A search for terms like arithmetic and natural on hackage reveals no shortage of libraries for handling the arithmetic of natural numbers. How is this library any different some of the others? It has a particular purpose: providing a foundation on top on which other libraries may define types indexed by sizes. This uses GHC's non-inductively-defined GHC.TypeNats.Nat. As a rule, this does not use unsafeCoerce internally anywhere. Perhaps the most direct competitor to `natural-arithmetic` is a typechecker plugin like type-nat-solver (https://github.com/yav/type-nat-solver). The big difference is that `type-nat-solver` can really only be used in application code, not in library code. This is because libraries should not require the presence of typechecker plugins. Technically, they can (you could document it), but many developers will not use libraries that have unusual install procedures like this. This library, in places, requires users to use the TypeApplications language extension. This is done when a number is only need at the type level (without a runtime witness). This library uses a non-minimal core, providing redundant primitives in Arithmetic.Lt and Arithmetic.Lte. This is done in the interest of making it easy for user to assemble proofs. Recall that proof assembly is done by hand rather than by an SMT solver, so removing some tediousness from this is helpful to users.
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