6.11.6. Implicit parameters — Glasgow Haskell Compiler 9.12.1 User's Guide (original) (raw)

ImplicitParams

Since:

6.8.1

Allow definition of functions expecting implicit parameters.

Implicit parameters are implemented as described in [Lewis2000] and enabled with the option ImplicitParams. (Most of the following, still rather incomplete, documentation is due to Jeff Lewis.)

[Lewis2000]

“Implicit parameters: dynamic scoping with static types”, J Lewis, MB Shields, E Meijer, J Launchbury,27th ACM Symposium on Principles of Programming Languages (POPL’00), Boston, Jan 2000.

A variable is called dynamically bound when it is bound by the calling context of a function and statically bound when bound by the callee’s context. In Haskell, all variables are statically bound. Dynamic binding of variables is a notion that goes back to Lisp, but was later discarded in more modern incarnations, such as Scheme. Dynamic binding can be very confusing in an untyped language, and unfortunately, typed languages, in particular Hindley-Milner typed languages like Haskell, only support static scoping of variables.

However, by a simple extension to the type class system of Haskell, we can support dynamic binding. Basically, we express the use of a dynamically bound variable as a constraint on the type. These constraints lead to types of the form (?x::t') => t, which says “this function uses a dynamically-bound variable ?x of type t'”. For example, the following expresses the type of a sort function, implicitly parameterised by a comparison function named cmp.

sort :: (?cmp :: a -> a -> Bool) => [a] -> [a]

The dynamic binding constraints are just a new form of predicate in the type class system.

An implicit parameter occurs in an expression using the special form?x, where x is any valid identifier (e.g. ord ?x is a valid expression). Use of this construct also introduces a new dynamic-binding constraint in the type of the expression. For example, the following definition shows how we can define an implicitly parameterised sort function in terms of an explicitly parameterised sortBy function:

sortBy :: (a -> a -> Bool) -> [a] -> [a]

sort :: (?cmp :: a -> a -> Bool) => [a] -> [a] sort = sortBy ?cmp

6.11.6.1. Implicit-parameter type constraints

Dynamic binding constraints behave just like other type class constraints in that they are automatically propagated. Thus, when a function is used, its implicit parameters are inherited by the function that called it. For example, our sort function might be used to pick out the least value in a list:

least :: (?cmp :: a -> a -> Bool) => [a] -> a least xs = head (sort xs)

Without lifting a finger, the ?cmp parameter is propagated to become a parameter of least as well. With explicit parameters, the default is that parameters must always be explicit propagated. With implicit parameters, the default is to always propagate them.

An implicit-parameter type constraint differs from other type class constraints in the following way: All uses of a particular implicit parameter must have the same type. This means that the type of(?x, ?x) is (?x::a) => (a,a), and not(?x::a, ?x::b) => (a, b), as would be the case for type class constraints.

You can’t have an implicit parameter in the context of a class or instance declaration. For example, both these declarations are illegal:

class (?x::Int) => C a where ... instance (?x::a) => Foo [a] where ...

Reason: exactly which implicit parameter you pick up depends on exactly where you invoke a function. But the “invocation” of instance declarations is done behind the scenes by the compiler, so it’s hard to figure out exactly where it is done. Easiest thing is to outlaw the offending types.

Implicit-parameter constraints do not cause ambiguity. For example, consider:

f :: (?x :: [a]) => Int -> Int f n = n + length ?x

g :: (Read a, Show a) => String -> String g s = show (read s)

Here, g has an ambiguous type, and is rejected, but f is fine. The binding for ?x at f‘s call site is quite unambiguous, and fixes the type a.

6.11.6.2. Implicit-parameter bindings

An implicit parameter is bound using the standard let or wherebinding forms. For example, we define the min function by bindingcmp.

min :: Ord a => [a] -> a min = let ?cmp = (<=) in least

A group of implicit-parameter bindings may occur anywhere a normal group of Haskell bindings can occur, except at top level. That is, they can occur in a let (including in a list comprehension, or do-notation, or pattern guards), or a where clause. Note the following points:

6.11.6.3. Implicit parameters and polymorphic recursion

Consider these two definitions:

len1 :: [a] -> Int len1 xs = let ?acc = 0 in len_acc1 xs

len_acc1 [] = ?acc len_acc1 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc1 xs

len2 :: [a] -> Int len2 xs = let ?acc = 0 in len_acc2 xs

len_acc2 :: (?acc :: Int) => [a] -> Int len_acc2 [] = ?acc len_acc2 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc2 xs

The only difference between the two groups is that in the second grouplen_acc is given a type signature. In the former case, len_acc1is monomorphic in its own right-hand side, so the implicit parameter?acc is not passed to the recursive call. In the latter case, because len_acc2 has a type signature, the recursive call is made to the polymorphic version, which takes ?acc as an implicit parameter. So we get the following results in GHCi:

Prog> len1 "hello" 0 Prog> len2 "hello" 5

Adding a type signature dramatically changes the result! This is a rather counter-intuitive phenomenon, worth watching out for.

6.11.6.4. Implicit parameters scoping guarantees

GHC always takes the most nested implicit parameter binding from the context to find the value. Consider the following code:

let ?f = 1 in let ?f = 2 in ?f

This expression will always return 2.

Another example of this rule is matching over constructors with constraints. For example:

data T where MkT :: (?f :: Int) => T

f :: T -> T -> Int f MkT MkT = ?f

Here GHC will always take ?f from the last match.

6.11.6.5. Implicit parameters and monomorphism

GHC applies the dreaded Monomorphism Restriction (section 4.5.5 of the Haskell Report) to implicit parameters. For example, consider:

f :: Int -> Int f v = let ?x = 0 in let y = ?x + v in let ?x = 5 in y

Since the binding for y falls under the Monomorphism Restriction it is not generalised, so the type of y is simply Int, not(?x::Int) => Int. Hence, (f 9) returns result 9. If you add a type signature for y, then y will get type(?x::Int) => Int, so the occurrence of y in the body of thelet will see the inner binding of ?x, so (f 9) will return14.