{ "id": "P151", "slug": "tax-brackets", "key": "P151-tax-brackets", "title": "Tax brackets", "summary": "Income bands written from a sentence and read four ways - closed, half-open, open, left-open - the incomes on a band's end, the slab tax the reading decides and the marginal tax it cannot change.", "entry": "main.eml", "ui": "terminal", "readme": "# P151 - Tax brackets\n\nIncome bands written from a sentence - 0-10000, 10000-40000, 40000-100000,\n100000 and above - read four ways, and the incomes that sit on a band's\nend.\n\n- `main.eml` - the menu, the bands under each reading, one income under\n each, the partition check over the incomes on file, and adding one\n- `bands.eml` - the bands, the readings, the incomes on file, whether a\n band takes an income, the bands that take it, the slab tax and the\n marginal tax\n\nHow each part works:\n\n- As in the corpus case `boundary-inclusive-or-not`, \"between\" is four\n questions - closed, half-open, open, left-open - and they part only at\n the ends: 0, 10000, 40000 and 100000. Every income in the middle lands in\n the same band under all four, which is why the difference survives every\n test there.\n- Consecutive bands read closed take the three inner ends twice; read open\n they take the four ends not at all; left-open misses only 0. Half-open\n alone puts every income in exactly one band: the bands are a partition.\n- The slab tax charges the whole income at its band's rate, so the reading\n decides it at an end: 10000 pays 0.00, 1000.00 or 3000.00 - read open no\n band takes it, and the else branch charges the top rate.\n- The marginal tax charges each slice at its own band's rate. It is the\n same under every reading, a slice's width not depending on which band\n owns its end, and it does not jump.\n\nWhat is checked: menu choices 1 to 5; an income from 0 to 9999999. An\nempty answer cancels.\n\nSessions: `sessions/basic.in` gives:\n- the bands; incomes 10000, 25000, 100000 and 0;\n- the incomes on file; 40000 added, and the incomes on file again.\n\n`sessions/bad-input.in` gives:\n- menu choices 0 and x;\n- incomes: a cancel, 12345678, 1e5 and -5;\n- adding: a cancel and x, then 99999; the incomes on file.\n\nBuilt on the verified corpus case `boundary-inclusive-or-not` (four\nreadings of a range, consecutive buckets that double-count or drop a\nboundary, and a partition check by counting).\n", "modules": [ { "name": "main.eml", "eml": "# P151 tax brackets: the bands and their four readings, one income under\n# each, the partition check over the incomes on file, and adding one.\nimport bands\n\ndef plain(s):\n 0 => i\n len(s) => j\n while i < j and s[i] == \" \":\n i + 1 => i\n while j > i and s[j - 1] == \" \":\n j - 1 => j\n return s[i:j]\n\ndef pad(s, n):\n s => out\n while len(out) < n:\n out + \" \" => out\n return out\n\ndef lpad(s, n):\n s => out\n while len(out) < n:\n \" \" + out => out\n return out\n\ndef money(c):\n c % 100 => p\n if p < 10:\n return str(int((c - p) / 100)) + \".0\" + str(p)\n return str(int((c - p) / 100)) + \".\" + str(p)\n\ndef interval(reading, b):\n if reading == \"closed\" or reading == \"half-open\":\n \"[\" => left\n else:\n \"(\" => left\n if b[1] < 0:\n return left + str(b[0]) + \", and up)\"\n if reading == \"closed\" or reading == \"left-open\":\n \"]\" => right\n else:\n \")\" => right\n return left + str(b[0]) + \", \" + str(b[1]) + right\n\ndef show_bands():\n \"The sentence: 0-10000 at 0%, 10000-40000 at 10%, 40000-100000 at 20%, 100000 and above at 30%.\" ^0\n (\" \" + pad(\"band\", 6) + pad(\"closed\", 18) + pad(\"half-open\", 18) + pad(\"open\", 18) + \"left-open\") ^0\n 1 => k\n for b in bands.bands():\n (\" \" + pad(str(k) + \" \" + str(b[2]) + \"%\", 6) + pad(interval(\"closed\", b), 18) + pad(interval(\"half-open\", b), 18) + pad(interval(\"open\", b), 18) + interval(\"left-open\", b)) ^0\n k + 1 => k\n\ndef names(ks):\n if len(ks) == 0:\n return \"none\"\n \"\" => out\n for k in ks:\n if out == \"\":\n str(k) => out\n else:\n out + \" and \" + str(k) => out\n return out\n\ndef one_income():\n plain(input(\"income (0 to 9999999)> \")) => t\n if t == \"\":\n \"Cancelled.\" ^0\n return\n if len(t) > 7:\n \"Type a whole number from 0 to 9999999.\" ^0\n return\n for c in t:\n if c < \"0\" or c > \"9\":\n \"Type a whole number from 0 to 9999999.\" ^0\n return\n int(t) => x\n show_income(x)\n\ndef show_income(x):\n (\"Income \" + str(x) + \":\") ^0\n (\" \" + pad(\"reading\", 11) + pad(\"bands that take it\", 20) + \"slab tax: the whole income at the band's rate\") ^0\n for r in bands.readings():\n bands.taking(r, x) => ks\n money(bands.slab(r, x)) => s\n if len(ks) == 0:\n s + \" - no band takes it, and the else branch charges the top rate\" => s\n elif len(ks) > 1:\n s + \" - band \" + str(ks[0]) + \", the first that takes it\" => s\n (\" \" + pad(r, 11) + pad(names(ks), 20) + s) ^0\n (\"Marginal tax, each slice at its own band's rate: \" + money(bands.marginal(x)) + \" under every reading: a slice's width does not depend on which band owns its end.\") ^0\n\ndef partition(xs):\n (\"Over the \" + str(len(xs)) + \" incomes on file:\") ^0\n (\" \" + pad(\"reading\", 11) + \"in no band in one in two slab tax in all\") ^0\n \"\" => exact\n for r in bands.readings():\n 0 => none\n 0 => one\n 0 => two\n 0 => total\n for x in xs:\n len(bands.taking(r, x)) => n\n if n == 0:\n none + 1 => none\n elif n == 1:\n one + 1 => one\n else:\n two + 1 => two\n total + bands.slab(r, x) => total\n (\" \" + pad(r, 11) + lpad(str(none), 10) + lpad(str(one), 8) + lpad(str(two), 8) + lpad(money(total), 18)) ^0\n if one == len(xs):\n if exact == \"\":\n r => exact\n else:\n exact + \" and \" + r => exact\n \"\" => edge\n [] => seen\n for x in xs:\n bands.taking(\"closed\", x) => a\n bands.taking(\"open\", x) => b\n False => dup\n for y in seen:\n if y == x:\n True => dup\n if (len(a) != 1 or len(b) != 1) and not dup:\n seen + [x] => seen\n if edge == \"\":\n str(x) => edge\n else:\n edge + \", \" + str(x) => edge\n if edge != \"\":\n (\"The readings part only at \" + edge + \": incomes on a band's end.\") ^0\n (\"Every income in exactly one band: \" + exact + \".\") ^0\n 0 => m\n for x in xs:\n m + bands.marginal(x) => m\n (\"Marginal tax in all: \" + money(m) + \", the same under every reading.\") ^0\n\ndef add(xs):\n plain(input(\"income (0 to 9999999)> \")) => t\n if t == \"\":\n \"Cancelled.\" ^0\n return xs\n if len(t) > 7:\n \"Type a whole number from 0 to 9999999.\" ^0\n return xs\n for c in t:\n if c < \"0\" or c > \"9\":\n \"Type a whole number from 0 to 9999999.\" ^0\n return xs\n int(t) => x\n (\"Income \" + str(x) + \" added; \" + str(len(xs) + 1) + \" on file.\") ^0\n return xs + [x]\n\nbands.incomes() => xs\n\n\"== Tax brackets ==\" ^0\n\"Bands written from a sentence, read four ways, and the incomes that sit on their ends.\" ^0\nTrue => running\nwhile running:\n \"\" ^0\n \"1) bands 2) one income 3) the incomes on file 4) add an income 5) quit\" ^0\n plain(input(\"choice> \")) => choice\n if choice == \"1\":\n show_bands()\n elif choice == \"2\":\n one_income()\n elif choice == \"3\":\n partition(xs)\n elif choice == \"4\":\n add(xs) => xs\n elif choice == \"5\":\n False => running\n else:\n \"Pick a number from 1 to 5.\" ^0\n\"Bye.\" ^0\n", "python": "import bands\n\ndef plain(s):\n i = 0\n j = len(s)\n while i < j and s[i] == \" \":\n i = i + 1\n while j > i and s[j - 1] == \" \":\n j = j - 1\n return s[i:j]\n\ndef pad(s, n):\n out = s\n while len(out) < n:\n out = out + \" \"\n return out\n\ndef lpad(s, n):\n out = s\n while len(out) < n:\n out = \" \" + out\n return out\n\ndef money(c):\n p = c % 100\n if p < 10:\n return str(int((c - p) / 100)) + \".0\" + str(p)\n return str(int((c - p) / 100)) + \".\" + str(p)\n\ndef interval(reading, b):\n if reading == \"closed\" or reading == \"half-open\":\n left = \"[\"\n else:\n left = \"(\"\n if b[1] < 0:\n return left + str(b[0]) + \", and up)\"\n if reading == \"closed\" or reading == \"left-open\":\n right = \"]\"\n else:\n right = \")\"\n return left + str(b[0]) + \", \" + str(b[1]) + right\n\ndef show_bands():\n print(\"The sentence: 0-10000 at 0%, 10000-40000 at 10%, 40000-100000 at 20%, 100000 and above at 30%.\")\n print(\" \" + pad(\"band\", 6) + pad(\"closed\", 18) + pad(\"half-open\", 18) + pad(\"open\", 18) + \"left-open\")\n k = 1\n for b in bands.bands():\n print(\" \" + pad(str(k) + \" \" + str(b[2]) + \"%\", 6) + pad(interval(\"closed\", b), 18) + pad(interval(\"half-open\", b), 18) + pad(interval(\"open\", b), 18) + interval(\"left-open\", b))\n k = k + 1\n\ndef names(ks):\n if len(ks) == 0:\n return \"none\"\n out = \"\"\n for k in ks:\n if out == \"\":\n out = str(k)\n else:\n out = out + \" and \" + str(k)\n return out\n\ndef one_income():\n t = plain(input(\"income (0 to 9999999)> \"))\n if t == \"\":\n print(\"Cancelled.\")\n return\n if len(t) > 7:\n print(\"Type a whole number from 0 to 9999999.\")\n return\n for c in t:\n if c < \"0\" or c > \"9\":\n print(\"Type a whole number from 0 to 9999999.\")\n return\n x = int(t)\n show_income(x)\n\ndef show_income(x):\n print(\"Income \" + str(x) + \":\")\n print(\" \" + pad(\"reading\", 11) + pad(\"bands that take it\", 20) + \"slab tax: the whole income at the band's rate\")\n for r in bands.readings():\n ks = bands.taking(r, x)\n s = money(bands.slab(r, x))\n if len(ks) == 0:\n s = s + \" - no band takes it, and the else branch charges the top rate\"\n elif len(ks) > 1:\n s = s + \" - band \" + str(ks[0]) + \", the first that takes it\"\n print(\" \" + pad(r, 11) + pad(names(ks), 20) + s)\n print(\"Marginal tax, each slice at its own band's rate: \" + money(bands.marginal(x)) + \" under every reading: a slice's width does not depend on which band owns its end.\")\n\ndef partition(xs):\n print(\"Over the \" + str(len(xs)) + \" incomes on file:\")\n print(\" \" + pad(\"reading\", 11) + \"in no band in one in two slab tax in all\")\n exact = \"\"\n for r in bands.readings():\n none = 0\n one = 0\n two = 0\n total = 0\n for x in xs:\n n = len(bands.taking(r, x))\n if n == 0:\n none = none + 1\n elif n == 1:\n one = one + 1\n else:\n two = two + 1\n total = total + bands.slab(r, x)\n print(\" \" + pad(r, 11) + lpad(str(none), 10) + lpad(str(one), 8) + lpad(str(two), 8) + lpad(money(total), 18))\n if one == len(xs):\n if exact == \"\":\n exact = r\n else:\n exact = exact + \" and \" + r\n edge = \"\"\n seen = []\n for x in xs:\n a = bands.taking(\"closed\", x)\n b = bands.taking(\"open\", x)\n dup = False\n for y in seen:\n if y == x:\n dup = True\n if (len(a) != 1 or len(b) != 1) and not dup:\n seen = seen + [x]\n if edge == \"\":\n edge = str(x)\n else:\n edge = edge + \", \" + str(x)\n if edge != \"\":\n print(\"The readings part only at \" + edge + \": incomes on a band's end.\")\n print(\"Every income in exactly one band: \" + exact + \".\")\n m = 0\n for x in xs:\n m = m + bands.marginal(x)\n print(\"Marginal tax in all: \" + money(m) + \", the same under every reading.\")\n\ndef add(xs):\n t = plain(input(\"income (0 to 9999999)> \"))\n if t == \"\":\n print(\"Cancelled.\")\n return xs\n if len(t) > 7:\n print(\"Type a whole number from 0 to 9999999.\")\n return xs\n for c in t:\n if c < \"0\" or c > \"9\":\n print(\"Type a whole number from 0 to 9999999.\")\n return xs\n x = int(t)\n print(\"Income \" + str(x) + \" added; \" + str(len(xs) + 1) + \" on file.\")\n return xs + [x]\n\nxs = bands.incomes()\nprint(\"== Tax brackets ==\")\nprint(\"Bands written from a sentence, read four ways, and the incomes that sit on their ends.\")\nrunning = True\nwhile running:\n print(\"\")\n print(\"1) bands 2) one income 3) the incomes on file 4) add an income 5) quit\")\n choice = plain(input(\"choice> \"))\n if choice == \"1\":\n show_bands()\n elif choice == \"2\":\n one_income()\n elif choice == \"3\":\n partition(xs)\n elif choice == \"4\":\n xs = add(xs)\n elif choice == \"5\":\n running = False\n else:\n print(\"Pick a number from 1 to 5.\")\nprint(\"Bye.\")\n" }, { "name": "bands.eml", "eml": "# P151 tax brackets - income bands written from a sentence, \"0-10000,\n# 10000-40000, 40000-100000, 100000 and above\", read four ways. As in the\n# corpus case boundary-inclusive-or-not, \"between\" is four questions -\n# closed, half-open, open, left-open - and they differ only at the end\n# points, which is why the difference survives every test in the middle.\n# Consecutive bands read closed take a boundary twice and read open take it\n# not at all; only half-open makes the bands a partition. A band is [low,\n# high, rate in percent]; the last has no high.\n\ndef bands():\n return [[0, 10000, 0], [10000, 40000, 10], [40000, 100000, 20], [100000, 0 - 1, 30]]\n\ndef readings():\n return [\"closed\", \"half-open\", \"open\", \"left-open\"]\n\ndef incomes():\n return [0, 8500, 10000, 25000, 40000, 40001, 72000, 100000, 150000]\n\ndef takes(reading, b, x):\n # does band b take income x under the reading\n if reading == \"closed\" or reading == \"half-open\":\n x >= b[0] => low_ok\n else:\n x > b[0] => low_ok\n if b[1] < 0:\n return low_ok\n if reading == \"closed\" or reading == \"left-open\":\n x <= b[1] => high_ok\n else:\n x < b[1] => high_ok\n return low_ok and high_ok\n\ndef taking(reading, x):\n # the numbers of the bands that take x, from 1\n [] => out\n 1 => k\n for b in bands():\n if takes(reading, b, x):\n out + [k] => out\n k + 1 => k\n return out\n\ndef slab(reading, x):\n # the whole income at the rate of the first band that takes it, in\n # cents; with no band the else branch charges the top rate\n for b in bands():\n if takes(reading, b, x):\n return x * b[2]\n return x * bands()[len(bands()) - 1][2]\n\ndef marginal(x):\n # each slice of the income at its own band's rate, in cents\n 0 => t\n for b in bands():\n x => top\n if b[1] >= 0 and b[1] < top:\n b[1] => top\n if top > b[0]:\n t + (top - b[0]) * b[2] => t\n return t\n", "python": "def bands():\n return [[0, 10000, 0], [10000, 40000, 10], [40000, 100000, 20], [100000, 0 - 1, 30]]\n\ndef readings():\n return [\"closed\", \"half-open\", \"open\", \"left-open\"]\n\ndef incomes():\n return [0, 8500, 10000, 25000, 40000, 40001, 72000, 100000, 150000]\n\ndef takes(reading, b, x):\n if reading == \"closed\" or reading == \"half-open\":\n low_ok = x >= b[0]\n else:\n low_ok = x > b[0]\n if b[1] < 0:\n return low_ok\n if reading == \"closed\" or reading == \"left-open\":\n high_ok = x <= b[1]\n else:\n high_ok = x < b[1]\n return low_ok and high_ok\n\ndef taking(reading, x):\n out = []\n k = 1\n for b in bands():\n if takes(reading, b, x):\n out = out + [k]\n k = k + 1\n return out\n\ndef slab(reading, x):\n for b in bands():\n if takes(reading, b, x):\n return x * b[2]\n return x * bands()[len(bands()) - 1][2]\n\ndef marginal(x):\n t = 0\n for b in bands():\n top = x\n if b[1] >= 0 and b[1] < top:\n top = b[1]\n if top > b[0]:\n t = t + (top - b[0]) * b[2]\n return t\n" } ], "sessions": [ { "name": "bad-input", "input": "0\nx\n2\n\n2\n12345678\n2\n1e5\n2\n-5\n4\n\n4\nx\n4\n99999\n3\n5\n", "screen": "== Tax brackets ==\nBands written from a sentence, read four ways, and the incomes that sit on their ends.\n\n1) bands 2) one income 3) the incomes on file 4) add an income 5) quit\nchoice> 0\nPick a number from 1 to 5.\n\n1) bands 2) one income 3) the incomes on file 4) add an income 5) quit\nchoice> x\nPick a number from 1 to 5.\n\n1) bands 2) one income 3) the incomes on file 4) add an income 5) quit\nchoice> 2\nincome (0 to 9999999)> \nCancelled.\n\n1) bands 2) one income 3) the incomes on file 4) add an income 5) quit\nchoice> 2\nincome (0 to 9999999)> 12345678\nType a whole number from 0 to 9999999.\n\n1) bands 2) one income 3) the incomes on file 4) add an income 5) quit\nchoice> 2\nincome (0 to 9999999)> 1e5\nType a whole number from 0 to 9999999.\n\n1) bands 2) one income 3) the incomes on file 4) add an income 5) quit\nchoice> 2\nincome (0 to 9999999)> -5\nType a whole number from 0 to 9999999.\n\n1) bands 2) one income 3) the incomes on file 4) add an income 5) quit\nchoice> 4\nincome (0 to 9999999)> \nCancelled.\n\n1) bands 2) one income 3) the incomes on file 4) add an income 5) quit\nchoice> 4\nincome (0 to 9999999)> x\nType a whole number from 0 to 9999999.\n\n1) bands 2) one income 3) the incomes on file 4) add an income 5) quit\nchoice> 4\nincome (0 to 9999999)> 99999\nIncome 99999 added; 10 on file.\n\n1) bands 2) one income 3) the incomes on file 4) add an income 5) quit\nchoice> 3\nOver the 10 incomes on file:\n reading in no band in one in two slab tax in all\n closed 0 7 3 113900.00\n half-open 0 10 0 128900.00\n open 4 6 0 134900.00\n left-open 1 9 0 113900.00\nThe readings part only at 0, 10000, 40000, 100000: incomes on a band's end.\nEvery income in exactly one band: half-open.\nMarginal tax in all: 76900.00, the same under every reading.\n\n1) bands 2) one income 3) the incomes on file 4) add an income 5) quit\nchoice> 5\nBye.\n", "interpreter": "equal" }, { "name": "basic", "input": "1\n2\n10000\n2\n25000\n2\n100000\n2\n0\n3\n4\n40000\n3\n5\n", "screen": "== Tax brackets ==\nBands written from a sentence, read four ways, and the incomes that sit on their ends.\n\n1) bands 2) one income 3) the incomes on file 4) add an income 5) quit\nchoice> 1\nThe sentence: 0-10000 at 0%, 10000-40000 at 10%, 40000-100000 at 20%, 100000 and above at 30%.\n band closed half-open open left-open\n 1 0% [0, 10000] [0, 10000) (0, 10000) (0, 10000]\n 2 10% [10000, 40000] [10000, 40000) (10000, 40000) (10000, 40000]\n 3 20% [40000, 100000] [40000, 100000) (40000, 100000) (40000, 100000]\n 4 30% [100000, and up) [100000, and up) (100000, and up) (100000, and up)\n\n1) bands 2) one income 3) the incomes on file 4) add an income 5) quit\nchoice> 2\nincome (0 to 9999999)> 10000\nIncome 10000:\n reading bands that take it slab tax: the whole income at the band's rate\n closed 1 and 2 0.00 - band 1, the first that takes it\n half-open 2 1000.00\n open none 3000.00 - no band takes it, and the else branch charges the top rate\n left-open 1 0.00\nMarginal tax, each slice at its own band's rate: 0.00 under every reading: a slice's width does not depend on which band owns its end.\n\n1) bands 2) one income 3) the incomes on file 4) add an income 5) quit\nchoice> 2\nincome (0 to 9999999)> 25000\nIncome 25000:\n reading bands that take it slab tax: the whole income at the band's rate\n closed 2 2500.00\n half-open 2 2500.00\n open 2 2500.00\n left-open 2 2500.00\nMarginal tax, each slice at its own band's rate: 1500.00 under every reading: a slice's width does not depend on which band owns its end.\n\n1) bands 2) one income 3) the incomes on file 4) add an income 5) quit\nchoice> 2\nincome (0 to 9999999)> 100000\nIncome 100000:\n reading bands that take it slab tax: the whole income at the band's rate\n closed 3 and 4 20000.00 - band 3, the first that takes it\n half-open 4 30000.00\n open none 30000.00 - no band takes it, and the else branch charges the top rate\n left-open 3 20000.00\nMarginal tax, each slice at its own band's rate: 15000.00 under every reading: a slice's width does not depend on which band owns its end.\n\n1) bands 2) one income 3) the incomes on file 4) add an income 5) quit\nchoice> 2\nincome (0 to 9999999)> 0\nIncome 0:\n reading bands that take it slab tax: the whole income at the band's rate\n closed 1 0.00\n half-open 1 0.00\n open none 0.00 - no band takes it, and the else branch charges the top rate\n left-open none 0.00 - no band takes it, and the else branch charges the top rate\nMarginal tax, each slice at its own band's rate: 0.00 under every reading: a slice's width does not depend on which band owns its end.\n\n1) bands 2) one income 3) the incomes on file 4) add an income 5) quit\nchoice> 3\nOver the 9 incomes on file:\n reading in no band in one in two slab tax in all\n closed 0 6 3 93900.20\n half-open 0 9 0 108900.20\n open 4 5 0 114900.20\n left-open 1 8 0 93900.20\nThe readings part only at 0, 10000, 40000, 100000: incomes on a band's end.\nEvery income in exactly one band: half-open.\nMarginal tax in all: 61900.20, the same under every reading.\n\n1) bands 2) one income 3) the incomes on file 4) add an income 5) quit\nchoice> 4\nincome (0 to 9999999)> 40000\nIncome 40000 added; 10 on file.\n\n1) bands 2) one income 3) the incomes on file 4) add an income 5) quit\nchoice> 3\nOver the 10 incomes on file:\n reading in no band in one in two slab tax in all\n closed 0 6 4 97900.20\n half-open 0 10 0 116900.20\n open 5 5 0 126900.20\n left-open 1 9 0 97900.20\nThe readings part only at 0, 10000, 40000, 100000: incomes on a band's end.\nEvery income in exactly one band: half-open.\nMarginal tax in all: 64900.20, the same under every reading.\n\n1) bands 2) one income 3) the incomes on file 4) add an income 5) quit\nchoice> 5\nBye.\n", "interpreter": "equal" } ], "builtOn": [ { "slug": "boundary-inclusive-or-not", "caseId": "233-boundary-inclusive-or-not", "title": "Four readings of one sentence, differing on two values" } ], "updated": "2026-10-18" }