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<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.html#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.html#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.html#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.html#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.html#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.html#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.html#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.html#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.html#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.html#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>
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<P>
<ADDRESS>
<A HREF="../index.html">Brian Harvey</A>,
<CODE>bh@cs.berkeley.edu</CODE>
</ADDRESS>
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