# Church numerals

### Traditional subs and sigils

```perl
constant $zero  = sub (Code $f) {
                  sub (     $x) { $x }}

constant $succ  = sub (Code $n) {
                  sub (Code $f) {
                  sub (     $x) { $f($n($f)($x)) }}}

constant $add   = sub (Code $n) {
                  sub (Code $m) {
                  sub (Code $f) {
                  sub (     $x) { $m($f)($n($f)($x)) }}}}

constant $mult  = sub (Code $n) {
                  sub (Code $m) {
                  sub (Code $f) {
                  sub (     $x) { $m($n($f))($x) }}}}

constant $power = sub (Code $b) {
                  sub (Code $e) { $e($b) }}

sub to_int (Code $f) {
    sub countup (Int $i) { $i + 1 }
    return $f(&countup).(0)
}

sub from_int (Int $x) {
    multi sub countdown (     0) { $zero }
    multi sub countdown (Int $i) { $succ( countdown($i - 1) ) }
    return countdown($x);
}

constant $three = $succ($succ($succ($zero)));
constant $four  = from_int(4);

say map &to_int,
    $add(   $three )( $four  ),
    $mult(  $three )( $four  ),
    $power( $four  )( $three ),
    $power( $three )( $four  ),
;
```

### Arrow subs without sigils

```perl
my \zero  = -> \f {                 -> \x { x               }}
my \succ  = -> \n {         -> \f { -> \x { f.(n.(f)(x))    }}}
my \add   = -> \n { -> \m { -> \f { -> \x { m.(f)(n.(f)(x)) }}}}
my \mult  = -> \n { -> \m { -> \f { -> \x { m.(n.(f))(x)    }}}}
my \power = -> \b {                 -> \e { e.(b)           }}

my \to_int   = -> \f { f.( -> \i { i + 1 } ).(0) }
my \from_int = -> \i { i == 0 ?? zero !! succ.( &?BLOCK(i - 1) ) }

my \three = succ.(succ.(succ.(zero)));
my \four  = from_int.(4);

say map -> \f { to_int.(f) },
    add.(   three )( four  ),
    mult.(  three )( four  ),
    power.( four  )( three ),
    power.( three )( four  ),
;
```

#### Output:

```
(7 12 64 81)
```
