diff options
| -rw-r--r-- | samples/rosetta/special_factorial.bruijn | 40 | ||||
| -rw-r--r-- | std/Math.bruijn | 31 |
2 files changed, 67 insertions, 4 deletions
diff --git a/samples/rosetta/special_factorial.bruijn b/samples/rosetta/special_factorial.bruijn new file mode 100644 index 0000000..588a95f --- /dev/null +++ b/samples/rosetta/special_factorial.bruijn @@ -0,0 +1,40 @@ +:import std/Combinator . +:import std/List . +:import std/Math . + +factorial [∏ (+1) → 0 | [0]] + +superfactorial [∏ (+1) → 0 | factorial] + +hyperfactorial [∏ (+1) → 0 | [0 ** 0]] + +alternating-factorial y [[=?0 0 ((factorial 0) - (1 --0))]] + +exponential-factorial y [[=?0 0 (0 ** (1 --0))]] + +:test ((factorial (+4)) =? (+24)) ([[1]]) +:test ((superfactorial (+4)) =? (+288)) ([[1]]) +:test ((hyperfactorial (+4)) =? (+27648)) ([[1]]) +:test ((alternating-factorial (+3)) =? (+5)) ([[1]]) +:test ((exponential-factorial (+4)) =? (+262144)) ([[1]]) + +invfac y [[[compare-case 1 (2 ++1 0) (-1) 0 (∏ (+0) → --1 | ++‣)]]] (+0) + +:test ((invfac (+1)) =? (+0)) ([[1]]) +:test ((invfac (+2)) =? (+2)) ([[1]]) +:test ((invfac (+6)) =? (+3)) ([[1]]) +:test ((invfac (+24)) =? (+4)) ([[1]]) +:test ((invfac (+120)) =? (+5)) ([[1]]) +:test ((invfac (+720)) =? (+6)) ([[1]]) +:test ((invfac (+5040)) =? (+7)) ([[1]]) +:test ((invfac (+40320)) =? (+8)) ([[1]]) +:test ((invfac (+362880)) =? (+9)) ([[1]]) +:test ((invfac (+3628800)) =? (+10)) ([[1]]) +:test ((invfac (+119)) =? (-1)) ([[1]]) + +seq-a [((superfactorial 0) : ((hyperfactorial 0) : {}(alternating-factorial 0)))] <$> (iterate ++‣ (+0)) + +seq-b exponential-factorial <$> (iterate ++‣ (+0)) + +# return first 10/4 elements of both sequences +main [(take (+10) seq-a) : {}(take (+5) seq-b)] diff --git a/std/Math.bruijn b/std/Math.bruijn index ec358fe..cfea07c 100644 --- a/std/Math.bruijn +++ b/std/Math.bruijn @@ -81,16 +81,39 @@ pow* z [[[rec]]] ⧗ Number → Number → Number primes nub ((…≠?… (+1)) ∘∘ gcd) (iterate ++‣ (+2)) ⧗ (List Number) # factorial function -# TODO: faster fac? fac [∏ (+1) → 0 | i] ⧗ Number → Number :test ((fac (+3)) =? (+6)) (true) +# super factorial function +superfac [∏ (+1) → 0 | fac] ⧗ Number → Number + +:test ((superfac (+4)) =? (+288)) ([[1]]) + # hyper factorial function -fac! [∏ (+1) → 0 | [0 ** 0]] ⧗ Number → Number +hyperfac [∏ (+1) → 0 | [0 ** 0]] ⧗ Number → Number + +:test ((hyperfac (+2)) =? (+4)) (true) +:test ((hyperfac (+3)) =? (+108)) (true) +:test ((hyperfac (+4)) =? (+27648)) ([[1]]) + +# alternate factorial function +altfac y [[=?0 0 ((fac 0) - (1 --0))]] + +:test ((altfac (+3)) =? (+5)) ([[1]]) + +# exponential factorial function +expfac y [[(0 =? (+1)) 0 (0 ** (1 --0))]] + +:test ((expfac (+4)) =? (+262144)) ([[1]]) + +# inverse factorial function +invfac y [[[compare-case 1 (2 ++1 0) (-1) 0 (∏ (+0) → --1 | ++‣)]]] (+0) -:test ((fac! (+2)) =? (+4)) (true) -:test ((fac! (+3)) =? (+108)) (true) +:test ((invfac (+1)) =? (+0)) ([[1]]) +:test ((invfac (+2)) =? (+2)) ([[1]]) +:test ((invfac (+120)) =? (+5)) ([[1]]) +:test ((invfac (+119)) =? (-1)) ([[1]]) # calculates a powertower # also: [[foldr pow (+1) (replicate 0 1)]] |