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CHANGELOG

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14 APR 2022 Version 1.4.0 Microkernel Pipeline:
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* Microkernel Architecture: Kernel, Proof Shell, and Tactics Server with open binary protocols
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* NixOS package /applications/science/logic/anders/ [@suhr]
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* Homotopy Library Manual: https://anders.groupoid.space/library/
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* CNAME Alias HOMOTOPY DEV
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* NixOS package /applications/science/logic/anders/
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* Homotopy Library Manual: https://anders.groupoid.space/lib/
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* CNAME Alias HOMOTOPY.DEV
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27 JAN 2022 Version 1.1.1 Univalence:
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LICENSE

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DHARMA License
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Copyright (c) 2016—2022 Groupoid Infinity
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Copyright (c) 2016—2025 Groupoid Infinity
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Permission to use, copy, modify, and/or distribute this software for any
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purpose with or without fee is hereby granted, provided that the above

README.md

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Benchmarks
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----------
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Intel i7-8700.
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Intel i5-12400.
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```
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$ time dune build
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real 0m1.456s
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user 0m2.794s
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sys 0m0.564s
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real 0m0.985s
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user 0m1.917s
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sys 0m0.570s
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```
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```
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$ time dune exec anders check library/book.anders
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$ time dune exec anders check lib/book.anders
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real 0m0.468s
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user 0m0.051s
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sys 0m0.032s
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real 0m0.268s
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user 0m0.017s
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sys 0m0.017s
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```
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# Anders: Homotopy Library

dune

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lib/foundations/modal/infinitesimal.anders
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lib/mathematics/algebra/algebra.anders
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lib/mathematics/analysis/real.anders
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lib/mathematics/analysis/topology.anders
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lib/mathematics/categories/category.anders
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lib/mathematics/categories/functor.anders
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lib/mathematics/categories/abelian.anders

lib/mathematics/analysis/topology.anders

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def Ω := U → 𝟐
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def ℙ (X: U₁) := X → Ω
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def isSet-ℙ (X: U₁) : isSet₁ (ℙ X)
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def isSet-ℙ (X: U₁)
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: isSet₁ (ℙ X)
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:= isSetPi₁ X (λ (x: X), Ω) (λ (x: X), isSetPi₁' U (λ (_: U), 𝟐) (λ (_: U), boolset))
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axiom specify (X: U₁) : (X → Ω) → ℙ X
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def ∅ (X: U₁) : ℙ X := \ (_: X) (_: U), false
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def total (X: U₁) : ℙ X := \ (_: X) (_: U), true
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def ∈ (X: U₁) (el: X) (set: ℙ X) : U₁ := Path₁ (U → 𝟐) (set el) (\(_: U), true)
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def ∉ (X: U₁) (el: X) (set: ℙ X) : U₁ := Path₁ (U → 𝟐) (set el) (\(_: U), false)
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def ⊆ (X: U₁) (A B: ℙ X) := Π (x: X), (∈ X x A) × (∈ X x B)
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def ∁ (X: U₁) : ℙ X → ℙ X -- not (complement)
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:= λ (h: ℙ X), λ (x: X) (Y: U), not (h x Y)
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def ∪ (X: U₁) : ℙ X → ℙ X → ℙ X -- or (union)
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:= λ (h1: ℙ X) (h2: ℙ X), λ (x: X) (Y: U), or (h1 x Y) (h2 x Y)
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def ∩ (X: U₁) : ℙ X → ℙ X → ℙ X -- and (intersection)
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:= λ (h1: ℙ X) (h2: ℙ X), λ (x: X) (Y: U), and (h1 x Y) (h2 x Y)
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def ∁ (X: U₁) : ℙ X → ℙ X := λ (h: ℙ X), λ (x: X) (Y: U), not (h x Y)
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def ∪ (X: U₁) : ℙ X → ℙ X → ℙ X := λ (h1: ℙ X) (h2: ℙ X), λ (x: X) (Y: U), or (h1 x Y) (h2 x Y)
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def ∩ (X: U₁) : ℙ X → ℙ X → ℙ X := λ (h1: ℙ X) (h2: ℙ X), λ (x: X) (Y: U), and (h1 x Y) (h2 x Y)

package.json

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{
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"name": "homotopy",
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"version": "1.3.0",
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"version": "1.4.0",
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"description": "Anders: Modal Homotopy Type System",
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"main": "",
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"scripts": {

src/frontend/anders.ml

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| Indices | Girard | Silent | Irrelevance
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let help =
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"\nhttps://homotopy.dev/library/
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"\nhttps://homotopy.dev/lib/
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invocation = anders | anders list
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list = [] | command list

src/frontend/repl.ml

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let banner =
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Printf.sprintf "Anders Proof Assistant version %Ld.%Ld.%Ld
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Copyright © 2021–2022 Groupoid Infinity."
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Fuze.year Fuze.month Fuze.patch
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Copyright © 2021–2022 Groupoid Infinity." 1L 4L 0L
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let loaded : Files.t ref = ref Files.empty
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