheet-array* n (make-vector 26)) (fill-row-with-cells (vector-ref *the-spreadsheet-array* n) 25) (fill-array-with-rows (- n 1))))) (define (<A NAME="g46"></A>fill-row-with-cells vec n) (if (< n 0) 'done (begin (vector-set! vec n (make-cell)) (fill-row-with-cells vec (- n 1))))) </PRE> <P> <P>That's the end of the project, apart from some straightforward procedures such as <CODE>letter->number</CODE> that you can look up in the complete listing if you're interested. <P><H2>Complete Program Listing</H2> <P><P><P><PRE> (define (spreadsheet) (init-array) (set-selection-cell-id! (make-id 1 1)) (set-screen-corner-cell-id! (make-id 1 1)) (command-loop)) (define (command-loop) (print-screen) (let ((command-or-formula (read))) (if (equal? command-or-formula 'exit) "Bye!" (begin (process-command command-or-formula) (command-loop))))) (define (process-command command-or-formula) (cond ((and (list? command-or-formula) (command? (car command-or-formula))) (execute-command command-or-formula)) ((command? command-or-formula) (execute-command (list command-or-formula 1))) (else (exhibit (ss-eval (pin-down command-or-formula (selection-cell-id))))))) (define (execute-command command) (apply (get-command (car command)) (cdr command))) (define (exhibit val) (show val) (show "Type RETURN to redraw screen") (read-line) (read-line)) ;;; Commands ;; Cell selection commands: F, B, N, P, and SELECT (define (prev-row delta) (let ((row (id-row (selection-cell-id)))) (if (< (- row delta) 1) (error "Already at top.") (set-selected-row! (- row delta))))) (define (next-row delta) (let ((row (id-row (selection-cell-id)))) (if (> (+ row delta) 30) (error "Already at bottom.") (set-selected-row! (+ row delta))))) (define (prev-col delta) (let ((col (id-column (selection-cell-id)))) (if (< (- col delta) 1) (error "Already at left.") (set-selected-column! (- col delta))))) (define (next-col delta) (let ((col (id-column (selection-cell-id)))) (if (> (+ col delta) 26) (error "Already at right.") (set-selected-column! (+ col delta))))) (define (set-selected-row! new-row) (select-id! (make-id (id-column (selection-cell-id)) new-row))) (define (set-selected-column! new-column) (select-id! (make-id new-column (id-row (selection-cell-id))))) (define (select-id! id) (set-selection-cell-id! id) (adjust-screen-boundaries)) (define (select cell-name) (select-id! (cell-name->id cell-name))) (define (adjust-screen-boundaries) (let ((row (id-row (selection-cell-id))) (col (id-column (selection-cell-id)))) (if (< row (id-row (screen-corner-cell-id))) (set-corner-row! row) 'do-nothing) (if (>= row (+ (id-row (screen-corner-cell-id)) 20)) (set-corner-row! (- row 19)) 'do-nothing) (if (< col (id-column (screen-corner-cell-id))) (set-corner-column! col) 'do-nothing) (if (>= col (+ (id-column (screen-corner-cell-id)) 6)) (set-corner-column! (- col 5)) 'do-nothing))) (define (set-corner-row! new-row) (set-screen-corner-cell-id! (make-id (id-column (screen-corner-cell-id)) new-row))) (define (set-corner-column! new-column) (set-screen-corner-cell-id! (make-id new-column (id-row (screen-corner-cell-id))))) ;; LOAD (define (spreadsheet-load filename) (let ((port (open-input-file filename))) (sl-helper port) (close-input-port port))) (define (sl-helper port) (let ((command (read port))) (if (eof-object? command) 'done (begin (show command) (process-command command) (sl-helper port))))) ;; PUT (define (put formula . where) (cond ((null? where) (put-formula-in-cell formula (selection-cell-id))) ((cell-name? (car where)) (put-formula-in-cell formula (cell-name->id (car where)))) ((number? (car where)) (put-all-cells-in-row formula (car where))) ((letter? (car where)) (put-all-cells-in-col formula (letter->number (car where)))) (else (error "Put it where?")))) (define (put-all-cells-in-row formula row) (put-all-helper formula (lambda (col) (make-id col row)) 1 26)) (define (put-all-cells-in-col formula col) (put-all-helper formula (lambda (row) (make-id col row)) 1 30)) (define (put-all-helper formula id-maker this max) (if (> this max) 'done (begin (try-putting formula (id-maker this)) (put-all-helper formula id-maker (+ 1 this) max)))) (define (try-putting formula id) (if (or (null? (cell-value id)) (null? formula)) (put-formula-in-cell formula id) 'do-nothing)) (define (put-formula-in-cell formula id) (put-expr (pin-down formula id) id)) ;;; The Association List of Commands (define (command? name) (assoc name *the-commands*)) (define (get-command name) (let ((result (assoc name *the-commands*))) (if (not result) #f (cadr result)))) (define *the-commands* (list (list 'p prev-row) (list 'n next-row) (list 'b prev-col) (list 'f next-col) (list 'select select) (list 'put put) (list 'load spreadsheet-load))) ;;; Pinning Down Formulas Into Expressions (define (pin-down formula id) (cond ((cell-name? formula) (cell-name->id formula)) ((word? formula) formula) ((null? formula) '()) ((equal? (car formula) 'cell) (pin-down-cell (cdr formula) id)) (else (bound-check (map (lambda (subformula) (pin-down subformula id)) formula))))) (define (bound-check form) (if (member 'out-of-bounds form) 'out-of-bounds form)) (define (pin-down-cell args reference-id) (cond ((null? args) (error "Bad cell specification: (cell)")) ((null? (cdr args)) (cond ((number? (car args)) ; they chose a row (make-id (id-column reference-id) (car args))) ((letter? (car args)) ; they chose a column (make-id (letter->number (car args)) (id-row reference-id))) (else (error "Bad cell specification:" (cons 'cell args))))) (else (let ((col (pin-down-col (car args) (id-column reference-id))) (row (pin-down-row (cadr args) (id-row reference-id)))) (if (and (>= col 1) (<= col 26) (>= row 1) (<= row 30)) (make-id col row) 'out-of-bounds))))) (define (pin-down-col new old) (cond ((equal? new '*) old) ((equal? (first new) '>) (+ old (bf new))) ((equal? (first new) '<) (- old (bf new))) ((letter? new) (letter->number new)) (else (error "What column?")))) (define (pin-down-row new old) (cond ((number? new) new) ((equal? new '*) old) ((equal? (first new) '>) (+ old (bf new))) ((equal? (first new) '<) (- old (bf new))) (else (error "What row?")))) ;;; Dependency Management (define (put-expr expr-or-out-of-bounds id) (let ((expr (if (equal? expr-or-out-of-bounds 'out-of-bounds) '() expr-or-out-of-bounds))) (for-each (lambda (old-parent) (set-cell-children! old-parent (remove id (cell-children old-parent)))) (cell-parents id)) (set-cell-expr! id expr) (set-cell-parents! id (remdup (extract-ids expr))) (for-each (lambda (new-parent) (set-cell-children! new-parent (cons id (cell-children new-parent)))) (cell-parents id)) (figure id))) (define (extract-ids expr) (cond ((id? expr) (list expr)) ((word? expr) '()) ((null? expr) '()) (else (append (extract-ids (car expr)) (extract-ids (cdr expr)))))) (define (figure id) (cond ((null? (cell-expr id)) (setvalue id '())) ((all-evaluated? (cell-parents id)) (setvalue id (ss-eval (cell-expr id)))) (else (setvalue id '())))) (define (all-evaluated? ids) (cond ((null? ids) #t) ((not (number? (cell-value (car ids)))) #f) (else (all-evaluated? (cdr ids))))) (define (setvalue id value) (let ((old (cell-value id))) (set-cell-value! id value) (if (not (equal? old value)) (for-each figure (cell-children id)) 'do-nothing))) ;;; Evaluating Expressions (define (ss-eval expr) (cond ((number? expr) expr) ((quoted? expr) (quoted-value expr)) ((id? expr) (cell-value expr)) ((invocation? expr) (apply (get-function (car expr)) (map ss-eval (cdr expr)))) (else (error "Invalid expression:" expr)))) (define (quoted? expr) (or (string? expr) (and (list? expr) (equal? (car expr) 'quote)))) (define (quoted-value expr) (if (string? expr) expr (cadr expr))) (define (invocation? expr) (list? expr)) (define (get-function name) (let ((result (assoc name *the-functions*))) (if (not result) (error "No such function: " name) (cadr result)))) (define *the-functions* (list (list '* *) (list '+ +) (list '- -) (list '/ /) (list 'abs abs) (list 'acos acos) (list 'asin asin) (list 'atan atan) (list 'ceiling ceiling) (list 'cos cos) (list 'count count) (list 'exp exp) (list 'expt expt) (list 'floor floor) (list 'gcd gcd) (list 'lcm lcm) (list 'log log) (list 'max max) (list 'min min) (list 'modulo modulo) (list 'quotient quotient) (list 'remainder remainder) (list 'round round) (list 'sin sin) (list 'sqrt sqrt) (list 'tan tan) (list 'truncate truncate))) ;;; Printing the Screen (define (print-screen) (newline) (newline) (newline) (show-column-labels (id-column (screen-corner-cell-id))) (show-rows 20 (id-column (screen-corner-cell-id)) (id-row (screen-corner-cell-id))) (display-cell-name (selection-cell-id)) (display ": ") (show (cell-value (selection-cell-id))) (display-expression (cell-expr (selection-cell-id))) (newline) (display "?? ")) (define (display-cell-name id) (display (number->letter (id-column id))) (display (id-row id))) (define (show-column-labels col-number) (display " ") (show-label 6 col-number) (newline)) (define (show-label to-go this-col-number) (cond ((= to-go 0) '()) (else (display " -----") (display (number->letter this-col-number)) (display "----") (show-label (- to-go 1) (+ 1 this-col-number))))) (define (show-rows to-go col row) (cond ((= to-go 0) 'done) (else (display (align row 2 0)) (display " ") (show-row 6 col row) (newline) (show-rows (- to-go 1) col (+ row 1))))) (define (show-row to-go col row) (cond ((= to-go 0) 'done) (else (display (if (selected-indices? col row) ">" " ")) (display-value (cell-value-from-indices col row)) (display (if (selected-indices? col row) "<" " ")) (show-row (- to-go 1) (+ 1 col) row)))) (define (selected-indices? col row) (and (= col (id-column (selection-cell-id))) (= row (id-row (selection-cell-id))))) (define (display-value val) (display (align (if (null? val) "" val) 10 2))) (define (display-expression expr) (cond ((null? expr) (display '())) ((quoted? expr) (display (quoted-value expr))) ((word? expr) (display expr)) ((id? expr) (display-cell-name expr)) (else (display-invocation expr)))) (define (display-invocation expr) (display "(") (display-expression (car expr)) (for-each (lambda (subexpr) (display " ") (display-expression subexpr)) (cdr expr)) (display ")")) ;;; Abstract Data Types ;; Special cells: the selected cell and the screen corner (define *special-cells* (make-vector 2)) (define (selection-cell-id) (vector-ref *special-cells* 0)) (define (set-selection-cell-id! new-id) (vector-set! *special-cells* 0 new-id)) (define (screen-corner-cell-id) (vector-ref *special-cells* 1)) (define (set-screen-corner-cell-id! new-id) (vector-set! *special-cells* 1 new-id)) ;; Cell names (define (cell-name? expr) (and (word? expr) (letter? (first expr)) (number? (bf expr)))) (define (cell-name-column cell-name) (letter->number (first cell-name))) (define (cell-name-row cell-name) (bf cell-name)) (define (cell-name->id cell-name) (make-id (cell-name-column cell-name) (cell-name-row cell-name))) ;; Cell IDs (define (make-id col row) (list 'id col row)) (define (id-column id) (cadr id)) (define (id-row id) (caddr id)) (define (id? x) (and (list? x) (not (null? x)) (equal? 'id (car x)))) ;; Cells (define (make-cell) (vector '() '() '() '())) (define (cell-value id) (vector-ref (cell-structure id) 0)) (define (cell-value-from-indices col row) (vector-ref (cell-structure-from-indices col row) 0)) (define (cell-expr id) (vector-ref (cell-structure id) 1)) (define (cell-parents id) (vector-ref (cell-structure id) 2)) (define (cell-children id) (vector-ref (cell-structure id) 3)) (define (set-cell-value! id val) (vector-set! (cell-structure id) 0 val)) (define (set-cell-expr! id val) (vector-set! (cell-structure id) 1 val)) (define (set-cell-parents! id val) (vector-set! (cell-structure id) 2 val)) (define (set-cell-children! id val) (vector-set! (cell-structure id) 3 val)) (define (cell-structure id) (global-array-lookup (id-column id) (id-row id))) (define (cell-structure-from-indices col row) (global-array-lookup col row)) (define *the-spreadsheet-array* (make-vector 30)) (define (global-array-lookup col row) (if (and (<= row 30) (<= col 26)) (vector-ref (vector-ref *the-spreadsheet-array* (- row 1)) (- col 1)) (error "Out of bounds"))) (define (init-array) (fill-array-with-rows 29)) (define (fill-array-with-rows n) (if (< n 0) 'done (begin (vector-set! *the-spreadsheet-array* n (make-vector 26)) (fill-row-with-cells (vector-ref *the-spreadsheet-array* n) 25) (fill-array-with-rows (- n 1))))) (define (fill-row-with-cells vec n) (if (< n 0) 'done (begin (vector-set! vec n (make-cell)) (fill-row-with-cells vec (- n 1))))) ;;; Utility Functions (define alphabet '#(a b c d e f g h i j k l m n o p q r s t u v w x y z)) (define (letter? something) (and (word? something) (= 1 (count something)) (vector-member something alphabet))) (define (number->letter num) (vector-ref alphabet (- num 1))) (define (letter->number letter) (+ (vector-member letter alphabet) 1)) (define (vector-member thing vector) (vector-member-helper thing vector 0)) (define (vector-member-helper thing vector index) (cond ((= index (vector-length vector)) #f) ((equal? thing (vector-ref vector index)) index) (else (vector-member-helper thing vector (+ 1 index))))) (define (remdup lst) (cond ((null? lst) '()) ((member (car lst) (cdr lst)) (remdup (cdr lst))) (else (cons (car lst) (remdup (cdr lst)))))) (define (remove bad-item lst) (filter (lambda (item) (not (equal? item bad-item))) lst)) </PRE><P> <P><H2>Exercises</H2> <P><B>25.1</B>  The "magic numbers" 26 and 30 (and some numbers derived from them) appear many times in the text of this program. It's easy to imagine wanting more rows or columns. <P>Create global variables <CODE>total-cols</CODE> and <CODE>total-rows</CODE> with values 26 and 30 respectively. Then modify the spreadsheet program to refer to these variables rather than to the numbers 26 and 30 directly. When you're done, redefine <CODE>total-rows</CODE> to be 40 and see if it works. <P> <B>25.2</B>  Suggest a way to notate columns beyond <CODE>z</CODE>. What procedures would have to change to accommodate this? <P> <B>25.3</B>  Modify the program so that the spreadsheet array is kept as a single vector of 780 elements, instead of a vector of 30 vectors of 26 vectors. What procedures do you have to change to make this work? (It shouldn't be very many.) <P> <B>25.4</B>  The procedures <CODE>get-function</CODE> and <CODE>get-command</CODE> are almost identical in structure; both look for an argument in an association list. They differ, however, in their handling of the situation in which the argument is not present in the list. Why? <P> <B>25.5</B>  The reason we had to include the word <CODE>id</CODE> in each cell ID was so we would be able to distinguish a list representing a cell ID from a list of some other kind in an expression. Another way to distinguish cell IDs would be to represent them as vectors, since vectors do not otherwise appear within expressions. Change the implementation of cell IDs from three-element lists to two-element vectors: <P><PRE>> (make-id 4 2) #(4 2) </PRE> <P>Make sure the rest of the program still works. <P> <B>25.6</B>  The <CODE>put</CODE> command can be used to label a cell by using a quoted word as the "formula." How does that work? For example, how is such a formula translated into an expression? How is that expression evaluated? What if the labeled cell has children? <P> <B>25.7</B>  Add commands to move the "window" of cells displayed on the screen without changing the selected cell. (There are a lot of possible user interfaces for this feature; pick anything reasonable.) <P> <B>25.8</B>  Modify the <CODE>put</CODE> command so that after doing its work it prints <P><PRE>14 cells modified </PRE> <P>(but, of course, using the actual number of cells modified instead of 14). This number may not be the entire length of a row or column because <CODE>put</CODE> doesn't change an existing formula in a cell when you ask it to set an entire row or column. <P> <B>25.9</B>  Modify the program so that each column remembers the number of digits that should be displayed after the decimal point (currently always 2). Add a command to set this value for a specified column. And, of course, modify <CODE>print-screen</CODE> to use this information. <P> <B>25.10</B>  Add an <CODE>undo</CODE> command, which causes the effect of the previous command to be nullified. That is, if the previous command was a cell selection command, <CODE>undo</CODE> will return to the previously selected cell. If the previous command was a <CODE>put</CODE>, <CODE>undo</CODE> will re-<CODE>put</CODE> the previous expressions in every affected cell. You don't need to undo <CODE>load</CODE> or <CODE>exit</CODE> commands. To do this, you'll need to modify the way the other commands work. <P> <B>25.11</B>  Add an <CODE>accumulate</CODE> procedure that can be used as a function in formulas. Instead of specifying a sequence of cells explicitly, in a formula like <P><PRE>(put (+ c2 c3 c4 c5 c6 c7) c10) </PRE> <P>we want to be able to say <P><PRE>(put (accumulate + c2 c7) c10) </PRE> <P>In general, the two cell names should be taken as corners of a rectangle, all of whose cells should be included, so these two commands are equivalent: <P><PRE>(put (accumulate * a3 c5) d7) (put (* a3 b3 c3 a4 b4 c4 a5 b5 c5) d7) </PRE> <P>Modify <CODE>pin-down</CODE> to convert the <CODE>accumulate</CODE> form into the corresponding spelled-out form. <P> <B>25.12</B>  Add variable-width columns to the spreadsheet. There should be a command to set the print width of a column. This may mean that the spreadsheet can display more or fewer than six columns. <P> <HR> <A NAME="ft1" HREF="spread-implement#text1">[1]</A> The vector elements are numbered from zero, but we number rows and columns from one, subtracting one in the selector that actually extracts information from the array of cells.<P> <A NAME="ft2" HREF="spread-implement#text2">[2]</A> Not every version of Scheme has this behavior. If you find that you have to hit <CODE>return</CODE> twice after exhibiting the value of a formula, take out one of the <CODE>read-line</CODE> invocations.<P> <A NAME="ft3" HREF="spread-implement#text3">[3]</A> We originally wrote two separate helper procedures for the two cases, like this: <P><PRE>(define (put-all-cells-in-row formula row) (row-helper formula 1 26 row)) (define (row-helper formula this-col max-col row) (if (> this-col max-col) 'done (begin (try-putting formula <B>(make-id this-col row)</B>) (row-helper formula (+ this-col 1) max-col row)))) (define (put-all-cells-in-col formula col) (column-helper formula 1 30 col)) (define (column-helper formula this-row max-row col) (if (> this-row max-row) 'done (begin (try-putting formula <B>(make-id col this-row)</B>) (column-helper formula (+ this-row 1) max-row col)))) </PRE> <P>but the procedures were so similar that we decided to generalize the pattern.<P> <A NAME="ft4" HREF="spread-implement#text4">[4]</A> In fact, <CODE>process-command</CODE> also invokes <CODE>pin-down</CODE> when the user types a formula in place of a command. In that situation, the result doesn't go into a cell but is immediately evaluated and printed.<P> <A NAME="ft5" HREF="spread-implement#text5">[5]</A> You can think of the <CODE>cell</CODE> notation in generalized formulas as a kind of special form, but <CODE>pin-down</CODE> has turned those into specific cell IDs before the formula is eligible for evaluation as an expression.<P> <P><A HREF="../ss-toc2.html">(back to Table of Contents)</A><P> <A HREF="../ssch24/spread.html"><STRONG>BACK</STRONG></A> chapter thread <A HREF="database.html"><STRONG>NEXT</STRONG></A> <P> <ADDRESS> <A HREF="../index.html">Brian Harvey</A>, <CODE>bh@cs.berkeley.edu</CODE> </ADDRESS> </BODY> </HTML>