diff options
Diffstat (limited to 'std/Math.bruijn')
| -rw-r--r-- | std/Math.bruijn | 43 |
1 files changed, 19 insertions, 24 deletions
diff --git a/std/Math.bruijn b/std/Math.bruijn index 7cf0af0..7b94283 100644 --- a/std/Math.bruijn +++ b/std/Math.bruijn @@ -1,27 +1,28 @@ # MIT License, Copyright (c) 2022 Marvin Borner :import std/List . + :input std/Number . # adds all values in list -sum foldl add (+0) +sum foldl add (+0) ⧗ (List Number) → Number ∑‣ sum :test (∑((+1) : ((+2) : ((+3) : empty)))) ((+6)) # returns max value of list -lmax foldl1 max +lmax foldl1 max ⧗ (List Number) → Number :test (lmax ((+1) : ((+3) : ((+2) : empty)))) ((+3)) # returns min value of list -lmin foldl1 min +lmin foldl1 min ⧗ (List Number) → Number :test (lmin ((+2) : ((+1) : ((+0) : empty)))) ((+0)) # list from num to num -{…→…} z [[[rec]]] +{…→…} z [[[rec]]] ⧗ Number → Number → (List Number) rec (1 =? ++0) case-end case-list case-list 1 : (2 ++1 0) case-end empty @@ -29,7 +30,7 @@ lmin foldl1 min :test ({ (+0) → (+2) }) ((+0) : ((+1) : ((+2) : empty))) # equivalent of mathematical sum function -∑…→…|… z [[[[[rec]]]]] (+0) +∑…→…|… z [[[[[rec]]]]] (+0) ⧗ Number → Number → (Number → Number) → Number rec (2 =? ++1) case-end case-sum case-sum 4 (3 + (0 2)) ++2 1 0 case-end 3 @@ -37,22 +38,22 @@ lmin foldl1 min :test (∑ (+1) → (+3) | ++‣) ((+9)) # multiplies all values in list -product foldl mul (+1) +product foldl mul (+1) ⧗ (List Number) → Number Π product :test (Π ((+1) : ((+2) : ((+3) : empty)))) ((+6)) # equivalent of mathematical product function -∏…→…|… z [[[[[rec]]]]] (+1) +∏…→…|… z [[[[[rec]]]]] (+1) ⧗ Number → Number → (Number → Number) → Number rec (2 =? ++1) case-end case-sum - case-sum 4 (3 * (0 2)) ++2 1 0 + case-sum 4 (3 ⋅ (0 2)) ++2 1 0 case-end 3 :test (∏ (+1) → (+3) | ++‣) ((+24)) # greatest common divisor -gcd z [[[(1 =? 0) case-eq ((1 >? 0) case-gre case-les)]]] +gcd z [[[(1 =? 0) case-eq ((1 >? 0) case-gre case-les)]]] ⧗ Number → Number → Number case-eq 1 case-gre 2 (1 - 0) 0 case-les 2 1 (0 - 1) @@ -62,40 +63,33 @@ gcd z [[[(1 =? 0) case-eq ((1 >? 0) case-gre case-les)]]] :test ((gcd (+3) (+8)) =? ((+1))) (true) # power function -pow […!!… (iterate (…*… 0) (+1))] +pow […!!… (iterate (…⋅… 0) (+1))] ⧗ Number → Number → Number …**… pow :test (((+2) ** (+3)) =? ((+8))) (true) -# power function using ternary exponentiation -# a 1 → b 0 -# pow' z [[[rec]]] -# rec =?0 case-end case-pow -# case-pow =?(lst 0) (mult ⊩r) ((mult ⊩r) ⋅ 1) -# mult [0 ⋅ 0 ⋅ 0] -# r 2 1 /³0 -# case-end (+1) -pow' z [[[rec]]] +# power function using ternary exponentiation (TODO: slow..) +pow' z [[[rec]]] ⧗ Number → Number → Number rec =?0 case-end case-pow case-pow =?(lst 0) (r ⋅ r ⋅ r) (r ⋅ r ⋅ r ⋅ 1) r 2 1 /³0 case-end (+1) # prime number sequence -primes nub ((…≠?… (+1)) ∘∘ gcd) (iterate ++‣ (+2)) +primes nub ((…≠?… (+1)) ∘∘ gcd) (iterate ++‣ (+2)) ⧗ (List Number) # factorial function # TODO: faster fac? -fac [∏ (+1) → 0 | i] +fac [∏ (+1) → 0 | i] ⧗ Number → Number :test ((fac (+3)) =? (+6)) (true) # fibonacci sequence # TODO: faster fib? -fibs fst <$> (iterate [~0 : (^0 + ~0)] ((+0) : (+1))) +fibs head <$> (iterate [~0 : (^0 + ~0)] ((+0) : (+1))) ⧗ (List Number) -fib [fibs !! ++0] +fib [fibs !! ++0] ⧗ Number :test (fib (+5)) ((+8)) @@ -106,7 +100,8 @@ pascal iterate [zip-with …+… ({ (+0) } ++ 0) (0 ; (+0))] ({ (+1) }) # π # q 3, r 2, t 1, i 0 # translation of unbounded spigot algorithm by Jeremy Gibbons -π g (+1) (+180) (+60) (+2) +# TODO: Fix/faster +π g (+1) (+180) (+60) (+2) ⧗ (List Number) g y [[[[[calc]]]]] calc b : (4 q r t i) a ↑⁰(↑⁺0 ⋅ (↑⁰0 + (+2))) |