extract from DomainSets package

.github/dependabot.yml

@@ -0,0 +1,7 @@
+# https://docs.github.com/github/administering-a-repository/configuration-options-for-dependency-updates
+version: 2
+updates:
+  - package-ecosystem: "github-actions"
+    directory: "/" # Location of package manifests
+    schedule:
+      interval: "weekly"

.github/workflows/CI.yml

@@ -0,0 +1,47 @@
+name: CI
+on:
+  push:
+    branches:
+      - main
+    tags: ['*']
+  pull_request:
+  workflow_dispatch:
+concurrency:
+  # Skip intermediate builds: always.
+  # Cancel intermediate builds: only if it is a pull request build.
+  group: ${{ github.workflow }}-${{ github.ref }}
+  cancel-in-progress: ${{ startsWith(github.ref, 'refs/pull/') }}
+jobs:
+  test:
+    name: Julia ${{ matrix.version }} - ${{ matrix.os }} - ${{ matrix.arch }}
+    runs-on: ${{ matrix.os }}
+    timeout-minutes: 60
+    permissions: # needed to allow julia-actions/cache to proactively delete old caches that it has created
+      actions: write
+      contents: read
+    strategy:
+      fail-fast: false
+      matrix:
+        version:
+          - '1.10'
+          - '1.11'
+          - 'pre'
+        os:
+          - ubuntu-latest
+        arch:
+          - x64
+    steps:
+      - uses: actions/checkout@v4
+      - uses: julia-actions/setup-julia@v2
+        with:
+          version: ${{ matrix.version }}
+          arch: ${{ matrix.arch }}
+      - uses: julia-actions/cache@v2
+      - uses: julia-actions/julia-buildpkg@v1
+      - uses: julia-actions/julia-runtest@v1
+      - uses: julia-actions/julia-processcoverage@v1
+      - uses: codecov/codecov-action@v4
+        with:
+          files: lcov.info
+          token: ${{ secrets.CODECOV_TOKEN }}
+          fail_ci_if_error: false

.github/workflows/CompatHelper.yml

@@ -0,0 +1,16 @@
+name: CompatHelper
+on:
+  schedule:
+    - cron: 0 0 * * *
+  workflow_dispatch:
+jobs:
+  CompatHelper:
+    runs-on: ubuntu-latest
+    steps:
+      - name: Pkg.add("CompatHelper")
+        run: julia -e 'using Pkg; Pkg.add("CompatHelper")'
+      - name: CompatHelper.main()
+        env:
+          GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }}
+          COMPATHELPER_PRIV: ${{ secrets.DOCUMENTER_KEY }}
+        run: julia -e 'using CompatHelper; CompatHelper.main()'

.github/workflows/TagBot.yml

@@ -0,0 +1,31 @@
+name: TagBot
+on:
+  issue_comment:
+    types:
+      - created
+  workflow_dispatch:
+    inputs:
+      lookback:
+        default: "3"
+permissions:
+  actions: read
+  checks: read
+  contents: write
+  deployments: read
+  issues: read
+  discussions: read
+  packages: read
+  pages: read
+  pull-requests: read
+  repository-projects: read
+  security-events: read
+  statuses: read
+jobs:
+  TagBot:
+    if: github.event_name == 'workflow_dispatch' || github.actor == 'JuliaTagBot'
+    runs-on: ubuntu-latest
+    steps:
+      - uses: JuliaRegistries/TagBot@v1
+        with:
+          token: ${{ secrets.GITHUB_TOKEN }}
+          ssh: ${{ secrets.DOCUMENTER_KEY }}

.gitignore

@@ -0,0 +1,6 @@
+*.jl.*.cov
+*.jl.cov
+*.jl.mem
+/Manifest.toml
+/docs/Manifest.toml
+/docs/build/

LICENSE

@@ -0,0 +1,21 @@
+MIT License
+
+Copyright (c) 2025 Daan Huybrechs <[email protected]> and contributors
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE.

Project.toml

@@ -0,0 +1,24 @@
+name = "FunctionMaps"
+uuid = "a85aefff-f8ca-4649-a888-c8e5398bc76c"
+authors = ["Daan Huybrechs <[email protected]> and contributors"]
+version = "0.1.0"
+
+[deps]
+CompositeTypes = "b152e2b5-7a66-4b01-a709-34e65c35f657"
+LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
+StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
+
+[compat]
+Aqua = "0.8"
+CompositeTypes = "0.1.3"
+LinearAlgebra = "1"
+StaticArrays = "1"
+Test = "1"
+julia = "1.10"
+
+[extras]
+Aqua = "4c88cf16-eb10-579e-8560-4a9242c79595"
+Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
+
+[targets]
+test = ["Test", "Aqua"]

README.md

@@ -0,0 +1,5 @@
+# FunctionMaps
+
+[![Build Status](https://github.com/daanhb/FunctionMaps.jl/actions/workflows/CI.yml/badge.svg?branch=main)](https://github.com/daanhb/FunctionMaps.jl/actions/workflows/CI.yml?query=branch%3Amain)
+[![Coverage](https://codecov.io/gh/daanhb/FunctionMaps.jl/branch/main/graph/badge.svg)](https://codecov.io/gh/daanhb/FunctionMaps.jl)
+[![Aqua QA](https://raw.githubusercontent.com/JuliaTesting/Aqua.jl/master/badge.svg)](https://github.com/JuliaTesting/Aqua.jl)

docs/Project.toml

@@ -0,0 +1,3 @@
+[deps]
+Documenter = "e30172f5-a6a5-5a46-863b-614d45cd2de4"
+FunctionMaps = "a85aefff-f8ca-4649-a888-c8e5398bc76c"

docs/make.jl

@@ -0,0 +1,17 @@
+using FunctionMaps
+using Documenter
+
+DocMeta.setdocmeta!(FunctionMaps, :DocTestSetup, :(using FunctionMaps); recursive=true)
+
+makedocs(;
+    modules=[FunctionMaps],
+    authors="Daan Huybrechs <[email protected]> and contributors",
+    sitename="FunctionMaps.jl",
+    format=Documenter.HTML(;
+        edit_link="main",
+        assets=String[],
+    ),
+    pages=[
+        "Home" => "index.md",
+    ],
+)

docs/src/index.md

@@ -0,0 +1,14 @@
+```@meta
+CurrentModule = FunctionMaps
+```
+
+# FunctionMaps
+
+Documentation for [FunctionMaps](https://github.com/daanhb/FunctionMaps.jl).
+
+```@index
+```
+
+```@autodocs
+Modules = [FunctionMaps]
+```

src/FunctionMaps.jl

@@ -0,0 +1,58 @@
+module FunctionMaps
+
+using CompositeTypes, CompositeTypes.Display, CompositeTypes.Indexing
+using LinearAlgebra
+using StaticArrays
+
+import Base:
+    convert, show,
+    ==, hash        # for the equality of maps
+
+import CompositeTypes: component, components
+
+# Exhaustive list of exports:
+
+# from util/common.jl
+export prectype, numtype
+
+# from generic/map.jl
+export Map, MapRef,
+    applymap, isequalmap,
+    domaintype, codomaintype,
+    inverse, leftinverse, rightinverse,
+    mapsize, jacobian, jacdet, diffvolume,
+    isrealmap
+# from generic/canonical.jl
+export canonicalmap
+# from generic/composite.jl
+export composedmap
+# from generic/product.jl
+export productmap
+
+# from types/basic.jl
+export IdentityMap,
+    StaticIdentityMap, VectorIdentityMap,
+    ZeroMap, UnityMap, ConstantMap,
+    isconstantmap, mapconstant
+# from types/affine.jl
+export AffineMap, Translation, LinearMap,
+    affinematrix, affinevector,
+    islinearmap, isaffinemap
+
+include("util/common.jl")
+
+include("generic/map.jl")
+include("generic/interface.jl")
+include("generic/canonical.jl")
+include("generic/lazy.jl")
+include("generic/inverse.jl")
+include("generic/jacobian.jl")
+include("generic/composite.jl")
+include("generic/product.jl")
+include("generic/isomorphism.jl")
+include("types/basic.jl")
+include("types/affine.jl")
+include("types/coordinates.jl")
+include("types/arithmetics.jl")
+
+end

src/generic/canonical.jl

@@ -0,0 +1,94 @@
+"""
+    canonicalmap([ctype::CanonicalType, ]map)
+
+Return an associated canonical map, if any, of the given map.
+
+Optionally, a canonical type argument may specify an alternative canonical map.
+Canonical maps help with converting between equal maps of different types.
+"""
+canonicalmap(m) = m
+
+"Does the map have a canonical map?"
+hascanonicalmap(m) = !(m === canonicalmap(m))
+
+
+"Supertype of different kinds of canonical objects."
+abstract type CanonicalType end
+
+canonicalmap(ctype::CanonicalType, m) = m
+hascanonicalmap(ctype::CanonicalType, m) = !(m === canonicalmap(ctype, m))
+
+
+"""
+    Equal <: CanonicalType
+
+A canonical object that is equal but simpler.
+"""
+struct Equal <: CanonicalType end
+
+canonicalmap(::Equal, m) = m
+equalmap(m) = canonicalmap(Equal(), m)
+hasequalmap(m) = hascanonicalmap(Equal(), m)
+
+"""
+    simplify(m)
+
+Simplify the given map to an equal map.
+"""
+simplify(m) = equalmap(m)
+"""
+    simplifies(m)
+
+Does the map simplify?
+"""
+simplifies(m) = hasequalmap(m)
+
+"Convert the given map to a map defined in FunctionMaps.jl."
+tofunctionmap(m::Map) = m
+tofunctionmap(m::MapRef) = tofunctionmap(functionmap(m))
+
+
+"""
+    Equivalent <: CanonicalType
+
+A canonical object that is equivalent but may have different type.
+"""
+struct Equivalent <: CanonicalType end
+
+canonicalmap(::Equivalent, m) = canonicalmap(Equal(), m)
+
+canonicalmap(::Equivalent, m::Map{<:StaticVector{1,T}}) where {T} = convert(Map{T}, m)
+canonicalmap(::Equivalent, m::Map{NTuple{N,T}}) where {N,T} = convert(Map{SVector{N,T}}, m)
+
+equivalentmap(m) = canonicalmap(Equivalent(), m)
+hasequivalentmap(m) = hascanonicalmap(Equivalent(), m)
+
+"""
+    CanonicalExtensionType <: CanonicalType
+
+Canonical types used to translate between packages.
+"""
+abstract type CanonicalExtensionType <: CanonicalType
+end
+
+"Return the extension type associated with the given object."
+canonicalextensiontype(m) = canonicalextensiontype(typeof(m))
+
+
+==(m1::Map, m2::Map) = isequalmap(m1, m2)   # Method from Base
+
+"""
+    isequalmap(map1, map2)
+
+Are the two given maps equal?
+"""
+isequalmap(m1, m2) = isequalmap1(m1, m2)
+isequalmap1(m1, m2) = simplifies(m1) ? isequalmap(simplify(m1), m2) : isequalmap2(m1, m2)
+isequalmap2(m1, m2) = simplifies(m2) ? isequalmap(m1, simplify(m2)) : default_isequalmap(m1, m2)
+default_isequalmap(m1, m2) = m1===m2
+
+# Associated with == we have to define the hashes of maps
+Base.hash(m::Map, h::UInt) = map_hash(m, h)
+
+map_hash(m) = map_hash(m, zero(UInt))
+map_hash(m, h::UInt) = invoke(hash, Tuple{Any,UInt}, m, h)