Des contraintes naît la beauté

This quote from Leonardo da Vinci “Beauty is born from constraints” was chosen by Alain Colmerauer as the motto for Prolog IV, the last iteration (for now) of the Prolog language, déveloped by Prologia in the early 1990’s.

Alain Colmerauer passed away this week. I have plenty of memories about him, starting from classes with him in Marseille, where his way to present constraint programming was as strange as it was passionate. Even before that, during my studies at Marseille’s Groupe d’Intelligence Artificielle, heavy on logic and Prolog, Alain Colmerauer was the name that made us all dream about research and fame.

Constraint programming at Prologia was intended to solve practical problems, in scheduling, optimization, and other NP-complete problems. That was fun for me, but Alain didn’t care: for him, what counted most was the beauty of the language, the ability to describe the language with the simplest theory possible. Prolog III, the first constraint language he developed, used linear programming on rational numbers, which could not solve all problems, but was mathematically exact.

In Prolog IV, we wanted to solve more general problems, and we started using intervals on less exact floating-point numbers. Alain was not enthusiastic at first, but things got better when we realized that floating-point numbers are actually rational numbers (i.e., exact numbers, not some approximation).

While I was writing my dissertation, I spent some evenings with Alain discussing potential formalizations of our constraints, and we ended up defining a notion of approximation to map a set to a smaller set of approximated values, and building something on it. I was quite proud of it, and I still am, but Alain was disappointed by the fact that the properties defining an approximation was too complex.

For me, that’s the legacy of Alain Colmerauer: even in the most complex thing, program, or language, a simple and elegant view of it is carefully hidden, and can be uncovered if you look for it carefully enough.

RIP, Alain.

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