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The Curry-Howard isomorphism states an amazing correspondence between systems of formal logic as encountered in proof theory and computational calculi as found in type theory. For instance,minimal propositional logic corresponds to simply typed lambda-calculus, first-order logic corresponds to dependent types, second-order logic corresponds to polymorphic types, sequent calculus is related to explicit substitution, etc.The isomorphism has many aspects, even at the syntactic level:formulas correspond to types, proofs correspond to terms, provability corresponds to inhabitation,

Curry-Howard isomorphism. --- Curry-Howard isomorphism. Lambda calculus. Proof theory. --- Lambda calculus. --- Proof theory. --- Curry-Howard isomorphism --- Lambda calculus --- Proof theory --- Mathematics --- Physical Sciences & Mathematics --- Mathematical Theory --- Calculus, Lambda --- Correspondence, Curry-Howard --- Curry-Howard correspondence --- Formulae-as-types principle --- Logic, Symbolic and mathematical --- Isomorphisms (Mathematics)