Sometimes, especially when dealing with business logic, we have to deal with data that comes in from the real world, or elsewhere, naturally very messily typed, leading to nasty type signatures and messes of macros or code generation to build data structures from a schema. Row polymorphism can help us by abstracting over the fields contained in a record type in the type signature, letting us define records based on data, concatenate records together, and define functions that are generic across any record containing the required fields, all without macros.

When designing interfaces, you may occasionally find a need to thread a proof of non-equality through API, and for ergonomics reasons, you would like that proof to be an auto implicit so the user doesn't have to generate the proof manually. Often, these proofs seem like they really should be trivial for the compiler to generate, but proof search will adamantly refuse to do so.

When programming, we quite frequently encounter the need for a data structure that can contain at most one of each given element. Typically, we might use a Set, which satisfies this constraint, but does so as a runtime invariant, which must be taken on trust, and results in ergonomic concerns when used as a component of API design. We introduce "Fresh Lists" as an alternative that provide a type-level guarantee of the uniqueness of each element, while also generalizing the notion of uniqueness and providing compile-time checking of literals.

While C can provide "convenient" string formatting by having hideously unsafe variadics, and dynamic languages, like python, can do the same, many type safe languages, such as Rust, are forced to provide such functionality through the use of a macro. Dependently typed languages, like Idris, can provide a printf like formatting interface, while maintaining both memory and type safety, without the need for macros. We will explore this by implementing a simplified version of printf in Idris from scratch.