The Petit Punch is a Mixed Drink which consists of Rum, Lime, and Sugar.
The Petit Punch is also known as a "Ti Punch".
FIELDING'S GUIDE TO THE CARIBBEAN, INCLUDING THE BAHAMAS (1968)
"Pg. 395 (Martinique): "Petit punch," the national drink, bears no resemblance to a martini in the making, yet somehow manages to create the same soul-soothing, nothing-quite-like-it effect; it looks much the same too. Risking the wrath of some theorists (every connoisseur swears his is the only proper way to make a "petit punch"), here is our favorite formula: to one part cane-sugar syrup (preboil a little more sugar than water together) add 5 parts white rum, 2 ice cubes, and a dash of West Indian, repeat, West Indian, green lime. Squeeze some of the juice into the glass, then drop the rest of the tiny fruit into the drink. (We can hear the screams from here: lime ruins vintage rum!) Nevertheless, with or without lime, merveilleux."
Dom Costa's Recipe (2002)
"Petit punch is the full name of a drink better known as "T'punch", yes it is originary from the French West Indies, and is made with a measure of rum "agricole" (white or gold, up to your taste), a teaspoon of brown sugar, and a quarter lime cut up in pieces and muddled, no ice."