Minor additions :)

samples/fun/goldbach.bruijn

@@ -0,0 +1,20 @@
+# Tromp's version, will reduce to [0] iff Goldbach conjecture is false
+:import std/Combinator .
+
+zero [[1]]
+
+one [[0]]
+
+sieve y [[[0 one (2 sn1 f)]]]
+	f y [sn2 0]
+		sn2 [[0 (0 4 1)] [[[[0 2 (1 3)]]]]]
+	sn1 [[0 (0 3 1)] [[[[0 2 (1 3)]]]]]
+
+zeroS [[[[0 zero (1 3)]]]]
+
+primes sieve zeroS
+
+check y [[[[[primes 0 (1 (4 0))] testp1]]]]
+	testp1 [0 0 2 [0 4] 0]
+
+main primes (check [[[[0]]]])

samples/fun/halting_problem.bruijn

@@ -0,0 +1,10 @@
+:import std/Logic .
+
+# hypothetical halting decider (shall not loop)
+# assuming (Program Arg) reduces to boolean
+halting [[halts (1 0)]] ⧗ Program → Arg → Boolean
+	halts [0 true false]
+
+# basically y combinator
+# paradox!
+e halting [¬(halting 0 0)] [¬(halting 0 0)]

samples/fun/huge.bruijn

@@ -1,4 +1,18 @@
 # "bruijn huge.bruijn"
+# some of the fastest growing functions per blc length
+
 # 55 bits inflating to 65536 bits, John Tromp
+huge-55 [[0 0 0 0 [[0 [[0]] 1]]] (+2u)
+
+# 64 bits inflating to ??? bits, John Tromp
+huge-64 [0 0 h 0 0 0] (+2u)
+	h [[[0 2 1 0]]]
+
+# 79 bits inflating to ??? bits, John Tromp and Bertram Felgenhauer
+huge-79 [0 0 e 0] (+2u)
+	e [0 g [[0]] d0 0]
+		g [[1 (d 0) (0 [0])]]
+			d [[[2 [2 0 1]]]]
+		d0 [[1 0 0]]
 
-main [[0 0 0 0 [[0 [[0]] 1]]] [[1 (1 0)]]]
+main huge-64

std/Math/Real.bruijn

@@ -151,9 +151,19 @@ hypot [[sqrt ((0 ⋅ 0) + (1 ⋅ 1))]] ⧗ Real → Real → Real
 		denom [N.mul 2 (N.mul 0 N.++0)] (N.mul (+2) 5)
 
 # ratio of circle's circumference to its diameter
-# TODO: Gauss-Legendre
 π π/2 ⋅ (+2.0r) ⧗ Real
 
+# Gauss-Legendre, quadratic convergence
+# Chudnovsky would be even faster but is ugly (i.e. magic numbers)
+π-gauss [L.nth-iterate &[[[[op]]]] start 0 final]
+	start [0 (+1.0q) Q.~(sqrt (+2.0r) 1) (+0.25q) (+1.0q)]
+	op [[1 0 b t p] a]
+		a Q.div (Q.add 4 3) (+2.0q)
+		b sqrt [Q.mul 6 5] 6
+		t Q.sub 3 (Q.mul 2 (Q.pow-n (Q.sub 5 0) (+2)))
+		p Q.mul (+2.0q) 2
+	final [[[[Q.div (Q.pow-n (Q.add 3 2) (+2)) (Q.mul (+4.0q) 1)]]]]
+
 # arctan by Taylor expansion, only for |x|<=1
 # tex: \sum_{n=0}^\infty(-1)^n \frac{x^{2n+1}}{2n+1}
 arctan* [[[L.nth-iterate &[[[[op]]]] start 1] (1 0) [[[[3]]]]]] ⧗ Real → Real