A derived instance is an instance declaration that is generated automatically in conjunction with a data or newtype declaration. The body of a derived instance declaration is derived syntactically from the definition of the associated type. Derived instances are possible only for classes known to the compiler: those defined in either the Prelude or a standard library. In this chapter, we describe the derivation of classes defined by the Prelude.
If T is an algebraic datatype declared by:
| data cx => T u1 ... uk | = | K1 t11 ... t1k1 | ...| Kn tn1 ... tnkn |
| deriving (C1, ..., Cm) |
(where m>=0 and the parentheses may be omitted if m=1) then a derived instance declaration is possible for a class C if these conditions hold:
If the deriving form is present, an instance declaration is automatically generated for T u1 ... uk over each class Ci. If the derived instance declaration is impossible for any of the Ci then a static error results. If no derived instances are required, the deriving form may be omitted or the form deriving () may be used.
Each derived instance declaration will have the form:
instance (cx, cx') => Ci (T u1 ... uk) where { d }
where d is derived automatically depending on Ci and the data type declaration for T (as will be described in the remainder of this section).
The context cx' is the smallest context satisfying point (2) above. For mutually recusive data types, the compiler may need to perform a fixpoint calculation to compute it.
The remaining details of the derived instances for each of the derivable Prelude classes are now given. Free variables and constructors used in these translations always refer to entities defined by the Prelude.
Derived comparisons always traverse constructors from left to right.
These examples illustrate this property:
(1,undefined) == (2,undefined) => False
(undefined,1) == (undefined,2) => _|_
All derived operations of class Eq and Ord are strict in both arguments.
For example, False <= _|_ is _|_, even though False is the first constructor
of the Bool type.
The nullary constructors are assumed to be numbered left-to-right with the indices 0 through n-1. The succ and pred operators give the successor and predecessor respectively of a value, under this numbering scheme. It is an error to apply succ to the maximum element, or pred to the minimum element.
The toEnum and fromEnum operators map enumerated values to and from the Int type; toEnum raises a runtime error if the Int argument is not the index of one of the constructors.
The definitions of the remaining methods are
enumFrom x = enumFromTo x lastCon
enumFromThen x y = enumFromThenTo x y bound
where
bound | fromEnum y >= fromEnum x = lastCon
| otherwise = firstCon
enumFromTo x y = map toEnum [fromEnum x .. fromEnum y]
enumFromThenTo x y z = map toEnum [fromEnum x, fromEnum y .. fromEnum z]
where firstCon and lastCon are respectively the first and last
constructors listed in the data declaration.
For example,
given the datatype:
data Color = Red | Orange | Yellow | Green deriving (Enum)
we would have:
[Orange ..] == [Orange, Yellow, Green]
fromEnum Yellow == 2
The function showsPrec d x r accepts a precedence level d (a number from 0 to 11), a value x, and a string r. It returns a string representing x concatenated to r. showsPrec satisfies the law:
showsPrec d x r ++ s == showsPrec d x (r ++ s)
The representation will be enclosed in parentheses if the precedence of the top-level constructor in x is less than d. Thus, if d is 0 then the result is never surrounded in parentheses; if d is 11 it is always surrounded in parentheses, unless it is an atomic expression (recall that function application has precedence 10). The extra parameter r is essential if tree-like structures are to be printed in linear time rather than time quadratic in the size of the tree.
The function readsPrec d s accepts a precedence level d (a number from 0 to 10) and a string s, and attempts to parse a value from the front of the string, returning a list of (parsed value, remaining string) pairs. If there is no successful parse, the returned list is empty. Parsing of an un-parenthesised infix operator application succeeds only if the precedence of the operator is greater than or equal to d.
It should be the case that
showList and readList allow lists of objects to be represented using non-standard denotations. This is especially useful for strings (lists of Char).
readsPrec will parse any valid representation of the standard types apart from strings, for which only quoted strings are accepted, and other lists, for which only the bracketed form [...] is accepted. See Chapter 8 for full details.
The result of show is a syntactically correct Haskell expression containing only constants, given the fixity declarations in force at the point where the type is declared. It contains only the constructor names defined in the data type, parentheses, and spaces. When labelled constructor fields are used, braces, commas, field names, and equal signs are also used. Parentheses are only added where needed, ignoring associativity. No line breaks are added. The result of show is readable by read if all component types are readable. (This is true for all instances defined in the Prelude but may not be true for user-defined instances.)
Derived instances of Read make the following assumptions, which derived instances of Show obey:
The derived Read and Show instances may be unsuitable for some uses. Some problems include:
As a complete example, consider a tree datatype:
data Tree a = Leaf a | Tree a :^: Tree a
deriving (Eq, Ord, Read, Show)
Automatic derivation of
instance
declarations for Bounded and Enum are not possible, as Tree is not
an enumeration or single-constructor datatype. The complete
instance declarations for Tree are shown in Figure 10.1,
Note the implicit use of default class method
definitions---for
example, only <= is defined for Ord, with the other
class methods (<, >, >=, max, and min) being defined by the defaults given in
the class declaration shown in Figure 6.1
(page ).