HCoop / hcoop / debian / mlton.git / blame
| Commit | Line | Data |
|---|---|---|
| 7f918cf1 CE |
1 | NumericLiteral |
| 2 | ============== | |
| 3 | ||
| 4 | Numeric literals in <:StandardML:Standard ML> can be written in either | |
| 5 | decimal or hexadecimal notation. Sometimes it can be convenient to | |
| 6 | write numbers down in other bases. Fortunately, using <:Fold:>, it is | |
| 7 | possible to define a concise syntax for numeric literals that allows | |
| 8 | one to write numeric constants in any base and of various types | |
| 9 | (`int`, `IntInf.int`, `word`, and more). | |
| 10 | ||
| 11 | We will define constants `I`, `II`, `W`, and +`+ so | |
| 12 | that, for example, | |
| 13 | [source,sml] | |
| 14 | ---- | |
| 15 | I 10 `1`2`3 $ | |
| 16 | ---- | |
| 17 | denotes `123:int` in base 10, while | |
| 18 | [source,sml] | |
| 19 | ---- | |
| 20 | II 8 `2`3 $ | |
| 21 | ---- | |
| 22 | denotes `19:IntInf.int` in base 8, and | |
| 23 | [source,sml] | |
| 24 | ---- | |
| 25 | W 2 `1`1`0`1 $ | |
| 26 | ---- | |
| 27 | denotes `0w13: word`. | |
| 28 | ||
| 29 | Here is the code. | |
| 30 | ||
| 31 | [source,sml] | |
| 32 | ---- | |
| 33 | structure Num = | |
| 34 | struct | |
| 35 | fun make (op *, op +, i2x) iBase = | |
| 36 | let | |
| 37 | val xBase = i2x iBase | |
| 38 | in | |
| 39 | Fold.fold | |
| 40 | ((i2x 0, | |
| 41 | fn (i, x) => | |
| 42 | if 0 <= i andalso i < iBase then | |
| 43 | x * xBase + i2x i | |
| 44 | else | |
| 45 | raise Fail (concat | |
| 46 | ["Num: ", Int.toString i, | |
| 47 | " is not a valid\ | |
| 48 | \ digit in base ", | |
| 49 | Int.toString iBase])), | |
| 50 | fst) | |
| 51 | end | |
| 52 | ||
| 53 | fun I ? = make (op *, op +, id) ? | |
| 54 | fun II ? = make (op *, op +, IntInf.fromInt) ? | |
| 55 | fun W ? = make (op *, op +, Word.fromInt) ? | |
| 56 | ||
| 57 | fun ` ? = Fold.step1 (fn (i, (x, step)) => | |
| 58 | (step (i, x), step)) ? | |
| 59 | ||
| 60 | val a = 10 | |
| 61 | val b = 11 | |
| 62 | val c = 12 | |
| 63 | val d = 13 | |
| 64 | val e = 14 | |
| 65 | val f = 15 | |
| 66 | end | |
| 67 | ---- | |
| 68 | where | |
| 69 | [source,sml] | |
| 70 | ---- | |
| 71 | fun fst (x, _) = x | |
| 72 | ---- | |
| 73 | ||
| 74 | The idea is for the fold to start with zero and to construct the | |
| 75 | result one digit at a time, with each stepper multiplying the previous | |
| 76 | result by the base and adding the next digit. The code is abstracted | |
| 77 | in two different ways for extra generality. First, the `make` | |
| 78 | function abstracts over the various primitive operations (addition, | |
| 79 | multiplication, etc) that are needed to construct a number. This | |
| 80 | allows the same code to be shared for constants `I`, `II`, `W` used to | |
| 81 | write down the various numeric types. It also allows users to add new | |
| 82 | constants for additional numeric types, by supplying the necessary | |
| 83 | arguments to make. | |
| 84 | ||
| 85 | Second, the step function, +`+, is abstracted over the actual | |
| 86 | construction operation, which is created by make, and passed along the | |
| 87 | fold. This allows the same constant, +`+, to be used for all | |
| 88 | numeric types. The alternative approach, having a different step | |
| 89 | function for each numeric type, would be more painful to use. | |
| 90 | ||
| 91 | On the surface, it appears that the code checks the digits dynamically | |
| 92 | to ensure they are valid for the base. However, MLton will simplify | |
| 93 | everything away at compile time, leaving just the final numeric | |
| 94 | constant. |