Standard ML does not have built-in support for optional arguments. Nevertheless, using Fold, it is easy to define functions that take optional arguments.
For example, suppose that we have the following definition of a
function f
.
fun f (i, r, s) =
concat [Int.toString i, ", ", Real.toString r, ", ", s]
Using the OptionalArg
structure described below, we can define a
function f'
, an optionalized version of f
, that takes 0, 1, 2, or
3 arguments. Embedded within f'
will be default values for i
,
r
, and s
. If f'
gets no arguments, then all the defaults are
used. If f'
gets one argument, then that will be used for i
. Two
arguments will be used for i
and r
respectively. Three arguments
will override all default values. Calls to f'
will look like the
following.
f' $
f' `2 $
f' `2 `3.0 $
f' `2 `3.0 `"four" $
The optional argument indicator, `
, is not special syntax ---
it is a normal SML value, defined in the OptionalArg
structure
below.
Here is the definition of f'
using the OptionalArg
structure, in
particular, OptionalArg.make
and OptionalArg.D
.
val f' =
fn z =>
let open OptionalArg in
make (D 1) (D 2.0) (D "three") $
end (fn i & r & s => f (i, r, s))
z
The definition of f'
is eta expanded as with all uses of fold. A
call to OptionalArg.make
is supplied with a variable number of
defaults (in this case, three), the end-of-arguments terminator, $
,
and the function to run, taking its arguments as an n-ary
product. In this case, the function simply converts
the product to an ordinary tuple and calls f
. Often, the function
body will simply be written directly.
In general, the definition of an optional-argument function looks like the following.
val f =
fn z =>
let open OptionalArg in
make (D <default1>) (D <default2>) ... (D <defaultn>) $
end (fn x1 & x2 & ... & xn =>
<function code goes here>)
z
Here is the definition of OptionalArg
.
structure OptionalArg =
struct
val make =
fn z =>
Fold.fold
((id, fn (f, x) => f x),
fn (d, r) => fn func =>
Fold.fold ((id, d ()), fn (f, d) =>
let
val d & () = r (id, f d)
in
func d
end))
z
fun D d = Fold.step0 (fn (f, r) =>
(fn ds => f (d & ds),
fn (f, a & b) => r (fn x => f a & x, b)))
val ` =
fn z =>
Fold.step1 (fn (x, (f, _ & d)) => (fn d => f (x & d), d))
z
end
OptionalArg.make
uses a nested fold. The first fold
accumulates
the default values in a product, associated to the right, and a
reversal function that converts a product (of the same arity as the
number of defaults) from right associativity to left associativity.
The accumulated defaults are used by the second fold, which recurs
over the product, replacing the appropriate component as it encounters
optional arguments. The second fold also constructs a "fill"
function, f
, that is used to reconstruct the product once the
end-of-arguments is reached. Finally, the finisher reconstructs the
product and uses the reversal function to convert the product from
right associative to left associative, at which point it is passed to
the user-supplied function.
Much of the complexity comes from the fact that while recurring over a product from left to right, one wants it to be right-associative, e.g., look like
a & (b & (c & d))
but the user function in the end wants the product to be left
associative, so that the product argument pattern can be written
without parentheses (since &
is left associative).
Labelled optional arguments
In addition to the positional optional arguments described above, it
is sometimes useful to have labelled optional arguments. These allow
one to define a function, f
, with defaults, say a
and b
. Then,
a caller of f
can supply values for a
and b
by name. If no
value is supplied then the default is used.
Labelled optional arguments are a simple extension of
FunctionalRecordUpdate using post composition. Suppose, for
example, that one wants a function f
with labelled optional
arguments a
and b
with default values 0
and 0.0
respectively.
If one has a functional-record-update function updateAB
for records
with a
and b
fields, then one can define f
in the following way.
val f =
fn z =>
Fold.post
(updateAB {a = 0, b = 0.0},
fn {a, b} => print (concat [Int.toString a, " ",
Real.toString b, "\n"]))
z
The idea is that f
is the post composition (using Fold.post
) of
the actual code for the function with a functional-record updater that
starts with the defaults.
Here are some example calls to f
.
val () = f $
val () = f (U#a 13) $
val () = f (U#a 13) (U#b 17.5) $
val () = f (U#b 17.5) (U#a 13) $
Notice that a caller can supply neither of the arguments, either of the arguments, or both of the arguments, and in either order. All that matter is that the arguments be labelled correctly (and of the right type, of course).
Here is another example.
val f =
fn z =>
Fold.post
(updateBCD {b = 0, c = 0.0, d = "<>"},
fn {b, c, d} =>
print (concat [Int.toString b, " ",
Real.toString c, " ",
d, "\n"]))
z
Here are some example calls.
val () = f $
val () = f (U#d "goodbye") $
val () = f (U#d "hello") (U#b 17) (U#c 19.3) $