7 files changed, 137 insertions, 10 deletions
diff --git a/std/Combinator.bruijn b/std/Combinator.bruijn
index 7199c77..470c574 100644
--- a/std/Combinator.bruijn
+++ b/std/Combinator.bruijn
@@ -118,9 +118,11 @@ o [[0 (1 0)]] ⧗ ((a → b) → a) → (a → b) → b
 # alternative name: starling prime: s'
 φ [[[[3 (2 0) (1 0)]]]] ⧗ (b → c → d) → (a → b) → (a → c) → a → d
 
-# psi combinator: on
+# psi combinator: on, (f ⋔ g) x y = f (g x) (g y)
 ψ [[[[3 (2 1) (2 0)]]]] ⧗ (b → b → c) → (a → b) → a → a → c
 
+…⋔… ψ
+
 ψ* [[[[[4 3 (2 1) (2 0)]]]]] ⧗ (c → b → b → d) → c → (a → b) → a → a → d
 
 # queer bird combinator: reverse function composition
diff --git a/std/List.bruijn b/std/List.bruijn
index 0d0a038..fe4b6f9 100644
--- a/std/List.bruijn
+++ b/std/List.bruijn
@@ -135,6 +135,18 @@ foldr1 [[foldl 1 ^0 ~0]] ⧗ (a → a → a) → (List a) → a
 # applies or to all list elements
 lor? foldr or? false ⧗ (List Boolean) → Boolean
 
+# largest element by compare function
+max-by [foldl1 max'] ⧗ (a → a → Number) → (List a) → a
+	max' [[>?(2 1 0) 1 0]]
+
+:test (max-by (compare ⋔ length) ("abc" : ("ab" : {}"abcd"))) ("abcd")
+
+# smallest element by compare function
+min-by [foldl1 min'] ⧗ (a → a → Number) → (List a) → a
+	min' [[<?(2 1 0) 1 0]]
+
+:test (min-by (compare ⋔ length) ("abc" : ("ab" : {}"abcd"))) ("ab")
+
 ⋁?‣ lor?
 
 :test (⋁?(true : {}true)) (true)
@@ -157,11 +169,8 @@ reverse foldl \cons empty ⧗ (List a) → (List a)
 
 :test (<~>((+1) : ((+2) : {}(+3)))) ((+3) : ((+2) : {}(+1)))
 
-# appends two lists
-append z [[[rec]]] ⧗ (List a) → (List a) → (List a)
-	rec 1 [[[case-append]]] case-end
-		case-append 2 : (5 1 3)
-		case-end 0
+# appends two lists (Tromp)
+append &(z [[[[[0 3 (2 4 1)]]]]]) ⧗ (List a) → (List a) → (List a)
 
 …++… append
 
diff --git a/std/Meta.bruijn b/std/Meta.bruijn
index 77027e9..e9ddea0 100644
--- a/std/Meta.bruijn
+++ b/std/Meta.bruijn
@@ -75,7 +75,7 @@ idx! [0 [0] 0 0] ⧗ Meta → Unary
 fold y [[[[[rec]]]]] ⧗ (Unary → a) → (a → a → a) → (a → a) → Meta → a
 	rec 0 case-idx case-app case-abs
 		case-idx 3
-		case-app ψ 2 (4 3 2 1)
+		case-app 2 ⋔ (4 3 2 1)
 		case-abs 1 ∘ (4 3 2 1)
 
 # calculates blc length of meta term
@@ -271,7 +271,7 @@ encode fold idx-cb app-cb abs-cb ⧗ Meta → Number
 decode y [[unpair-ternary 0 go]] ⧗ Number → Meta
 	go [[(case-idx : (case-app : {}case-abs)) !! 1 0]]
 		case-idx idx ∘ ternary→unary
-		case-app [unpair-ternary 0 (ψ app 4)]
+		case-app [unpair-ternary 0 (app ⋔ 4)]
 		case-abs abs ∘ 3
 
 :test (decode (+0)) (`0)
diff --git a/std/Number/Binary.bruijn b/std/Number/Binary.bruijn
index 648af29..fcbe264 100644
--- a/std/Number/Binary.bruijn
+++ b/std/Number/Binary.bruijn
@@ -6,6 +6,11 @@
 :import std/List .
 :import std/Logic .
 
+# TODO: remove ternary conversion shortcuts
+# TODO: then move functions to reflect order of std/Ternary
+
+:import std/Number/Ternary T
+
 # bit indicating a one, compatible with std/Logic
 b¹ true ⧗ Bit
 
@@ -252,6 +257,17 @@ sub [[(0 =? 1) (+0b) -((pad 1 0) + -(pad 0 1))]] ⧗ Binary → Binary → Binar
 :test ((+3b) - (+0b) =? (+3b)) (true)
 :test ((+3b) - (+2b) =? (+1b)) (true)
 
+# muls two binary numbers (can introduce leading 0s)
+mul [[1 z a¹ a⁰]] ⧗ Number → Number → Number
+	z (+0b)
+	a¹ [↑⁰0 + 1]
+	a⁰ [↑⁰0]
+
+…⋅… mul
+
+:test ((+42b) ⋅ (+0b) =? (+0b)) (true)
+:test ((+3b) ⋅ (+11b) =? (+33b)) (true)
+
 # rshifts least significant bit of a binary number
 div² [~(0 z a¹ a⁰)] ⧗ Binary → Binary
 	z (+0b) : (+0b)
@@ -282,3 +298,70 @@ odd? lsb ⧗ Binary → Boolean
 :test (odd? (+1b)) (true)
 :test (odd? (+41b)) (true)
 :test (odd? (+42b)) (false)
+
+# TODO: Remove (duplicate of std/Conversion because of dep loop)
+binary→ternary [y [[[rec]]] [0] 0 (+0t)] ⧗ Binary → Ternary
+	rec zero? 0 case-end case-rec
+		case-rec odd? 0 (2 (1 ∘ T.inc) (dec 0)) (2 (1 ∘ (T.mul (+2t))) (div² 0))
+		case-end 1
+
+# returns true if number is greater than other number
+# TODO: remove ternary conversion
+gre? T.gre? ⋔ binary→ternary ⧗ Binary → Binary → Boolean
+
+…>?… gre?
+
+:test ((+1b) >? (+2b)) (false)
+:test ((+2b) >? (+2b)) (false)
+:test ((+3b) >? (+2b)) (true)
+
+# returns true if number is less than other number
+les? \gre? ⧗ Binary → Binary → Boolean
+
+…<?… les?
+
+:test ((+1b) <? (+2b)) (true)
+:test ((+2b) <? (+2b)) (false)
+:test ((+3b) <? (+2b)) (false)
+
+# returns true if number is less than or equal to other number
+leq? not! ∘∘ gre? ⧗ Binary → Binary → Boolean
+
+…≤?… leq?
+
+:test ((+1b) ≤? (+2b)) (true)
+:test ((+2b) ≤? (+2b)) (true)
+:test ((+3b) ≤? (+2b)) (false)
+
+# returns true if number is greater than or equal to other number
+geq? \leq? ⧗ Binary → Binary → Boolean
+
+…≥?… geq?
+
+:test ((+1b) ≥? (+2b)) (false)
+:test ((+2b) ≥? (+2b)) (true)
+:test ((+3b) ≥? (+2b)) (true)
+
+# returns eq, lt, gt 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
+
+# returns 1 if a>b, -1 if a<b and 0 if a=b
+# also: spaceship operator
+compare compare-case (+0) (+1) (-1) ⧗ Binary → Binary → Binary
+
+:test (compare (+2b) (+2b)) ((+0))
+:test (compare (+2b) (+1b)) ((+1))
+:test (compare (+1b) (+2b)) ((-1))
+
+…<=>… compare
+
+# returns max number of two
+max [[(1 ≤? 0) 0 1]] ⧗ Binary → Binary → Binary
+
+:test (max (+5b) (+2b)) ((+5b))
+
+# returns min number of two
+min [[(1 ≤? 0) 1 0]] ⧗ Binary → Binary → Binary
+
+:test (min (+5b) (+2b)) ((+2b))
diff --git a/std/Number/Bruijn.bruijn b/std/Number/Bruijn.bruijn
new file mode 100644
index 0000000..744d9a1
--- /dev/null
+++ b/std/Number/Bruijn.bruijn
@@ -0,0 +1,23 @@
+# MIT License, Copyright (c) 2023 Marvin Borner
+# De Bruijn numeral system (named by me)
+# proof that this numeral system does not support zero/eq/sub/etc. is in
+#   Wadsworth, Christopher. "Some unusual λ-calculus numeral systems."
+# very sad indeed
+
+:import std/Combinator . 
+
+# increments De Bruijn numeral
+inc [[[2 1]]]
+
+++‣ inc
+
+:test (++(+0d)) ((+1d))
+:test (++(+5d)) ((+6d))
+
+# decrements De Bruijn numeral
+dec [[1 0 0]]
+
+--‣ dec
+
+:test (--(+1d)) ((+0d))
+:test (--(+5d)) ((+4d))
diff --git a/std/Number/Conversion.bruijn b/std/Number/Conversion.bruijn
index c79e53f..0057310 100644
--- a/std/Number/Conversion.bruijn
+++ b/std/Number/Conversion.bruijn
@@ -27,3 +27,13 @@ binary→ternary [y [[[rec]]] [0] 0 (+0t)] ⧗ Binary → Ternary
 
 :test (T.eq? (binary→ternary (+0b)) (+0t)) ([[1]])
 :test (T.eq? (binary→ternary (+42b)) (+42t)) ([[1]])
+
+# converts numbers to binary
+# constructs reversed path of composed functions and applies to ternary
+ternary→binary [y [[[rec]]] [0] 0 (+0b)] ⧗ Ternary → Binary
+	rec T.zero? 0 case-end case-rec
+		case-rec T.odd? 0 (2 (1 ∘ B.inc) (T.dec 0)) (2 (1 ∘ (B.mul (+2b))) (T.div² 0))
+		case-end 1
+
+:test (B.eq? (ternary→binary (+0t)) (+0b)) ([[1]])
+:test (B.eq? (ternary→binary (+42t)) (+42b)) ([[1]])
diff --git a/std/test_all.sh b/std/test_all.sh
index c61a575..32619f3 100755
--- a/std/test_all.sh
+++ b/std/test_all.sh
@@ -18,8 +18,8 @@ done
 echo >>All.bruijn
 echo "main [[0]]" >>All.bruijn
 
-if bruijn -v All.bruijn -r "$1" | tee /dev/fd/2 | grep -q "ERROR"; then
+if cat /dev/null | bruijn -v All.bruijn -r "$1" | tee /dev/fd/2 | grep -q "ERROR"; then
 	exit 1
 fi
 
-hyperfine --warmup 5 --runs 20 "bruijn -r $1 All.bruijn"
+hyperfine --warmup 5 --runs 20 "cat /dev/null | bruijn -r $1 All.bruijn"