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agda-experiments/MLTT/Universes.agda
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agda-experiments/MLTT/Universes.agda
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{-# OPTIONS --safe --without-K #-}
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module MLTT.Universes where
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open import Agda.Primitive public
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using (_⊔_)
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renaming (lzero to 𝓤₀
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; lsuc to _⁺
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; Level to Universe
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; Setω to 𝓤ω
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)
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variable
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𝓤 𝓥 𝓦 𝓣 𝓤' 𝓥' 𝓦' 𝓣' : Universe
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_̇ : (𝓤 : Universe) → Set (𝓤 ⁺)
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𝓤 ̇ = Set 𝓤
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𝓤₁ = 𝓤₀ ⁺
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𝓤₂ = 𝓤₁ ⁺
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_⁺⁺ : Universe → Universe
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𝓤 ⁺⁺ = 𝓤 ⁺ ⁺
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infix 1 _̇
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agda-experiments/about-agda-experiments.md
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agda-experiments/about-agda-experiments.md
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# Installing Agda
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I added these lines to my configuration.nixos to get a workable Agda installation:
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(agda.withPackages (p: [ p.standard-library ]))
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but there were a few issues, so I removed that and installed with
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cabal update
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cabal install Agda
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which seemed to work nicely after some hackery with zlib, and installing the standard libraries.
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# Owen's Geolog definitions
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Owen.agda : Definitions fom Owen's first two lectures about Geolog.
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These set up the basic machinery for contexts (signatures), theories and interpolation.
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Compile with:
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agda -c --no-main Owen.agda
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# HoTT definitions from Martin Escardo's book "Univalent Foundations" https://arxiv.org/pdf/1911.00580
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agda -c --no-main MLTT/Universe.agda
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Escardo defines everything from the ground up with his own concepts of sets, universes etc.,
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independently of the standard library.
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