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import Foundation

     

       
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/// Pterodactyl has two sizes of small things: little and moderate. Beyond these, we have things that are not types but rather “type schemes”.

     

       
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/// Pterodactyl has two sizes of small things: ``little(universe:)`` and ``big``. Beyond these, we have things that are not types but rather “type schemes”.

     

       
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public enum Size<Universe> {

     

       
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	/// A “little” thing is something classified by a universe. Universes form a countable hierarchy.

     

       
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	/// A “little” type is something classified by a universe. Universes form a countable hierarchy.

     

       
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	case little(universe: Universe)

     

       
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	/// A “moderate” type is something classified by `Type`.

     

       
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	case moderate

     

       
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	/// A “big” type is something classified by `Type`.

     

       
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	case big

     

       
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}

     

       
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	public static func == (lhs: Size<Universe>, rhs: Size<Universe>) -> Bool {

     

       
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		switch (lhs, rhs) {

     

       
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		case (.little, .little): true

     

       
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		case (.moderate, .moderate): true

     

       
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		case (.big, .big): true

     

       
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		default: false

     

       
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		}

     

       
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	}

     
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	func map<U>(_ f: (Universe) -> U) -> Size<U> {

     

       
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		switch self {

     

       
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		case let .little(universe: universe): .little(universe: f(universe))

     

       
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		case .moderate: .moderate

     

       
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		case .big: .big

     

       
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		}

     

       
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	}

     

       
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}

     

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		switch await type.whnf() {

     

       
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		// In principle the type of universes could be small, but I am worried about about the strictness of the semilattice operations. I know how to interpret them if universeType is exoNat as in 2LTT, but in that case universeType probably should not be fibrant.

     

       
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		case .universeType, .universeCodes(size: .moderate):

     

       
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		case .universeType, .universeCodes(size: .big):

     

       
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			throw SizeError()

     

       
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		case let .universeCodes(size: .little(universe: littleUniverse)):

     
···

       
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	func assertLeq(size1: Size<Value>, size2: Size<Value>) async throws {

     

       
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		switch (size1, size2) {

     

       
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		case (_, .moderate): ()

     

       
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		case (_, .big): ()

     

       
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		case let (.little(universe: universe1), .little(universe: universe2)):

     

       
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			try await assertLeq(universe1: universe1, universe2: universe2)

     

       
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		default:

     

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		let analysis = LocalAnalysis()

     

       
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		await #expect(throws: Never.self) {

     

       
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			try await analysis.assertLeq(size1: .moderate, size2: .moderate)

     

       
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			try await analysis.assertLeq(size1: .big, size2: .big)

     

       
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		}

     

       
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	}

     

       
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		let analysis = LocalAnalysis()

     

       
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		await #expect(throws: LocalAnalysis.SizeError.self) {

     

       
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			try await analysis.assertLeq(size1: .moderate, size2: .little(universe: .universeZero))

     

       
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			try await analysis.assertLeq(size1: .big, size2: .little(universe: .universeZero))

     

       
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		}

     

       
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	}

     

       
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