# 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.

## Integers¶

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.

with Ada.Text_IO; use Ada.Text_IO; procedure Integer_Type_Example is -- Declare a signed integer type, and give the bounds type My_Int is range -1 .. 20; -- ^ High bound -- ^ Low bound -- Like variables, type declarations can only appear in -- declarative regions begin for I in My_Int loop Put_Line (My_Int'Image (I)); -- ^ 'Image attribute, converts a value to a -- String end loop; end Integer_Type_Example;

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 the type.

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 My_Int'Image (I) expression. 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 value for Integer is $$-2^{31}$$, and the last valid value is $$2^{31}-1$$.

Ada does not mandate the range of the built-in type Integer. An implementation for a 16-bit target would likely choose the range $$-2^{15}$$ through $$2^{15}-1$$.

### Operational semantics¶

Unlike some other languages, Ada requires that operations on integers should be checked for overflow.

procedure Main is A : Integer := Integer'Last; B : Integer; begin B := A + 5; -- This operation will overflow, eg. it will -- raise an exception at run time. end Main;

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:

with Ada.Text_IO; use Ada.Text_IO; procedure Main is type My_Int is range 1 .. 20; A : My_Int := 12; B : My_Int := 15; M : My_Int := (A + B) / 2; -- No overflow here, overflow checks are done at -- specific boundaries. begin for I in 1 .. M loop Put_Line ("Hello, World!"); end loop; -- Loop body executed 13 times end Main;

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.

## Unsigned types¶

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 2**32, this mimics the most common implementation behavior of unsigned types. However, an advantage of Ada is that the modulus is more general:

with Ada.Text_IO; use Ada.Text_IO; procedure Main is type Mod_Int is mod 2 ** 5; -- ^ Range is 0 .. 31 A : Mod_Int := 20; B : Mod_Int := 15; M : Mod_Int := A + B; -- No overflow here, M = (20 + 15) mod 32 = 3 begin for I in 1 .. M loop Put_Line ("Hello, World!"); end loop; end Main;

Unlike in C/C++, since this 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.

## Enumerations¶

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.

with Ada.Text_IO; use Ada.Text_IO; procedure Enumeration_Example is type Days is (Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday); -- An enumeration type begin for I in Days loop case I is when Saturday .. Sunday => Put_Line ("Week end!"); when Monday .. Friday => Put_Line ("Hello on " & Days'Image (I)); -- 'Image attribute, works on enums too end case; end loop; end Enumeration_Example;

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.

## Floating-point types¶

### Basic properties¶

Like most languages, Ada supports floating-point types. The most commonly used floating-point type is Float:

with Ada.Text_IO; use Ada.Text_IO; procedure Floating_Point_Demo is A : Float := 2.5; begin Put_Line ("The value of A is " & Float'Image (A)); end Floating_Point_Demo;

The application will display 2.5 as the value of A.

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:

with Ada.Text_IO; use Ada.Text_IO; procedure Floating_Point_Operations is A : Float := 2.5; begin A := abs (A - 4.5); Put_Line ("The value of A is " & Float'Image (A)); A := A ** 2 + 1.0; Put_Line ("The value of A is " & Float'Image (A)); end Floating_Point_Operations;

The value of A is 2.0 after the first operation and 5.0 after the second operation.

In addition to Float, an Ada implementation may offer data types with higher precision such as Long_Float and Long_Long_Float. Like 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 precision of 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:

with Ada.Text_IO; use Ada.Text_IO; procedure Custom_Floating_Types is type T3 is digits 3; type T15 is digits 15; type T18 is digits 18; begin Put_Line ("T3 requires " & Integer'Image (T3'Size) & " bits"); Put_Line ("T15 requires " & Integer'Image (T15'Size) & " bits"); Put_Line ("T18 requires " & Integer'Image (T18'Size) & " bits"); end Custom_Floating_Types;

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 bits for 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:

with Ada.Text_IO; use Ada.Text_IO; procedure Display_Custom_Floating_Types is type T3 is digits 3; type T18 is digits 18; C1 : constant := 1.0e-4; A : T3 := 1.0 + C1; B : T18 := 1.0 + C1; begin Put_Line ("The value of A is " & T3'Image (A)); Put_Line ("The value of B is " & T18'Image (B)); end Display_Custom_Floating_Types;

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 between -1.0 and 1.0:

with Ada.Text_IO; use Ada.Text_IO; procedure Floating_Point_Range is type T_Norm is new Float range -1.0 .. 1.0; A : T_Norm; begin A := 1.0; Put_Line ("The value of A is " & T_Norm'Image (A)); end Floating_Point_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 exception Constraint_Error is raised when assigning 2.0 to the variable A:

with Ada.Text_IO; use Ada.Text_IO; procedure Floating_Point_Range_Exception is type T_Norm is new Float range -1.0 .. 1.0; A : T_Norm; begin A := 2.0; Put_Line ("The value of A is " & T_Norm'Image (A)); end Floating_Point_Range_Exception;

Ranges can also be specified for custom floating-point types. For example:

with Ada.Text_IO; use Ada.Text_IO; with Ada.Numerics; use Ada.Numerics; procedure Custom_Range_Types is type T6_Inv_Trig is digits 6 range -Pi / 2.0 .. Pi / 2.0; begin null; end Custom_Range_Types;

In this example, we are defining a type called T6_Inv_Trig, which has a range from $$-\pi/2$$ to $$\pi/2$$ with a minimum precision of 6 digits. (Pi is defined in the predefined package Ada.Numerics.)

## Strong typing¶

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:

with Ada.Text_IO; use Ada.Text_IO; procedure Illegal_Example is -- Declare two different floating point types type Meters is new Float; type Miles is new Float; Dist_Imperial : Miles; -- Declare a constant Dist_Metric : constant Meters := 100.0; begin -- Not correct: types mismatch Dist_Imperial := (Dist_Metric * 1609.0) / 1000.0; Put_Line (Miles'Image (Dist_Imperial)); end Illegal_Example;

A consequence of these rules is that, in the general case, a "mixed mode" expression like 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:

with Ada.Text_IO; use Ada.Text_IO; procedure Conv is type Meters is new Float; type Miles is new Float; Dist_Imperial : Miles; Dist_Metric : constant Meters := 100.0; begin Dist_Imperial := (Miles (Dist_Metric) * 1609.0) / 1000.0; -- ^ Type conversion, from Meters to Miles -- Now the code is correct Put_Line (Miles'Image (Dist_Imperial)); end Conv;

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.

with Ada.Text_IO; use Ada.Text_IO; procedure Conv is type Meters is new Float; type Miles is new Float; -- Function declaration, like procedure but returns a value. function To_Miles (M : Meters) return Miles is -- ^ Return type begin return (Miles (M) * 1609.0) / 1000.0; end To_Miles; Dist_Imperial : Miles; Dist_Metric : constant Meters := 100.0; begin Dist_Imperial := To_Miles (Dist_Metric); Put_Line (Miles'Image (Dist_Imperial)); end Conv;

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 a 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:

procedure Main is A : Integer := 3; B : Integer := 2; F : Float; begin F := A / B; end Main;

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.

## Derived types¶

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.

procedure Main is -- ID card number type, incompatible with Integer. type Social_Security_Number is new Integer range 0 .. 999_99_9999; -- ^ Since a SSN has 9 digits max, and cannot be -- negative, we enforce a validity constraint. SSN : Social_Security_Number := 555_55_5555; -- ^ You can put underscores as formatting in -- any number. I : Integer; Invalid : Social_Security_Number := -1; -- ^ This will cause a runtime error -- (and a compile time warning with -- GNAT) begin I := SSN; -- Illegal, they have different types SSN := I; -- Likewise illegal I := Integer (SSN); -- OK with explicit conversion SSN := Social_Security_Number (I); -- Likewise OK end Main;

The type 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:

with Ada.Text_IO; use Ada.Text_IO; procedure Greet is type Days is (Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday); type Weekend_Days is new Days range Saturday .. Sunday; -- New type, where only Saturday and Sunday are valid literals. begin null; end Greet;

## Subtypes¶

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.

with Ada.Text_IO; use Ada.Text_IO; procedure Greet is type Days is (Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday); -- Declaration of a subtype subtype Weekend_Days is Days range Saturday .. Sunday; -- ^ Constraint of the subtype M : Days := Sunday; S : Weekend_Days := M; -- No error here, Days and Weekend_Days are of the same type. begin for I in Days loop case I is -- Just like a type, a subtype can be used as a -- range when Weekend_Days => Put_Line ("Week end!"); when others => Put_Line ("Hello on " & Days'Image (I)); end case; end loop; end Greet;

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.

with Ada.Text_IO; use Ada.Text_IO; procedure Greet is type Days is (Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday); subtype Weekend_Days is Days range Saturday .. Sunday; Day : Days := Saturday; Weekend : Weekend_Days; begin Weekend := Day; -- ^ Correct: Same type, subtype constraints are respected Weekend := Monday; -- ^ Wrong value for the subtype -- Compiles, but exception at runtime end Greet;