5 files changed, 30 insertions, 12 deletions
diff --git a/samples/fun/interpreter.bruijn b/samples/fun/interpreter.bruijn
index 0691f4a..c2b8020 100644
--- a/samples/fun/interpreter.bruijn
+++ b/samples/fun/interpreter.bruijn
@@ -7,7 +7,6 @@
 :import std/List .
 :import std/Char C
 
-# TODO: finish types
 uni [0 0] int [0 Ω] ⧗ (List Bit) → Term
 	int [[[0 go (2 2) 1]]]
 		go [[[[2 match]]]]
diff --git a/src/Binary.hs b/src/Binary.hs
index 3f77d4a..acf20d4 100644
--- a/src/Binary.hs
+++ b/src/Binary.hs
@@ -61,8 +61,6 @@ fromJot = worker . reverse
   k = Function $ NormalFunction "k"
   worker ('0' : xs) = Application (Application (worker xs) s) k
   worker ('1' : xs) = Application s (Application k (worker xs))
-  -- worker ('1' : xs) = Abstraction
-  --   (Abstraction (Application (worker xs) (Application (Bruijn 1) (Bruijn 0))))
   worker _          = Abstraction (Bruijn 0)
 
 
diff --git a/std/Combinator.bruijn b/std/Combinator.bruijn
index 8efc534..71ad078 100644
--- a/std/Combinator.bruijn
+++ b/std/Combinator.bruijn
@@ -7,16 +7,22 @@ b [[[2 (1 0)]]] ⧗ (b → c) → (a → b) → a → c
 
 …∘… b
 
+∘‣ b
+
 # blackbird combinator: 2x function composition: (f ∘∘ g) x y = f (g x y)
 b' [[[[3 (2 1 0)]]]] ⧗ (c → d) → (a → b → c) → a → b → d
 
 …∘∘… b'
 
+∘∘‣ b'
+
 # bunting combinator: 3x function composition: (f ∘∘∘ g) x y z = f (g x y z)
 b'' [[[[[4 (3 2 1 0)]]]]] ⧗ (d → e) → (a → b → c → d) → a → b → c → e
 
 …∘∘∘… b''
 
+∘∘∘‣ b''
+
 # becard combinator
 b''' [[[[3 (2 (1 0))]]]] ⧗ (c → d) → (b → c) → (a → b) → a → d
 
@@ -117,7 +123,7 @@ o [[0 (1 0)]] ⧗ ((a → b) → a) → (a → b) → b
 
 ψ* [[[[[4 3 (2 1) (2 0)]]]]] ⧗ (c → b → b → d) → c → (a → b) → a → a → d
 
-# queer bird combinator: reverse function composition: (f , g) x = g (f x)
+# queer bird combinator: reverse function composition
 q [[[1 (2 0)]]] ⧗ (a → b) → (b → c) → a → c
 
 # quixotic bird combinator
diff --git a/std/Number/Ternary.bruijn b/std/Number/Ternary.bruijn
index a0fd796..e9b402c 100644
--- a/std/Number/Ternary.bruijn
+++ b/std/Number/Ternary.bruijn
@@ -282,7 +282,7 @@ sub [[1 + -0]] ⧗ Number → Number → Number
 :test ((+42) - (+1) =? (+41)) (true)
 
 # returns true if number is greater than other number
-gre? [[>?(1 - 0)]] ⧗ Number → Number → Boolean
+gre? positive? ∘∘ sub ⧗ Number → Number → Boolean
 
 …>?… gre?
 
@@ -300,7 +300,7 @@ les? \gre? ⧗ Number → Number → Boolean
 :test ((+3) <? (+2)) (false)
 
 # returns true if number is less than or equal to other number
-leq? [[¬(1 >? 0)]] ⧗ Number → Number → Boolean
+leq? not! ∘∘ gre? ⧗ Number → Number → Boolean
 
 …≤?… leq?
 
@@ -317,7 +317,7 @@ geq? \leq? ⧗ Number → Number → Boolean
 :test ((+2) ≥? (+2)) (true)
 :test ((+3) ≥? (+2)) (true)
 
-# returns eq, lt, gt depending on comparison of two functions
+# returns eq, lt, gt depending on comparison of two numbers
 compare-case [[[[[go (1 - 0)]]]]] ⧗ a → b → c → Number → Number → d
 	go [=?0 5 (>?0 4 3)]
 
diff --git a/std/Number/Unary.bruijn b/std/Number/Unary.bruijn
index f5de3e2..6ace440 100644
--- a/std/Number/Unary.bruijn
+++ b/std/Number/Unary.bruijn
@@ -63,7 +63,7 @@ sub [[0 dec 1]] ⧗ Unary → Unary → Unary
 :test ((+5u) - (+3u)) ((+2u))
 
 # returns true if number is less than or equal to other number
-leq? [[=?(1 - 0)]] ⧗ Unary → Unary → Boolean
+leq? zero? ∘∘ sub ⧗ Unary → Unary → Boolean
 
 …≤?… leq?
 
@@ -82,7 +82,7 @@ geq? \leq? ⧗ Unary → Unary → Boolean
 
 # returns true if number is greater than other number
 # larger numbers should be second argument (performance)
-gre? [[¬(1 ≤? 0)]] ⧗ Unary → Unary → Boolean
+gre? not! ∘∘ leq? ⧗ Unary → Unary → Boolean
 
 …>?… gre?
 
@@ -101,12 +101,13 @@ les? \gre? ⧗ Unary → Unary → Boolean
 :test ((+3u) <? (+2u)) (false)
 
 # returns true if two unary numbers are equal
-eq? [[(0 ≥? 1) ⋀? (0 ≤? 1)]] ⧗ Unary → Unary → Boolean
+eq? [[=?(1 - 0) ⋀? =?(0 - 1)]] ⧗ Unary → Unary → Boolean
 
 …=?… eq?
 
 :test ((+1u) =? (+0u)) (false)
 :test ((+1u) =? (+1u)) (true)
+:test ((+1u) =? (+2u)) (false)
 :test ((+42u) =? (+42u)) (true)
 
 # returns true if two unary numbers are not equal
@@ -118,6 +119,20 @@ not-eq? not! ∘∘ eq? ⧗ Unary → Unary → Boolean
 :test ((+1u) ≠? (+1u)) (false)
 :test ((+42u) ≠? (+42u)) (false)
 
+# returns eq, lt, gt depending on comparison of two numbers
+compare-case [[[[[go (1 - 0) (0 - 1)]]]]] ⧗ a → b → c → Unary → Unary → d
+	go [[=?0 (=?1 6 5) 4]]
+
+# returns ternary 1 if a>b, -1 if a<b and 0 if a=b
+# also: spaceship operator
+compare compare-case (+0) (+1) (-1) ⧗ Unary → Unary → Number
+
+:test (compare (+2u) (+2u)) ((+0))
+:test (compare (+2u) (+1u)) ((+1))
+:test (compare (+1u) (+2u)) ((-1))
+
+…<=>… compare
+
 # muls two unary numbers
 mul …∘… ⧗ Unary → Unary → Unary
 
@@ -136,7 +151,7 @@ div [[[[3 [[0 1]] [1] (3 [3 [[0 1]] [3 (0 1)] [0]] 0)]]]] ⧗ Unary → Unary �
 :test ((+2u) / (+2u)) ((+1u))
 :test ((+2u) / (+3u)) ((+0u))
 
-# slower div
+# slower div (more obvious impl)
 div* [z rec ++0] ⧗ Unary → Unary → Unary
 	rec [[[[[[=?0 ((+0u) 2 1) (2 (5 0 3 2 1))] (3 - 2)]]]]]
 
@@ -148,7 +163,7 @@ mod [[[[3 [0 [[1]]] (3 [3 [[[0 (2 (5 1)) 1]]] [1] 1] [1]) [[0]]]]]] ⧗ Unary �
 :test ((+10u) % (+3u)) ((+1u))
 :test ((+3u) % (+5u)) ((+3u))
 
-# slower mod
+# slower mod (more obvious impl)
 mod* [[1 [0 [[(0 ⋀? (3 ≤? 1)) case-rec case-end]]] (1 : true) [[1]]]] ⧗ Unary → Unary → Unary
 	case-rec (1 - 3) : true
 	case-end 1 : false