Numeric literals in Standard ML can be written in either
decimal or hexadecimal notation. Sometimes it can be convenient to
write numbers down in other bases. Fortunately, using Fold, it is
possible to define a concise syntax for numeric literals that allows
one to write numeric constants in any base and of various types
(int
, IntInf.int
, word
, and more).
We will define constants I
, II
, W
, and `
so
that, for example,
I 10 `1`2`3 $
denotes 123:int
in base 10, while
II 8 `2`3 $
denotes 19:IntInf.int
in base 8, and
W 2 `1`1`0`1 $
denotes 0w13: word
.
Here is the code.
structure Num =
struct
fun make (op *, op +, i2x) iBase =
let
val xBase = i2x iBase
in
Fold.fold
((i2x 0,
fn (i, x) =>
if 0 <= i andalso i < iBase then
x * xBase + i2x i
else
raise Fail (concat
["Num: ", Int.toString i,
" is not a valid\
\ digit in base ",
Int.toString iBase])),
fst)
end
fun I ? = make (op *, op +, id) ?
fun II ? = make (op *, op +, IntInf.fromInt) ?
fun W ? = make (op *, op +, Word.fromInt) ?
fun ` ? = Fold.step1 (fn (i, (x, step)) =>
(step (i, x), step)) ?
val a = 10
val b = 11
val c = 12
val d = 13
val e = 14
val f = 15
end
where
fun fst (x, _) = x
The idea is for the fold to start with zero and to construct the
result one digit at a time, with each stepper multiplying the previous
result by the base and adding the next digit. The code is abstracted
in two different ways for extra generality. First, the make
function abstracts over the various primitive operations (addition,
multiplication, etc) that are needed to construct a number. This
allows the same code to be shared for constants I
, II
, W
used to
write down the various numeric types. It also allows users to add new
constants for additional numeric types, by supplying the necessary
arguments to make.
Second, the step function, `
, is abstracted over the actual
construction operation, which is created by make, and passed along the
fold. This allows the same constant, `
, to be used for all
numeric types. The alternative approach, having a different step
function for each numeric type, would be more painful to use.
On the surface, it appears that the code checks the digits dynamically to ensure they are valid for the base. However, MLton will simplify everything away at compile time, leaving just the final numeric constant.