diff options
Diffstat (limited to 'std/Math.bruijn')
| -rw-r--r-- | std/Math.bruijn | 30 |
1 files changed, 29 insertions, 1 deletions
diff --git a/std/Math.bruijn b/std/Math.bruijn index 156e1c8..07a9a9b 100644 --- a/std/Math.bruijn +++ b/std/Math.bruijn @@ -85,6 +85,35 @@ fac [∏ (+1) → 0 | i] ⧗ Number → Number :test ((fac (+3)) =? (+6)) (true) +# hyper factorial function +fac! [∏ (+1) → 0 | [0 ** 0]] ⧗ Number → Number + +:test ((fac! (+2)) =? (+4)) (true) +:test ((fac! (+3)) =? (+108)) (true) + +# calculates a powertower +# also: [[foldr pow (+1) (replicate 0 1)]] +powertower z [[[rec]]] ⧗ Number → Number → Number + rec =?0 case-end case-rec + case-end (+1) + case-rec 1 ** (2 1 --0) + +:test ((powertower (+2) (+1)) =? (+2)) (true) +:test ((powertower (+2) (+2)) =? (+4)) (true) +:test ((powertower (+2) (+3)) =? (+16)) (true) +:test ((powertower (+2) (+4)) =? (+65536)) (true) + +# knuth's up-arrow notation +# arrow count → base → exponent +arrow z [[[[rec]]]] ⧗ Number → Number → Number → Number + rec =?2 case-end case-rec + case-end 1 ⋅ 0 + case-rec foldr (3 --2) 1 (replicate --0 1) + +:test ((arrow (+1) (+1) (+1)) =? (+1)) (true) +:test ((arrow (+1) (+2) (+4)) =? (+16)) (true) +:test ((arrow (+2) (+2) (+4)) =? (+65536)) (true) + # fibonacci sequence # TODO: faster fib? fibs head <$> (iterate [~0 : (^0 + ~0)] ((+0) : (+1))) ⧗ (List Number) @@ -124,7 +153,6 @@ log* [z [[rec]] --0] ⧗ Number → Number :test ((log* (+65537)) =? (+5)) (true) # pascal triangle - # TODO: something is wrong in here pascal iterate [zip-with …+… ({}(+0) ++ 0) (0 ; (+0))] ({}(+1)) |