Synthesis is harder than analysis

Over the years, mathematicians, logicians and computer scientists have developed various calculi . If you have a background in computer science, you’ve likely heard of the lambda calculus, a model of computation that was developed by Alonzo Church. If databases are more your thing, then you’ve been exposed to the relational calculus without even knowing it, since SQL is based on the relational calculus. If you are into formal methods, then you’ve worked with the predicate calculus, better known as first-order logic. Finally, if you enjoy reading academic papers on programming languages, you’ve almost certainly run into the sequent calculus. However, when someone says “calculus” without modification (e.g., “I’m taking calculus next semester”), there’s no ambiguity about which calculus they are referring to: it’s always one particular calculus. Or, rather, two calculi that happen to be deeply related to each other: differential calculus and integral calculus.