Programming languages based on dependent type theory promise two great advances: flexibility and security. With the type-level computation afforded by dependent types, algorithms can be more generic, as the type system can express flexible interfaces via programming. Likewise, type-level computation can also express data structure invariants, so that programs can be proved correct through type checking. Furthermore, despite these extensions, programmers already know everything. Via the Curry-Howard isomorphism, the language of type-level computation and the verification logic is the programming language itself.
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