Fun new tupling technique

samples/fun/goldbach.bruijn

@@ -18,4 +18,4 @@ primes sieve zeroS
 check y [[[[[primes 0 (1 (4 0))] testp1]]]]
 	testp1 [0 0 2 [0 4] 0]
 
-main primes (check [[[[0]]]])
+main [primes (check [[[[0]]]])]

samples/rosetta/variadic_fixed-point_combinator.bruijn

@@ -1,22 +1,83 @@
+:import std/Combinator .
 :import std/Number .
 :import std/List .
 
-y* [[[0 1] <$> 0] ([[1 <! ([[1 2 0]] <$> 0)]] <$> 0)]
+# ---------------
+# explicit Church
+# ---------------
 
-# --- example usage ---
-# mutual recurrence relation of odd?/even?
+# passes all functions explicitly
+explicit-y* [[[0 1] <$> 0] ([[1 <! ([[1 2 0]] <$> 0)]] <$> 0)]
 
 # even x = if x == 0 then true else odd? (x-1)
 g [[[=?0 [[1]] (1 --0)]]]
 
 # odd x = if x == 0 then false else even? (x-1)
 h [[[=?0 [[0]] (2 --0)]]]
 
-even? ^(y* (g : {}h))
+# merged even/odd
+rec explicit-y* (g : {}h)
 
-odd? _(y* (g : {}h))
+:test (^rec (+5)) ([[0]])
+:test (_rec (+5)) ([[1]])
 
-:test (even? (+5)) ([[0]])
-:test (odd? (+5)) ([[1]])
+# n % 3
+mod3 ^(explicit-y* (zero : (one : {}two)))
+	zero [[[[=?0 (+0) (2 --0)]]]]
+	one [[[[=?0 (+1) (1 --0)]]]]
+	two [[[[=?0 (+2) (3 --0)]]]]
 
-main [[0]]
+:test ((mod3 (+5)) =? (+2)) ([[1]])
+
+# ----------------
+# explicit tupling
+# ----------------
+
+# passes all functions explicitly
+# requires a tuple mapping function first
+tupled-y* [y [[2 (1 0) 0]]]
+
+# merged even odd
+rec tupled-y* map [0 g h]
+	map [&[[[0 (3 2) (3 1)]]]]
+
+# [[1]] / [[0]] are tuple selectors:
+
+:test (rec [[1]] (+5)) ([[0]])
+:test (rec [[0]] (+5)) ([[1]])
+
+# n % 3, [[[2]]] selects first tuple element
+mod3 tupled-y* map [0 zero one two] [[[2]]]
+	map [&[[[[0 (4 3) (4 2) (4 1)]]]]]
+	zero [[[[=?0 (+0) (2 --0)]]]]
+	one [[[[=?0 (+1) (1 --0)]]]]
+	two [[[[=?0 (+2) (3 --0)]]]]
+
+:test ((mod3 (+5)) =? (+2)) ([[1]])
+
+# ---------------
+# implicit Church
+# ---------------
+
+# passes all functions in a single list
+implicit-y* y [[&(1 0) <$> 0]]
+
+# even x = if x == 0 then true else odd? (x-1)
+g [[=?0 [[1]] (_1 --0)]]
+
+# odd x = if x == 0 then false else even? (x-1)
+h [[=?0 [[0]] (^1 --0)]]
+
+# merged even/odd
+rec implicit-y* (g : {}h)
+
+:test (^rec (+5)) ([[0]])
+:test (_rec (+5)) ([[1]])
+
+# n % 3
+mod3 ^(implicit-y* (zero : (one : {}two)))
+	zero [[=?0 (+0) (_1 --0)]]
+	one [[=?0 (+1) (^(~1) --0)]]
+	two [[=?0 (+2) (^1 --0)]]
+
+:test ((mod3 (+5)) =? (+2)) ([[1]])

std/List/Church.bruijn

@@ -532,7 +532,6 @@ enumerate zip (iterate ++‣ (+0)) ⧗ (List a) → (List (Pair Number a))
 :test (enumerate "abc") (((+0) : 'a') : (((+1) : 'b') : {}((+2) : 'c')))
 
 # calculates all fixed points of given functions as a list
-y* [[[0 1] <$> 0] xs] ⧗ (List a) → (List b)
-	xs [[1 <! ([[1 2 0]] <$> 0)]] <$> 0
+y* y [[&(1 0) <$> 0]]
 
 :test (&(+5) <$> (y* ([[[=?0 true (1 --0)]]] : {}[[[=?0 false (2 --0)]]]))) (false : {}true)