Cool/cool-manual.pdf.txt

CoolAid: The Cool Reference Manual∗

1

Introduction

This manual describes the programming language Cool: the Classroom Object-Oriented Language. Cool
is a small language that can be implemented with reasonable effort in a one semester course. Still, Cool
retains many of the features of modern programming languages including objects, static typing, and
automatic memory management.

Cool programs are sets of classes. A class encapsulates the variables and procedures of a data type.
Instances of a class are objects. In Cool, classes and types are identified; i.e., every class defines a type.
Classes permit programmers to define new types and associated procedures (or methods) specific to those
types. Inheritance allows new types to extend the behavior of existing types.

Cool is an expression language. Most Cool constructs are expressions, and every expression has a
value and a type. Cool is type safe: procedures are guaranteed to be applied to data of the correct type.
While static typing imposes a strong discipline on programming in Cool, it guarantees that no runtime
type errors can arise in the execution of Cool programs.

This manual is divided into informal and formal components. For a short, informal overview, the first

12 pages (through Section 9) suffices. The formal description begins with Section 10.

2 Getting Started

The reader who wants to get a sense for Cool at the outset should begin by reading, and then write their
own cool-programs and run them. Cool source files have extension .cl and Cool assembly files have
extension .s. The Cool compiler is coolc (note that cool is a Linux-binary file). To compile a program:

coolc [ -o fileout ] file1.cl file2.cl ... filen.cl

The compiler compiles the files file1.cl through filen.cl as if they were concatenated together.
Each file must define a set of complete classes—class definitions may not be split across files. The -o
option specifies an optional name to use for the output assembly code. If fileout is not supplied, the
output assembly is named file1.s.

The coolc compiler generates MIPS assembly code. Because not all of the machines the course is
using are MIPS-based, Cool programs are run on a MIPS simulator called spim. To run a cool program,
type

% spim
(spim) load "file.s"
(spim) run

∗Copyright c(cid:176)1995-2000 by Alex Aiken. All rights reserved.

1

To run a different program during the same spim session, it is necessary to reinitialize the state of the
simulator before loading the new assembly file:

(spim) reinit

An alternative—and faster—way to invoke spim is with a file:

spim -file file.s

This form loads the file, runs the program, and exits spim when the program terminates. Be sure that
the spim we provided is actually used. There may be another version of spim installed in on some
systems, but it will not execute Cool programs. The spim manual is available in the resources folder of
the repository.

The following is a complete transcript of the compilation and execution of list.cl. This program is

very silly, but it does serve to illustrate many of the features of Cool.

% coolc list.cl
% spim
SPIM Version 5.4 of Jan. 17, 1994
Copyright 1990-1994 by James R. Larus ([email protected]).
All Rights Reserved.
See the file README a full copyright notice.
Loaded: /usa/pollock/public/cool02/lib/trap.handler

(spim) load "list.s"
(spim) run
How many numbers to sort?5
0
1
2
3
4
COOL program successfully executed
(spim) exit
%

3 Classes

All code in Cool is organized into classes. Each class definition must be contained in a single source file,
but multiple classes may be defined in the same file. Class definitions have the form:

class <type> [ inherits <type> ] {

<feature_list>

};

The notation [ ...] denotes an optional construct. All class names are globally visible. Class names

begin with an uppercase letter. Classes may not be redefined.

2

3.1 Features

The body of a class definition consists of a list of feature definitions. A feature is either an attribute or
a method. An attribute of class A specifies a variable that is part of the state of objects of class A. A
method of class A is a procedure that may manipulate the variables and objects of class A.

One of the major themes of modern programming languages is information hiding, which is the idea
that certain aspects of a data type’s implementation should be abstract and hidden from users of the
data type. Cool supports information hiding through a simple mechanism: all attributes have scope local
to the class, and all methods have global scope. Thus, the only way to provide access to object state in
Cool is through methods.

Feature names must begin with a lowercase letter. No method name may be defined multiple times in
a class, and no attribute name may be defined multiple times in a class, but a method and an attribute
may have the same name.

A fragment from list.cl illustrates simple cases of both attributes and methods:

class Cons inherits List {
xcar : Int;
xcdr : List;

isNil() : Bool { false };

init(hd : Int, tl : List) : Cons {

xcar <- hd;
xcdr <- tl;
self;

{

}

}
...
};

In this example, the class Cons has two attributes xcar and xcdr and two methods isNil and init.
Note that the types of attributes, as well as the types of formal parameters and return types of methods,
are explicitly declared by the programmer.

Given object c of class Cons and object l of class List, we can set the xcar and xcdr fields by using

the method init:

c.init(1,l)

This notation is object-oriented dispatch. There may be many definitions of init methods in many
different classes. The dispatch looks up the class of the object c to decide which init method to invoke.
Because the class of c is Cons, the init method in the Cons class is invoked. Within the invocation, the
variables xcar and xcdr refer to c’s attributes. The special variable self refers to the object on which
the method was dispatched, which, in the example, is c itself.

There is a special form new C that generates a fresh object of class C. An object can be thought of as
a record that has a slot for each of the attributes of the class as well as pointers to the methods of the
class. A typical dispatch for the init method is:

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(new Cons).init(1,new Nil)

This example creates a new cons cell and initializes the “car” of the cons cell to be 1 and the “cdr” to
be new Nil.1 There is no mechanism in Cool for programmers to deallocate objects. Cool has automatic
memory management; objects that cannot be used by the program are deallocated by a runtime garbage
collector.

Attributes are discussed further in Section 5 and methods are discussed further in Section 6.

3.2 Inheritance

If a class definition has the form

class A inherits B { ... };

then class A inherits the features of B. In this case B is the parent class of A and A is a child class of B.

The semantics of A inherits B is that A has all of the features defined in B in addition to its own
features. In the case that a parent and child both define the same method name, then the definition
given in the child class takes precedence. It is illegal to redefine attribute names. Furthermore, for type
safety, it is necessary to place some restrictions on how methods may be redefined (see Section 6).

There is a distinguished class Object. If a class definition does not specify a parent class, then the
class inherits from Object by default. A class may inherit only from a single class; this is aptly called
“single inheritance.”2 The parent-child relation on classes defines a graph. This graph may not contain
cycles. For example, if A inherits from B, then B must not inherit from A. Furthermore, if A inherits from
B, then B must have a class definition somewhere in the program. Because Cool has single inheritance, it
follows that if both of these restrictions are satisfied, then the inheritance graph forms a tree with Object
as the root.

In addition to Object, Cool has four other basic classes: Int, String, Bool, and IO. The basic classes

are discussed in Section 8.

4 Types

In Cool, every class name is also a type. In addition, there is a type SELF TYPE that can be used in
special circumstances.

A type declaration has the form x:C, where x is a variable and C is a type. Every variable must have a
type declaration at the point it is introduced, whether that is in a let, case, or as the formal parameter
of a method. The types of all attributes must also be declared.

The basic type rule in Cool is that if a method or variable expects a value of type A, then any value
of type B may be used instead, provided that A is an ancestor of B in the class hierarchy. In other words,
if B inherits from A, either directly or indirectly, then a B can be used wherever an A would suffice.

When an object of class B may be used in place of an object of class A, we say that B conforms to A

or that B ≤ A. As discussed above, conformance is defined in terms of the inheritance graph.

Definition 4.1 (Conformance) Let A, B, and C be types.

• A ≤ A for all types A

1In this example, Nil is assumed to be a subtype of List.
2Some object-oriented languages allow a class to inherit from multiple classes, which is equally aptly called “multiple

inheritance.”

4

• if A inherits from B, then A ≤ B

• if A ≤ B and B ≤ C then A ≤ C

Because Object is the root of the class hierarchy, it follows that A ≤ Object for all types A.

4.1 SELF TYPE

The type SELF TYPE is used to refer to the type of the self variable. This is useful in classes that will
be inherited by other classes, because it allows the programmer to avoid specifying a fixed final type at
the time the class is written. For example, the program

class Silly {

copy() : SELF_TYPE { self };

};

class Sally inherits Silly { };

class Main {

x : Sally <- (new Sally).copy();

main() : Sally { x };

};

Because SELF TYPE is used in the definition of the copy method, we know that the result of copy is the
same as the type of the self parameter. Thus, it follows that (new Sally).copy() has type Sally,
which conforms to the declaration of attribute x.

Note that the meaning of SELF TYPE is not fixed, but depends on the class in which it is used. In
general, SELF TYPE may refer to the class C in which it appears, or any class that conforms to C. When it
is useful to make explicit what SELF TYPE may refer to, we use the name of the class C in which SELF TYPE
appears as an index SELF TYPEC. This subscript notation is not part of Cool syntax—it is used merely
to make clear in what class a particular occurrence of SELF TYPE appears.

From Definition 4.1, it follows that SELF TYPEX ≤ SELF TYPEX. There is also a special conformance

rule for SELF TYPE:

SELF TYPEC ≤ B if C ≤ B

Finally, SELF TYPE may be used in the following places: new SELF TYPE, as the return type of a
method, as the declared type of a let variable, or as the declared type of an attribute. No other uses of
SELF TYPE are permitted.

4.2 Type Checking

The Cool type system guarantees at compile time that execution of a program cannot result in runtime
type errors. Using the type declarations for identifiers supplied by the programmer, the type checker
infers a type for every expression in the program.

It is important to distinguish between the type assigned by the type checker to an expression at compile
time, which we shall call the static type of the expression, and the type(s) to which the expression may
evaluate during execution, which we shall call the dynamic types.

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The distinction between static and dynamic types is needed because the type checker cannot, at
compile time, have perfect information about what values will be computed at runtime. Thus, in general,
the static and dynamic types may be different. What we require, however, is that the type checker’s
static types be sound with respect to the dynamic types.

Definition 4.2 For any expression e, let De be a dynamic type of e and let Se be the static type inferred
by the type checker. Then the type checker is sound if for all expressions e it is the case that De ≤ Se.

Put another way, we require that the type checker err on the side of overestimating the type of an
expression in those cases where perfect accuracy is not possible. Such a type checker will never accept
a program that contains type errors. However, the price paid is that the type checker will reject some
programs that would actually execute without runtime errors.

5 Attributes

An attribute definition has the form

<id> : <type> [ <- <expr> ];

The expression is optional initialization that is executed when a new object is created. The static type
of the expression must conform to the declared type of the attribute. If no initialization is supplied, then
the default initialization is used (see below).

When a new object of a class is created, all of the inherited and local attributes must be initialized.
Inherited attributes are initialized first in inheritance order beginning with the attributes of the greatest
ancestor class. Within a given class, attributes are initialized in the order they appear in the source text.
Attributes are local to the class in which they are defined or inherited. Inherited attributes cannot

be redefined.

5.1 Void

All variables in Cool are initialized to contain values of the appropriate type. The special value void
is a member of all types and is used as the default initialization for variables where no initialization is
supplied by the user. Note that there is no name for void in Cool; the only way to create a void value
is to declare a variable of some class other than Int, String, or Bool and allow the default initialization
to occur.

There is a special form isvoid expr that tests whether a value is void (see Section 7.11). In addition,
void values may be tested for equality. A void value may be passed as an argument, assigned to a variable,
or otherwise used in any context where any value is legitimate, except that a dispatch to or case on void
generates a runtime error.

Variables of the basic classes Int, Bool, and String are initialized specially; see Section 8.

6 Methods

A method definition has the form

<id>(<id> : <type>,...,<id> : <type>): <type> { <expr> };

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There may be zero or more formal parameters. The identifiers used in the formal parameter list must
be distinct. The type of the method body must conform to the declared return type. When a method is
invoked, the formal parameters are bound to the actual arguments and the expression is evaluated; the
resulting value is the meaning of the method invocation. A formal parameter hides any definition of an
attribute of the same name.

To ensure type safety, there are restrictions on the redefinition of inherited methods. The rule is
simple: If a class A inherits a method f from an ancestor class B, then A may override the inherited
definition of f provided the number of arguments, the types of the formal parameters, and the return
type are exactly the same in both definitions.

To see why some restriction is necessary on the redefinition of inherited methods, consider the following

example:

class A {

f(): Int { 1 };

};

class B inherits A {

f(): String { "1" };

};

Let a be an object with dynamic type A. Then

a.f() + 1

is a well-formed expression with value 2. However, we cannot substitute a value of type B for a, as it would
result in adding a string to a number. Thus, if methods can be redefined arbitrarily, then subclasses may
not simply extend the behavior of their parents, and much of the usefulness of inheritance, as well as
type safety, is lost.

7 Expressions

Expressions are the largest syntactic category in Cool.

7.1 Constants

The simplest expressions are constants. The boolean constants are true and false. Integer constants are
unsigned strings of digits such as 0, 123, and 007. String constants are sequences of characters enclosed
in double quotes, such as "This is a string." String constants may be at most 1024 characters long.
There are other restrictions on strings; see Section 10.

The constants belong to the basic classes Bool, Int, and String. The value of a constant is an object

of the appropriate basic class.

7.2 Identifiers

The names of local variables, formal parameters of methods, self, and class attributes are all expressions.
The identifier self may be referenced, but it is an error to assign to self or to bind self in a let, a
case, or as a formal parameter. It is also illegal to have attributes named self.

7

Local variables and formal parameters have lexical scope. Attributes are visible throughout a class in
which they are declared or inherited, although they may be hidden by local declarations within expres-
sions. The binding of an identifier reference is the innermost scope that contains a declaration for that
identifier, or to the attribute of the same name if there is no other declaration. The exception to this
rule is the identifier self, which is implicitly bound in every class.

7.3 Assignment

An assignment has the form

<id> <- <expr>

The static type of the expression must conform to the declared type of the identifier. The value is the
value of the expression. The static type of an assignment is the static type of <expr>.

7.4 Dispatch

There are three forms of dispatch in Cool. The three forms differ only in how the called method is
selected. The most commonly used form of dispatch is

<expr>.<id>(<expr>,...,<expr>)

Consider the dispatch e0.f(e1, . . . , en). To evaluate this expression, the arguments are evaluated in left-
to-right order, from e1 to en. Next, e0 is evaluated and its class C noted (if e0 is void a runtime error is
generated). Finally, the method f in class C is invoked, with the value of e0 bound to self in the body
of f and the actual arguments bound to the formals as usual. The value of the expression is the value
returned by the method invocation.

Type checking a dispatch involves several steps. Assume e0 has static type A. (Recall that this type
is not necessarily the same as the type C above. A is the type inferred by the type checker; C is the class
of the object computed at runtime, which is potentially any subclass of A.) Class A must have a method
f, the dispatch and the definition of f must have the same number of arguments, and the static type of
the ith actual parameter must conform to the declared type of the ith formal parameter.

If f has return type B and B is a class name, then the static type of the dispatch is B. Otherwise, if f
has return type SELF TYPE, then the static type of the dispatch is A. To see why this is sound, note that
the self parameter of the method f conforms to type A. Therefore, because f returns SELF TYPE, we can
infer that the result must also conform to A. Inferring accurate static types for dispatch expressions is
what justifies including SELF TYPE in the Cool type system.

The other forms of dispatch are:

<id>(<expr>,...,<expr>)
<expr>@<type>.id(<expr>,...,<expr>)

The first form is shorthand for self.<id>(<expr>,...,<expr>).

The second form provides a way of accessing methods of parent classes that have been hidden by
redefinitions in child classes.
Instead of using the class of the leftmost expression to determine the
method, the method of the class explicitly specified is used. For example, [email protected]() invokes the method
f in class B on the object that is the value of e. For this form of dispatch, the static type to the left of
“@”must conform to the type specified to the right of “@”.

8

7.5 Conditionals

A conditional has the form

if <expr> then <expr> else <expr> fi

The semantics of conditionals is standard. The predicate is evaluated first. If the predicate is true,
then the then branch is evaluated. If the predicate is false, then the else branch is evaluated. The
value of the conditional is the value of the evaluated branch.

The predicate must have static type Bool. The branches may have any static types. To specify the
static type of the conditional, we define an operation (cid:116) (pronounced “join”) on types as follows. Let
A,B,D be any types other than SELF TYPE. The least type of a set of types means the least element with
respect to the conformance relation ≤.

A (cid:116) B = the least type C such that A ≤ C and B ≤ C

SELF TYPED (cid:116) SELF TYPED = SELF TYPED

SELF TYPED (cid:116) A = D (cid:116) A
A (cid:116) SELF TYPED = A (cid:116) D

Let T and F be the static types of the branches of the conditional. Then the static type of the

conditional is T (cid:116) F.

7.6 Loops

A loop has the form

while <expr> loop <expr> pool

The predicate is evaluated before each iteration of the loop. If the predicate is false, the loop terminates
and void is returned. If the predicate is true, the body of the loop is evaluated and the process repeats.
The predicate must have static type Bool. The body may have any static type. The static type of a

loop expression is Object.

7.7 Blocks

A block has the form

{ <expr>; ... <expr>; }

The expressions are evaluated in left-to-right order. Every block has at least one expression; the value
of a block is the value of the last expression. The expressions of a block may have any static types. The
static type of a block is the static type of the last expression.

An occasional source of confusion in Cool is the use of semi-colons. Semi-colons are used as terminators
in lists of expressions (e.g., the block syntax above) and not as expression separators. Semi-colons also
terminate other Cool constructs, see Section 11 for details.

9

7.8 Let

A let expression has the form

let <id1> : <type1> [ <- <expr1> ], ..., <idn> : <typen> [ <- <exprn> ] in <expr>

The optional expressions are initialization; the other expression is the body. A let is evaluated as
follows. First <expr1> is evaluated and the result bound to <id1>. Then <expr2> is evaluated and the
result bound to <id2>, and so on, until all of the variables in the let are initialized. (If the initialization
of <idk> is omitted, the default initialization of type <typek> is used.) Next the body of the let is
evaluated. The value of the let is the value of the body.

The let identifiers <id1>,...,<idn> are visible in the body of the let. Furthermore, identifiers

<id1>,...,<idk> are visible in the initialization of <idm> for any m > k.

If an identifier is defined multiple times in a let, later bindings hide earlier ones. Identifiers introduced
by let also hide any definitions for the same names in containing scopes. Every let expression must
introduce at least one identifier.

The type of an initialization expression must conform to the declared type of the identifier. The type

of let is the type of the body.

The scope of a let extends as far (encompasses as many tokens) as possible.

7.9 Case

A case expression has the form

case <expr0> of

<id1> : <type1> => <expr1>;
. . .
<idn> : <typen> => <exprn>;

esac

Case expressions provide runtime type tests on objects. First, expr0 is evaluated and its dynamic type
C noted (if expr0 evaluates to void a run-time error is produced). Next, from among the branches the
branch with the least type <typek> such that C ≤ <typek> is selected. The identifier <idk> is bound
to the value of <expr0> and the expression <exprk> is evaluated. The result of the case is the value
of <exprk>.
If no branch can be selected for evaluation, a run-time error is generated. Every case
expression must have at least one branch.

For each branch, let Ti be the static type of <expri>. The static type of a case expression is

1≤i≤n Ti.
The identifier id introduced by a branch of a case hides any variable or attribute definition for id visible
in the containing scope.

(cid:70)

The case expression has no special construct for a “default” or “otherwise” branch. The same affect

is achieved by including a branch

x : Object => ...

because every type is ≤ to Object.

The case expression provides programmers a way to insert explicit runtime type checks in situa-
tions where static types inferred by the type checker are too conservative. A typical situation is that
a programmer writes an expression e and type checking infers that e has static type A. However, the
programmer may know that, in fact, the dynamic type of e is always B for some B ≤ A. This information
can be captured using a case expression:

10

case e of x : B => ...

In the branch the variable x is bound to the value of e but has the more specific static type B.

7.10 New

A new expression has the form

new <type>

The value is a fresh object of the appropriate class. If the type is SELF TYPE, then the value is a fresh
object of the class of self in the current scope. The static type is <type>.

7.11 Isvoid

The expression

isvoid expr

evaluates to true if expr is void and evaluates to false if expr is not void.

7.12 Arithmetic and Comparison Operations

Cool has four binary arithmetic operations: +, -, *, /. The syntax is

expr1 <op> expr2

To evaluate such an expression first expr1 is evaluated and then expr2. The result of the operation is
the result of the expression.

The static types of the two sub-expressions must be Int. The static type of the expression is Int.

Cool has only integer division.

Cool has three comparison operations: <, <=, =. For < and <= the rules are exactly the same as
for the binary arithmetic operations, except that the result is a Bool. The comparison = is a special
case. If either <expr1> or <expr2> has static type Int, Bool, or String, then the other must have the
same static type. Any other types, including SELF TYPE, may be freely compared. On non-basic objects,
equality simply checks for pointer equality (i.e., whether the memory addresses of the objects are the
same). Equality is defined for void.

In principle, there is nothing wrong with permitting equality tests between, for example, Bool and
Int. However, such a test must always be false and almost certainly indicates some sort of programming
error. The Cool type checking rules catch such errors at compile-time instead of waiting until runtime.

Finally, there is one arithmetic and one logical unary operator. The expression ~<expr> is the integer
complement of <expr>. The expression <expr> must have static type Int and the entire expression
has static type Int. The expression not <expr> is the boolean complement of <expr>. The expression
<expr> must have static type Bool and the entire expression has static type Bool.

11

8 Basic Classes

8.1 Object

The Object class is the root of the inheritance graph. Methods with the following declarations are
defined:

abort() : Object
type_name() : String
copy() : SELF_TYPE

The method abort halts program execution with an error message. The method type name returns a
string with the name of the class of the object. The method copy produces a shallow copy of the object.3

8.2 IO

The IO class provides the following methods for performing simple input and output operations:

out_string(x : String) : SELF_TYPE
out_int(x : Int) : SELF_TYPE
in_string() : String
in_int() : Int

The methods out string and out int print their argument and return their self parameter. The
method in string reads a string from the standard input, up to but not including a newline character.
The method in int reads a single integer, which may be preceded by whitespace. Any characters following
the integer, up to and including the next newline, are discarded by in int.

A class can make use of the methods in the IO class by inheriting from IO. It is an error to redefine

the IO class.

8.3 Int

The Int class provides integers. There are no methods special to Int. The default initialization for
variables of type Int is 0 (not void). It is an error to inherit from or redefine Int.

8.4 String

The String class provides strings. The following methods are defined:

length() : Int
concat(s : String) : String
substr(i : Int, l : Int) : String

The method length returns the length of the self parameter. The method concat returns the string
formed by concatenating s after self. The method substr returns the substring of its self parameter
beginning at position i with length l; string positions are numbered beginning at 0. A runtime error is
generated if the specified substring is out of range.

The default initialization for variables of type String is "" (not void). It is an error to inherit from

or redefine String.

3A shallow copy of a copies a itself, but does not recursively copy objects that a points to.

12

8.5 Bool

The Bool class provides true and false. The default initialization for variables of type Bool is false
(not void). It is an error to inherit from or redefine Bool.

9 Main Class

Every program must have a class Main. Furthermore, the Main class must have a method main that
takes no formal parameters. The main method must be defined in class Main (not inherited from another
class). A program is executed by evaluating (new Main).main().

The remaining sections of this manual provide a more formal definition of Cool. There are four sections
covering lexical structure (Section 10), grammar (Section 11), type rules (Section 12), and operational
semantics (Section 13).

10 Lexical Structure

The lexical units of Cool are integers, type identifiers, object identifiers, special notation, strings, key-
words, and white space.

10.1 Integers, Identifiers, and Special Notation

Integers are non-empty strings of digits 0-9. Identifiers are strings (other than keywords) consisting of
letters, digits, and the underscore character. Type identifiers begin with a capital letter; object identifiers
begin with a lower case letter. There are two other identifiers, self and SELF TYPE that are treated
specially by Cool but are not treated as keywords. The special syntactic symbols (e.g., parentheses,
assignment operator, etc.) are given in Figure 1.

10.2 Strings

Strings are enclosed in double quotes "...". Within a string, a sequence ‘\c’ denotes the character ‘c’,
with the exception of the following:

\b backspace
tab
\t
\n newline
\f

formfeed

A non-escaped newline character may not appear in a string:

"This is not
OK"

A string may not contain EOF. A string may not contain the null (character \0). Any other character

may be included in a string. Strings cannot cross file boundaries.

13

10.3 Comments

There are two forms of comments in Cool. Any characters between two dashes “ – –” and the next
newline (or EOF, if there is no next newline) are treated as comments. Comments may also be written
by enclosing text in (∗ . . . ∗). The latter form of comment may be nested. Comments cannot cross file
boundaries.

10.4 Keywords

The keywords of cool are: class, else, false, fi, if, in, inherits, isvoid, let, loop, pool, then, while,
case, esac, new, of, not, true. Except for the constants true and false, keywords are case insensitive.
To conform to the rules for other objects, the first letter of true and false must be lowercase; the trailing
letters may be upper or lower case.

10.5 White Space

White space consists of any sequence of the characters: blank, newline, \f, \r, \t, \v.

11 Cool Syntax

Figure 1 provides a specification of Cool syntax. The specification is not context-free; for convenience,
we also use some regular expression notation. Specifically, A∗ means zero or more A’s in succession; A+
means one or more A’s. The special notation A;∗ means zero or more A’s terminated by semicolons. The
special notation A,∗ means zero or more A’s separated by commas. Separators differ from terminators
in that the terminator always appears at the end of the list; a separator is never included at the end of
a list. In Cool, semicolons are always terminators and commas are always separators. Items in square
brackets [. . .] are optional. Double braces [[ ]] are not part of Cool; they are used in the grammar as a
meta-symbol to show association of grammar operations.

11.1 Precedence

The precedence of infix binary and prefix unary operations, from highest to lowest, is given by the
following table:

.
@
~
isvoid
* /
+ -
<=
not
<-

< =

All binary operations are left-associative, with the exception of assignment, which is right-associative,
and the three comparison operations, which do not associate.

14

program ::= class;+

class

::= class TYPE [inherits TYPE] { feature;∗ }

feature ::= ID(formal,∗ ) : TYPE { expr }

|

ID : TYPE [ <- expr ]

formal

::= ID : TYPE

expr

::= ID <- expr

|

|

|

expr[@TYPE].ID(expr,∗ )
ID(expr,∗ )
if expr then expr else expr fi

| while expr loop expr pool

|

|

|

|

|

|

|

|

|

|

|

|

|

|

|

|

|

|

|

|

{ expr;+ }
let [[ID : TYPE [ <- expr ], ]]+ in expr
case expr of [[ID : TYPE => expr; ]]+esac
new TYPE

isvoid expr

expr + expr

expr − expr

expr ∗ expr

expr / expr

˜expr

expr < expr

expr <= expr

expr = expr

not expr

(expr)

ID

integer

string

true

false

Figure 1: Cool syntax.

15

12 Type Rules

This section formally defines the type rules of Cool. The type rules define the type of every Cool expression
in a given context. The context is the type environment, which describes the type of every unbound
identifier appearing in an expression. The type environment is described in Section 12.1. Section 12.2
gives the type rules.

12.1 Type Environments

To a first approximation, type checking in Cool can be thought of as a bottom-up algorithm: the type of
an expression e is computed from the (previously computed) types of e’s subexpressions. For example,
an integer 1 has type Int; there are no subexpressions in this case. As another example, if en has type
X, then the expression { e1; . . . ; en; } has type X.

A complication arises in the case of an expression v, where v is an object identifier. It is not possible
to say what the type of v is in a strictly bottom-up algorithm; we need to know the type declared for v
in the larger expression. Such a declaration must exist for every object identifier in valid Cool programs.
To capture information about the types of identifiers, we use a type environment. The environment
consists of three parts: a method environment M , an object environment O, and the name of the
current class in which the expression appears. The method environment and object environment are
both functions (also called mappings). The object environment is a function of the form

O(v) = T

which assigns the type T to object identifier v. The method environment is more complex; it is a function
of the form

M (C, f ) = (T1, . . . , Tn−1, Tn)

where C is a class name (a type), f is a method name, and t1, . . . , tn are types. The tuple of types is
the signature of the method. The interpretation of signatures is that in class C the method f has formal
parameters of types (t1, . . . , tn−1)—in that order—and a return type tn.

Two mappings are required instead of one because object names and method names do not clash—i.e.,

there may be a method and an object identifier of the same name.

The third component of the type environment is the name of the current class, which is needed for

type rules involving SELF TYPE.

Every expression e is type checked in a type environment; the subexpressions of e may be type
checked in the same environment or, if e introduces a new object identifier, in a modified environment.
For example, consider the expression

let c : Int <- 33 in

...

The let expression introduces a new variable c with type Int. Let O be the object component of the
type environment for the let. Then the body of the let is type checked in the object type environment

where the notation O[T /c] is defined as follows:

O[Int/c]

O[T /c](c) = T

O[T /c](d) = O(d) if d (cid:54)= c

16

12.2 Type Checking Rules

The general form a type checking rule is:

...
O, M, C (cid:96) e : T

The rule should be read: In the type environment for objects O, methods M , and containing class C, the
expression e has type T . The dots above the horizontal bar stand for other statements about the types
of sub-expressions of e. These other statements are hypotheses of the rule; if the hypotheses are satisfied,
then the statement below the bar is true.

The rule for object identifiers is simply that if the environment assigns an identifier Id type T , then

Id has type T .

The rule for assignment to a variable is more complex:

O(Id) = T
O, M, C (cid:96) Id : T

O(Id) = T
O, M, C (cid:96) e1 : T (cid:48)
T (cid:48) ≤ T

O, M, C (cid:96) Id ← e1 : T (cid:48)

[Var]

[ASSIGN]

Note that this type rule—as well as others—use the conformance relation ≤ (see Section 3.2). The rule
says that the assigned expression e1 must have a type T (cid:48) that conforms to the type T of the identifier Id
in the type environment. The type of the whole expression is T (cid:48).

The type rules for constants are all easy:

O, M, C (cid:96) true : Bool

O, M, C (cid:96) f alse : Bool

i is an integer constant
O, M, C (cid:96) i : Int

s is a string constant
O, M, C (cid:96) s : String

There are two cases for new, one for new SELF TYPE and one for any other form:

(cid:40)

T (cid:48) =

SELF TYPEC if T = SELF TYPE
T otherwise
O, M, C (cid:96) new T : T (cid:48)

[True]

[False]

[Int]

[String]

[New]

17

Dispatch expressions are the most complex to type check.

O, M, C (cid:96) e0 : T0
O, M, C (cid:96) e1 : T1
...
O, M, C (cid:96) en : Tn

(cid:40)

T (cid:48)
0 =

C if T0 = SELF TYPEC
T0 otherwise
1, . . . , T (cid:48)

n, T (cid:48)

n+1)

M (T (cid:48)
Ti ≤ T (cid:48)
i

0, f ) = (T (cid:48)
(cid:40)

Tn+1 =

1 ≤ i ≤ n
if T (cid:48)
T0
T (cid:48)
n+1 otherwise
O, M, C (cid:96) e0.f (e1, . . . , en) : Tn+1

n+1 = SELF TYPE

O, M, C (cid:96) e0 : T0
O, M, C (cid:96) e1 : T1
...
O, M, C (cid:96) en : Tn
T0 ≤ T
M (T, f ) = (T (cid:48)
Ti ≤ T (cid:48)
i

1, . . . , T (cid:48)

n, T (cid:48)

n+1)

Tn+1 =

(cid:40)

1 ≤ i ≤ n
if T (cid:48)
T0
T (cid:48)
n+1 otherwise
O, M, C (cid:96) [email protected] (e1, . . . , en) : Tn+1

n+1 = SELF TYPE

[Dispatch]

[StaticDispatch]

To type check a dispatch, each of the subexpressions must first be type checked. The type T0 of e0
determines the which declaration of the method f is used. The argument types of the dispatch must
conform to the declared argument types. Note that the type of the result of the dispatch is either the
declared return type or T0 in the case that the declared return type is SELF TYPE. The only difference in
type checking a static dispatch is that the class T of the method f is given in the dispatch, and the type
T0 must conform to T .

The type checking rules for if and {-} expressions are straightforward. See Section 7.5 for the

definition of the (cid:116) operation.

O, M, C (cid:96) e1 : Bool
O, M, C (cid:96) e2 : T2
O, M, C (cid:96) e3 : T3
O, M, C (cid:96) if e1 then e2 else e3 fi : T2 (cid:116) T3

O, M, C (cid:96) e1 : T1
O, M, C (cid:96) e2 : T2
...
O, M, C (cid:96) en : Tn
O, M, C (cid:96) { e1; e2; . . . en; } : Tn

18

[If]

[Sequence]

The let rule has some interesting aspects.

(cid:40)

T (cid:48)
0 =

SELF TYPEC if T0 = SELF TYPE
T0 otherwise

O, M, C (cid:96) e1 : T1
T1 ≤ T (cid:48)
0
O[T (cid:48)

0/x], M, C (cid:96) e2 : T2
O, M, C (cid:96) let x : T0 ← e1 in e2 : T2
First, the initialization e1 is type checked in an environment without a definition for x. Thus, the variable
x cannot be used in e1 unless it already has a definition in an outer scope. Second, the body e2 is type
checked in the environment O extended with the typing x : T (cid:48)
0. Third, note that the type of x may be
SELF TYPE.

[Let-Init]

(cid:40)

T (cid:48)
0 =

SELF TYPEC if T0 = SELF TYPE
T0 otherwise

O[T (cid:48)

0/x], M, C (cid:96) e1 : T1

O, M, C (cid:96) let x : T0 in e1 : T1
The rule for let with no initialization simply omits the conformance requirement. We give type rules
only for a let with a single variable. Typing a multiple let

[Let-No-Init]

let x1 : T1 [← e1], x2 : T2 [← e2], . . . , xn : Tn [← en] in e

is defined to be the same as typing

let x1 : T1 [← e1] in (let x2 : T2 [← e2], . . . , xn : Tn [← en] in e )

O, M, C (cid:96) e0 : T0
O[T1/x1], M, C (cid:96) e1 : T (cid:48)
1
...
O[Tn/xn], M, C (cid:96) en : T (cid:48)
n

O, M, C (cid:96) case e0 of x1 : T1 ⇒ e1; . . . xn : Tn ⇒ en; esac :

(cid:70)

1≤i≤n T (cid:48)
i

[Case]

Each branch of a case is type checked in an environment where variable xi has type Ti. The type of
the entire case is the join of the types of its branches. The variables declared on each branch of a case
must all have distinct types.

O, M, C (cid:96) while e1 loop e2 pool : Object
The predicate of a loop must have type Bool; the type of the entire loop is always Object. An isvoid
test has type Bool:

[Loop]

[Isvoid]

O, M, C (cid:96) e1 : Bool
O, M, C (cid:96) e2 : T2

O, M, C (cid:96) e1 : T1
O, M, C (cid:96) isvoid e1 : Bool

With the exception of the rule for equality, the type checking rules for the primitive logical, compar-

ison, and arithmetic operations are easy.

O, M, C (cid:96) e1 : Bool
O, M, C (cid:96) ¬e1 : Bool

19

[Not]

O, M, C (cid:96) e1 : Int
O, M, C (cid:96) e2 : Int
op ∈ {<, ≤}

O, M, C (cid:96) e1 op e2 : Bool

O, M, C (cid:96) e1 : Int
O, M, C (cid:96) ˜e1 : Int

O, M, C (cid:96) e1 : Int
O, M, C (cid:96) e2 : Int
op ∈ {∗, +, −, /}
O, M, C (cid:96) e1 op e2 : Int

[Compare]

[Neg]

[Arith]

The wrinkle in the rule for equality is that any types may be freely compared except Int, String

and Bool, which may only be compared with objects of the same type.

O, M, C (cid:96) e1 : T1
O, M, C (cid:96) e2 : T2
T1 ∈ {Int, String, Bool} ∨ T2 ∈ {Int, String, Bool} ⇒ T1 = T2
O, M, C (cid:96) e1 = e2 : Bool

[Equal]

The final cases are type checking rules for attributes and methods. For a class C, let the object
environment OC give the types of all attributes of C (including any inherited attributes). More formally,
if x is an attribute (inherited or not) of C, and the declaration of x is x : T , then
(cid:40)

OC(x) =

SELF TYPEC if T = SELF TYPE
T otherwise

The method environment M is global to the entire program and defines for every class C the signatures

of all of the methods of C (including any inherited methods).

The two rules for type checking attribute defininitions are similar the rules for let. The essential
difference is that attributes are visible within their initialization expressions. Note that self is bound in
the initialization.

OC(x) = T0
OC[SELF TYPEC/self], M, C (cid:96) e1 : T1
T1 ≤ T0

OC, M, C (cid:96) x : T0 ← e1;

OC(x) = T
OC, M, C (cid:96) x : T ;

[Attr-Init]

[Attr-No-Init]

The rule for typing methods checks the body of the method in an environment where OC is extended
with bindings for the formal parameters and self. The type of the method body must conform to the
declared return type.

M (C, f ) = (T1, . . . , Tn, T0)
OC[SELF TYPEC/self][T1/x1] . . . [Tn/xn], M, C (cid:96) e : T (cid:48)
0

(cid:40)

T (cid:48)
0 ≤

SELF TYPEC if T0 = SELF TYPE
T0 otherwise

OC, M, C (cid:96) f (x1 : T1, . . . , xn : Tn) : T0 { e };

20

[Method]

13 Operational Semantics

This section contains a mostly formal presentation of the operational semantics for the Cool language. The
operational semantics define for every Cool expression what value it should produce in a given context.
The context has three components: an environment, a store, and a self object. These components are
described in the next section. Section 13.2 defines the syntax used to refer to Cool objects, and Section
13.3 defines the syntax used to refer to class definitions.

Keep in mind that a formal semantics is a specification only—it does not describe an implementation.
The purpose of presenting the formal semantics is to make clear all the details of the behavior of Cool
expressions. How this behavior is implemented is another matter.

13.1 Environment and the Store

Before we can present a semantics for Cool we need a number of concepts and a considerable amount of
notation. An environment is a mapping of variable identifiers to locations. Intuitively, an environment
tells us for a given identifier the address of the memory location where that identifier’s value is stored.
For a given expression, the environment must assign a location to all identifiers to which the expression
may refer. For the expression, e.g., a + b, we need an environment that maps a to some location and b
to some location. We’ll use the following syntax to describe environments, which is very similar to the
syntax of type assumptions used in Section 12.

E = [a : l1, b : l2]

This environment maps a to location l1, and b to location l2.

The second component of the context for the evaluation of an expression is the store. The store maps
locations to values, where values in Cool are just objects. Intuitively, a store tells us what value is stored
in a given memory location. For the moment, assume all values are integers. A store is similar to an
environment:

S = [l1 → 55, l2 → 77]

This store maps location l1 to value 55 and location l2 to value 77.

Given an environment and a store, the value of an identifier can be found by first looking up the

location that the identifier maps to in the environment and then looking up the location in the store.

E(a) = l1
S(l1) = 55

Together, the environment and the store define the execution state at a particular step of the evaluation
of a Cool expression. The double indirection from identifiers to locations to values allows us to model
variables. Consider what happens if the value 99 is assigned variable a in the environment and store
defined above. Assigning to a variable means changing the value to which it refers but not its location.
To perform the assignment, we look up the location for a in the environment E and then change the
mapping for the obtained location to the new value, giving a new store S(cid:48).

E(a) = l1

S(cid:48) = S[99/l1]

The syntax S[v/l] denotes a new store that is identical to the store S, except that S(cid:48) maps location l to
value v. For all locations l(cid:48) where l(cid:48) (cid:54)= l, we still have S(cid:48)(l(cid:48)) = S(l(cid:48)).

21

The store models the contents of memory of the computer during program execution. Assigning to a

variable modifies the store.

There are also situations in which the environment is modified. Consider the following Cool fragment:

let c : Int <- 33 in

c

When evaluating this expression, we must introduce the new identifier c into the environment before
evaluating the body of the let. If the current environment and state are E and S, then we create a new
environment E(cid:48) and a new store S(cid:48) defined by:

lc = newloc(S)
E(cid:48) = E[lc/c]
S(cid:48) = S[33/lc]

The first step is to allocate a location for the variable c. The location should be fresh, meaning that the
current store does not have a mapping for it. The function newloc() applied to a store gives us an unused
location in that store. We then create a new environment E(cid:48), which maps c to lc but also contains all
of the mappings of E for identifiers other than c. Note that if c already has a mapping in E, the new
environment E(cid:48) hides this old mapping. We must also update the store to map the new location to a
value. In this case lc maps to the value 33, which is the initial value for c as defined by the let-expression.
The example in this subsection oversimplifies Cool environments and stores a bit, because simple

integers are not Cool values. Even integers are full-fledged objects in Cool.

13.2 Syntax for Cool Objects

Every Cool value is an object. Objects contain a list of named attributes, a bit like records in C. In
addition, each object belongs to a class. We use the following syntax for values in Cool:

v = X(a1 = l1, a2 = l2, . . . , an = ln)

Read the syntax as follows: The value v is a member of class X containing the attributes a1, . . . , an whose
locations are l1, . . . , ln. Note that the attributes have an associated location. Intuitively this means that
there is some space in memory reserved for each attribute.

For base objects of Cool (i.e., Ints, Strings, and Bools) we use a special case of the above syntax.
Base objects have a class name, but their attributes are not like attributes of normal classes, because
they cannot be modified. Therefore, we describe base objects using the following syntax:

Int(5)
Bool(true)
String(4, "Cool")

For Ints and Bools, the meaning is obvious. Strings contain two parts, the length and the actual

sequence of ASCII characters.

13.3 Class definitions

In the rules presented in the next section, we need a way to refer to the definitions of attributes and
methods for classes. Suppose we have the following Cool class definition:

22

class B {

s : String <- "Hello";
g (y:String) : Int {

y.concat(s)

};
f (x:Int) : Int {

x+1

};

};

class A inherits B {

a : Int;
b : B <- new B;
f(x:Int) : Int {

x+a

};

};

Two mappings, called class and implementation, are associated with class definitions. The class

mapping is used to get the attributes, as well as their types and initializations, of a particular class:

class(A) = (s : String ← "Hello", a : Int ← 0, b : B ← new B)

Note that the information for class A contains everything that it inherited from class B, as well as its own
definitions. If B had inherited other attributes, those attributes would also appear in the information for
A. The attributes are listed in the order they are inherited and then in source order: all the attributes
from the greatest ancestor are listed first in the order in which they textually appear, then the attributes
of the next greatest ancestor, and so on, on down to the attributes defined in the particular class. We
rely on this order in describing how new objects are initialized.

The general form of a class mapping is:

class(X) = (a1 : T1 ← e1, . . . , an : Tn ← en)

Note that every attribute has an initializing expression, even if the Cool program does not specify one for
each attribute. The default initialization for a variable or attribute is the default of its type. The default
of Int is 0, the default of String is "", the default of Bool is false, and the default of any other type
is void.4 The default of type T is written DT .

The implementation mapping gives information about the methods of a class. For the above example,

implementation of A is defined as follows:

implementation(A, f ) = (x, x + a)
implementation(A, g) = (y, y.concat(s))

In general, for a class X and a method m,

implementation(X, m) = (x1, x2, . . . , xn, ebody)

specifies that method m when invoked from class X, has formal parameters x1, . . . , xn, and the body of
the method is expression ebody.

4A tiny point: We are allowing void to be used as an expression here. There is no expression for void available to Cool

programmers.

23

13.4 Operational Rules

Equipped with environments, stores, objects, and class definitions, we can now attack the operational
semantics for Cool. The operational semantics is described by rules similar to the rules used in type
checking. The general form of the rules is:

...
so, S, E (cid:96) e1 : v, S(cid:48)

The rule should be read as: In the context where self is the object so, the store is S, and the environment
is E, the expression e1 evaluates to object v and the new store is S(cid:48). The dots above the horizontal bar
stand for other statements about the evaluation of sub-expressions of e1.

Besides an environment and a store, the evaluation context contains a self object so. The self object
is just the object to which the identifier self refers if self appears in the expression. We do not place
self in the environment and store because self is not a variable—it cannot be assigned to. Note that
the rules specify a new store after the evaluation of an expression. The new store contains all changes to
memory resulting as side effects of evaluating expression e1.

The rest of this section presents and briefly discusses each of the operational rules. A few cases are

not covered; these are discussed at the end of the section.

so, S1, E (cid:96) e1 : v1, S2
E(Id) = l1
S3 = S2[v1/l1]

so, S1, E (cid:96) Id ← e1 : v1, S3

[Assign]

An assignment first evaluates the expression on the right-hand side, yielding a value v1. This value is
stored in memory at the address for the identifier.

The rules for identifier references, self, and constants are straightforward:

E(Id) = l
S(l) = v
so, S, E (cid:96) Id : v, S

so, S, E (cid:96) self : so, S

so, S, E (cid:96) true : Bool(true), S

so, S, E (cid:96) false : Bool(f alse), S

i is an integer constant
so, S, E (cid:96) i : Int(i), S

s is a string constant
l = length(s)

so, S, E (cid:96) s : String(l, s), S

24

[Var]

[Self]

[True]

[False]

[Int]

[String]

A new expression is more complicated than one might expect:

(cid:40)

T0 =

X if T = SELF TYPE and so = X(. . .)
T otherwise

class(T0) = (a1 : T1 ← e1, . . . , an : Tn ← en)
li = newloc(S1), for i = 1 . . . n and each li is diistinct
v1 = T0(a1 = l1, . . . , an = ln)
S2 = S1[DT1/l1, . . . , DTn/ln]
v1, S2, [a1 : l1, . . . , an : ln] (cid:96) {a1 ← e1; . . . ; an ← en; } : v2, S3
so, S1, E (cid:96) new T : v1, S3

[New]

The tricky thing in a new expression is to initialize the attributes in the right order. Note also that,
during initialization, attributes are bound to the default of the appropriate class.

so, S1, E (cid:96) e1 : v1, S2
so, S2, E (cid:96) e2 : v2, S3
...
so, Sn, E (cid:96) en : vn, Sn+1
so, Sn+1, E (cid:96) e0 : v0, Sn+2
v0 = X(a1 = la1, . . . , am = lam)
implementation(X, f ) = (x1, . . . , xn, en+1)
lxi = newloc(Sn+2), for i = 1 . . . n and each lxi is distinct
Sn+3 = Sn+2[v1/lx1, . . . , vn/lxn]
v0, Sn+3, [a1 : la1, . . . , am : lam, x1 : lx1, . . . , xn : lxn] (cid:96) en+1 : vn+1, Sn+4
so, S1, E (cid:96) e0.f (e1, . . . , en) : vn+1, Sn+4

so, S1, E (cid:96) e1 : v1, S2
so, S2, E (cid:96) e2 : v2, S3
...
so, Sn, E (cid:96) en : vn, Sn+1
so, Sn+1, E (cid:96) e0 : v0, Sn+2
v0 = X(a1 = la1, . . . , am = lam)
implementation(T, f ) = (x1, . . . , xn, en+1)
lxi = newloc(Sn+2), for i = 1 . . . n and each lxi is distinct
Sn+3 = Sn+2[v1/lx1, . . . , vn/lxn]
v0, Sn+3, [a1 : la1, . . . , am : lam, x1 : lx1, . . . , xn : lxn] (cid:96) en+1 : vn+1, Sn+4
so, S1, E (cid:96) [email protected] (e1, . . . , en) : vn+1, Sn+4

[Dispatch]

[StaticDispatch]

The two dispatch rules do what one would expect. The arguments are evaluated and saved. Next, the
expression on the left-hand side of the “.” is evaluated. In a normal dispatch, the class of this expression
is used to determine the method to invoke; otherwise the class is specified in the dispatch itself.

so, S1, E (cid:96) e1 : Bool(true), S2
so, S2, E (cid:96) e2 : v2, S3

so, S1, E (cid:96) if e1 then e2 else e3 fi : v2, S3

[If-True]

25

so, S1, E (cid:96) e1 : Bool(f alse), S2
so, S2, E (cid:96) e3 : v3, S3

so, S1, E (cid:96) if e1 then e2 else e3 fi : v3, S3
There are no surprises in the if-then-else rules. Note that value of the predicate is a Bool object, not a
boolean.

[If-False]

so, S1, E (cid:96) e1 : v1, S2
so, S2, E (cid:96) e2 : v2, S3
...
so, Sn, E (cid:96) en : vn, Sn+1
so, S1, E (cid:96) { e1; e2; . . . ; en; } : vn, Sn+1
Blocks are evaluated from the first expression to the last expression, in order. The result is the result of
the last expression.

[Sequence]

so, S1, E (cid:96) e1 : v1, S2
l1 = newloc(S2)
S3 = S2[v1/l1]
E(cid:48) = E[l1/Id]
so, S3, E(cid:48) (cid:96) e2 : v2, S4
so, S1, E (cid:96) let Id : T1 ← e1 in e2 : v2, S4
A let evaluates any initialization code, assigns the result to the variable at a fresh location, and evaluates
the body of the let. (If there is no initialization, the variable is initialized to the default value of T1.)
We give the operational semantics only for the case of let with a single variable. The semantics of a
multiple let

[Let]

let x1 : T1 ← e1, x2 : T2 ← e2, . . . , xn : Tn ← en in e

is defined to be the same as

let x1 : T1 ← e1 in (let x2 : T2 ← e2, . . . , xn : Tn ← en in e )

so, S1, E (cid:96) e0 : v0, S2
v0 = X(. . .)
Ti = closest ancestor of X in {T1, . . . , Tn}
l0 = newloc(S2)
S3 = S2[v0/l0]
E(cid:48) = E[l0/Idi]
so, S3, E(cid:48) (cid:96) ei : v1, S4

so, S1, E (cid:96) case e0 of Id1 : T1 ⇒ e1; . . . ; Idn : Tn ⇒ en; esac : v1, S4
Note that the case rule requires that the class hierarchy be available in some form at runtime, so that
the correct branch of the case can be selected. This rule is otherwise straightforward.

[Case]

so, S1, E (cid:96) e1 : Bool(true), S2
so, S2, E (cid:96) e2 : v2, S3
so, S3, E (cid:96) while e1 loop e2 pool : void, S4
so, S1, E (cid:96) while e1 loop e2 pool : void, S4

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[Loop-True]

so, S1, E (cid:96) e1 : Bool(f alse), S2
so, S1, E (cid:96) while e1 loop e2 pool : void, S2
There are two rules for while: one for the case where the predicate is true and one for the case where the
predicate is false. Both cases are straightforward. The two rules for isvoid are also straightforward:

[Loop-False]

so, S1, E (cid:96) e1 : void, S2
so, S1, E (cid:96) isvoid e1 : Bool(true), S2

[IsVoid-True]

so, S1, E (cid:96) e1 : X(. . .), S2
so, S1, E (cid:96) isvoid e1 : Bool(f alse), S2
The remainder of the rules are for the primitive arithmetic, logical, and comparison operations except
equality. These are all easy rules.

[IsVoid-False]

so, S1, E (cid:96) e1 : Bool(b), S2
v1 = Bool(¬b)
so, S1, E (cid:96) not e1 : v1, S2

so, S1, E (cid:96) e1 : Int(i1), S2
so, S2, E (cid:96) e2 : Int(i2), S3
op ∈ {≤, <}
(cid:40)

v1 =

Bool(true), if i1 op i2
Bool(f alse), otherwise

so, S1, E (cid:96) e1 op e2 : v1, S3

so, S1, E (cid:96) e1 : Int(i1), S2
v1 = Int(−i1)

so, S1, E (cid:96) ˜e1 : v1, S2

[Not]

[Comp]

[Neg]

so, S1, E (cid:96) e1 : Int(i1), S2
so, S2, E (cid:96) e2 : Int(i2), S3
op ∈ {∗, +, −, /}
v1 = Int(i1 op i2)
so, S1, E (cid:96) e1 op e2 : v1, S3
Cool Ints are 32-bit two’s complement signed integers; the arithmetic operations are defined accordingly.
The notation and rules given above are not powerful enough to describe how objects are tested for

[Arith]

equality, or how runtime exceptions are handled. For these cases we resort to an English description.

In e1 = e2, first e1 is evaluated and then e2 is evaluated. The two objects are compared for equality
by first comparing their pointers (addresses). If they are the same, the objects are equal. The value
void is not equal to any object except itself. If the two objects are of type String, Bool, or Int, their
respective contents are compared.

In addition, the operational rules do not specify what happens in the event of a runtime error.

Execution aborts when a runtime error occurs. The following list specifies all possible runtime errors.

1. A dispatch (static or dynamic) on void.

2. A case on void.

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3. Execution of a case statement without a matching branch.

4. Division by zero.

5. Substring out of range.

6. Heap overflow.

Finally, the rules given above do not explain the execution behaviour for dispatches to primitive
methods defined in the Object, IO, or String classes. Descriptions of these primitive methods are given
in Sections 8.3-8.5.

14 Acknowledgements

Cool is based on Sather164, which is itself based on the language Sather. Portions of this document
were cribbed from the Sather164 manual; in turn, portions of the Sather164 manual are based on Sather
documentation written by Stephen M. Omohundro.

A number people have contributed to the design and implementation of Cool, including Manuel
F¨ahndrich, David Gay, Douglas Hauge, Megan Jacoby, Tendo Kayiira, Carleton Miyamoto, and Michael
Stoddart. Joe Darcy updated Cool to the current version.

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