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Defines unary Peano numerals with two recursive functions for
arithmetic:
type peano = Zero | Succ of peano
let rec plus a b = match a with
| Zero -> b
| Succ a' -> Succ (plus a' b)
let rec mul a b = match a with
| Zero -> Zero
| Succ a' -> plus b (mul a' b)
mul is defined inductively: mul Zero _ = Zero; mul (Succ a) b =
b + (a * b).
to_int (mul (from_int 5) (from_int 6)) = 30
The result is a Peano value with 30 nested Succ wrappers; to_int
unrolls them to a host int. Tests recursive ADT with a single-arg
constructor + four mutually-defined recursive functions (no rec/and
needed since each is defined separately).
80 baseline programs total — milestone.
22 lines
389 B
OCaml
22 lines
389 B
OCaml
type peano = Zero | Succ of peano
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let rec to_int p = match p with
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| Zero -> 0
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| Succ p' -> 1 + to_int p'
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let rec from_int n =
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if n = 0 then Zero
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else Succ (from_int (n - 1))
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let rec plus a b = match a with
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| Zero -> b
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| Succ a' -> Succ (plus a' b)
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let rec mul a b = match a with
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| Zero -> Zero
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| Succ a' -> plus b (mul a' b)
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;;
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to_int (mul (from_int 5) (from_int 6))
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