Computational Trilogy

See also Curry-Howard Correspondence.

“A profound cross-disciplinary insight has emerged – starting in the late 1970s, with core refinements in recent years – observing that three superficially different-looking fields of mathematics,

• computation/programming languages
• formal logic/type theory
• ∞-category theory/∞-topos theory (algebraic topology)

are but three different perspectives on a single underlying phenomenon at the foundations of mathematics:

… spaces <=> computation <=> logic <=> spaces … [this is supposed to be a circle]”