Comment by its-summertime 5 hours ago
It all goes over my head, but, what does the distribution of values look like? e.g. for unsigned integers its completely flat, for floating point its far too many zeros, and most of the numbers are centered around 0, what do these systems end up looking like?
Let me go ahead and compute that for all halting lambda terms of length at most 33 bits. The output I got from a modified BB.lhs is (giving the normal form size and the number of terms with that normal form size):
4x208506 6x203638 7x93072 8x202741 9x62039 10x189422 11x101450 12x183896 13x96804 14x167842 15x103631 16x131387 17x100319 18x161560 19x148361 20x180227 21x117866 22x82568 23x90577 24x136315 25x158660 26x207930 27x181334 28x33308 29x33331 30x52430 31x80559 32x140753 33x231169 34x3643 35x1356 36x2817 37x1162 38x2067 39x707 40x1820 41x414 42x1316 43x226 44x1026 45x230 46x663 47x142 48x189 49x150 50x189 51x63 52x102 53x169 54x161 55x24 56x71 57x88 58x48 59x6 60x63 61x11 62x19 63x3 64x18 65x11 66x20 67x10 68x13 69x4 70x6 71x11 72x8 73x12 74x10 75x7 76x9 77x5 78x6 79x5 80x4 81x3 82x9 84x6 85x2 86x3 87x3 88x13 89x3 90x6 92x5 94x3 95x2 96x9 101x1 102x3 103x1 106x2 108x2 109x1 111x3 112x1 113x3 115x1 117x1 118x1 120x2 121x1 122x1 124x1 127x3 128x1 130x2 132x1 133x1 134x3 141x1 142x3 143x2 144x1 146x1 148x1 149x2 158x1 159x1 160x3 161x1 162x7 164x3 166x1 179x1 180x1 187x2 199x1 202x2 203x1 217x1 223x1 225x1 227x4 242x1 247x2 267x1 268x1 269x1 280x1 296x1 298x1 331x1 363x1 394x1 432x1 475x1 484x1 544x1 673x1 708x1 820x1 1364x1 1812x1