Numbers, Expressions, Simple Programs

DrScheme looks like this:

Beware!If your window does not sayin the lower window like the above picture, then see the IMPORTANT note in Preparing DrScheme.Language: Beginning Student

The top area, the *definitions window*, is for defining new
programs. We'll explain how to use this window later, in
Variables and Programs.

To type Scheme numbers into DrScheme, first click in DrScheme's bottom
area, the *interactions window*, to set the keyboard focus to a point
after the ``> '' prompt.

After typing a Scheme expression, type ENTER (a.k.a. RETURN). If you type a number, DrScheme echoes the number back. If you type a more complex expression, DrScheme prints the expression's value. For example, evaluatingBeware!The insertion caret (the focus point for typing) must be placed after the space following the last ``>'' in the window; otherwise, DrScheme won't let you type a new expression. You can still select old expressions and results for copying, but they cannot be modified.

`(+ 5 5)`

in DrScheme looks like this:

**Numbers**

Scheme numbers are printed in the standard way, but spaces are not
allowed within a number. Thus, `-5`

, with no space between the
`-`

and `5`

, is the negative integer -5. But `- 5`

,
with a space in between, is two separate expressions: the minus
operator and the number 5. Similarly, `3/2`

is the fraction
3/2, while `3 / 2`

is three separate expressions: the number 3,
the division operator, and the number 2.

There is no limit on the size of exact numbers in Scheme. Try giving
DrScheme the number `123456789012345678901234567890`

.

Try the number `10/12`

. DrScheme echoes back the repeating
decimal 0.83 with a line over the 3. If you right-click the
number (Mac OS: control-click), then you can choose to display the
number in fraction form, 5/6. Note that DrScheme automatically puts
the displayed fraction in its simplest form.

DrScheme also accepts decimal numbers, such as `3.2`

, and
treats them in the same way as fractions.

To change the default method for printing numbers (fractions versus
decimals), open the ** Choose Language** dialog, click the

DrScheme always prints inexact results with a leading `#i`

to
alert you that the number is inexact. For example, an abbreviation
for pi (the ratio between a circle's circumference and diameter)
is built into DrScheme, and the input `pi`

produces the output
`#i3.14159`

(perhaps with more digits).

For the Especially Curious:Inexact numbers have a limited size as well as a limited precision. Thus,`(expt #i2 #i5000)`

calculates the inexact value of 2^{5000}to be`#i+inf.0`

, which means ``roughly infinity'' -- very inexact, indeed!

**Numeric Expressions**

Every numeric expression that is not a number must start with an open
parenthesis `(`

and end with a close parenthesis
`)`

. If, instead of `(+ 1 2)`

, you type `+ 1 2`

or `1 + 2`

, DrScheme echos back each of the three separate
pieces: `1`

, `+`

, and `2`

.

To help you match parentheses, DrScheme highlights parenthesis-balanced expressions with a gray background when the insertion caret is immediately before an open parenthesis or after a close parenthesis. However, this highlighting is only an indicator. The highlight does not actually select any text; in particular, the copy and cut commands do not apply to the highlighted region. The normal caret, which is used to select text for cut and paste poerations, is still visible as a blinking black line on the end of the highlighted region.Beware!If you type an open parenthesis without a matching close parenthesis (or vice versa), DrScheme does not even try to evaluate the malformed expression; instead, typing ENTER creates a new line for typing.

If a numeric expression starts with an open parenthesis, an operator
must follow the parenthesis. Unlike arithmetic, where extra
parentheses are always allowed, extra parentheses are illegal in a
Scheme expression. Thus, `(1)`

is not a numeric expression,
neither is `(+ (1) 2)`

, and neither is `((+ 1 2))`

. If
you give DrScheme the expression `(1)`

, it replies with the
error ``First term after parenthesis is illegal in an application.''
In other words, since `1`

appears after the parenthesis,
DrScheme thinks you want to apply the ``operator'' `1`

to some
arguments. But `1`

is not an operator, so it is illegal for
`1`

to follow an open parenthesis. DrScheme gives the same
error message for `((+ 1 2))`

because `(+ 1 2)`

is also
not an operator.

When typing a compound expression, you may accidentally omit a set of
internal parentheses. In this case, DrScheme may report an error that
a primitive operation was received when a number was expected. For
example:

> (* (+ 2 - 4 5) 43 5) +: expects type <number> as 2nd argument; given -; other arguments were: 2 4 5

When an error occurs, DrScheme highlights the erroneous expression in pink. In the above example,

`(+ 2 - 4 5)`

is highlighted,
pinpointing the specific part of the expression that contained the
error: parentheses are missing around the sub-expression ```
- 4
5
```

.
An expression like `(+ 1 2 3)`

does not signal an error because
the standard arithmetic operations accept more than two
arguments. `(+ 1 2 3)`

is legal Scheme notation for 1 + 2 +
3, `(- 1 2 3)`

means (1 `-` 2) `-` 3, `(* 1 2 3)`

means
1 * 2 * 3, and `(/ 1 2 3)`

means (1 / 2) / 3.

**Stepping**

DrScheme provides a ** Step** tool that shows how a complex
expression is evaluated, step-by-step. For example, given the
expression

(+ 2 (* 3 4))

DrScheme must evaluate the

`(* 3 4)`

expression first to get
`12`

. Then, it can evaluate `(+ 2 12)`

to get
`14`

.
To use the ** Step** tool, put the expression(s) you want to
evaluate into DrScheme's top area, the definitions window, then click
the

When you click ** Step**, a new window appears with three
parts:

The top part contains values and definitions that have already been processed by the stepper. Unless the definition window contains function definitions (discussed in the next section), the top part of the stepper window is initially empty.

The middle part shows a single step in evaluating an expression. The left-hand side of this part shows the expression before the step, with a green highlight for the relevant subexpression. The right-hand side shows the expression after a single step, with a result highlighted in purple corresponding to the green subexpression on the left.

Clicking the

button moves the right-hand expression to the left, highlights a new subexpression in green, and shows the next step in evaluation on the right.`Next`Clicking the

button undoes one step, showing the previous step again.`Previous`Clicking the

button starts returns to the very first evaluation step.`Home`The bottom part contains expressions to be evaluated later.

If you change the content of the definitions window, you must close
the current stepper window and click ** Step** again to step
through the new expression.

Type program definitions in DrScheme's top area, the definitions window, like this:

After the definition is complete, click the ** Execute**
button. DrScheme creates a new prompt in the bottom window and
starts evaluating expressions from the definitions window. If there
are no errors in the definitions window, then the defined program can
be tested the interactions window at the prompt. If there are errors
in the definitions window, an error message is printed in the
interactions window and the offending expression is highlighted with
pink in the definitions window. After fixing an error in the
definitions window, click

After your program has been executed, evaluate test expressions in the
interactions window, e.g., `(area-of-disk 3)`

. Test
expressions can also appear in the definitions window. In this case,
when the ** Execute** button is clicked, the value of each test
expression is displayed in the interactions window.

If the definitions window is modified and you type an expression into
the interactions window without clicking ** Execute**, DrScheme
warns you that

Don't forget to save your work. When the definitions window is
modified, a ** Save** button appears in the top left corner of
DrScheme's window. Click the button to save your definitions to a
file, and use the filename extension ``.scm'' for definition files.

**The Shape of Definitions**

The location of parentheses in a definition must match the following
pattern *exactly*:

.-- start definition | | .-- start program and input names | | | | .- end input names v v v (define (f arg ...) expression) ^- end definition

Compare this pattern to the

`area-of-disk`

program:
(define (area-of-disk r) (* 3.14 (* r r)))

In `area-of-disk`

, the expression is `(* 3.14 (* r r))`

.
No extra parentheses are added to this expression.

If the parentheses for `define`

are not correct, DrScheme
reports the error ``Malformed define''. When this error occurs, check
that a single set of parentheses surrounds the program name and
argument list, and that a *single* body expression is provided
(perhaps with its own set of parentheses, but with no extra
parentheses).

The following is *not* a legal definition in the
** Beginning Student** language level:

`(define (f) expr)`

because no arguments have been specified. (If DrScheme accepts this definition, double-check that the current language level is

**Formatting Definitions**

DrScheme helps you format your definitions in a standard, easy-to-read
way. After typing the first line of a definition:

`(define (area-of-disk r)`

when you type ENTER, DrScheme automatically inserts some space at the beginning of the next line. Whenever the indentation of a line is incorrect, typing TAB with the caret anywhere in the line re-indents the line. Multiple lines can be reformatted by selecting the lines and typing TAB. DrScheme's

After a while, you will become used to the standard way of formatting definitions and expressions. When ENTER or TAB does not produce the indentation you expect, check the expression to make sure that parentheses are inserted at the right places. Strange indentation is a sign that your expression has the wrong shape.

**Variable Names**

Unlike most programming languages, program and variable names in
Scheme can contain almost any character. For example, the following
are legal names:

a-b in->ft my-2nd-program positive? [email protected]$%^&/*~program

The name

`a-b`

does not mean `a`

minus `b`

; it's
just a name. Even `*3.14`

is a name. Suppose that you forget
the space between `*`

and `3.14`

when defining
`area-of-disk`

:
(define (area-of-disk r) (*3.14 (* r r)))

When you test this definition of

`area-of-disk`

, DrScheme
reports that the name `*3.14`

is undefined.
Avoid the following characters in variable names:

" ' ` , # ; | \

Since quotes cannot be used in names, do not attempt to use

`x'`

as ``x prime.'' The pairs of bracket characters
`[`

`]`

and `{`

`}`

are also special:
they act just like parenthesis pairs `(`

`)`

.
Names are case-sensitive, i.e., an upper-case letter is treated
different from a lower-case letter in a name. For example, the name
`area-of-disk`

is different from the name
`Area-Of-Disk`

.

**Interactions Window Tips**

When you click the ** Execute** button, the interactions window
is cleared, but your old test expressions are not lost. In the
interactions window, typing ESC-P copies the most recent test
expression to the current prompt. (``ESC-P'' means ``push the ESC
key, let go, and then push the p key''.) Typing ESC-P multiple times
produces older and older expressions from the history of interaction
expressions, while ESC-N produces newer expressions. Alternatively,
place the insertion caret at the end of any old expression in the
interactions window and type ENTER to copy the expression down to the
current prompt. Of course, cut and paste work as usual.

**Exercise Notes**

**Exercise 2.2.1** To use the
** convert.ss** teachpack in DrScheme, choose the

After clicking ** Execute**, the definitions window shows

A teachpack extends the set of built-in operations and programs
provided by DrScheme. After the ** convert.ss** teachpack is
selected, DrScheme provides the

`convert-gui`

,
`convert-repl`

, and `convert-file`

programs.More than one teachpack can be loaded at a time. The current set of teachpacks is stored as a preference, so even if you quit and restart DrScheme, the selected set is preserved. If you open multiple windows in DrScheme, the teachpack selection applies to all windows.

DrScheme's ** Language** menu provides a menu item for each
selected teachpack that clears it from the selected set, plus a

**Exercise 2.2.5** Scheme has a built-in `square`

operator. In futrure versions of DrScheme (startign with version
200), the operator's name will change to `sqr`

.

*No DrScheme notes for this section.*

When an error occurs, DrScheme highlights the source of the error,
whether it is in the definitions window or the interactions
window. For example, typing `(/ 1 0)`

in the interactions
window causes that expression to be highlighted (and also produces the
error message ``/: division by zero'').

**Exercise Notes**

**Exercise 2.4.1** If DrScheme gives the error message
``procedure application: expected procedure'' for the expression
`(+ (10) 20)`

make sure that the language level is set to
** Beginning Student**, as described in Preparing
DrScheme. The correct error message is more
specific: ``First term after parenthesis is illegal in an
application''.

Contracts are specified in the following format:

```
````;; program : input1 input2 ... -> output `

but DrScheme cannot check the format of your contracts. In Scheme, a semi-colon

`;`

starts a comment that extends to the next
linefeed (i.e., the end of the line if the program text is not
automatically line-wrapped). DrScheme ignores anything between the
first semi-colon in a line and the end of the line.
DrScheme can insert semi-colons at the start of lines for you. Select
all of the lines to be ``commented out'' and select the
** Scheme|Comment Out** menu item. Leading semi-colons are
removed from all selected lines by the

You can also write a contract inside a text box. To insert a text
box into your program, choose the ** Edit|Insert Text Box**
menu item. It inserts a text box wherever the caret is sitting.

Unlike comments, a text box is not ignored by DrScheme. Instead, it acts like a constant expression (just like a number), so DrScheme shows contract text boxes at the top of the interactions window whenBeware!If you use text boxes to enter contracts, DrScheme saves your program file in a special format, instead of the normal text format. Only DrScheme can read this special format.

In addition to line-based comments using `;`

, DrScheme ignores
block comments starting with `#|`

and ending with `|#`

:

`#| This is a multi-line block comment. |#`

Block comments using

`#|`

and `|#`

can be nested.
For the testing phase, a useful trick is to move the commented-out
examples below the program definition, uncomment them, and put quotes
around the `=`

intact between the test expression and its
result. Then, when you click ** Execute** DrScheme will run all
the tests, printing the actual result, a

`"="`

(read as ``should
be equal to''), and the expected result. For example,
(define (plus-ten n) (+ n 10)) ;; Tests: (plus-ten 4) "=" 14 (plus-ten -4) "=" -6 ;; oops!

produces the output

14 "=" 14 6 "=" -6

in the interactions window when

`6`

is not `-6`

, so
either the program or the test case must be wrong. The string
`"should be"`

is often better than `"="`

, since it
clarifies which is the program result and which is the predicted
result.Test cases written as above must follow the program being tested. However, program implementors should always create the test cases as examples, before the program is written.