Sentient Lang.

Self-enumerating pangram

The following program finds self-enumerating pangrams.

function^ pangram () {
  function^ main () {
    array26<int7> sentenceSeed, letterCounts;

    numberOfPlurals = letterCounts.countBy(*moreThanOne?);
    lettersForEachNumber = letterCounts.map(*lettersForNumberWord);

    numberOfEachLetter = lettersForEachNumber.transpose.map(*sum);
    numberOfEachLetter = numberOfEachLetter.map(*addMandatoryLetter);
    numberOfEachLetter = numberOfEachLetter.addArray(sentenceSeed);
    numberOfEachLetter = numberOfEachLetter.addPlurals(numberOfPlurals);

    invariant numberOfEachLetter == letterCounts;
    invariant sentenceSeed.all?(*inBounds?);
    invariant letterCounts.all?(*inBounds?);

    expose sentenceSeed, letterCounts;

  function moreThanOne? (n) {
    return n > 1;

  # ... more functions


lookupTable = [
  # Each index maps to an array of characters for that number-word, e.g.
  # 1 -> O, N, E
  # 2 -> T, W, O
  # ...


Here is the full source code and compiled program on Github. This program takes a minute or two to run with the lingeling solver. Here is a solution:

This pangram lists four a's, one b, one c, two d's, twenty-two e's, seven f's, two g's, two h's, nine i's, one j, one k, two l's, two m's, twenty n's, nineteen o's, two p's, one q, five r's, twenty-six s's, twenty-two t's, four u's, five v's, fourteen w's, two x's, five y's and one z.

How does it work?

We start by declaring arrays for the ‘sentenceSeed’ and ‘letterCounts’. The ‘sentenceSeed’ counts how many of each letter appear in ‘This sentence contains … and’, or whichever seed is (assigned)[../cli/assign] at runtime. The ‘letterCounts’ array contains the expected number of each letter that appears in the sentence.

We then use ‘letterCounts’ to determine the actual number of each letter. Later on, we specify that the expected ‘letterCounts’ must equal the actual ‘numberOfEachLetter’, which is the crux of this problem. We also check that all elements in these arrays are in bounds, which helps the optimiser simplify the program.

To calculate the actual number of each letter, we use the ‘lookupTable’ to map ‘letterCounts’ to the number of letters that appear in the number-words (e.g ‘ONE’, ‘TWO’). We sum these for each letter and add the ‘mandatoryLetter’ that must appear in the sentence, e.g. (one a, two b’s). We add the ‘sentenceSeed’ and the ‘numberOfPlurals’ that follow each term in the sentence (e.g two b’s, three c’s).

CLI example

Here is an example of running this program with the command-line interface:

sentient                               \
  --run self-enumerating-pangram.json  \
  --assign-file assignment.json        \
  --machine lingeling

# assignment.json
  // This pangram lists ... and

# standard output:

The above example uses the assign-file option which is convenient for large inputs.