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binop.t
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$ cat >nat.ny <<EOF
> def ℕ : Type := data [ zero. | suc. (_ : ℕ) ]
> def O : ℕ := zero.
> def S : ℕ → ℕ := n ↦ suc. n
> def plus : ℕ → ℕ → ℕ := m n ↦ match n [ | zero. ↦ m | suc. n ↦ suc. (plus m n) ]
> def times : ℕ → ℕ → ℕ := m n ↦ match n [ | zero. ↦ zero. | suc. n ↦ plus (times m n) m ]
> notation 0 plus : m "+" n … ≔ plus m n
> notation 1 times : m "*" n … ≔ times m n
> echo (S O) + (S (S O)) + (S (S (S O)))
> echo S (S O) * S (S O) + S (S O)
> echo S (S O) * (S (S O) + S (S O))
> def six : ℕ := 6
> axiom m : ℕ
> axiom n : ℕ
> echo m+n
> echo m+n*n
> echo m*(m+n*n)
> echo m + suc. n
> echo (m+n)*(m+n)
> echo n + n + n + n + n + n + n + n + n + n + n + n + n + n + n + n + n + n + n + n + n + n + n + n + n + n + n + n + n + n + n + n + n + n + n + n
> echo n + n * n + n * n * n + n * n * n * n + n + n * n * n * n * n * n * n + n * n + n * n * n + n * n * n * n + n + n * n * n * n * n * n * n
$ narya -v nat.ny
￫ info[I0000]
￮ constant ℕ defined
￫ info[I0000]
￮ constant O defined
￫ info[I0000]
￮ constant S defined
￫ info[I0000]
￮ constant plus defined
￫ info[I0000]
￮ constant times defined
￫ info[I0002]
￮ notation plus defined
￫ info[I0002]
￮ notation times defined
6
: ℕ
6
: ℕ
8
: ℕ
￫ info[I0000]
￮ constant six defined
￫ info[I0001]
￮ axiom m assumed
￫ info[I0001]
￮ axiom n assumed
m + n
: ℕ
m + n * n
: ℕ
m * (m + n * n)
: ℕ
suc. (m + n)
: ℕ
(m + n) * (m + n)
: ℕ
n
+ n
+ n
+ n
+ n
+ n
+ n
+ n
+ n
+ n
+ n
+ n
+ n
+ n
+ n
+ n
+ n
+ n
+ n
+ n
+ n
+ n
+ n
+ n
+ n
+ n
+ n
+ n
+ n
+ n
+ n
+ n
+ n
+ n
+ n
+ n
: ℕ
n
+ n * n
+ n * n * n
+ n * n * n * n
+ n
+ n * n * n * n * n * n * n
+ n * n
+ n * n * n
+ n * n * n * n
+ n
+ n * n * n * n * n * n * n
: ℕ