diff options
Diffstat (limited to 'std/Number.bruijn')
| -rw-r--r-- | std/Number.bruijn | 178 |
1 files changed, 89 insertions, 89 deletions
diff --git a/std/Number.bruijn b/std/Number.bruijn index bd54232..de56762 100644 --- a/std/Number.bruijn +++ b/std/Number.bruijn @@ -1,5 +1,5 @@ # MIT License, Copyright (c) 2022 Marvin Borner -# According to works of T.Æ. Mogensen +# Heavily inspired by the works of T.Æ. Mogensen (see refs in README) :import std/Combinator . @@ -11,29 +11,29 @@ trit-neg [[[2]]] # returns whether a trit is negative -trit-neg? [0 T F F] +trit-neg? [0 true false false] # positive trit indicating coeffecient of (+1) trit-pos [[[1]]] # returns whether a trit is positive -trit-pos? [0 F T F] +trit-pos? [0 false true false] # zero trit indicating coeffecient of 0 trit-zero [[[0]]] # returns whether a trit is zero -trit-zero? [0 F F T] - -:test (trit-neg? trit-neg) (T) -:test (trit-neg? trit-pos) (F) -:test (trit-neg? trit-zero) (F) -:test (trit-pos? trit-neg) (F) -:test (trit-pos? trit-pos) (T) -:test (trit-pos? trit-zero) (F) -:test (trit-zero? trit-neg) (F) -:test (trit-zero? trit-pos) (F) -:test (trit-zero? trit-zero) (T) +trit-zero? [0 false false true] + +:test (trit-neg? trit-neg) (true) +:test (trit-neg? trit-pos) (false) +:test (trit-neg? trit-zero) (false) +:test (trit-pos? trit-neg) (false) +:test (trit-pos? trit-pos) (true) +:test (trit-pos? trit-zero) (false) +:test (trit-zero? trit-neg) (false) +:test (trit-zero? trit-pos) (false) +:test (trit-zero? trit-zero) (true) # shifts a negative trit into a balanced ternary number up-neg [[[[[2 (4 3 2 1 0)]]]]] @@ -71,10 +71,10 @@ up [[[[[[5 2 1 0 (4 3 2 1 0)]]]]]] # shifts the least significant trit out - basically div by 3 down [snd (0 z neg pos zero)] - z pair (+0) (+0) - neg [0 [[pair (^<1) 1]]] - pos [0 [[pair (^>1) 1]]] - zero [0 [[pair (^=1) 1]]] + z (+0) : (+0) + neg [0 [[(^<1) : 1]]] + pos [0 [[(^>1) : 1]]] + zero [0 [[(^=1) : 1]]] # negates a balanced ternary number negate [[[[[4 3 1 2 0]]]]] @@ -87,19 +87,19 @@ negate [[[[[4 3 1 2 0]]]]] # converts a balanced ternary number to a list of trits list! [0 z neg pos zero] - z F - neg [[pair trit-neg 1]] - pos [[pair trit-pos 1]] - zero [[pair trit-zero 1]] + z true + neg [[trit-neg : 1]] + pos [[trit-pos : 1]] + zero [[trit-zero : 1]] # TODO: Tests! # strips leading 0s from balanced ternary number strip [fst (0 z neg pos zero)] - z pair (+0) T - neg [0 [[pair (^<1) F]]] - pos [0 [[pair (^>1) F]]] - zero [0 [[pair (0 (+0) (^=1)) 0]]] + z (+0) : true + neg [0 [[(^<1) : false]]] + pos [0 [[(^>1) : false]]] + zero [0 [[(0 (+0) (^=1)) : 0]]] ~( strip @@ -133,30 +133,30 @@ negative? [trit-neg? (mst 0)] <?( negative? -:test (<?(+0)) (F) -:test (<?(-1)) (T) -:test (<?(+1)) (F) -:test (<?(+42)) (F) +:test (<?(+0)) (false) +:test (<?(-1)) (true) +:test (<?(+1)) (false) +:test (<?(+42)) (false) # returns whether balanced ternary number is positive positive? [trit-pos? (mst 0)] >?( positive? -:test (>?(+0)) (F) -:test (>?(-1)) (F) -:test (>?(+1)) (T) -:test (>?(+42)) (T) +:test (>?(+0)) (false) +:test (>?(-1)) (false) +:test (>?(+1)) (true) +:test (>?(+42)) (true) # checks whether balanced ternary number is zero -zero? [0 T [F] [F] I] +zero? [0 true [false] [false] I] =?( zero? -:test (=?(+0)) (T) -:test (=?(-1)) (F) -:test (=?(+1)) (F) -:test (=?(+42)) (F) +:test (=?(+0)) (true) +:test (=?(-1)) (false) +:test (=?(+1)) (false) +:test (=?(+42)) (false) # converts the normal balanced ternary representation into abstract # -> the abstract representation is used in add/sub/mul @@ -183,21 +183,21 @@ normal! ω rec # -> ignores leading 0s! eq? [[abs 1 (abstract! 0)]] z [zero? (normal! 0)] - neg [[0 F [2 0] [F] [F]]] - pos [[0 F [F] [2 0] [F]]] - zero [[0 (1 0) [F] [F] [2 0]]] + neg [[0 false [2 0] [false] [false]]] + pos [[0 false [false] [2 0] [false]]] + zero [[0 (1 0) [false] [false] [2 0]]] abs [0 z neg pos zero] (=?) eq? -:test ((-42) =? (-42)) (T) -:test ((-1) =? (-1)) (T) -:test ((-1) =? (+0)) (F) -:test ((+0) =? (+0)) (T) -:test ((+1) =? (+0)) (F) -:test ((+1) =? (+1)) (T) -:test ((+42) =? (+42)) (T) -:test ([[[[(1 (0 (0 (0 (0 3)))))]]]] =? (+1)) (T) +:test ((-42) =? (-42)) (true) +:test ((-1) =? (-1)) (true) +:test ((-1) =? (+0)) (false) +:test ((+0) =? (+0)) (true) +:test ((+1) =? (+0)) (false) +:test ((+1) =? (+1)) (true) +:test ((+42) =? (+42)) (true) +:test ([[[[(1 (0 (0 (0 (0 3)))))]]]] =? (+1)) (true) # I believe Mogensen's Paper has an error in its inc/dec/add/mul/eq definitions. # They use 3 instead of 2 abstractions in the functions, also we use switched @@ -206,39 +206,39 @@ eq? [[abs 1 (abstract! 0)]] # adds (+1) to a balanced ternary number (can introduce leading 0s) inc [snd (0 z neg pos zero)] - z pair (+0) (+1) - neg [0 [[pair (^<1) (^=1)]]] - zero [0 [[pair (^=1) (^>1)]]] - pos [0 [[pair (^>1) (^<0)]]] + z (+0) : (+1) + neg [0 [[(^<1) : (^=1)]]] + zero [0 [[(^=1) : (^>1)]]] + pos [0 [[(^>1) : (^<0)]]] ++( inc # adds (+1) to a balanced ternary number and strips leading 0s -ssinc [~(++0)] +ssinc strip . inc -:test ((++(-42)) =? (-41)) (T) -:test ((++(-1)) =? (+0)) (T) -:test ((++(+0)) =? (+1)) (T) -:test ((++(++(++(++(++(+0)))))) =? (+5)) (T) -:test ((++(+42)) =? (+43)) (T) +:test ((++(-42)) =? (-41)) (true) +:test ((++(-1)) =? (+0)) (true) +:test ((++(+0)) =? (+1)) (true) +:test ((++(++(++(++(++(+0)))))) =? (+5)) (true) +:test ((++(+42)) =? (+43)) (true) # subs (+1) from a balanced ternary number (can introduce leading 0s) dec [snd (0 dec-z dec-neg dec-pos dec-zero)] - dec-z pair (+0) (-1) - dec-neg [0 [[pair (^<1) (^>0)]]] - dec-zero [0 [[pair (^=1) (^<1)]]] - dec-pos [0 [[pair (^>1) (^=1)]]] + dec-z (+0) : (-1) + dec-neg [0 [[(^<1) : (^>0)]]] + dec-zero [0 [[(^=1) : (^<1)]]] + dec-pos [0 [[(^>1) : (^=1)]]] --( dec # subs (+1) from a balanced ternary number and strips leading 0s -ssub [~(--0)] +sdec strip . dec -:test ((--(-42)) =? (-43)) (T) -:test ((--(+0)) =? (-1)) (T) -:test ((--(--(--(--(--(+5)))))) =? (+0)) (T) -:test ((--(+1)) =? (+0)) (T) -:test ((--(+42)) =? (+41)) (T) +:test ((--(-42)) =? (-43)) (true) +:test ((--(+0)) =? (-1)) (true) +:test ((--(--(--(--(--(+5)))))) =? (+0)) (true) +:test ((--(+1)) =? (+0)) (true) +:test ((--(+42)) =? (+41)) (true) # adds two balanced ternary numbers (can introduce leading 0s) add [[abs 1 (abstract! 0)]] @@ -257,14 +257,14 @@ add [[abs 1 (abstract! 0)]] (+) add # adds two balanced ternary numbers and strips leading 0s -sadd [[~(1 + 0)]] +sadd strip ... add -:test (((-42) + (-1)) =? (-43)) (T) -:test (((-5) + (+6)) =? (+1)) (T) -:test (((-1) + (+0)) =? (-1)) (T) -:test (((+0) + (+0)) =? (+0)) (T) -:test (((+1) + (+2)) =? (+3)) (T) -:test (((+42) + (+1)) =? (+43)) (T) +:test (((-42) + (-1)) =? (-43)) (true) +:test (((-5) + (+6)) =? (+1)) (true) +:test (((-1) + (+0)) =? (-1)) (true) +:test (((+0) + (+0)) =? (+0)) (true) +:test (((+1) + (+2)) =? (+3)) (true) +:test (((+42) + (+1)) =? (+43)) (true) # subs two balanced ternary numbers (can introduce leading 0s) sub [[1 + -0]] @@ -272,14 +272,14 @@ sub [[1 + -0]] (-) sub # subs two balanced ternary numbers and strips leading 0s -ssub [[~(1 - 0)]] +ssub strip ... sub -:test (((-42) - (-1)) =? (-41)) (T) -:test (((-5) - (+6)) =? (-11)) (T) -:test (((-1) - (+0)) =? (-1)) (T) -:test (((+0) - (+0)) =? (+0)) (T) -:test (((+1) - (+2)) =? (-1)) (T) -:test (((+42) - (+1)) =? (+41)) (T) +:test (((-42) - (-1)) =? (-41)) (true) +:test (((-5) - (+6)) =? (-11)) (true) +:test (((-1) - (+0)) =? (-1)) (true) +:test (((+0) - (+0)) =? (+0)) (true) +:test (((+1) - (+2)) =? (-1)) (true) +:test (((+42) - (+1)) =? (+41)) (true) # returns whether number is greater than other number gre? [[negative? (sub 0 1)]] @@ -299,9 +299,9 @@ mul [[1 (+0) neg pos zero]] (*) mul -smul [[strip (mul 1 0)]] +smul strip ... mul -:test (((+42) * (+0)) =? (+0)) (T) -:test (((-1) * (+42)) =? (-42)) (T) -:test (((+3) * (+11)) =? (+33)) (T) -:test (((+42) * (-4)) =? (-168)) (T) +:test (((+42) * (+0)) =? (+0)) (true) +:test (((-1) * (+42)) =? (-42)) (true) +:test (((+3) * (+11)) =? (+33)) (true) +:test (((+42) * (-4)) =? (-168)) (true) |