Strongly typed language¶
Ada is a strongly typed language. It is interestingly modern in that respect: strong static typing has been increasing in popularity in programming language design, owing to factors such as the growth of statically typed functional programming, a big push from the research community in the typing domain, and many practical languages with strong type systems.
What is a type?¶
In statically typed languages, a type is mainly (but not only) a compile time construct. It is a construct to enforce invariants about the behavior of a program. Invariants are unchangeable properties that hold for all variables of a given type. Enforcing them ensures, for example, that variables of a data type never have invalid values.
A type is used to reason about the objects a program manipulates (an object is a variable or a constant). The aim is to classify objects by what you can accomplish with them (i.e., the operations that are permitted), and this way you can reason about the correctness of the objects' values.
A nice feature of Ada is that you can define your own integer types, based on the requirements of your program (i.e., the range of values that makes sense). In fact, the definitional mechanism that Ada provides forms the semantic basis for the predefined integer types. There is no "magical" built-in type in that regard, which is unlike most languages, and arguably very elegant.
This example illustrates the declaration of a signed integer type, and several things we can do with them.
Every type declaration in Ada starts with the
type keyword (except for
task types). After the type, we can see a range that looks
a lot like
the ranges that we use in for loops, that defines the low and high bound of the
type. Every integer in the inclusive range of the bounds is a valid value for
Ada integer types
In Ada, an integer type is not specified in terms of its machine representation, but rather by its range. The compiler will then choose the most appropriate representation.
Another point to note in the above example is the
Name'Attribute (optional params) notation is used for
what is called an attribute in Ada. An attribute is a
built-in operation on a type, a value, or some other program entity. It is
accessed by using a
' symbol (the ASCII apostrophe).
Ada has several types available as "built-ins";
Integer is one of
them. Here is how
Integer might be defined for a typical processor:
type Integer is range -(2 ** 31) .. +(2 ** 31 - 1);
** is the exponent operator, which means that the first valid
Integer is -231, and the last valid value is
231 - 1.
Ada does not mandate the range of the built-in type Integer. An implementation for a 16-bit target would likely choose the range -215 through 215 - 1.
Unlike some other languages, Ada requires that operations on integers should be checked for overflow.
There are two types of overflow checks:
Machine-level overflow, when the result of an operation exceeds the maximum value (or is less than the minimum value) that can be represented in the storage reserved for an object of the type, and
Type-level overflow, when the result of an operation is outside the range defined for the type.
Mainly for efficiency reasons, while machine level overflow always results in an exception, type level overflows will only be checked at specific boundaries, like assignment:
Type level overflow will only be checked at specific points in the execution. The result, as we see above, is that you might have an operation that overflows in an intermediate computation, but no exception will be raised because the final result does not overflow.
Ada also features unsigned Integer types. They're called modular types in Ada parlance. The reason for this designation is due to their behavior in case of overflow: They simply "wrap around", as if a modulo operation was applied.
For machine sized modular types, for example a modulus of 232, this mimics the most common implementation behavior of unsigned types. However, an advantage of Ada is that the modulus is more general:
Unlike in C/C++, since this wraparound behavior is guaranteed by the Ada specification, you can rely on it to implement portable code. Also, being able to leverage the wrapping on arbitrary bounds is very useful — the modulus does not need to be a power of 2 — to implement certain algorithms and data structures, such as ring buffers.
Enumeration types are another nicety of Ada's type system. Unlike C's enums, they are not integers, and each new enumeration type is incompatible with other enumeration types. Enumeration types are part of the bigger family of discrete types, which makes them usable in certain situations that we will describe later but one context that we have already seen is a case statement.
Enumeration types are powerful enough that, unlike in most languages, they're used to define the standard Boolean type:
type Boolean is (False, True);
As mentioned previously, every "built-in" type in Ada is defined with facilities generally available to the user.
Like most languages, Ada supports floating-point types. The most commonly used
floating-point type is
The application will display
2.5 as the value of
The Ada language does not specify the precision (number of decimal digits in the mantissa) for Float; on a typical 32-bit machine the precision will be 6.
All common operations that could be expected for floating-point types are available, including absolute value and exponentiation. For example:
The value of
2.0 after the first operation and
after the second operation.
In addition to
Float, an Ada implementation may offer data types with
higher precision such as
Float, the standard does not indicate the exact precision of these types: it
only guarantees that the type
Long_Float, for example, has at least the
Float. In order to guarantee that a certain precision
requirement is met, we can define custom floating-point types, as we will see
in the next section.
Precision of floating-point types¶
Ada allows the user to specify the precision for a floating-point type, expressed in terms of decimal digits. Operations on these custom types will then have at least the specified precision. The syntax for a simple floating-point type declaration is:
type T is digits <number_of_decimal_digits>;
The compiler will choose a floating-point representation that supports the required precision. For example:
In this example, the attribute
'Size is used to retrieve the number of
bits used for the specified data type. As we can see by running this example,
the compiler allocates 32 bits for
T3, 64 bits for
T15 and 128
T18. This includes both the mantissa and the exponent.
The number of digits specified in the data type is also used in the format when displaying floating-point variables. For example:
As expected, the application will display the variables according to specified precision (1.00E+00 and 1.00010000000000000E+00).
Range of floating-point types¶
In addition to the precision, a range can also be specified for a
floating-point type. The syntax is similar to the one used for integer data
types — using the
range keyword. This simple example creates a new
floating-point type based on the type
Float, for a normalized range
The application is responsible for ensuring that variables of this type stay
within this range; otherwise an exception is raised. In this example, the
Constraint_Error is raised when assigning
2.0 to the
Ranges can also be specified for custom floating-point types. For example:
In this example, we are defining a type called
T6_Inv_Trig, which has a
range from -π / 2 to π / 2 with a minimum precision of 6
Pi is defined in the predefined package
As noted earlier, Ada is strongly typed. As a result, different types of the same family are incompatible with each other; a value of one type cannot be assigned to a variable from the other type. For example:
A consequence of these rules is that, in the general case, a "mixed mode"
2 * 3.0 will trigger a compilation error. In a language
like C or Python, such expressions are made valid by implicit conversions. In
Ada, such conversions must be made explicit:
Of course, we probably do not want to write the conversion code every time we convert from meters to miles. The idiomatic Ada way in that case would be to introduce conversion functions along with the types.
If you write a lot of numeric code, having to explicitly provide such conversions might seem painful at first. However, this approach brings some advantages. Notably, you can rely on the absence of implicit conversions, which will in turn prevent some subtle errors.
In other languages
In C, for example, the rules for implicit conversions may not always be completely obvious. In Ada, however, the code will always do exactly what it seems to do. For example:
int a = 3, b = 2; float f = a / b;
This code will compile fine, but the result of
f will be 1.0 instead
of 1.5, because the compiler will generate an integer division (three
divided by two) that results in one. The software developer must be
aware of data conversion issues and use an appropriate casting:
int a = 3, b = 2; float f = (float)a / b;
In the corrected example, the compiler will convert both variables to their corresponding floating-point representation before performing the division. This will produce the expected result.
This example is very simple, and experienced C developers will probably
notice and correct it before it creates bigger
problems. However, in more complex applications where the type
declaration is not always visible — e.g. when referring to elements of
struct — this situation might not always be evident and quickly
lead to software defects that can be harder to find.
The Ada compiler, in contrast, will always reject code that mixes floating-point and integer variables without explicit conversion. The following Ada code, based on the erroneous example in C, will not compile:
The offending line must be changed to
F := Float (A) / Float (B);
in order to be accepted by the compiler.
You can use Ada's strong typing to help enforce invariants in your code, as in the example above: Since Miles and Meters are two different types, you cannot mistakenly convert an instance of one to an instance of the other.
In Ada you can create new types based on existing ones. This is very useful: you get a type that has the same properties as some existing type but is treated as a distinct type in the interest of strong typing.
Social_Security is said to be a derived type;
its parent type is Integer.
As illustrated in this example, you can refine the valid range when defining a derived scalar type (such as integer, floating-point and enumeration).
The syntax for enumerations uses the
range <range> syntax:
As we are starting to see, types may be used in Ada to enforce constraints on the valid range of values. However, we sometimes want to enforce constraints on some values while staying within a single type. This is where subtypes come into play. A subtype does not introduce a new type.
Several subtypes are predefined in the standard package in Ada, and are automatically available to you:
subtype Natural is Integer range 0 .. Integer'Last; subtype Positive is Integer range 1 .. Integer'Last;
While subtypes of a type are statically compatible with each other, constraints are enforced at run time: if you violate a subtype constraint, an exception will be raised.
Subtypes as type aliases¶
Previously, we've seen that we can create new types by declaring
type Miles is new Float. We could also create type aliases, which
generate alternative names — aliases — for known types. Note that
type aliases are sometimes called type synonyms.
We achieve this in Ada by using subtypes without new constraints. In this case, however, we don't get all of the benefits of Ada's strong type checking. Let's rewrite an example using type aliases:
In the example above, the fact that both
Float allows us to mix variables of both types without
type conversion. This, however, can lead to all sorts of programming mistakes
that we'd like to avoid, as we can see in the undetected error highlighted in
the code above. In that example, the error in the assignment of a value in
meters to a variable meant to store values in miles remains undetected because
Miles are subtypes of
the recommendation is to use strong typing — via
type X is new Y
— for cases such as the one above.
There are, however, many situations where type aliases are useful. For example, in an application that uses floating-point types in multiple contexts, we could use type aliases to indicate additional meaning to the types or to avoid long variable names. For example, instead of writing:
Paid_Amount, Due_Amount : Float;
We could write:
subtype Amount is Float; Paid, Due : Amount;
In other languages
In C, for example, we can use a
typedef declaration to create a type
alias. For example:
typedef float meters;
This corresponds to the declaration that we've seen above using subtypes. Other programming languages include this concept in similar ways. For example:
using meters = float;
typealias Meters = Double
typealias Meters = Double
type Meters = Float
Note, however, that subtypes in Ada correspond to type aliases if, and only
if, they don't have new constraints. Thus, if we add a new constraint to a
subtype declaration, we don't have a type alias anymore. For example, the
following declaration can't be consider a type alias of
subtype Meters is Float range 0.0 .. 1_000_000.0;
Let's look at another example:
subtype Degree_Celsius is Float; subtype Liquid_Water_Temperature is Degree_Celsius range 0.0 .. 100.0; subtype Running_Water_Temperature is Liquid_Water_Temperature;
In this example,
Liquid_Water_Temperature isn't an alias of
Degree_Celsius, since it adds a new constraint that wasn't part of the
declaration of the
Degree_Celsius. However, we do have two type aliases
Degree_Celsiusis an alias of
Running_Water_Temperatureis an alias of
Liquid_Water_Temperature, even if
Liquid_Water_Temperatureitself has a constrained range.