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10.2 Instance declarations

Once the interface of the type class has been defined in the typeclass declaration, we can use an instance declaration to define how a particular type (or sequence of types) satisfies the interface declared in the typeclass declaration.

An instance declaration has the form

:- instance classname(typename(typevar, …), …)
        where [methoddefinition, methoddefinition, …].

An ‘instance’ declaration gives a type for each parameter of the type class. Each of these types must be either a type with no arguments, or a polymorphic type whose arguments are all type variables. For example int, list(T), bintree(K, V) and bintree(T, T) are allowed, but T and list(int) are not. The types in an instance declaration must not be abstract types which are elsewhere defined as equivalence types. A program may not contain more than one instance declaration for a particular type (or sequence of types, in the case of a multi-parameter type class) and typeclass. These restrictions ensure that there are no overlapping instance declarations, i.e. for each typeclass there is at most one instance declaration that may be applied to any type (or sequence of types).

Each methoddefinition entry in the ‘where […]’ part of an instance declaration defines the implementation of one of the class methods for this instance. There are two ways of defining methods. The first way is to define a method by giving the name of the predicate or function which implements that method. In this case, the methoddefinition must have one of the following forms:

pred(methodname/arity) is predname
func(methodname/arity) is funcname

The predname or funcname must name a function or predicate of the specified arity whose type, modes, determinism, and purity are at least as permissive as the declared type, modes, determinism, and purity of the class method with the specified methodname and arity, after the types of the arguments in the instance declaration have been substituted in place of the parameters in the type class declaration.

The second way of defining methods is by listing the clauses for the definition inside the instance declaration. A methoddefinition can be a clause. These clauses are just like the clauses used to define ordinary predicates or functions (see Items), and so they can be facts, rules, or DCG rules. The only difference is that in instance declarations, clauses are separated by commas rather than being terminated by periods, and so rules and DCG rules in instance declarations must normally be enclosed in parentheses. As with ordinary predicates, you can have more than one clause for each method. The clauses must satisfy the declared type, modes, determinism and purity for the method, after the types of the arguments in the instance declaration have been substituted in place of the parameters in the type class declaration.

These two ways are mutually exclusive: each method must be defined either by a single naming definition (using the ‘pred(…) is predname’ or ‘func(…) is funcname’ form), or by a set of one or more clauses, but not both.

Here’s an example of an instance declaration and the different kinds of method definitions that it can contain:

:- typeclass foo(T) where [
	func method1(T, T) = int,
	func method2(T) = int,
	pred method3(T::in, int::out) is det,
	pred method4(T::in, io.state::di, io.state::uo) is det,
	func method5(bool, T) = T

:- instance foo(int) where [
	% method defined by naming the implementation
	func(method1/2) is (+),

	% method defined by a fact
	method2(X) = X + 1,

	% method defined by a rule
	(method3(X, Y) :- Y = X + 2),

	% method defined by a DCG rule
	(method4(X) --> io.print(X),,

	% method defined by multiple clauses
	method5(no, _) = 0,
	(method5(yes, X) = Y :- X + Y = 0)

Each ‘instance’ declaration must define an implementation for every method declared in the corresponding ‘typeclass’ declaration. It is an error to define more than one implementation for the same method within a single ‘instance’ declaration.

Any call to a method must have argument types (and in the case of functions, return type) which are constrained to be a member of that method’s type class, or which match one of the instance declarations visible at the point of the call. A method call will invoke the predicate or function specified for that method in the instance declaration that matches the types of the arguments to the call.

Note that even if a type class has no methods, an explicit instance declaration is required for a type to be considered an instance of that type class.

Here’s an example of some code using an instance declaration:

:- type coordinate
        ---> coordinate(
                float,           % X coordinate
                float            % Y coordinate

:- instance point(coordinate) where [
        pred(coords/3) is coordinate_coords,
        func(translate/3) is coordinate_translate

:- pred coordinate_coords(coordinate, float, float).
:- mode coordinate_coords(in, out, out) is det.

coordinate_coords(coordinate(X, Y), X, Y).

:- func coordinate_translate(coordinate, float, float) = coordinate.

coordinate_translate(coordinate(X, Y), Dx, Dy) = coordinate(X + Dx, Y + Dy).

We have now made the coordinate type an instance of the point type class. If we introduce a new type, coloured_coordinate which represents a point in two dimensional space with a colour associated with it, it can also become an instance of the type class:

:- type rgb
        ---> rgb(

:- type coloured_coordinate
        ---> coloured_coordinate(

:- instance point(coloured_coordinate) where [
        pred(coords/3) is coloured_coordinate_coords,
        func(translate/3) is coloured_coordinate_translate

:- pred coloured_coordinate_coords(coloured_coordinate, float, float).
:- mode coloured_coordinate_coords(in, out, out) is det.

coloured_coordinate_coords(coloured_coordinate(X, Y, _), X, Y).

:- func coloured_coordinate_translate(coloured_coordinate, float, float) 
        = coloured_coordinate.

coloured_coordinate_translate(coloured_coordinate(X, Y, Colour), Dx, Dy) 
        = coloured_coordinate(X + Dx, Y + Dy, Colour).

If we call ‘translate/3’ with the first argument having type ‘coloured_coordinate’, this will invoke ‘coloured_coordinate_translate’. Likewise, if we call ‘translate/3’ with the first argument having type ‘coordinate’, this will invoke ‘coordinate_translate’.

Further instances of the type class could be made, e.g. a type that represents the point using polar coordinates.

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