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Dependent Types Explained
- Dependent types allow types to depend on values, making types first-class citizens like functions in functional programming.
- This lets programmers describe data more precisely, such as a list's length encoded in its type.
Programs as Proofs
- Programs in dependent type systems are also proofs under the Curry–Howard correspondence.
- A function, like sorting a list, simultaneously acts as a proof the algorithm works and as the implementation itself.
Totality vs Turing Completeness
- Total functional languages like Idris ensure every program terminates, unlike Turing complete languages.
- Idris aims for "Packman completeness": practical usefulness over theoretical Turing completeness.