Sequent calculus is, in essence, a style of formal logical argumentation where every line of a proof is a conditional tautology (called a sequent by Gerhard Gentzen) instead of an unconditional tautology. Each conditional tautology is inferred from other conditional tautologies on earlier lines in a formal argument according to rules and procedures of inference, giving a better approximation to the style of natural deduction used by mathematicians than David Hilbert's earlier style of formal logic where every line was an unconditional tautology. There may be more subtle distinctions to be made...

In type theory and functional programming, Hindley–Milner (HM), also known as Damas–Milner or Damas–Hindley–Milner, is a classical type system for the lambda calculus with parametric polymorphism, first described by J. Roger Hindley and later rediscovered by Robin Milner. Luis Damas contributed a close formal analysis and proof of the method in his PhD thesis. Among HM's more notable properties are its completeness and its ability to deduce the most general type of a given program without the need of any type annotations or other hints supplied by the programmer. Algorithm W is a fast algorithm...