diff options
Diffstat (limited to 'std')
| -rw-r--r-- | std/List.bruijn | 9 | ||||
| -rw-r--r-- | std/Math.bruijn | 42 | ||||
| -rw-r--r-- | std/Meta.bruijn | 2 | ||||
| -rw-r--r-- | std/Number/Binary.bruijn | 9 | ||||
| -rw-r--r-- | std/Number/Bruijn.bruijn | 2 | ||||
| -rw-r--r-- | std/Number/Ternary.bruijn | 15 | ||||
| -rw-r--r-- | std/Number/Unary.bruijn | 2 | ||||
| -rw-r--r-- | std/String.bruijn | 53 |
8 files changed, 105 insertions, 29 deletions
diff --git a/std/List.bruijn b/std/List.bruijn index d355ea9..a240e3d 100644 --- a/std/List.bruijn +++ b/std/List.bruijn @@ -420,6 +420,15 @@ eq? ⋀?‣ ∘∘∘ zip-with ⧗ (a → a → Boolean) → (List a) → Boolea :test (eq? …=?… ((+1) : {}(+2)) ((+2) : {}(+2))) (false) :test (eq? …=?… empty empty) (true) +# returns eq, lt, gt depending on comparison of two lists and comparison function +compare-case z [[[[[[[rec]]]]]]] ⧗ (a → a → Boolean) → c → d → e → (List a) → (List a) → Boolean + rec ∅?1 (∅?0 4 3) (∅?0 2 go) + go [=?0 (7 6 5 4 3 ~2 ~1) 0] (5 ^1 ^0) + +# returns 1 if a>b, -1 if a<b and 0 if a=b +# also: spaceship operator +compare [compare-case 0 (+0) (+1) (-1)] ⧗ (a → a → Boolean) → Binary → Binary → Number + # returns true if list is prefix of other list prefix? z [[[[rec]]]] ⧗ (a → a → Boolean) → (List a) → (List a) → Boolean rec ∅?1 true (∅?0 false go) diff --git a/std/Math.bruijn b/std/Math.bruijn index 62d04e0..78e3006 100644 --- a/std/Math.bruijn +++ b/std/Math.bruijn @@ -3,14 +3,14 @@ :input std/Number -:import std/List . +:import std/List L # adds all values in list -sum foldl add (+0) ⧗ (List Number) → Number +sum L.foldl add (+0) ⧗ (List Number) → Number ∑‣ sum -:test (∑((+1) : ((+2) : {}(+3)))) ((+6)) +:test (∑((+1) : ((+2) : L.{}(+3)))) ((+6)) # digit sum of all values digit-sum sum ∘ number→list ⧗ Number → Number @@ -20,48 +20,48 @@ digit-sum sum ∘ number→list ⧗ Number → Number :test ((digit-sum (+19)) =? (+10)) (true) # returns max value of list -lmax foldl1 max ⧗ (List Number) → Number +lmax L.foldl1 max ⧗ (List Number) → Number -:test (lmax ((+1) : ((+3) : {}(+2)))) ((+3)) +:test (lmax ((+1) : ((+3) : L.{}(+2)))) ((+3)) # returns min value of list -lmin foldl1 min ⧗ (List Number) → Number +lmin L.foldl1 min ⧗ (List Number) → Number -:test (lmin ((+2) : ((+1) : {}(+0)))) ((+0)) +:test (lmin ((+2) : ((+1) : L.{}(+0)))) ((+0)) # list from num to num {…→…} z [[[rec]]] ⧗ Number → Number → (List Number) - rec (1 =? ++0) case-end case-list + rec 1 =? ++0 case-end case-list case-list 1 : (2 ++1 0) - case-end empty + case-end L.empty -:test ({ (+0) → (+2) }) ((+0) : ((+1) : {}(+2))) +:test ({ (+0) → (+2) }) ((+0) : ((+1) : L.{}(+2))) # equivalent of mathematical sum function ∑…→…|… z [[[[[rec]]]]] (+0) ⧗ Number → Number → (Number → Number) → Number - rec (2 =? ++1) case-end case-sum + rec 2 =? ++1 case-end case-sum case-sum 4 (3 + (0 2)) ++2 1 0 case-end 3 :test (∑ (+1) → (+3) | ++‣) ((+9)) # multiplies all values in list -product foldl mul (+1) ⧗ (List Number) → Number +product L.foldl mul (+1) ⧗ (List Number) → Number ∏‣ product -:test (∏((+1) : ((+2) : {}(+3)))) ((+6)) +:test (∏((+1) : ((+2) : L.{}(+3)))) ((+6)) # equivalent of mathematical product function ∏…→…|… z [[[[[rec]]]]] (+1) ⧗ Number → Number → (Number → Number) → Number - rec (2 =? ++1) case-end case-sum + rec 2 =? ++1 case-end case-sum 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)]]] ⧗ Number → Number → Number +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) @@ -136,7 +136,7 @@ powertower z [[[rec]]] ⧗ Number → Number → Number 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) + case-rec L.foldr (3 --2) 1 (L.replicate --0 1) :test ((arrow (+1) (+1) (+1)) =? (+1)) (true) :test ((arrow (+1) (+2) (+4)) =? (+16)) (true) @@ -144,9 +144,9 @@ arrow z [[[[rec]]]] ⧗ Number → Number → Number → Number # fibonacci sequence # TODO: faster fib? -fibs head <$> (iterate &[[0 : (1 + 0)]] ((+0) : (+1))) ⧗ (List Number) +fibs L.map L.head (L.iterate &[[0 : (1 + 0)]] ((+0) : (+1))) ⧗ (List Number) -fib [fibs !! ++0] ⧗ Number +fib [L.index ++0 fibs] ⧗ Number :test (fib (+5)) ((+8)) @@ -194,7 +194,7 @@ log* [z [[rec]] --0] ⧗ Number → Number # pascal triangle # TODO: something is wrong in here -pascal iterate [zip-with …+… ({}(+0) ++ 0) (0 ; (+0))] ({}(+1)) +pascal L.iterate [L.zip-with …+… (L.{}(+0) ++ 0) (0 ; (+0))] (L.{}(+1)) # characteristic prime sequence by Tromp characteristic-primes ki : (ki : (sieve s0)) ⧗ (List Bool) @@ -204,10 +204,10 @@ characteristic-primes ki : (ki : (sieve s0)) ⧗ (List Bool) s0 [[[ki : (0 2)]]] # prime number sequence -primes map fst (filter snd (zip (iterate ++‣ (+0)) characteristic-primes)) ⧗ (List Number) +primes L.map fst (L.filter snd (L.zip (L.iterate ++‣ (+0)) characteristic-primes)) ⧗ (List Number) # slower but cooler prime number sequence -primes* nub ((…≠?… (+1)) ∘∘ gcd) (iterate ++‣ (+2)) ⧗ (List Number) +primes* L.nub ((…≠?… (+1)) ∘∘ gcd) (L.iterate ++‣ (+2)) ⧗ (List Number) # π as a list of decimal digits # translation of unbounded spigot algorithm by Jeremy Gibbons diff --git a/std/Meta.bruijn b/std/Meta.bruijn index e9ddea0..bf55b86 100644 --- a/std/Meta.bruijn +++ b/std/Meta.bruijn @@ -3,8 +3,8 @@ :import std/Logic . :import std/Combinator . -:import std/Number/Unary . :import std/List . +:import std/Number/Unary . :import std/Number/Pairing . :import std/Number/Conversion . :import std/Pair P diff --git a/std/Number/Binary.bruijn b/std/Number/Binary.bruijn index 77ce09c..064889d 100644 --- a/std/Number/Binary.bruijn +++ b/std/Number/Binary.bruijn @@ -359,7 +359,7 @@ geq? \leq? ⧗ Binary → Binary → Boolean :test ((+2b) ≥? (+2b)) (true) :test ((+3b) ≥? (+2b)) (true) -# returns eq, lt, gt depending on comparison of two numbers +# returns eq, gt, lt depending on comparison of two numbers # TODO: remove ternary conversion compare-case [[[(T.compare-case 2 1 0) ⋔ binary→ternary]]] ⧗ a → b → c → Binary → Binary → d @@ -367,12 +367,15 @@ compare-case [[[(T.compare-case 2 1 0) ⋔ binary→ternary]]] ⧗ a → b → c # also: spaceship operator compare compare-case (+0) (+1) (-1) ⧗ Binary → Binary → Number +…<=>… compare + +<=>‣ &compare + :test (compare (+2b) (+2b)) ((+0)) :test (compare (+2b) (+1b)) ((+1)) :test (compare (+1b) (+2b)) ((-1)) -…<=>… compare - +# prefix for comparing functions # returns max number of two max [[(1 ≤? 0) 0 1]] ⧗ Binary → Binary → Binary diff --git a/std/Number/Bruijn.bruijn b/std/Number/Bruijn.bruijn index 744d9a1..131a1a3 100644 --- a/std/Number/Bruijn.bruijn +++ b/std/Number/Bruijn.bruijn @@ -4,8 +4,6 @@ # Wadsworth, Christopher. "Some unusual λ-calculus numeral systems." # very sad indeed -:import std/Combinator . - # increments De Bruijn numeral inc [[[2 1]]] diff --git a/std/Number/Ternary.bruijn b/std/Number/Ternary.bruijn index 8cf891f..5e93c66 100644 --- a/std/Number/Ternary.bruijn +++ b/std/Number/Ternary.bruijn @@ -348,7 +348,7 @@ geq? \leq? ⧗ Number → Number → Boolean :test ((+2) ≥? (+2)) (true) :test ((+3) ≥? (+2)) (true) -# returns eq, lt, gt depending on comparison of two numbers +# returns eq, gt, lt depending on comparison of two numbers compare-case [[[[[go (1 - 0)]]]]] ⧗ a → b → c → Number → Number → d go [=?0 5 (>?0 4 3)] @@ -356,11 +356,22 @@ compare-case [[[[[go (1 - 0)]]]]] ⧗ a → b → c → Number → Number → d # also: spaceship operator compare compare-case (+0) (+1) (-1) ⧗ Number → Number → Number +…<=>… compare + +<=>‣ &compare + :test (compare (+2) (+2)) ((+0)) :test (compare (+2) (+1)) ((+1)) :test (compare (+1) (+2)) ((-1)) -…<=>… compare +# returns true if comparison result is equal (EQ) +c-eq? eq? (+0) ⧗ Number → Number + +# returns true if comparison result is less than (LT) +c-les? eq? (-1) ⧗ Number → Number + +# returns true if comparison result is greater than (GT) +c-gre? eq? (+1) ⧗ Number → Number # negates a balanced ternary number if <0 abs [<?0 -0 0] ⧗ Number → Number diff --git a/std/Number/Unary.bruijn b/std/Number/Unary.bruijn index 81af007..5041614 100644 --- a/std/Number/Unary.bruijn +++ b/std/Number/Unary.bruijn @@ -136,6 +136,8 @@ compare compare-case (+0) (+1) (-1) ⧗ Unary → Unary → Number …<=>… compare +<=>‣ &compare + # muls two unary numbers mul …∘… ⧗ Unary → Unary → Unary diff --git a/std/String.bruijn b/std/String.bruijn index 645eda3..e1f4f4b 100644 --- a/std/String.bruijn +++ b/std/String.bruijn @@ -17,6 +17,59 @@ eq? eq? B.eq? ⧗ String → String → Boolean # prefix for comparing functions ?‣ &eq? +# returns eq, gt, lt depending on comparison of two numbers +compare-case B.<=>compare-case ⧗ a → b → c → String → String → d + +# returns 1 if a>b, -1 if a<b and 0 if a=b +# also: spaceship operator +compare compare-case (+0) (+1) (-1) ⧗ String → String → Number + +…<=>… compare + +<=>‣ &compare + +:test (compare "2" "2") ((+0)) +:test (compare "2" "1") ((+1)) +:test (compare "1" "2") ((-1)) +:test (compare "12" "1") ((-1)) +:test (compare "1" "12") ((+1)) + +# returns true if string is lexically less than other string +les? c-les? ∘∘ compare ⧗ String → String → Boolean + +…<?… les? + +:test ("1" <? "2") (true) +:test ("2" <? "2") (false) +:test ("3" <? "2") (false) + +# returns true if string is lexically greater than other string +gre? \les? ⧗ String → String → Boolean + +…>?… gre? + +:test ("1" >? "2") (false) +:test ("2" >? "2") (false) +:test ("3" >? "2") (true) + +# returns true if string is lexically less than or equal to other string +leq? not! ∘∘ gre? ⧗ String → String → Boolean + +…≤?… leq? + +:test ("1" ≤? "2") (true) +:test ("2" ≤? "2") (true) +:test ("3" ≤? "2") (false) + +# returns true if number is greater than or equal to other string +geq? \leq? ⧗ String → String → Boolean + +…≥?… geq? + +:test ("1" ≥? "2") (false) +:test ("2" ≥? "2") (true) +:test ("3" ≥? "2") (true) + # returns true if character is part of a string in? B.?in? ⧗ Char → String → Boolean |