Implicit parameters are implemented as described in
“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.
Note however that the binding syntax in that paper,
using keywords dlet and with,
has been replaced by the form presented below.
(Most of the following, still rather incomplete, documentation is due to Jeff Lewis.)
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, as dynamic binding can be very confusing in an untyped language. 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 parameterized 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 parameterized sort function in
terms of an explicitly parameterized sortBy function:
sortBy :: (a -> a -> Bool) -> [a] -> [a] sort :: (?cmp :: a -> a -> Bool) => [a] -> [a] sort = sortBy ?cmp
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 = fst (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 explicitly 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. The 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.
An implicit parameter is bound using the standard
let or where binding forms.
For example, we define the min function by binding
cmp:
min :: [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 a where clause.
Note the following points:
An implicit-parameter binding group must be a collection of simple bindings to implicit-style variables (no function-style bindings, and no type signatures); these bindings are neither polymorphic or recursive.
You may not mix implicit-parameter bindings with ordinary bindings in a
single let expression;
use two nested lets instead.
(In the case of where you are stuck,
since you can't nest where clauses.)
You may put multiple implicit-parameter bindings in a single binding group;
but they are not treated as a mutually recursive group
(as ordinary let bindings are).
Instead they are treated as a non-recursive group,
simultaneously binding all the implicit parameters.
The bindings are not nested, and may be re-ordered without changing
the meaning of the program.
For example, consider:
f t = let { ?x = t; ?y = ?x+(1::Int) } in ?x + ?y
The use of ?x in the binding for ?y
does not “see” the binding for ?x,
so the type of f is
f :: (?x::Int) => Int -> Int