docs/Zipper.ipynb

   1 {
   2  "cells": [
   3   {
   4    "cell_type": "markdown",
   5    "metadata": {},
   6    "source": [
   7     "# Traversing Datastructures with Zippers\n",
   8     "This notebook is about using the \"zipper\" with joy datastructures.  See the [Zipper wikipedia entry](https://en.wikipedia.org/wiki/Zipper_%28data_structure%29) or the original paper: [\"FUNCTIONAL PEARL The Zipper\" by Gérard Huet](https://www.st.cs.uni-saarland.de/edu/seminare/2005/advanced-fp/docs/huet-zipper.pdf)\n",
   9     "\n",
  10     "\n",
  11     "Given a datastructure on the stack we can navigate through it, modify it, and rebuild it using the \"zipper\" technique."
  12    ]
  13   },
  14   {
  15    "cell_type": "markdown",
  16    "metadata": {},
  17    "source": [
  18     "## Trees\n",
  19     "In Joypy there aren't any complex datastructures, just ints, floats, strings, Symbols (strings that are names of functions) and sequences (aka lists, aka quoted literals, aka aggregates, etc...), but we can build [trees](https://en.wikipedia.org/wiki/Tree_%28data_structure%29) out of sequences."
  20    ]
  21   },
  22   {
  23    "cell_type": "code",
  24    "execution_count": 1,
  25    "metadata": {},
  26    "outputs": [
  27     {
  28      "name": "stdout",
  29      "output_type": "stream",
  30      "text": [
  31       "[1 [2 [3 4 25 6] 7] 8]"
  32      ]
  33     }
  34    ],
  35    "source": [
  36     "[1 [2 [3 4 25 6] 7] 8]"
  37    ]
  38   },
  39   {
  40    "cell_type": "markdown",
  41    "metadata": {},
  42    "source": [
  43     "## Zipper in Joy\n",
  44     "Zippers work by keeping track of the current item, the already-seen items, and the yet-to-be seen items as you traverse a datastructure (the datastructure used to keep track of these items is the zipper.)\n",
  45     "\n",
  46     "In Joy we can do this with the following words:\n",
  47     "\n",
  48     "    z-down == [] swap uncons swap\n",
  49     "    z-up == swons swap shunt\n",
  50     "    z-right == [swons] cons dip uncons swap\n",
  51     "    z-left == swons [uncons swap] dip swap\n",
  52     "\n",
  53     "Let's use them to change 25 into 625.  The first time a word is used I show the trace so you can see how it works.  If we were going to use these a lot it would make sense to write Python versions for efficiency, but see below."
  54    ]
  55   },
  56   {
  57    "cell_type": "code",
  58    "execution_count": 2,
  59    "metadata": {},
  60    "outputs": [
  61     {
  62      "name": "stdout",
  63      "output_type": "stream",
  64      "text": [
  65       "[1 [2 [3 4 25 6] 7] 8]"
  66      ]
  67     }
  68    ],
  69    "source": [
  70     "[z-down [] swap uncons swap] inscribe\n",
  71     "[z-up swons swap shunt] inscribe\n",
  72     "[z-right [swons] cons dip uncons swap] inscribe\n",
  73     "[z-left swons [uncons swap] dip swap] inscribe"
  74    ]
  75   },
  76   {
  77    "cell_type": "code",
  78    "execution_count": 3,
  79    "metadata": {},
  80    "outputs": [
  81     {
  82      "name": "stdout",
  83      "output_type": "stream",
  84      "text": [
  85       "   [1 [2 [3 4 25 6] 7] 8] • z-down\n",
  86       "   [1 [2 [3 4 25 6] 7] 8] • [] swap uncons swap\n",
  87       "[1 [2 [3 4 25 6] 7] 8] [] • swap uncons swap\n",
  88       "[] [1 [2 [3 4 25 6] 7] 8] • uncons swap\n",
  89       "[] 1 [[2 [3 4 25 6] 7] 8] • swap\n",
  90       "[] [[2 [3 4 25 6] 7] 8] 1 • \n",
  91       "\n",
  92       "[] [[2 [3 4 25 6] 7] 8] 1"
  93      ]
  94     }
  95    ],
  96    "source": [
  97     "[z-down] trace"
  98    ]
  99   },
 100   {
 101    "cell_type": "code",
 102    "execution_count": 4,
 103    "metadata": {},
 104    "outputs": [
 105     {
 106      "name": "stdout",
 107      "output_type": "stream",
 108      "text": [
 109       "        [] [[2 [3 4 25 6] 7] 8] 1 • z-right\n",
 110       "        [] [[2 [3 4 25 6] 7] 8] 1 • [swons] cons dip uncons swap\n",
 111       "[] [[2 [3 4 25 6] 7] 8] 1 [swons] • cons dip uncons swap\n",
 112       "[] [[2 [3 4 25 6] 7] 8] [1 swons] • dip uncons swap\n",
 113       "                               [] • 1 swons [[2 [3 4 25 6] 7] 8] uncons swap\n",
 114       "                             [] 1 • swons [[2 [3 4 25 6] 7] 8] uncons swap\n",
 115       "                              [1] • [[2 [3 4 25 6] 7] 8] uncons swap\n",
 116       "         [1] [[2 [3 4 25 6] 7] 8] • uncons swap\n",
 117       "         [1] [2 [3 4 25 6] 7] [8] • swap\n",
 118       "         [1] [8] [2 [3 4 25 6] 7] • \n",
 119       "\n",
 120       "[1] [8] [2 [3 4 25 6] 7]"
 121      ]
 122     }
 123    ],
 124    "source": [
 125     "[z-right] trace"
 126    ]
 127   },
 128   {
 129    "cell_type": "code",
 130    "execution_count": 5,
 131    "metadata": {},
 132    "outputs": [
 133     {
 134      "name": "stdout",
 135      "output_type": "stream",
 136      "text": [
 137       "[1] [8] [] [[3 4 25 6] 7] 2"
 138      ]
 139     }
 140    ],
 141    "source": [
 142     "z-down"
 143    ]
 144   },
 145   {
 146    "cell_type": "code",
 147    "execution_count": 6,
 148    "metadata": {},
 149    "outputs": [
 150     {
 151      "name": "stdout",
 152      "output_type": "stream",
 153      "text": [
 154       "[1] [8] [2] [7] [3 4 25 6]"
 155      ]
 156     }
 157    ],
 158    "source": [
 159     "z-right"
 160    ]
 161   },
 162   {
 163    "cell_type": "code",
 164    "execution_count": 7,
 165    "metadata": {},
 166    "outputs": [
 167     {
 168      "name": "stdout",
 169      "output_type": "stream",
 170      "text": [
 171       "[1] [8] [2] [7] [] [4 25 6] 3"
 172      ]
 173     }
 174    ],
 175    "source": [
 176     "z-down"
 177    ]
 178   },
 179   {
 180    "cell_type": "code",
 181    "execution_count": 8,
 182    "metadata": {},
 183    "outputs": [
 184     {
 185      "name": "stdout",
 186      "output_type": "stream",
 187      "text": [
 188       "[1] [8] [2] [7] [3] [25 6] 4"
 189      ]
 190     }
 191    ],
 192    "source": [
 193     "z-right"
 194    ]
 195   },
 196   {
 197    "cell_type": "code",
 198    "execution_count": 9,
 199    "metadata": {},
 200    "outputs": [
 201     {
 202      "name": "stdout",
 203      "output_type": "stream",
 204      "text": [
 205       "[1] [8] [2] [7] [4 3] [6] 25"
 206      ]
 207     }
 208    ],
 209    "source": [
 210     "z-right"
 211    ]
 212   },
 213   {
 214    "cell_type": "code",
 215    "execution_count": 10,
 216    "metadata": {},
 217    "outputs": [
 218     {
 219      "name": "stdout",
 220      "output_type": "stream",
 221      "text": [
 222       "[1] [8] [2] [7] [4 3] [6] 625"
 223      ]
 224     }
 225    ],
 226    "source": [
 227     "sqr"
 228    ]
 229   },
 230   {
 231    "cell_type": "code",
 232    "execution_count": 11,
 233    "metadata": {},
 234    "outputs": [
 235     {
 236      "name": "stdout",
 237      "output_type": "stream",
 238      "text": [
 239       "[1] [8] [2] [7] [4 3] [6] 625 • z-up\n",
 240       "[1] [8] [2] [7] [4 3] [6] 625 • swons swap shunt\n",
 241       "[1] [8] [2] [7] [4 3] [625 6] • swap shunt\n",
 242       "[1] [8] [2] [7] [625 6] [4 3] • shunt\n",
 243       "  [1] [8] [2] [7] [3 4 625 6] • \n",
 244       "\n",
 245       "[1] [8] [2] [7] [3 4 625 6]"
 246      ]
 247     }
 248    ],
 249    "source": [
 250     "[z-up] trace"
 251    ]
 252   },
 253   {
 254    "cell_type": "code",
 255    "execution_count": 12,
 256    "metadata": {},
 257    "outputs": [
 258     {
 259      "name": "stdout",
 260      "output_type": "stream",
 261      "text": [
 262       "[1] [8] [2 [3 4 625 6] 7]"
 263      ]
 264     }
 265    ],
 266    "source": [
 267     "z-up"
 268    ]
 269   },
 270   {
 271    "cell_type": "code",
 272    "execution_count": 13,
 273    "metadata": {},
 274    "outputs": [
 275     {
 276      "name": "stdout",
 277      "output_type": "stream",
 278      "text": [
 279       "[1 [2 [3 4 625 6] 7] 8]"
 280      ]
 281     }
 282    ],
 283    "source": [
 284     "z-up"
 285    ]
 286   },
 287   {
 288    "cell_type": "markdown",
 289    "metadata": {},
 290    "source": [
 291     "## `dip` and `infra`\n",
 292     "In Joy we have the `dip` and `infra` combinators which can \"target\" or \"address\" any particular item in a Joy tree structure."
 293    ]
 294   },
 295   {
 296    "cell_type": "code",
 297    "execution_count": 14,
 298    "metadata": {},
 299    "outputs": [
 300     {
 301      "name": "stdout",
 302      "output_type": "stream",
 303      "text": [
 304       "[1 [2 [3 4 625 6] 7] 8] [[[[[[sqr] dipd] infra] dip] infra] dip] • infra\n",
 305       "                                           8 [2 [3 4 625 6] 7] 1 • [[[[[sqr] dipd] infra] dip] infra] dip [] swaack\n",
 306       "        8 [2 [3 4 625 6] 7] 1 [[[[[sqr] dipd] infra] dip] infra] • dip [] swaack\n",
 307       "                                             8 [2 [3 4 625 6] 7] • [[[[sqr] dipd] infra] dip] infra 1 [] swaack\n",
 308       "                  8 [2 [3 4 625 6] 7] [[[[sqr] dipd] infra] dip] • infra 1 [] swaack\n",
 309       "                                                 7 [3 4 625 6] 2 • [[[sqr] dipd] infra] dip [8] swaack 1 [] swaack\n",
 310       "                            7 [3 4 625 6] 2 [[[sqr] dipd] infra] • dip [8] swaack 1 [] swaack\n",
 311       "                                                   7 [3 4 625 6] • [[sqr] dipd] infra 2 [8] swaack 1 [] swaack\n",
 312       "                                      7 [3 4 625 6] [[sqr] dipd] • infra 2 [8] swaack 1 [] swaack\n",
 313       "                                                       6 625 4 3 • [sqr] dipd [7] swaack 2 [8] swaack 1 [] swaack\n",
 314       "                                                 6 625 4 3 [sqr] • dipd [7] swaack 2 [8] swaack 1 [] swaack\n",
 315       "                                                           6 625 • sqr 4 3 [7] swaack 2 [8] swaack 1 [] swaack\n",
 316       "                                                           6 625 • dup * 4 3 [7] swaack 2 [8] swaack 1 [] swaack\n",
 317       "                                                       6 625 625 • * 4 3 [7] swaack 2 [8] swaack 1 [] swaack\n",
 318       "                                                        6 390625 • 4 3 [7] swaack 2 [8] swaack 1 [] swaack\n",
 319       "                                                      6 390625 4 • 3 [7] swaack 2 [8] swaack 1 [] swaack\n",
 320       "                                                    6 390625 4 3 • [7] swaack 2 [8] swaack 1 [] swaack\n",
 321       "                                                6 390625 4 3 [7] • swaack 2 [8] swaack 1 [] swaack\n",
 322       "                                                7 [3 4 390625 6] • 2 [8] swaack 1 [] swaack\n",
 323       "                                              7 [3 4 390625 6] 2 • [8] swaack 1 [] swaack\n",
 324       "                                          7 [3 4 390625 6] 2 [8] • swaack 1 [] swaack\n",
 325       "                                          8 [2 [3 4 390625 6] 7] • 1 [] swaack\n",
 326       "                                        8 [2 [3 4 390625 6] 7] 1 • [] swaack\n",
 327       "                                     8 [2 [3 4 390625 6] 7] 1 [] • swaack\n",
 328       "                                      [1 [2 [3 4 390625 6] 7] 8] • \n",
 329       "\n",
 330       "[1 [2 [3 4 390625 6] 7] 8]"
 331      ]
 332     }
 333    ],
 334    "source": [
 335     "[[[[[[sqr] dipd] infra] dip] infra] dip] [infra] trace"
 336    ]
 337   },
 338   {
 339    "cell_type": "markdown",
 340    "metadata": {},
 341    "source": [
 342     "If you read the trace carefully you'll see that about half of it is the `dip` and `infra` combinators de-quoting programs and \"digging\" into the subject datastructure.  Instead of maintaining temporary results on the stack they are pushed into the pending expression (continuation).  When `sqr` has run the rest of the pending expression  rebuilds the datastructure.\n",
 343     "\n",
 344     "## `Z`\n",
 345     "Imagine a function `Z` that accepts a sequence of `dip` and `infra` combinators, a quoted program `[Q]`, and a datastructure to work on.  It would effectively execute the quoted program as if it had been embedded in a nested series of quoted programs, e.g.:\n",
 346     "\n",
 347     "       [...] [Q] [dip dip infra dip infra dip infra] Z\n",
 348     "    -------------------------------------------------------------\n",
 349     "       [...] [[[[[[[Q] dip] dip] infra] dip] infra] dip] infra\n",
 350     "       \n",
 351     "The `Z` function isn't hard to make."
 352    ]
 353   },
 354   {
 355    "cell_type": "code",
 356    "execution_count": 4,
 357    "metadata": {},
 358    "outputs": [
 359     {
 360      "name": "stdout",
 361      "output_type": "stream",
 362      "text": []
 363     }
 364    ],
 365    "source": [
 366     "clear"
 367    ]
 368   },
 369   {
 370    "cell_type": "code",
 371    "execution_count": 2,
 372    "metadata": {},
 373    "outputs": [
 374     {
 375      "name": "stdout",
 376      "output_type": "stream",
 377      "text": [
 378       "[Q] [dip dip infra dip infra dip infra]"
 379      ]
 380     }
 381    ],
 382    "source": [
 383     "[Q] [dip dip infra dip infra dip infra]"
 384    ]
 385   },
 386   {
 387    "cell_type": "code",
 388    "execution_count": null,
 389    "metadata": {},
 390    "outputs": [],
 391    "source": [
 392     "[unit cons] step"
 393    ]
 394   },
 395   {
 396    "cell_type": "markdown",
 397    "metadata": {},
 398    "source": [
 399     "So that's broken with the current definition of `step` but this works:"
 400    ]
 401   },
 402   {
 403    "cell_type": "code",
 404    "execution_count": 6,
 405    "metadata": {},
 406    "outputs": [
 407     {
 408      "name": "stdout",
 409      "output_type": "stream",
 410      "text": []
 411     }
 412    ],
 413    "source": [
 414     "clear"
 415    ]
 416   },
 417   {
 418    "cell_type": "code",
 419    "execution_count": 7,
 420    "metadata": {},
 421    "outputs": [
 422     {
 423      "name": "stdout",
 424      "output_type": "stream",
 425      "text": [
 426       "[Q] [[dip] [dip] [infra] [dip] [infra] [dip] [infra]]"
 427      ]
 428     }
 429    ],
 430    "source": [
 431     "[Q] [[dip] [dip] [infra] [dip] [infra] [dip] [infra]]"
 432    ]
 433   },
 434   {
 435    "cell_type": "code",
 436    "execution_count": 8,
 437    "metadata": {},
 438    "outputs": [
 439     {
 440      "name": "stdout",
 441      "output_type": "stream",
 442      "text": [
 443       "[[[[[[[[Q] dip] dip] infra] dip] infra] dip] infra]"
 444      ]
 445     }
 446    ],
 447    "source": [
 448     "[cons] step"
 449    ]
 450   },
 451   {
 452    "cell_type": "markdown",
 453    "metadata": {},
 454    "source": [
 455     "Do I want to revisit `step` def?  Insist that `Z` use `[[A][B][C]...]` rather than `[A B C ...]`?  Seems clunky, special-cased, and not in the spirit of the thing, eh?\n",
 456     "\n",
 457     "Arguably,\n",
 458     "\n",
 459     "    [dip dip infra dip infra dip infra] [unit cons] step\n",
 460     "\n",
 461     "*should* work, yes?\n",
 462     "\n",
 463     "\n",
 464     "           ... [] [Q] . step\n",
 465     "        -----------------------\n",
 466     "              ... .\n",
 467     "\n",
 468     "\n",
 469     "           ... [a] [Q] . step\n",
 470     "        ------------------------\n",
 471     "             ... a . Q\n",
 472     "\n",
 473     "\n",
 474     "           ... [a b c] [Q] . step\n",
 475     "        ----------------------------------------\n",
 476     "                 ... a . Q [b c] [Q] step\n",
 477     "\n"
 478    ]
 479   },
 480   {
 481    "cell_type": "code",
 482    "execution_count": 9,
 483    "metadata": {},
 484    "outputs": [
 485     {
 486      "name": "stdout",
 487      "output_type": "stream",
 488      "text": []
 489     }
 490    ],
 491    "source": [
 492     "clear"
 493    ]
 494   },
 495   {
 496    "cell_type": "code",
 497    "execution_count": 10,
 498    "metadata": {},
 499    "outputs": [
 500     {
 501      "name": "stdout",
 502      "output_type": "stream",
 503      "text": [
 504       "[dip dip infra dip infra dip infra]"
 505      ]
 506     }
 507    ],
 508    "source": [
 509     "[dip dip infra dip infra dip infra]"
 510    ]
 511   },
 512   {
 513    "cell_type": "code",
 514    "execution_count": 11,
 515    "metadata": {},
 516    "outputs": [
 517     {
 518      "name": "stdout",
 519      "output_type": "stream",
 520      "text": [
 521       "[[dip] dip infra dip infra dip infra]"
 522      ]
 523     }
 524    ],
 525    "source": [
 526     "[unit] infra"
 527    ]
 528   },
 529   {
 530    "cell_type": "code",
 531    "execution_count": null,
 532    "metadata": {},
 533    "outputs": [],
 534    "source": []
 535   },
 536   {
 537    "cell_type": "code",
 538    "execution_count": null,
 539    "metadata": {},
 540    "outputs": [],
 541    "source": []
 542   },
 543   {
 544    "cell_type": "code",
 545    "execution_count": null,
 546    "metadata": {},
 547    "outputs": [],
 548    "source": []
 549   },
 550   {
 551    "cell_type": "code",
 552    "execution_count": null,
 553    "metadata": {},
 554    "outputs": [],
 555    "source": []
 556   },
 557   {
 558    "cell_type": "code",
 559    "execution_count": null,
 560    "metadata": {},
 561    "outputs": [],
 562    "source": []
 563   },
 564   {
 565    "cell_type": "code",
 566    "execution_count": null,
 567    "metadata": {},
 568    "outputs": [],
 569    "source": []
 570   },
 571   {
 572    "cell_type": "code",
 573    "execution_count": null,
 574    "metadata": {},
 575    "outputs": [],
 576    "source": []
 577   },
 578   {
 579    "cell_type": "code",
 580    "execution_count": null,
 581    "metadata": {},
 582    "outputs": [],
 583    "source": []
 584   },
 585   {
 586    "cell_type": "code",
 587    "execution_count": null,
 588    "metadata": {},
 589    "outputs": [],
 590    "source": []
 591   },
 592   {
 593    "cell_type": "code",
 594    "execution_count": 6,
 595    "metadata": {},
 596    "outputs": [
 597     {
 598      "name": "stdout",
 599      "output_type": "stream",
 600      "text": []
 601     }
 602    ],
 603    "source": [
 604     "[Z [[] ccons] step i] inscribe"
 605    ]
 606   },
 607   {
 608    "cell_type": "markdown",
 609    "metadata": {},
 610    "source": [
 611     "Here it is in action in a simplified scenario."
 612    ]
 613   },
 614   {
 615    "cell_type": "code",
 616    "execution_count": 7,
 617    "metadata": {},
 618    "outputs": [
 619     {
 620      "name": "stdout",
 621      "output_type": "stream",
 622      "text": [
 623       "                                                                                   1 [2 3 4] • Z\n",
 624       "                                                                                   1 [2 3 4] • [[] ccons] step i\n",
 625       "                                                                        1 [2 3 4] [[] ccons] • step i\n",
 626       "                                                                        1 [2 3 4] [[] ccons] • [_step0] x i\n",
 627       "                                                               1 [2 3 4] [[] ccons] [_step0] • x i\n",
 628       "                                                               1 [2 3 4] [[] ccons] [_step0] • dup i i\n",
 629       "                                                      1 [2 3 4] [[] ccons] [_step0] [_step0] • i i\n",
 630       "                                                               1 [2 3 4] [[] ccons] [_step0] • _step0 i\n",
 631       "                                                               1 [2 3 4] [[] ccons] [_step0] • _step1 [popopop] [_stept] branch i\n",
 632       "                                                               1 [2 3 4] [[] ccons] [_step0] • [?] dipd roll< [popopop] [_stept] branch i\n",
 633       "                                                           1 [2 3 4] [[] ccons] [_step0] [?] • dipd roll< [popopop] [_stept] branch i\n",
 634       "                                                           1 [2 3 4] [[] ccons] [_step0] [?] • [dip] codi roll< [popopop] [_stept] branch i\n",
 635       "                                                     1 [2 3 4] [[] ccons] [_step0] [?] [dip] • codi roll< [popopop] [_stept] branch i\n",
 636       "                                                     1 [2 3 4] [[] ccons] [_step0] [?] [dip] • cons dip roll< [popopop] [_stept] branch i\n",
 637       "                                                     1 [2 3 4] [[] ccons] [_step0] [[?] dip] • dip roll< [popopop] [_stept] branch i\n",
 638       "                                                                        1 [2 3 4] [[] ccons] • [?] dip [_step0] roll< [popopop] [_stept] branch i\n",
 639       "                                                                    1 [2 3 4] [[] ccons] [?] • dip [_step0] roll< [popopop] [_stept] branch i\n",
 640       "                                                                                   1 [2 3 4] • ? [[] ccons] [_step0] roll< [popopop] [_stept] branch i\n",
 641       "                                                                                   1 [2 3 4] • dup bool [[] ccons] [_step0] roll< [popopop] [_stept] branch i\n",
 642       "                                                                           1 [2 3 4] [2 3 4] • bool [[] ccons] [_step0] roll< [popopop] [_stept] branch i\n",
 643       "                                                                              1 [2 3 4] true • [[] ccons] [_step0] roll< [popopop] [_stept] branch i\n",
 644       "                                                                   1 [2 3 4] true [[] ccons] • [_step0] roll< [popopop] [_stept] branch i\n",
 645       "                                                          1 [2 3 4] true [[] ccons] [_step0] • roll< [popopop] [_stept] branch i\n",
 646       "                                                          1 [2 3 4] true [[] ccons] [_step0] • swapd swap [popopop] [_stept] branch i\n",
 647       "                                                          1 [2 3 4] true [[] ccons] [_step0] • [swap] dip swap [popopop] [_stept] branch i\n",
 648       "                                                   1 [2 3 4] true [[] ccons] [_step0] [swap] • dip swap [popopop] [_stept] branch i\n",
 649       "                                                                   1 [2 3 4] true [[] ccons] • swap [_step0] swap [popopop] [_stept] branch i\n",
 650       "                                                                   1 [2 3 4] [[] ccons] true • [_step0] swap [popopop] [_stept] branch i\n",
 651       "                                                          1 [2 3 4] [[] ccons] true [_step0] • swap [popopop] [_stept] branch i\n",
 652       "                                                          1 [2 3 4] [[] ccons] [_step0] true • [popopop] [_stept] branch i\n",
 653       "                                                1 [2 3 4] [[] ccons] [_step0] true [popopop] • [_stept] branch i\n",
 654       "                                       1 [2 3 4] [[] ccons] [_step0] true [popopop] [_stept] • branch i\n",
 655       "                                                               1 [2 3 4] [[] ccons] [_step0] • _stept i\n",
 656       "                                                               1 [2 3 4] [[] ccons] [_step0] • [uncons] dipd [dupdipd] dip x i\n",
 657       "                                                      1 [2 3 4] [[] ccons] [_step0] [uncons] • dipd [dupdipd] dip x i\n",
 658       "                                                      1 [2 3 4] [[] ccons] [_step0] [uncons] • [dip] codi [dupdipd] dip x i\n",
 659       "                                                1 [2 3 4] [[] ccons] [_step0] [uncons] [dip] • codi [dupdipd] dip x i\n",
 660       "                                                1 [2 3 4] [[] ccons] [_step0] [uncons] [dip] • cons dip [dupdipd] dip x i\n",
 661       "                                                1 [2 3 4] [[] ccons] [_step0] [[uncons] dip] • dip [dupdipd] dip x i\n",
 662       "                                                                        1 [2 3 4] [[] ccons] • [uncons] dip [_step0] [dupdipd] dip x i\n",
 663       "                                                               1 [2 3 4] [[] ccons] [uncons] • dip [_step0] [dupdipd] dip x i\n",
 664       "                                                                                   1 [2 3 4] • uncons [[] ccons] [_step0] [dupdipd] dip x i\n",
 665       "                                                                                   1 [2 3 4] • [first] [rest] cleave [[] ccons] [_step0] [dupdipd] dip x i\n",
 666       "                                                                           1 [2 3 4] [first] • [rest] cleave [[] ccons] [_step0] [dupdipd] dip x i\n",
 667       "                                                                    1 [2 3 4] [first] [rest] • cleave [[] ccons] [_step0] [dupdipd] dip x i\n",
 668       "                                                                    1 [2 3 4] [first] [rest] • fork popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 669       "                                                                    1 [2 3 4] [first] [rest] • [i] app2 popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 670       "                                                                1 [2 3 4] [first] [rest] [i] • app2 popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 671       "                                                                1 [2 3 4] [first] [rest] [i] • [grba swap grba swap] dip [infrst] cons ii popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 672       "                                          1 [2 3 4] [first] [rest] [i] [grba swap grba swap] • dip [infrst] cons ii popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 673       "                                                                    1 [2 3 4] [first] [rest] • grba swap grba swap [i] [infrst] cons ii popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 674       "                                                                    1 [2 3 4] [first] [rest] • [stack popd] dip swap grba swap [i] [infrst] cons ii popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 675       "                                                       1 [2 3 4] [first] [rest] [stack popd] • dip swap grba swap [i] [infrst] cons ii popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 676       "                                                                           1 [2 3 4] [first] • stack popd [rest] swap grba swap [i] [infrst] cons ii popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 677       "                                                       1 [2 3 4] [first] [[first] [2 3 4] 1] • popd [rest] swap grba swap [i] [infrst] cons ii popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 678       "                                                       1 [2 3 4] [first] [[first] [2 3 4] 1] • [pop] dip [rest] swap grba swap [i] [infrst] cons ii popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 679       "                                                 1 [2 3 4] [first] [[first] [2 3 4] 1] [pop] • dip [rest] swap grba swap [i] [infrst] cons ii popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 680       "                                                                           1 [2 3 4] [first] • pop [[first] [2 3 4] 1] [rest] swap grba swap [i] [infrst] cons ii popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 681       "                                                                                   1 [2 3 4] • [[first] [2 3 4] 1] [rest] swap grba swap [i] [infrst] cons ii popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 682       "                                                               1 [2 3 4] [[first] [2 3 4] 1] • [rest] swap grba swap [i] [infrst] cons ii popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 683       "                                                        1 [2 3 4] [[first] [2 3 4] 1] [rest] • swap grba swap [i] [infrst] cons ii popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 684       "                                                        1 [2 3 4] [rest] [[first] [2 3 4] 1] • grba swap [i] [infrst] cons ii popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 685       "                                                        1 [2 3 4] [rest] [[first] [2 3 4] 1] • [stack popd] dip swap [i] [infrst] cons ii popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 686       "                                           1 [2 3 4] [rest] [[first] [2 3 4] 1] [stack popd] • dip swap [i] [infrst] cons ii popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 687       "                                                                            1 [2 3 4] [rest] • stack popd [[first] [2 3 4] 1] swap [i] [infrst] cons ii popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 688       "                                                         1 [2 3 4] [rest] [[rest] [2 3 4] 1] • popd [[first] [2 3 4] 1] swap [i] [infrst] cons ii popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 689       "                                                         1 [2 3 4] [rest] [[rest] [2 3 4] 1] • [pop] dip [[first] [2 3 4] 1] swap [i] [infrst] cons ii popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 690       "                                                   1 [2 3 4] [rest] [[rest] [2 3 4] 1] [pop] • dip [[first] [2 3 4] 1] swap [i] [infrst] cons ii popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 691       "                                                                            1 [2 3 4] [rest] • pop [[rest] [2 3 4] 1] [[first] [2 3 4] 1] swap [i] [infrst] cons ii popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 692       "                                                                                   1 [2 3 4] • [[rest] [2 3 4] 1] [[first] [2 3 4] 1] swap [i] [infrst] cons ii popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 693       "                                                                1 [2 3 4] [[rest] [2 3 4] 1] • [[first] [2 3 4] 1] swap [i] [infrst] cons ii popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 694       "                                            1 [2 3 4] [[rest] [2 3 4] 1] [[first] [2 3 4] 1] • swap [i] [infrst] cons ii popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 695       "                                            1 [2 3 4] [[first] [2 3 4] 1] [[rest] [2 3 4] 1] • [i] [infrst] cons ii popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 696       "                                        1 [2 3 4] [[first] [2 3 4] 1] [[rest] [2 3 4] 1] [i] • [infrst] cons ii popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 697       "                               1 [2 3 4] [[first] [2 3 4] 1] [[rest] [2 3 4] 1] [i] [infrst] • cons ii popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 698       "                               1 [2 3 4] [[first] [2 3 4] 1] [[rest] [2 3 4] 1] [[i] infrst] • ii popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 699       "                               1 [2 3 4] [[first] [2 3 4] 1] [[rest] [2 3 4] 1] [[i] infrst] • [dip] dupdip i popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 700       "                         1 [2 3 4] [[first] [2 3 4] 1] [[rest] [2 3 4] 1] [[i] infrst] [dip] • dupdip i popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 701       "                         1 [2 3 4] [[first] [2 3 4] 1] [[rest] [2 3 4] 1] [[i] infrst] [dip] • dupd dip i popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 702       "                         1 [2 3 4] [[first] [2 3 4] 1] [[rest] [2 3 4] 1] [[i] infrst] [dip] • [dup] dip dip i popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 703       "                   1 [2 3 4] [[first] [2 3 4] 1] [[rest] [2 3 4] 1] [[i] infrst] [dip] [dup] • dip dip i popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 704       "                               1 [2 3 4] [[first] [2 3 4] 1] [[rest] [2 3 4] 1] [[i] infrst] • dup [dip] dip i popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 705       "                  1 [2 3 4] [[first] [2 3 4] 1] [[rest] [2 3 4] 1] [[i] infrst] [[i] infrst] • [dip] dip i popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 706       "            1 [2 3 4] [[first] [2 3 4] 1] [[rest] [2 3 4] 1] [[i] infrst] [[i] infrst] [dip] • dip i popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 707       "                               1 [2 3 4] [[first] [2 3 4] 1] [[rest] [2 3 4] 1] [[i] infrst] • dip [[i] infrst] i popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 708       "                                                               1 [2 3 4] [[first] [2 3 4] 1] • [i] infrst [[rest] [2 3 4] 1] [[i] infrst] i popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 709       "                                                           1 [2 3 4] [[first] [2 3 4] 1] [i] • infrst [[rest] [2 3 4] 1] [[i] infrst] i popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 710       "                                                           1 [2 3 4] [[first] [2 3 4] 1] [i] • infra first [[rest] [2 3 4] 1] [[i] infrst] i popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 711       "                                                           1 [2 3 4] [[first] [2 3 4] 1] [i] • swons swaack [i] dip swaack first [[rest] [2 3 4] 1] [[i] infrst] i popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 712       "                                                           1 [2 3 4] [[first] [2 3 4] 1] [i] • swap cons swaack [i] dip swaack first [[rest] [2 3 4] 1] [[i] infrst] i popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 713       "                                                           1 [2 3 4] [i] [[first] [2 3 4] 1] • cons swaack [i] dip swaack first [[rest] [2 3 4] 1] [[i] infrst] i popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 714       "                                                           1 [2 3 4] [[i] [first] [2 3 4] 1] • swaack [i] dip swaack first [[rest] [2 3 4] 1] [[i] infrst] i popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 715       "                                                           1 [2 3 4] [first] [i] [[2 3 4] 1] • [i] dip swaack first [[rest] [2 3 4] 1] [[i] infrst] i popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 716       "                                                       1 [2 3 4] [first] [i] [[2 3 4] 1] [i] • dip swaack first [[rest] [2 3 4] 1] [[i] infrst] i popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 717       "                                                                       1 [2 3 4] [first] [i] • i [[2 3 4] 1] swaack first [[rest] [2 3 4] 1] [[i] infrst] i popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 718       "                                                                           1 [2 3 4] [first] • i [[2 3 4] 1] swaack first [[rest] [2 3 4] 1] [[i] infrst] i popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 719       "                                                                                   1 [2 3 4] • first [[2 3 4] 1] swaack first [[rest] [2 3 4] 1] [[i] infrst] i popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 720       "                                                                                         1 2 • [[2 3 4] 1] swaack first [[rest] [2 3 4] 1] [[i] infrst] i popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 721       "                                                                             1 2 [[2 3 4] 1] • swaack first [[rest] [2 3 4] 1] [[i] infrst] i popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 722       "                                                                             1 [2 3 4] [2 1] • first [[rest] [2 3 4] 1] [[i] infrst] i popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 723       "                                                                                 1 [2 3 4] 2 • [[rest] [2 3 4] 1] [[i] infrst] i popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 724       "                                                              1 [2 3 4] 2 [[rest] [2 3 4] 1] • [[i] infrst] i popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 725       "                                                 1 [2 3 4] 2 [[rest] [2 3 4] 1] [[i] infrst] • i popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 726       "                                                              1 [2 3 4] 2 [[rest] [2 3 4] 1] • [i] infrst popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 727       "                                                          1 [2 3 4] 2 [[rest] [2 3 4] 1] [i] • infrst popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 728       "                                                          1 [2 3 4] 2 [[rest] [2 3 4] 1] [i] • infra first popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 729       "                                                          1 [2 3 4] 2 [[rest] [2 3 4] 1] [i] • swons swaack [i] dip swaack first popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 730       "                                                          1 [2 3 4] 2 [[rest] [2 3 4] 1] [i] • swap cons swaack [i] dip swaack first popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 731       "                                                          1 [2 3 4] 2 [i] [[rest] [2 3 4] 1] • cons swaack [i] dip swaack first popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 732       "                                                          1 [2 3 4] 2 [[i] [rest] [2 3 4] 1] • swaack [i] dip swaack first popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 733       "                                                          1 [2 3 4] [rest] [i] [2 [2 3 4] 1] • [i] dip swaack first popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 734       "                                                      1 [2 3 4] [rest] [i] [2 [2 3 4] 1] [i] • dip swaack first popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 735       "                                                                        1 [2 3 4] [rest] [i] • i [2 [2 3 4] 1] swaack first popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 736       "                                                                            1 [2 3 4] [rest] • i [2 [2 3 4] 1] swaack first popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 737       "                                                                                   1 [2 3 4] • rest [2 [2 3 4] 1] swaack first popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 738       "                                                                                   1 [2 3 4] • [pop] infra [2 [2 3 4] 1] swaack first popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 739       "                                                                             1 [2 3 4] [pop] • infra [2 [2 3 4] 1] swaack first popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 740       "                                                                             1 [2 3 4] [pop] • swons swaack [i] dip swaack [2 [2 3 4] 1] swaack first popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 741       "                                                                             1 [2 3 4] [pop] • swap cons swaack [i] dip swaack [2 [2 3 4] 1] swaack first popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 742       "                                                                             1 [pop] [2 3 4] • cons swaack [i] dip swaack [2 [2 3 4] 1] swaack first popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 743       "                                                                             1 [[pop] 2 3 4] • swaack [i] dip swaack [2 [2 3 4] 1] swaack first popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 744       "                                                                             4 3 2 [pop] [1] • [i] dip swaack [2 [2 3 4] 1] swaack first popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 745       "                                                                         4 3 2 [pop] [1] [i] • dip swaack [2 [2 3 4] 1] swaack first popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 746       "                                                                                 4 3 2 [pop] • i [1] swaack [2 [2 3 4] 1] swaack first popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 747       "                                                                                       4 3 2 • pop [1] swaack [2 [2 3 4] 1] swaack first popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 748       "                                                                                         4 3 • [1] swaack [2 [2 3 4] 1] swaack first popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 749       "                                                                                     4 3 [1] • swaack [2 [2 3 4] 1] swaack first popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 750       "                                                                                     1 [3 4] • [2 [2 3 4] 1] swaack first popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 751       "                                                                       1 [3 4] [2 [2 3 4] 1] • swaack first popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 752       "                                                                       1 [2 3 4] 2 [[3 4] 1] • first popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 753       "                                                                           1 [2 3 4] 2 [3 4] • popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 754       "                                                                           1 [2 3 4] 2 [3 4] • [pop] dipd [[] ccons] [_step0] [dupdipd] dip x i\n",
 755       "                                                                     1 [2 3 4] 2 [3 4] [pop] • dipd [[] ccons] [_step0] [dupdipd] dip x i\n",
 756       "                                                                     1 [2 3 4] 2 [3 4] [pop] • [dip] codi [[] ccons] [_step0] [dupdipd] dip x i\n",
 757       "                                                               1 [2 3 4] 2 [3 4] [pop] [dip] • codi [[] ccons] [_step0] [dupdipd] dip x i\n",
 758       "                                                               1 [2 3 4] 2 [3 4] [pop] [dip] • cons dip [[] ccons] [_step0] [dupdipd] dip x i\n",
 759       "                                                               1 [2 3 4] 2 [3 4] [[pop] dip] • dip [[] ccons] [_step0] [dupdipd] dip x i\n",
 760       "                                                                                 1 [2 3 4] 2 • [pop] dip [3 4] [[] ccons] [_step0] [dupdipd] dip x i\n",
 761       "                                                                           1 [2 3 4] 2 [pop] • dip [3 4] [[] ccons] [_step0] [dupdipd] dip x i\n",
 762       "                                                                                   1 [2 3 4] • pop 2 [3 4] [[] ccons] [_step0] [dupdipd] dip x i\n",
 763       "                                                                                           1 • 2 [3 4] [[] ccons] [_step0] [dupdipd] dip x i\n",
 764       "                                                                                         1 2 • [3 4] [[] ccons] [_step0] [dupdipd] dip x i\n",
 765       "                                                                                   1 2 [3 4] • [[] ccons] [_step0] [dupdipd] dip x i\n",
 766       "                                                                        1 2 [3 4] [[] ccons] • [_step0] [dupdipd] dip x i\n",
 767       "                                                               1 2 [3 4] [[] ccons] [_step0] • [dupdipd] dip x i\n",
 768       "                                                     1 2 [3 4] [[] ccons] [_step0] [dupdipd] • dip x i\n",
 769       "                                                                        1 2 [3 4] [[] ccons] • dupdipd [_step0] x i\n",
 770       "                                                                        1 2 [3 4] [[] ccons] • dup dipd [_step0] x i\n",
 771       "                                                             1 2 [3 4] [[] ccons] [[] ccons] • dipd [_step0] x i\n",
 772       "                                                             1 2 [3 4] [[] ccons] [[] ccons] • [dip] codi [_step0] x i\n",
 773       "                                                       1 2 [3 4] [[] ccons] [[] ccons] [dip] • codi [_step0] x i\n",
 774       "                                                       1 2 [3 4] [[] ccons] [[] ccons] [dip] • cons dip [_step0] x i\n",
 775       "                                                       1 2 [3 4] [[] ccons] [[[] ccons] dip] • dip [_step0] x i\n",
 776       "                                                                                   1 2 [3 4] • [[] ccons] dip [[] ccons] [_step0] x i\n",
 777       "                                                                        1 2 [3 4] [[] ccons] • dip [[] ccons] [_step0] x i\n",
 778       "                                                                                         1 2 • [] ccons [3 4] [[] ccons] [_step0] x i\n",
 779       "                                                                                      1 2 [] • ccons [3 4] [[] ccons] [_step0] x i\n",
 780       "                                                                                      1 2 [] • cons cons [3 4] [[] ccons] [_step0] x i\n",
 781       "                                                                                       1 [2] • cons [3 4] [[] ccons] [_step0] x i\n",
 782       "                                                                                       [1 2] • [3 4] [[] ccons] [_step0] x i\n",
 783       "                                                                                 [1 2] [3 4] • [[] ccons] [_step0] x i\n",
 784       "                                                                      [1 2] [3 4] [[] ccons] • [_step0] x i\n",
 785       "                                                             [1 2] [3 4] [[] ccons] [_step0] • x i\n",
 786       "                                                             [1 2] [3 4] [[] ccons] [_step0] • dup i i\n",
 787       "                                                    [1 2] [3 4] [[] ccons] [_step0] [_step0] • i i\n",
 788       "                                                             [1 2] [3 4] [[] ccons] [_step0] • _step0 i\n",
 789       "                                                             [1 2] [3 4] [[] ccons] [_step0] • _step1 [popopop] [_stept] branch i\n",
 790       "                                                             [1 2] [3 4] [[] ccons] [_step0] • [?] dipd roll< [popopop] [_stept] branch i\n",
 791       "                                                         [1 2] [3 4] [[] ccons] [_step0] [?] • dipd roll< [popopop] [_stept] branch i\n",
 792       "                                                         [1 2] [3 4] [[] ccons] [_step0] [?] • [dip] codi roll< [popopop] [_stept] branch i\n",
 793       "                                                   [1 2] [3 4] [[] ccons] [_step0] [?] [dip] • codi roll< [popopop] [_stept] branch i\n",
 794       "                                                   [1 2] [3 4] [[] ccons] [_step0] [?] [dip] • cons dip roll< [popopop] [_stept] branch i\n",
 795       "                                                   [1 2] [3 4] [[] ccons] [_step0] [[?] dip] • dip roll< [popopop] [_stept] branch i\n",
 796       "                                                                      [1 2] [3 4] [[] ccons] • [?] dip [_step0] roll< [popopop] [_stept] branch i\n",
 797       "                                                                  [1 2] [3 4] [[] ccons] [?] • dip [_step0] roll< [popopop] [_stept] branch i\n",
 798       "                                                                                 [1 2] [3 4] • ? [[] ccons] [_step0] roll< [popopop] [_stept] branch i\n",
 799       "                                                                                 [1 2] [3 4] • dup bool [[] ccons] [_step0] roll< [popopop] [_stept] branch i\n",
 800       "                                                                           [1 2] [3 4] [3 4] • bool [[] ccons] [_step0] roll< [popopop] [_stept] branch i\n",
 801       "                                                                            [1 2] [3 4] true • [[] ccons] [_step0] roll< [popopop] [_stept] branch i\n",
 802       "                                                                 [1 2] [3 4] true [[] ccons] • [_step0] roll< [popopop] [_stept] branch i\n",
 803       "                                                        [1 2] [3 4] true [[] ccons] [_step0] • roll< [popopop] [_stept] branch i\n",
 804       "                                                        [1 2] [3 4] true [[] ccons] [_step0] • swapd swap [popopop] [_stept] branch i\n",
 805       "                                                        [1 2] [3 4] true [[] ccons] [_step0] • [swap] dip swap [popopop] [_stept] branch i\n",
 806       "                                                 [1 2] [3 4] true [[] ccons] [_step0] [swap] • dip swap [popopop] [_stept] branch i\n",
 807       "                                                                 [1 2] [3 4] true [[] ccons] • swap [_step0] swap [popopop] [_stept] branch i\n",
 808       "                                                                 [1 2] [3 4] [[] ccons] true • [_step0] swap [popopop] [_stept] branch i\n",
 809       "                                                        [1 2] [3 4] [[] ccons] true [_step0] • swap [popopop] [_stept] branch i\n",
 810       "                                                        [1 2] [3 4] [[] ccons] [_step0] true • [popopop] [_stept] branch i\n",
 811       "                                              [1 2] [3 4] [[] ccons] [_step0] true [popopop] • [_stept] branch i\n",
 812       "                                     [1 2] [3 4] [[] ccons] [_step0] true [popopop] [_stept] • branch i\n",
 813       "                                                             [1 2] [3 4] [[] ccons] [_step0] • _stept i\n",
 814       "                                                             [1 2] [3 4] [[] ccons] [_step0] • [uncons] dipd [dupdipd] dip x i\n",
 815       "                                                    [1 2] [3 4] [[] ccons] [_step0] [uncons] • dipd [dupdipd] dip x i\n",
 816       "                                                    [1 2] [3 4] [[] ccons] [_step0] [uncons] • [dip] codi [dupdipd] dip x i\n",
 817       "                                              [1 2] [3 4] [[] ccons] [_step0] [uncons] [dip] • codi [dupdipd] dip x i\n",
 818       "                                              [1 2] [3 4] [[] ccons] [_step0] [uncons] [dip] • cons dip [dupdipd] dip x i\n",
 819       "                                              [1 2] [3 4] [[] ccons] [_step0] [[uncons] dip] • dip [dupdipd] dip x i\n",
 820       "                                                                      [1 2] [3 4] [[] ccons] • [uncons] dip [_step0] [dupdipd] dip x i\n",
 821       "                                                             [1 2] [3 4] [[] ccons] [uncons] • dip [_step0] [dupdipd] dip x i\n",
 822       "                                                                                 [1 2] [3 4] • uncons [[] ccons] [_step0] [dupdipd] dip x i\n",
 823       "                                                                                 [1 2] [3 4] • [first] [rest] cleave [[] ccons] [_step0] [dupdipd] dip x i\n",
 824       "                                                                         [1 2] [3 4] [first] • [rest] cleave [[] ccons] [_step0] [dupdipd] dip x i\n",
 825       "                                                                  [1 2] [3 4] [first] [rest] • cleave [[] ccons] [_step0] [dupdipd] dip x i\n",
 826       "                                                                  [1 2] [3 4] [first] [rest] • fork popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 827       "                                                                  [1 2] [3 4] [first] [rest] • [i] app2 popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 828       "                                                              [1 2] [3 4] [first] [rest] [i] • app2 popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 829       "                                                              [1 2] [3 4] [first] [rest] [i] • [grba swap grba swap] dip [infrst] cons ii popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 830       "                                        [1 2] [3 4] [first] [rest] [i] [grba swap grba swap] • dip [infrst] cons ii popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 831       "                                                                  [1 2] [3 4] [first] [rest] • grba swap grba swap [i] [infrst] cons ii popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 832       "                                                                  [1 2] [3 4] [first] [rest] • [stack popd] dip swap grba swap [i] [infrst] cons ii popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 833       "                                                     [1 2] [3 4] [first] [rest] [stack popd] • dip swap grba swap [i] [infrst] cons ii popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 834       "                                                                         [1 2] [3 4] [first] • stack popd [rest] swap grba swap [i] [infrst] cons ii popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 835       "                                                   [1 2] [3 4] [first] [[first] [3 4] [1 2]] • popd [rest] swap grba swap [i] [infrst] cons ii popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 836       "                                                   [1 2] [3 4] [first] [[first] [3 4] [1 2]] • [pop] dip [rest] swap grba swap [i] [infrst] cons ii popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 837       "                                             [1 2] [3 4] [first] [[first] [3 4] [1 2]] [pop] • dip [rest] swap grba swap [i] [infrst] cons ii popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 838       "                                                                         [1 2] [3 4] [first] • pop [[first] [3 4] [1 2]] [rest] swap grba swap [i] [infrst] cons ii popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 839       "                                                                                 [1 2] [3 4] • [[first] [3 4] [1 2]] [rest] swap grba swap [i] [infrst] cons ii popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 840       "                                                           [1 2] [3 4] [[first] [3 4] [1 2]] • [rest] swap grba swap [i] [infrst] cons ii popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 841       "                                                    [1 2] [3 4] [[first] [3 4] [1 2]] [rest] • swap grba swap [i] [infrst] cons ii popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 842       "                                                    [1 2] [3 4] [rest] [[first] [3 4] [1 2]] • grba swap [i] [infrst] cons ii popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 843       "                                                    [1 2] [3 4] [rest] [[first] [3 4] [1 2]] • [stack popd] dip swap [i] [infrst] cons ii popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 844       "                                       [1 2] [3 4] [rest] [[first] [3 4] [1 2]] [stack popd] • dip swap [i] [infrst] cons ii popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 845       "                                                                          [1 2] [3 4] [rest] • stack popd [[first] [3 4] [1 2]] swap [i] [infrst] cons ii popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 846       "                                                     [1 2] [3 4] [rest] [[rest] [3 4] [1 2]] • popd [[first] [3 4] [1 2]] swap [i] [infrst] cons ii popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 847       "                                                     [1 2] [3 4] [rest] [[rest] [3 4] [1 2]] • [pop] dip [[first] [3 4] [1 2]] swap [i] [infrst] cons ii popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 848       "                                               [1 2] [3 4] [rest] [[rest] [3 4] [1 2]] [pop] • dip [[first] [3 4] [1 2]] swap [i] [infrst] cons ii popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 849       "                                                                          [1 2] [3 4] [rest] • pop [[rest] [3 4] [1 2]] [[first] [3 4] [1 2]] swap [i] [infrst] cons ii popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 850       "                                                                                 [1 2] [3 4] • [[rest] [3 4] [1 2]] [[first] [3 4] [1 2]] swap [i] [infrst] cons ii popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 851       "                                                            [1 2] [3 4] [[rest] [3 4] [1 2]] • [[first] [3 4] [1 2]] swap [i] [infrst] cons ii popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 852       "                                      [1 2] [3 4] [[rest] [3 4] [1 2]] [[first] [3 4] [1 2]] • swap [i] [infrst] cons ii popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 853       "                                      [1 2] [3 4] [[first] [3 4] [1 2]] [[rest] [3 4] [1 2]] • [i] [infrst] cons ii popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 854       "                                  [1 2] [3 4] [[first] [3 4] [1 2]] [[rest] [3 4] [1 2]] [i] • [infrst] cons ii popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 855       "                         [1 2] [3 4] [[first] [3 4] [1 2]] [[rest] [3 4] [1 2]] [i] [infrst] • cons ii popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 856       "                         [1 2] [3 4] [[first] [3 4] [1 2]] [[rest] [3 4] [1 2]] [[i] infrst] • ii popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 857       "                         [1 2] [3 4] [[first] [3 4] [1 2]] [[rest] [3 4] [1 2]] [[i] infrst] • [dip] dupdip i popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 858       "                   [1 2] [3 4] [[first] [3 4] [1 2]] [[rest] [3 4] [1 2]] [[i] infrst] [dip] • dupdip i popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 859       "                   [1 2] [3 4] [[first] [3 4] [1 2]] [[rest] [3 4] [1 2]] [[i] infrst] [dip] • dupd dip i popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 860       "                   [1 2] [3 4] [[first] [3 4] [1 2]] [[rest] [3 4] [1 2]] [[i] infrst] [dip] • [dup] dip dip i popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 861       "             [1 2] [3 4] [[first] [3 4] [1 2]] [[rest] [3 4] [1 2]] [[i] infrst] [dip] [dup] • dip dip i popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 862       "                         [1 2] [3 4] [[first] [3 4] [1 2]] [[rest] [3 4] [1 2]] [[i] infrst] • dup [dip] dip i popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 863       "            [1 2] [3 4] [[first] [3 4] [1 2]] [[rest] [3 4] [1 2]] [[i] infrst] [[i] infrst] • [dip] dip i popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 864       "      [1 2] [3 4] [[first] [3 4] [1 2]] [[rest] [3 4] [1 2]] [[i] infrst] [[i] infrst] [dip] • dip i popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 865       "                         [1 2] [3 4] [[first] [3 4] [1 2]] [[rest] [3 4] [1 2]] [[i] infrst] • dip [[i] infrst] i popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 866       "                                                           [1 2] [3 4] [[first] [3 4] [1 2]] • [i] infrst [[rest] [3 4] [1 2]] [[i] infrst] i popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 867       "                                                       [1 2] [3 4] [[first] [3 4] [1 2]] [i] • infrst [[rest] [3 4] [1 2]] [[i] infrst] i popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 868       "                                                       [1 2] [3 4] [[first] [3 4] [1 2]] [i] • infra first [[rest] [3 4] [1 2]] [[i] infrst] i popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 869       "                                                       [1 2] [3 4] [[first] [3 4] [1 2]] [i] • swons swaack [i] dip swaack first [[rest] [3 4] [1 2]] [[i] infrst] i popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 870       "                                                       [1 2] [3 4] [[first] [3 4] [1 2]] [i] • swap cons swaack [i] dip swaack first [[rest] [3 4] [1 2]] [[i] infrst] i popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 871       "                                                       [1 2] [3 4] [i] [[first] [3 4] [1 2]] • cons swaack [i] dip swaack first [[rest] [3 4] [1 2]] [[i] infrst] i popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 872       "                                                       [1 2] [3 4] [[i] [first] [3 4] [1 2]] • swaack [i] dip swaack first [[rest] [3 4] [1 2]] [[i] infrst] i popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 873       "                                                       [1 2] [3 4] [first] [i] [[3 4] [1 2]] • [i] dip swaack first [[rest] [3 4] [1 2]] [[i] infrst] i popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 874       "                                                   [1 2] [3 4] [first] [i] [[3 4] [1 2]] [i] • dip swaack first [[rest] [3 4] [1 2]] [[i] infrst] i popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 875       "                                                                     [1 2] [3 4] [first] [i] • i [[3 4] [1 2]] swaack first [[rest] [3 4] [1 2]] [[i] infrst] i popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 876       "                                                                         [1 2] [3 4] [first] • i [[3 4] [1 2]] swaack first [[rest] [3 4] [1 2]] [[i] infrst] i popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 877       "                                                                                 [1 2] [3 4] • first [[3 4] [1 2]] swaack first [[rest] [3 4] [1 2]] [[i] infrst] i popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 878       "                                                                                     [1 2] 3 • [[3 4] [1 2]] swaack first [[rest] [3 4] [1 2]] [[i] infrst] i popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 879       "                                                                       [1 2] 3 [[3 4] [1 2]] • swaack first [[rest] [3 4] [1 2]] [[i] infrst] i popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 880       "                                                                       [1 2] [3 4] [3 [1 2]] • first [[rest] [3 4] [1 2]] [[i] infrst] i popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 881       "                                                                               [1 2] [3 4] 3 • [[rest] [3 4] [1 2]] [[i] infrst] i popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 882       "                                                          [1 2] [3 4] 3 [[rest] [3 4] [1 2]] • [[i] infrst] i popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 883       "                                             [1 2] [3 4] 3 [[rest] [3 4] [1 2]] [[i] infrst] • i popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 884       "                                                          [1 2] [3 4] 3 [[rest] [3 4] [1 2]] • [i] infrst popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 885       "                                                      [1 2] [3 4] 3 [[rest] [3 4] [1 2]] [i] • infrst popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 886       "                                                      [1 2] [3 4] 3 [[rest] [3 4] [1 2]] [i] • infra first popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 887       "                                                      [1 2] [3 4] 3 [[rest] [3 4] [1 2]] [i] • swons swaack [i] dip swaack first popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 888       "                                                      [1 2] [3 4] 3 [[rest] [3 4] [1 2]] [i] • swap cons swaack [i] dip swaack first popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 889       "                                                      [1 2] [3 4] 3 [i] [[rest] [3 4] [1 2]] • cons swaack [i] dip swaack first popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 890       "                                                      [1 2] [3 4] 3 [[i] [rest] [3 4] [1 2]] • swaack [i] dip swaack first popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 891       "                                                      [1 2] [3 4] [rest] [i] [3 [3 4] [1 2]] • [i] dip swaack first popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 892       "                                                  [1 2] [3 4] [rest] [i] [3 [3 4] [1 2]] [i] • dip swaack first popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 893       "                                                                      [1 2] [3 4] [rest] [i] • i [3 [3 4] [1 2]] swaack first popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 894       "                                                                          [1 2] [3 4] [rest] • i [3 [3 4] [1 2]] swaack first popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 895       "                                                                                 [1 2] [3 4] • rest [3 [3 4] [1 2]] swaack first popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 896       "                                                                                 [1 2] [3 4] • [pop] infra [3 [3 4] [1 2]] swaack first popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 897       "                                                                           [1 2] [3 4] [pop] • infra [3 [3 4] [1 2]] swaack first popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 898       "                                                                           [1 2] [3 4] [pop] • swons swaack [i] dip swaack [3 [3 4] [1 2]] swaack first popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 899       "                                                                           [1 2] [3 4] [pop] • swap cons swaack [i] dip swaack [3 [3 4] [1 2]] swaack first popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 900       "                                                                           [1 2] [pop] [3 4] • cons swaack [i] dip swaack [3 [3 4] [1 2]] swaack first popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 901       "                                                                           [1 2] [[pop] 3 4] • swaack [i] dip swaack [3 [3 4] [1 2]] swaack first popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 902       "                                                                           4 3 [pop] [[1 2]] • [i] dip swaack [3 [3 4] [1 2]] swaack first popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 903       "                                                                       4 3 [pop] [[1 2]] [i] • dip swaack [3 [3 4] [1 2]] swaack first popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 904       "                                                                                   4 3 [pop] • i [[1 2]] swaack [3 [3 4] [1 2]] swaack first popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 905       "                                                                                         4 3 • pop [[1 2]] swaack [3 [3 4] [1 2]] swaack first popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 906       "                                                                                           4 • [[1 2]] swaack [3 [3 4] [1 2]] swaack first popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 907       "                                                                                   4 [[1 2]] • swaack [3 [3 4] [1 2]] swaack first popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 908       "                                                                                   [1 2] [4] • [3 [3 4] [1 2]] swaack first popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 909       "                                                                   [1 2] [4] [3 [3 4] [1 2]] • swaack first popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 910       "                                                                   [1 2] [3 4] 3 [[4] [1 2]] • first popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 911       "                                                                           [1 2] [3 4] 3 [4] • popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 912       "                                                                           [1 2] [3 4] 3 [4] • [pop] dipd [[] ccons] [_step0] [dupdipd] dip x i\n",
 913       "                                                                     [1 2] [3 4] 3 [4] [pop] • dipd [[] ccons] [_step0] [dupdipd] dip x i\n",
 914       "                                                                     [1 2] [3 4] 3 [4] [pop] • [dip] codi [[] ccons] [_step0] [dupdipd] dip x i\n",
 915       "                                                               [1 2] [3 4] 3 [4] [pop] [dip] • codi [[] ccons] [_step0] [dupdipd] dip x i\n",
 916       "                                                               [1 2] [3 4] 3 [4] [pop] [dip] • cons dip [[] ccons] [_step0] [dupdipd] dip x i\n",
 917       "                                                               [1 2] [3 4] 3 [4] [[pop] dip] • dip [[] ccons] [_step0] [dupdipd] dip x i\n",
 918       "                                                                               [1 2] [3 4] 3 • [pop] dip [4] [[] ccons] [_step0] [dupdipd] dip x i\n",
 919       "                                                                         [1 2] [3 4] 3 [pop] • dip [4] [[] ccons] [_step0] [dupdipd] dip x i\n",
 920       "                                                                                 [1 2] [3 4] • pop 3 [4] [[] ccons] [_step0] [dupdipd] dip x i\n",
 921       "                                                                                       [1 2] • 3 [4] [[] ccons] [_step0] [dupdipd] dip x i\n",
 922       "                                                                                     [1 2] 3 • [4] [[] ccons] [_step0] [dupdipd] dip x i\n",
 923       "                                                                                 [1 2] 3 [4] • [[] ccons] [_step0] [dupdipd] dip x i\n",
 924       "                                                                      [1 2] 3 [4] [[] ccons] • [_step0] [dupdipd] dip x i\n",
 925       "                                                             [1 2] 3 [4] [[] ccons] [_step0] • [dupdipd] dip x i\n",
 926       "                                                   [1 2] 3 [4] [[] ccons] [_step0] [dupdipd] • dip x i\n",
 927       "                                                                      [1 2] 3 [4] [[] ccons] • dupdipd [_step0] x i\n",
 928       "                                                                      [1 2] 3 [4] [[] ccons] • dup dipd [_step0] x i\n",
 929       "                                                           [1 2] 3 [4] [[] ccons] [[] ccons] • dipd [_step0] x i\n",
 930       "                                                           [1 2] 3 [4] [[] ccons] [[] ccons] • [dip] codi [_step0] x i\n",
 931       "                                                     [1 2] 3 [4] [[] ccons] [[] ccons] [dip] • codi [_step0] x i\n",
 932       "                                                     [1 2] 3 [4] [[] ccons] [[] ccons] [dip] • cons dip [_step0] x i\n",
 933       "                                                     [1 2] 3 [4] [[] ccons] [[[] ccons] dip] • dip [_step0] x i\n",
 934       "                                                                                 [1 2] 3 [4] • [[] ccons] dip [[] ccons] [_step0] x i\n",
 935       "                                                                      [1 2] 3 [4] [[] ccons] • dip [[] ccons] [_step0] x i\n",
 936       "                                                                                     [1 2] 3 • [] ccons [4] [[] ccons] [_step0] x i\n",
 937       "                                                                                  [1 2] 3 [] • ccons [4] [[] ccons] [_step0] x i\n",
 938       "                                                                                  [1 2] 3 [] • cons cons [4] [[] ccons] [_step0] x i\n",
 939       "                                                                                   [1 2] [3] • cons [4] [[] ccons] [_step0] x i\n",
 940       "                                                                                   [[1 2] 3] • [4] [[] ccons] [_step0] x i\n",
 941       "                                                                               [[1 2] 3] [4] • [[] ccons] [_step0] x i\n",
 942       "                                                                    [[1 2] 3] [4] [[] ccons] • [_step0] x i\n",
 943       "                                                           [[1 2] 3] [4] [[] ccons] [_step0] • x i\n",
 944       "                                                           [[1 2] 3] [4] [[] ccons] [_step0] • dup i i\n",
 945       "                                                  [[1 2] 3] [4] [[] ccons] [_step0] [_step0] • i i\n",
 946       "                                                           [[1 2] 3] [4] [[] ccons] [_step0] • _step0 i\n",
 947       "                                                           [[1 2] 3] [4] [[] ccons] [_step0] • _step1 [popopop] [_stept] branch i\n",
 948       "                                                           [[1 2] 3] [4] [[] ccons] [_step0] • [?] dipd roll< [popopop] [_stept] branch i\n",
 949       "                                                       [[1 2] 3] [4] [[] ccons] [_step0] [?] • dipd roll< [popopop] [_stept] branch i\n",
 950       "                                                       [[1 2] 3] [4] [[] ccons] [_step0] [?] • [dip] codi roll< [popopop] [_stept] branch i\n",
 951       "                                                 [[1 2] 3] [4] [[] ccons] [_step0] [?] [dip] • codi roll< [popopop] [_stept] branch i\n",
 952       "                                                 [[1 2] 3] [4] [[] ccons] [_step0] [?] [dip] • cons dip roll< [popopop] [_stept] branch i\n",
 953       "                                                 [[1 2] 3] [4] [[] ccons] [_step0] [[?] dip] • dip roll< [popopop] [_stept] branch i\n",
 954       "                                                                    [[1 2] 3] [4] [[] ccons] • [?] dip [_step0] roll< [popopop] [_stept] branch i\n",
 955       "                                                                [[1 2] 3] [4] [[] ccons] [?] • dip [_step0] roll< [popopop] [_stept] branch i\n",
 956       "                                                                               [[1 2] 3] [4] • ? [[] ccons] [_step0] roll< [popopop] [_stept] branch i\n",
 957       "                                                                               [[1 2] 3] [4] • dup bool [[] ccons] [_step0] roll< [popopop] [_stept] branch i\n",
 958       "                                                                           [[1 2] 3] [4] [4] • bool [[] ccons] [_step0] roll< [popopop] [_stept] branch i\n",
 959       "                                                                          [[1 2] 3] [4] true • [[] ccons] [_step0] roll< [popopop] [_stept] branch i\n",
 960       "                                                               [[1 2] 3] [4] true [[] ccons] • [_step0] roll< [popopop] [_stept] branch i\n",
 961       "                                                      [[1 2] 3] [4] true [[] ccons] [_step0] • roll< [popopop] [_stept] branch i\n",
 962       "                                                      [[1 2] 3] [4] true [[] ccons] [_step0] • swapd swap [popopop] [_stept] branch i\n",
 963       "                                                      [[1 2] 3] [4] true [[] ccons] [_step0] • [swap] dip swap [popopop] [_stept] branch i\n",
 964       "                                               [[1 2] 3] [4] true [[] ccons] [_step0] [swap] • dip swap [popopop] [_stept] branch i\n",
 965       "                                                               [[1 2] 3] [4] true [[] ccons] • swap [_step0] swap [popopop] [_stept] branch i\n",
 966       "                                                               [[1 2] 3] [4] [[] ccons] true • [_step0] swap [popopop] [_stept] branch i\n",
 967       "                                                      [[1 2] 3] [4] [[] ccons] true [_step0] • swap [popopop] [_stept] branch i\n",
 968       "                                                      [[1 2] 3] [4] [[] ccons] [_step0] true • [popopop] [_stept] branch i\n",
 969       "                                            [[1 2] 3] [4] [[] ccons] [_step0] true [popopop] • [_stept] branch i\n",
 970       "                                   [[1 2] 3] [4] [[] ccons] [_step0] true [popopop] [_stept] • branch i\n",
 971       "                                                           [[1 2] 3] [4] [[] ccons] [_step0] • _stept i\n",
 972       "                                                           [[1 2] 3] [4] [[] ccons] [_step0] • [uncons] dipd [dupdipd] dip x i\n",
 973       "                                                  [[1 2] 3] [4] [[] ccons] [_step0] [uncons] • dipd [dupdipd] dip x i\n",
 974       "                                                  [[1 2] 3] [4] [[] ccons] [_step0] [uncons] • [dip] codi [dupdipd] dip x i\n",
 975       "                                            [[1 2] 3] [4] [[] ccons] [_step0] [uncons] [dip] • codi [dupdipd] dip x i\n",
 976       "                                            [[1 2] 3] [4] [[] ccons] [_step0] [uncons] [dip] • cons dip [dupdipd] dip x i\n",
 977       "                                            [[1 2] 3] [4] [[] ccons] [_step0] [[uncons] dip] • dip [dupdipd] dip x i\n",
 978       "                                                                    [[1 2] 3] [4] [[] ccons] • [uncons] dip [_step0] [dupdipd] dip x i\n",
 979       "                                                           [[1 2] 3] [4] [[] ccons] [uncons] • dip [_step0] [dupdipd] dip x i\n",
 980       "                                                                               [[1 2] 3] [4] • uncons [[] ccons] [_step0] [dupdipd] dip x i\n",
 981       "                                                                               [[1 2] 3] [4] • [first] [rest] cleave [[] ccons] [_step0] [dupdipd] dip x i\n",
 982       "                                                                       [[1 2] 3] [4] [first] • [rest] cleave [[] ccons] [_step0] [dupdipd] dip x i\n",
 983       "                                                                [[1 2] 3] [4] [first] [rest] • cleave [[] ccons] [_step0] [dupdipd] dip x i\n",
 984       "                                                                [[1 2] 3] [4] [first] [rest] • fork popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 985       "                                                                [[1 2] 3] [4] [first] [rest] • [i] app2 popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 986       "                                                            [[1 2] 3] [4] [first] [rest] [i] • app2 popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 987       "                                                            [[1 2] 3] [4] [first] [rest] [i] • [grba swap grba swap] dip [infrst] cons ii popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 988       "                                      [[1 2] 3] [4] [first] [rest] [i] [grba swap grba swap] • dip [infrst] cons ii popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 989       "                                                                [[1 2] 3] [4] [first] [rest] • grba swap grba swap [i] [infrst] cons ii popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 990       "                                                                [[1 2] 3] [4] [first] [rest] • [stack popd] dip swap grba swap [i] [infrst] cons ii popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 991       "                                                   [[1 2] 3] [4] [first] [rest] [stack popd] • dip swap grba swap [i] [infrst] cons ii popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 992       "                                                                       [[1 2] 3] [4] [first] • stack popd [rest] swap grba swap [i] [infrst] cons ii popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 993       "                                               [[1 2] 3] [4] [first] [[first] [4] [[1 2] 3]] • popd [rest] swap grba swap [i] [infrst] cons ii popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 994       "                                               [[1 2] 3] [4] [first] [[first] [4] [[1 2] 3]] • [pop] dip [rest] swap grba swap [i] [infrst] cons ii popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 995       "                                         [[1 2] 3] [4] [first] [[first] [4] [[1 2] 3]] [pop] • dip [rest] swap grba swap [i] [infrst] cons ii popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 996       "                                                                       [[1 2] 3] [4] [first] • pop [[first] [4] [[1 2] 3]] [rest] swap grba swap [i] [infrst] cons ii popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 997       "                                                                               [[1 2] 3] [4] • [[first] [4] [[1 2] 3]] [rest] swap grba swap [i] [infrst] cons ii popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 998       "                                                       [[1 2] 3] [4] [[first] [4] [[1 2] 3]] • [rest] swap grba swap [i] [infrst] cons ii popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
 999       "                                                [[1 2] 3] [4] [[first] [4] [[1 2] 3]] [rest] • swap grba swap [i] [infrst] cons ii popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
1000       "                                                [[1 2] 3] [4] [rest] [[first] [4] [[1 2] 3]] • grba swap [i] [infrst] cons ii popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
1001       "                                                [[1 2] 3] [4] [rest] [[first] [4] [[1 2] 3]] • [stack popd] dip swap [i] [infrst] cons ii popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
1002       "                                   [[1 2] 3] [4] [rest] [[first] [4] [[1 2] 3]] [stack popd] • dip swap [i] [infrst] cons ii popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
1003       "                                                                        [[1 2] 3] [4] [rest] • stack popd [[first] [4] [[1 2] 3]] swap [i] [infrst] cons ii popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
1004       "                                                 [[1 2] 3] [4] [rest] [[rest] [4] [[1 2] 3]] • popd [[first] [4] [[1 2] 3]] swap [i] [infrst] cons ii popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
1005       "                                                 [[1 2] 3] [4] [rest] [[rest] [4] [[1 2] 3]] • [pop] dip [[first] [4] [[1 2] 3]] swap [i] [infrst] cons ii popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
1006       "                                           [[1 2] 3] [4] [rest] [[rest] [4] [[1 2] 3]] [pop] • dip [[first] [4] [[1 2] 3]] swap [i] [infrst] cons ii popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
1007       "                                                                        [[1 2] 3] [4] [rest] • pop [[rest] [4] [[1 2] 3]] [[first] [4] [[1 2] 3]] swap [i] [infrst] cons ii popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
1008       "                                                                               [[1 2] 3] [4] • [[rest] [4] [[1 2] 3]] [[first] [4] [[1 2] 3]] swap [i] [infrst] cons ii popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
1009       "                                                        [[1 2] 3] [4] [[rest] [4] [[1 2] 3]] • [[first] [4] [[1 2] 3]] swap [i] [infrst] cons ii popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
1010       "                                [[1 2] 3] [4] [[rest] [4] [[1 2] 3]] [[first] [4] [[1 2] 3]] • swap [i] [infrst] cons ii popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
1011       "                                [[1 2] 3] [4] [[first] [4] [[1 2] 3]] [[rest] [4] [[1 2] 3]] • [i] [infrst] cons ii popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
1012       "                            [[1 2] 3] [4] [[first] [4] [[1 2] 3]] [[rest] [4] [[1 2] 3]] [i] • [infrst] cons ii popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
1013       "                   [[1 2] 3] [4] [[first] [4] [[1 2] 3]] [[rest] [4] [[1 2] 3]] [i] [infrst] • cons ii popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
1014       "                   [[1 2] 3] [4] [[first] [4] [[1 2] 3]] [[rest] [4] [[1 2] 3]] [[i] infrst] • ii popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
1015       "                   [[1 2] 3] [4] [[first] [4] [[1 2] 3]] [[rest] [4] [[1 2] 3]] [[i] infrst] • [dip] dupdip i popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
1016       "             [[1 2] 3] [4] [[first] [4] [[1 2] 3]] [[rest] [4] [[1 2] 3]] [[i] infrst] [dip] • dupdip i popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
1017       "             [[1 2] 3] [4] [[first] [4] [[1 2] 3]] [[rest] [4] [[1 2] 3]] [[i] infrst] [dip] • dupd dip i popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
1018       "             [[1 2] 3] [4] [[first] [4] [[1 2] 3]] [[rest] [4] [[1 2] 3]] [[i] infrst] [dip] • [dup] dip dip i popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
1019       "       [[1 2] 3] [4] [[first] [4] [[1 2] 3]] [[rest] [4] [[1 2] 3]] [[i] infrst] [dip] [dup] • dip dip i popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
1020       "                   [[1 2] 3] [4] [[first] [4] [[1 2] 3]] [[rest] [4] [[1 2] 3]] [[i] infrst] • dup [dip] dip i popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
1021       "      [[1 2] 3] [4] [[first] [4] [[1 2] 3]] [[rest] [4] [[1 2] 3]] [[i] infrst] [[i] infrst] • [dip] dip i popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
1022       "[[1 2] 3] [4] [[first] [4] [[1 2] 3]] [[rest] [4] [[1 2] 3]] [[i] infrst] [[i] infrst] [dip] • dip i popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
1023       "                   [[1 2] 3] [4] [[first] [4] [[1 2] 3]] [[rest] [4] [[1 2] 3]] [[i] infrst] • dip [[i] infrst] i popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
1024       "                                                       [[1 2] 3] [4] [[first] [4] [[1 2] 3]] • [i] infrst [[rest] [4] [[1 2] 3]] [[i] infrst] i popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
1025       "                                                   [[1 2] 3] [4] [[first] [4] [[1 2] 3]] [i] • infrst [[rest] [4] [[1 2] 3]] [[i] infrst] i popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
1026       "                                                   [[1 2] 3] [4] [[first] [4] [[1 2] 3]] [i] • infra first [[rest] [4] [[1 2] 3]] [[i] infrst] i popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
1027       "                                                   [[1 2] 3] [4] [[first] [4] [[1 2] 3]] [i] • swons swaack [i] dip swaack first [[rest] [4] [[1 2] 3]] [[i] infrst] i popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
1028       "                                                   [[1 2] 3] [4] [[first] [4] [[1 2] 3]] [i] • swap cons swaack [i] dip swaack first [[rest] [4] [[1 2] 3]] [[i] infrst] i popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
1029       "                                                   [[1 2] 3] [4] [i] [[first] [4] [[1 2] 3]] • cons swaack [i] dip swaack first [[rest] [4] [[1 2] 3]] [[i] infrst] i popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
1030       "                                                   [[1 2] 3] [4] [[i] [first] [4] [[1 2] 3]] • swaack [i] dip swaack first [[rest] [4] [[1 2] 3]] [[i] infrst] i popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
1031       "                                                   [[1 2] 3] [4] [first] [i] [[4] [[1 2] 3]] • [i] dip swaack first [[rest] [4] [[1 2] 3]] [[i] infrst] i popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
1032       "                                               [[1 2] 3] [4] [first] [i] [[4] [[1 2] 3]] [i] • dip swaack first [[rest] [4] [[1 2] 3]] [[i] infrst] i popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
1033       "                                                                   [[1 2] 3] [4] [first] [i] • i [[4] [[1 2] 3]] swaack first [[rest] [4] [[1 2] 3]] [[i] infrst] i popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
1034       "                                                                       [[1 2] 3] [4] [first] • i [[4] [[1 2] 3]] swaack first [[rest] [4] [[1 2] 3]] [[i] infrst] i popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
1035       "                                                                               [[1 2] 3] [4] • first [[4] [[1 2] 3]] swaack first [[rest] [4] [[1 2] 3]] [[i] infrst] i popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
1036       "                                                                                 [[1 2] 3] 4 • [[4] [[1 2] 3]] swaack first [[rest] [4] [[1 2] 3]] [[i] infrst] i popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
1037       "                                                                 [[1 2] 3] 4 [[4] [[1 2] 3]] • swaack first [[rest] [4] [[1 2] 3]] [[i] infrst] i popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
1038       "                                                                 [[1 2] 3] [4] [4 [[1 2] 3]] • first [[rest] [4] [[1 2] 3]] [[i] infrst] i popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
1039       "                                                                             [[1 2] 3] [4] 4 • [[rest] [4] [[1 2] 3]] [[i] infrst] i popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
1040       "                                                      [[1 2] 3] [4] 4 [[rest] [4] [[1 2] 3]] • [[i] infrst] i popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
1041       "                                         [[1 2] 3] [4] 4 [[rest] [4] [[1 2] 3]] [[i] infrst] • i popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
1042       "                                                      [[1 2] 3] [4] 4 [[rest] [4] [[1 2] 3]] • [i] infrst popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
1043       "                                                  [[1 2] 3] [4] 4 [[rest] [4] [[1 2] 3]] [i] • infrst popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
1044       "                                                  [[1 2] 3] [4] 4 [[rest] [4] [[1 2] 3]] [i] • infra first popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
1045       "                                                  [[1 2] 3] [4] 4 [[rest] [4] [[1 2] 3]] [i] • swons swaack [i] dip swaack first popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
1046       "                                                  [[1 2] 3] [4] 4 [[rest] [4] [[1 2] 3]] [i] • swap cons swaack [i] dip swaack first popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
1047       "                                                  [[1 2] 3] [4] 4 [i] [[rest] [4] [[1 2] 3]] • cons swaack [i] dip swaack first popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
1048       "                                                  [[1 2] 3] [4] 4 [[i] [rest] [4] [[1 2] 3]] • swaack [i] dip swaack first popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
1049       "                                                  [[1 2] 3] [4] [rest] [i] [4 [4] [[1 2] 3]] • [i] dip swaack first popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
1050       "                                              [[1 2] 3] [4] [rest] [i] [4 [4] [[1 2] 3]] [i] • dip swaack first popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
1051       "                                                                    [[1 2] 3] [4] [rest] [i] • i [4 [4] [[1 2] 3]] swaack first popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
1052       "                                                                        [[1 2] 3] [4] [rest] • i [4 [4] [[1 2] 3]] swaack first popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
1053       "                                                                               [[1 2] 3] [4] • rest [4 [4] [[1 2] 3]] swaack first popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
1054       "                                                                               [[1 2] 3] [4] • [pop] infra [4 [4] [[1 2] 3]] swaack first popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
1055       "                                                                         [[1 2] 3] [4] [pop] • infra [4 [4] [[1 2] 3]] swaack first popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
1056       "                                                                         [[1 2] 3] [4] [pop] • swons swaack [i] dip swaack [4 [4] [[1 2] 3]] swaack first popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
1057       "                                                                         [[1 2] 3] [4] [pop] • swap cons swaack [i] dip swaack [4 [4] [[1 2] 3]] swaack first popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
1058       "                                                                         [[1 2] 3] [pop] [4] • cons swaack [i] dip swaack [4 [4] [[1 2] 3]] swaack first popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
1059       "                                                                         [[1 2] 3] [[pop] 4] • swaack [i] dip swaack [4 [4] [[1 2] 3]] swaack first popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
1060       "                                                                         4 [pop] [[[1 2] 3]] • [i] dip swaack [4 [4] [[1 2] 3]] swaack first popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
1061       "                                                                     4 [pop] [[[1 2] 3]] [i] • dip swaack [4 [4] [[1 2] 3]] swaack first popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
1062       "                                                                                     4 [pop] • i [[[1 2] 3]] swaack [4 [4] [[1 2] 3]] swaack first popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
1063       "                                                                                           4 • pop [[[1 2] 3]] swaack [4 [4] [[1 2] 3]] swaack first popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
1064       "                                                                                             • [[[1 2] 3]] swaack [4 [4] [[1 2] 3]] swaack first popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
1065       "                                                                                 [[[1 2] 3]] • swaack [4 [4] [[1 2] 3]] swaack first popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
1066       "                                                                                [[1 2] 3] [] • [4 [4] [[1 2] 3]] swaack first popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
1067       "                                                              [[1 2] 3] [] [4 [4] [[1 2] 3]] • swaack first popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
1068       "                                                              [[1 2] 3] [4] 4 [[] [[1 2] 3]] • first popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
1069       "                                                                          [[1 2] 3] [4] 4 [] • popdd [[] ccons] [_step0] [dupdipd] dip x i\n",
1070       "                                                                          [[1 2] 3] [4] 4 [] • [pop] dipd [[] ccons] [_step0] [dupdipd] dip x i\n",
1071       "                                                                    [[1 2] 3] [4] 4 [] [pop] • dipd [[] ccons] [_step0] [dupdipd] dip x i\n",
1072       "                                                                    [[1 2] 3] [4] 4 [] [pop] • [dip] codi [[] ccons] [_step0] [dupdipd] dip x i\n",
1073       "                                                              [[1 2] 3] [4] 4 [] [pop] [dip] • codi [[] ccons] [_step0] [dupdipd] dip x i\n",
1074       "                                                              [[1 2] 3] [4] 4 [] [pop] [dip] • cons dip [[] ccons] [_step0] [dupdipd] dip x i\n",
1075       "                                                              [[1 2] 3] [4] 4 [] [[pop] dip] • dip [[] ccons] [_step0] [dupdipd] dip x i\n",
1076       "                                                                             [[1 2] 3] [4] 4 • [pop] dip [] [[] ccons] [_step0] [dupdipd] dip x i\n",
1077       "                                                                       [[1 2] 3] [4] 4 [pop] • dip [] [[] ccons] [_step0] [dupdipd] dip x i\n",
1078       "                                                                               [[1 2] 3] [4] • pop 4 [] [[] ccons] [_step0] [dupdipd] dip x i\n",
1079       "                                                                                   [[1 2] 3] • 4 [] [[] ccons] [_step0] [dupdipd] dip x i\n",
1080       "                                                                                 [[1 2] 3] 4 • [] [[] ccons] [_step0] [dupdipd] dip x i\n",
1081       "                                                                              [[1 2] 3] 4 [] • [[] ccons] [_step0] [dupdipd] dip x i\n",
1082       "                                                                   [[1 2] 3] 4 [] [[] ccons] • [_step0] [dupdipd] dip x i\n",
1083       "                                                          [[1 2] 3] 4 [] [[] ccons] [_step0] • [dupdipd] dip x i\n",
1084       "                                                [[1 2] 3] 4 [] [[] ccons] [_step0] [dupdipd] • dip x i\n",
1085       "                                                                   [[1 2] 3] 4 [] [[] ccons] • dupdipd [_step0] x i\n",
1086       "                                                                   [[1 2] 3] 4 [] [[] ccons] • dup dipd [_step0] x i\n",
1087       "                                                        [[1 2] 3] 4 [] [[] ccons] [[] ccons] • dipd [_step0] x i\n",
1088       "                                                        [[1 2] 3] 4 [] [[] ccons] [[] ccons] • [dip] codi [_step0] x i\n",
1089       "                                                  [[1 2] 3] 4 [] [[] ccons] [[] ccons] [dip] • codi [_step0] x i\n",
1090       "                                                  [[1 2] 3] 4 [] [[] ccons] [[] ccons] [dip] • cons dip [_step0] x i\n",
1091       "                                                  [[1 2] 3] 4 [] [[] ccons] [[[] ccons] dip] • dip [_step0] x i\n",
1092       "                                                                              [[1 2] 3] 4 [] • [[] ccons] dip [[] ccons] [_step0] x i\n",
1093       "                                                                   [[1 2] 3] 4 [] [[] ccons] • dip [[] ccons] [_step0] x i\n",
1094       "                                                                                 [[1 2] 3] 4 • [] ccons [] [[] ccons] [_step0] x i\n",
1095       "                                                                              [[1 2] 3] 4 [] • ccons [] [[] ccons] [_step0] x i\n",
1096       "                                                                              [[1 2] 3] 4 [] • cons cons [] [[] ccons] [_step0] x i\n",
1097       "                                                                               [[1 2] 3] [4] • cons [] [[] ccons] [_step0] x i\n",
1098       "                                                                               [[[1 2] 3] 4] • [] [[] ccons] [_step0] x i\n",
1099       "                                                                            [[[1 2] 3] 4] [] • [[] ccons] [_step0] x i\n",
1100       "                                                                 [[[1 2] 3] 4] [] [[] ccons] • [_step0] x i\n",
1101       "                                                        [[[1 2] 3] 4] [] [[] ccons] [_step0] • x i\n",
1102       "                                                        [[[1 2] 3] 4] [] [[] ccons] [_step0] • dup i i\n",
1103       "                                               [[[1 2] 3] 4] [] [[] ccons] [_step0] [_step0] • i i\n",
1104       "                                                        [[[1 2] 3] 4] [] [[] ccons] [_step0] • _step0 i\n",
1105       "                                                        [[[1 2] 3] 4] [] [[] ccons] [_step0] • _step1 [popopop] [_stept] branch i\n",
1106       "                                                        [[[1 2] 3] 4] [] [[] ccons] [_step0] • [?] dipd roll< [popopop] [_stept] branch i\n",
1107       "                                                    [[[1 2] 3] 4] [] [[] ccons] [_step0] [?] • dipd roll< [popopop] [_stept] branch i\n",
1108       "                                                    [[[1 2] 3] 4] [] [[] ccons] [_step0] [?] • [dip] codi roll< [popopop] [_stept] branch i\n",
1109       "                                              [[[1 2] 3] 4] [] [[] ccons] [_step0] [?] [dip] • codi roll< [popopop] [_stept] branch i\n",
1110       "                                              [[[1 2] 3] 4] [] [[] ccons] [_step0] [?] [dip] • cons dip roll< [popopop] [_stept] branch i\n",
1111       "                                              [[[1 2] 3] 4] [] [[] ccons] [_step0] [[?] dip] • dip roll< [popopop] [_stept] branch i\n",
1112       "                                                                 [[[1 2] 3] 4] [] [[] ccons] • [?] dip [_step0] roll< [popopop] [_stept] branch i\n",
1113       "                                                             [[[1 2] 3] 4] [] [[] ccons] [?] • dip [_step0] roll< [popopop] [_stept] branch i\n",
1114       "                                                                            [[[1 2] 3] 4] [] • ? [[] ccons] [_step0] roll< [popopop] [_stept] branch i\n",
1115       "                                                                            [[[1 2] 3] 4] [] • dup bool [[] ccons] [_step0] roll< [popopop] [_stept] branch i\n",
1116       "                                                                         [[[1 2] 3] 4] [] [] • bool [[] ccons] [_step0] roll< [popopop] [_stept] branch i\n",
1117       "                                                                      [[[1 2] 3] 4] [] false • [[] ccons] [_step0] roll< [popopop] [_stept] branch i\n",
1118       "                                                           [[[1 2] 3] 4] [] false [[] ccons] • [_step0] roll< [popopop] [_stept] branch i\n",
1119       "                                                  [[[1 2] 3] 4] [] false [[] ccons] [_step0] • roll< [popopop] [_stept] branch i\n",
1120       "                                                  [[[1 2] 3] 4] [] false [[] ccons] [_step0] • swapd swap [popopop] [_stept] branch i\n",
1121       "                                                  [[[1 2] 3] 4] [] false [[] ccons] [_step0] • [swap] dip swap [popopop] [_stept] branch i\n",
1122       "                                           [[[1 2] 3] 4] [] false [[] ccons] [_step0] [swap] • dip swap [popopop] [_stept] branch i\n",
1123       "                                                           [[[1 2] 3] 4] [] false [[] ccons] • swap [_step0] swap [popopop] [_stept] branch i\n",
1124       "                                                           [[[1 2] 3] 4] [] [[] ccons] false • [_step0] swap [popopop] [_stept] branch i\n",
1125       "                                                  [[[1 2] 3] 4] [] [[] ccons] false [_step0] • swap [popopop] [_stept] branch i\n",
1126       "                                                  [[[1 2] 3] 4] [] [[] ccons] [_step0] false • [popopop] [_stept] branch i\n",
1127       "                                        [[[1 2] 3] 4] [] [[] ccons] [_step0] false [popopop] • [_stept] branch i\n",
1128       "                               [[[1 2] 3] 4] [] [[] ccons] [_step0] false [popopop] [_stept] • branch i\n",
1129       "                                                        [[[1 2] 3] 4] [] [[] ccons] [_step0] • popopop i\n",
1130       "                                                        [[[1 2] 3] 4] [] [[] ccons] [_step0] • pop popop i\n",
1131       "                                                                 [[[1 2] 3] 4] [] [[] ccons] • popop i\n",
1132       "                                                                 [[[1 2] 3] 4] [] [[] ccons] • pop pop i\n",
1133       "                                                                            [[[1 2] 3] 4] [] • pop i\n",
1134       "                                                                               [[[1 2] 3] 4] • i\n",
1135       "                                                                                             • [[1 2] 3] 4\n",
1136       "                                                                                   [[1 2] 3] • 4\n",
1137       "                                                                                 [[1 2] 3] 4 • \n",
1138       "\n",
1139       "[[1 2] 3] 4"
1140      ]
1141     }
1142    ],
1143    "source": [
1144     "1 [2 3 4] [Z] trace"
1145    ]
1146   },
1147   {
1148    "cell_type": "code",
1149    "execution_count": 19,
1150    "metadata": {},
1151    "outputs": [
1152     {
1153      "name": "stdout",
1154      "output_type": "stream",
1155      "text": []
1156     }
1157    ],
1158    "source": [
1159     "clear"
1160    ]
1161   },
1162   {
1163    "cell_type": "markdown",
1164    "metadata": {},
1165    "source": [
1166     "And here it is doing the thing."
1167    ]
1168   },
1169   {
1170    "cell_type": "code",
1171    "execution_count": 20,
1172    "metadata": {},
1173    "outputs": [
1174     {
1175      "name": "stdout",
1176      "output_type": "stream",
1177      "text": [
1178       "[1 [2 [3 4 25 6] 7] 8] [sqr] [dip dip infra dip infra dip infra]"
1179      ]
1180     }
1181    ],
1182    "source": [
1183     "[1 [2 [3 4 25 6] 7] 8] [sqr] [dip dip infra dip infra dip infra]"
1184    ]
1185   },
1186   {
1187    "cell_type": "code",
1188    "execution_count": null,
1189    "metadata": {},
1190    "outputs": [],
1191    "source": [
1192     " [[[] ccons] step i] trace"
1193    ]
1194   },
1195   {
1196    "cell_type": "markdown",
1197    "metadata": {},
1198    "source": [
1199     "## Addressing\n",
1200     "Because we are only using two combinators we could replace the list with a string made from only two characters.\n",
1201     "\n",
1202     "       [...] [Q] 'ddididi' Zstr\n",
1203     "    -------------------------------------------------------------\n",
1204     "       [...] [[[[[[[Q] dip] dip] infra] dip] infra] dip] infra\n",
1205     "\n",
1206     "The string can be considered a name or address for an item in the subject datastructure.\n",
1207     "\n",
1208     "## Determining the right \"path\" for an item in a tree.\n",
1209     "It's easy to read off (in reverse) the right sequence of \"d\" and \"i\" from the subject datastructure:\n",
1210     "\n",
1211     "    [ n [ n [ n n x ...\n",
1212     "    i d i d i d d Bingo!"
1213    ]
1214   }
1215  ],
1216  "metadata": {
1217   "kernelspec": {
1218    "display_name": "Joypy",
1219    "language": "",
1220    "name": "thun"
1221   },
1222   "language_info": {
1223    "file_extension": ".joy",
1224    "mimetype": "text/plain",
1225    "name": "Joy"
1226   }
1227  },
1228  "nbformat": 4,
1229  "nbformat_minor": 2
1230 }