3.3.1. Decoder: build the choices first🔗

The decoder represents a partial match as a pair containing the captures found so far and the unconsumed remainder. It explores the input from left to right:

1. Sign consumes -. Its absent alternative cannot continue because Natural requires a digit.

2. Natural can initially consume 1 or 12. The 1 branch leaves 2.34, so the following dot fails. The 12 branch reaches the dot.

3. Fraction can consume 3, leaving 4, or consume 34, leaving nothing.

The following checked equation exposes the two candidates that reach the root:

Triptych.decode constructs this candidate list, keeps only entries with an empty remainder, and returns the first one. The first candidate above is discarded; the second yields the captures Sign = "-", Natural = "12", and Fraction = "34".

3.3.2. Scanner: ask the rest immediately🔗

The complete scanner does not first construct that list. Whenever it finds a possible prefix, it immediately calls the continuation for the rest of the grammar:

Natural = "1"  -> try "." next -> fail immediately
Natural = "12" -> try "." next -> continue
Fraction = "3" -> root sees remainder "4" -> fail immediately
Fraction = "34" -> root sees no remainder -> return success

This is the same ordered search, but failed choices are discarded as soon as their continuation fails, and the successful choice stops the search.

Decimal also passes Triptych.Grammar.staticUnique, so its normal runtime path is even more direct. The scanner sees that Natural is followed by the literal dot, consumes the digit run up to that dot, and then consumes the final fraction to the end of the input. It obtains the successful captures without complete-candidate backtracking.

The two implementations therefore return exactly the same observable result:

The generated parser then checks the constraints and computes the value from this one capture map. Neither the decoder nor the scanner itself decides what the Decimal value means.