Pluto.jl
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Published
20 hours ago •
fonsp
fonsp
Function wrapping not working for big plotting cell
#720 is not working properly in this notebook:
The first interactive board takes 130ms when I move the slider, but when I replace it with exactly the same code wrapped in a function (zzz below the cell), it only takes 50ms.
### A Pluto.jl notebook ###
# v0.19.25
#> [frontmatter]
#> chapter = 1
#> video = "https://www.youtube.com/watch?v=KyBXJV1zFlo"
#> image = "https://user-images.githubusercontent.com/6933510/136196599-c6ae60f0-9269-4134-bb0d-5bcab928bd2b.gif"
#> section = 7
#> order = 7
#> title = "Dynamic Programming"
#> layout = "layout.jlhtml"
#> youtube_id = "KyBXJV1zFlo"
#> description = ""
#> tags = ["lecture", "module1"]
using Markdown
using InteractiveUtils
# This Pluto notebook uses @bind for interactivity. When running this notebook outside of Pluto, the following 'mock version' of @bind gives bound variables a default value (instead of an error).
macro bind(def, element)
quote
local iv = try Base.loaded_modules[Base.PkgId(Base.UUID("6e696c72-6542-2067-7265-42206c756150"), "AbstractPlutoDingetjes")].Bonds.initial_value catch; b -> missing; end
local el = $(esc(element))
global $(esc(def)) = Core.applicable(Base.get, el) ? Base.get(el) : iv(el)
el
end
end
# ╔═╡ 71b53b98-8038-11eb-0ea5-d953294e9f35
begin
import ImageIO
using Plots, PlutoUI, Colors, Images
end
# ╔═╡ 938107f0-80ee-11eb-18cf-775802c43c2f
md"""
What is dynamic programming? The word "programming" here is a rather archaic word (but still in use) for an **optimization problem**, as used, for example, in the phrase
"linear programming." Probably the word "programming" should be abandoned in this context, but no doubt it is too late.
"""
# ╔═╡ eb043a90-8102-11eb-3b78-d590a23c83f4
md"""
## Summing over paths problem
"""
# ╔═╡ 5994117c-8102-11eb-1b05-671b7cf87a7e
md"""
Let's start by looking at the following problem.
> Given a matrix, we follow a path from top to bottom.
> The paths start at one of the square on the top, and can only go downwards, either **South-East**, **South**, or **South-West**.
>
> We will **add up** the numbers visited along each path. Our goal is to find the path that has the **_smallest_ sum**.
This is indeed an optimization problem: in the set of all possible paths, we want to find a path that **minimizes** the sum of visited squares.
"""
# ╔═╡ b2c90407-ca04-4f96-a640-d197be02d155
md"""
### Try it yourself!
"""
# ╔═╡ b4558306-804a-11eb-2719-5fd37c6fa281
md"""
Board size: $(@bind n Slider(2:12, show_value = true, default=8))
"""
# ╔═╡ bc631086-804a-11eb-216e-c955e2115f55
M = rand( 0:9, n, n)
# ╔═╡ 5dd22d0e-80d6-11eb-0541-d77668309f6c
# normally you would just do
# @bind whichpath Slider(1:numpaths)
# but that would not work on PlutoSliderServer, because then the bond for n would
# define this bond for whichpath (because n defines numpaths).
# This trick avoids the dependency. But it's not nice that the arrow keys don't take a single step anymore.
md"""
Path: $( @bind whichpath_float Slider(0:0.00005:1) )
"""
# ╔═╡ fdfa9f4f-35ea-4578-8fd1-358aaf3eac23
# zzz(M, paths, whichpath, setup_board, draw_path!, path_text, winner)
# ╔═╡ b086bb69-7194-4fb3-95fb-2403761468fd
# function zzz(M, paths, whichpath, setup_board, draw_path!, path_text, winner)
# let
# path = paths[whichpath]
# values = [ M[i,path[i]] for i=1:n]
# nv = length(values)
# rectangle(w, h, x, y) = Shape(x .+ [0,w,w,0], y .+ [0,0,h,h])
# p = setup_board(M)
# # The winning path
# draw_path!(p, winner;
# color=RGB(1,.6,.6),
# )
# # your path
# draw_path!(p, path;
# color=:black,
# )
# # text
# plot!(p, title=path_text(values))
# plot!(p, xlabel=path_text([ M[i,winner[i]] for i=1:n]), xguidefontcolor=RGB(1,.5,.5))
# p
# end
# end
# ╔═╡ 4e4d333e-8102-11eb-0ba1-0f0183d0d3c2
md"""
One way to solve this problem is the naive algorithm where we enumerate *all* the paths, calculate the sum for each, and take the minimum.
However, as the matrix gets larger the total number of paths grows *exponentially*.
"""
# ╔═╡ 0f0e7456-8104-11eb-1d90-e9f0009e8789
md"""
[Possible research problem: Investigate the statistics of the sums over all possible paths.]
"""
# ╔═╡ 4f969032-80e9-11eb-1ada-d1aa64960967
md"""
## Fixing a single point on a path
"""
# ╔═╡ 28f18aa2-8104-11eb-0c01-dbd14c760ecf
md"""
Let's fix a given point $(i, j)$ and focus only on all those paths that pass through $(i, j)$.
"""
# ╔═╡ 37ebfa3e-80e5-11eb-166c-4ff3471ab12d
md"""
i= $(@bind fixi Scrubbable(1:n))
j= $(@bind fixj Scrubbable(1:n))
"""
# ╔═╡ d0eb5a08-149b-40e8-9fbe-14ace325e335
md"""
Path: $( @bind whichfixedpath_float Slider(0:0.0001:1) )
"""
# ╔═╡ 4d81a6f4-8104-11eb-1f06-5bb7a56c8406
md"""
Suppose we fix the point on the penultimate row (last but one). When we look at the paths below the fixed value, we're doing the same calculation over and over again. It doesn't seem sensible to keep re-doing these calculations. The same holds as we move the fixed point further upwards.
So instead of calculating by working "forwards", for each box we look at the minimum below it.
"""
# ╔═╡ d9265982-80ed-11eb-3a5f-27712a23506b
md"""
## The idea of *overlapping subproblems*
"""
# ╔═╡ ba4acb08-8104-11eb-1771-15bc5d8076fd
md"""
The key point in this problem is that there are *overlapping subproblems*: there are calculations that we don't need to repeat.
The idea of dynamic programming is to remember the solution of those subproblems to get an exponential speed-up in the calculation speed.
"""
# ╔═╡ 163bf8fe-80d0-11eb-2066-75439a533513
begin
struct Paths
m::Int
n::Int
end
Base.iterate(p::Paths) = fill(1,p.m), fill(1,p.m) #start the iteration with 1's
Base.IteratorSize(::Type{Paths}) = SizeUnknown()
function Base.iterate(p::Paths, state)
if state ≠ fill(p.n,p.m) # end when each row has an n
newstate = next(state,p.n)
return newstate, newstate
end
end
function next(path,n)
k = length(path)
# start from the end and find the first element that can be updated by adding 1
while k≥2 && ( path[k]==n || path[k]+1 > path[k-1]+1 )
k -= 1
end
path[k] +=1 #add the one then reset the following elements
for j = k+1 : length(path)
path[j] = max(path[j-1]-1,1)
end
return(path)
end
function allpaths(m,n)
v=Vector{Int}[]
paths = Paths(m,n)
for p ∈ paths
push!(v,copy(p))
end
v
end
end
# ╔═╡ d1c851ee-80d5-11eb-1ce4-357dfb1e638e
begin
paths = allpaths(n,n)
numpaths = length(paths)
md"There are **$numpaths paths** to check."
end
# ╔═╡ 92605063-f0f6-4619-8a0a-e4b18e4c6f88
whichpath = round(Int64, 1 + whichpath_float * (numpaths-1) )
# ╔═╡ 84bb1f5c-80e5-11eb-0e55-83068948870c
begin
fixedpaths = [p for p∈paths if p[fixi]==fixj]
number_of_fixedpaths = length(fixedpaths)
md"Number of fixed paths = $number_of_fixedpaths"
end
# ╔═╡ a307eafd-056d-47ca-a7ab-b6438960355e
whichfixedpath = round(Int64, 1 + whichfixedpath_float * (number_of_fixedpaths-1) )
# ╔═╡ 4e8c8052-8102-11eb-3e9f-01494b525ba0
md"""
### Summing Paths Demo
"""
# ╔═╡ bfa04a82-80d8-11eb-277a-f74429b09870
begin
winnernum = argmin([sum( M[i,p[i]] for i=1:n) for p∈paths])
winner = paths[winnernum]
winnertotal = sum( M[i,winner[i]] for i=1:n);
end
# ╔═╡ 7191b674-80dc-11eb-24b3-518de83f465a
md"""
Our goal is to add the numbers on a path and find the minimal path.
The winner is number $winnernum.
"""
# ╔═╡ f30776b8-abe9-4b9d-b60a-65e8c31c8480
function setup_board(M)
n = size(M,1)
rectangle(w, h, x, y) = Shape(x .+ [0,w,w,0], y .+ [0,0,h,h])
p = plot()
# the board
for i=1:n, j=1:n
if rem(i+j,2) == 0
plot!(p, rectangle(1,1,i,j), opacity=.2, color=:red)
end
end
for i=1:n, j=1:n
annotate!(p, (j+.5),n+2-(i+.5), M[i,j])
end
plot!(p, legend=false, aspectratio=1, xlims=(1,n+1), ylims=(1,n+1), axis=nothing)
return p
end
# ╔═╡ e04331b8-8331-4c7e-bf62-83e3b55206df
rectangle(w, h, x, y) = Shape(x .+ [0,w,w,0], y .+ [0,0,h,h])
# ╔═╡ 59b6694f-e851-42e3-ae53-d826bd6b7792
function draw_path!(p, path, indices=1:n; kwargs...)
# draw the line
plot!(p,
path[indices] .+ .5,
(n + 1 .- indices) .+ .5;
linewidth=4, kwargs...
)
# add little squares as background for the number in a square
for j in n + 1 .- indices
i = path[1+n-j]
plot!(p, rectangle(.4,.4,i+.3,j+.3), opacity=1, color=RGB(0,1,0), linewidth=0,fillcolor=ifelse(rem(i+j,2) == 0, RGBA(1,.85,.85,.2), :white))
end
p
end
# ╔═╡ 4f72bfb4-b6b5-4824-81d6-acbf30b44c56
path_text(values) = "$(join(values, " + ")) = $(sum(values))"
# ╔═╡ 75d6f388-d057-4d8f-bb5f-78b757dacb41
let
path = paths[whichpath]
values = [ M[i,path[i]] for i=1:n]
nv = length(values)
rectangle(w, h, x, y) = Shape(x .+ [0,w,w,0], y .+ [0,0,h,h])
p = setup_board(M)
# The winning path
draw_path!(p, winner;
color=RGB(1,.6,.6),
)
# your path
draw_path!(p, path;
color=:black,
)
# text
plot!(p, title=path_text(values))
plot!(p, xlabel=path_text([ M[i,winner[i]] for i=1:n]), xguidefontcolor=RGB(1,.5,.5))
p
end
# ╔═╡ e5367534-80e5-11eb-341d-7b3e6ca4f111
let
path = fixedpaths[whichfixedpath]
values = [ M[i,path[i]] for i=1:n]
p = setup_board(M)
annotate!(p, (fixj+.5),n+2-(fixi+.5), M[fixi,fixj], :red)
draw_path!(p, path, 1:fixi; color=:black)
draw_path!(p, path, fixi:n; color=:blue)
plot!(p; title=path_text(values))
end
# ╔═╡ 00000000-0000-0000-0000-000000000001
PLUTO_PROJECT_TOML_CONTENTS = """
[deps]
Colors = "5ae59095-9a9b-59fe-a467-6f913c188581"
ImageIO = "82e4d734-157c-48bb-816b-45c225c6df19"
Images = "916415d5-f1e6-5110-898d-aaa5f9f070e0"
Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
PlutoUI = "7f904dfe-b85e-4ff6-b463-dae2292396a8"
[compat]
Colors = "~0.12.8"
ImageIO = "~0.6.6"
Images = "~0.25.2"
Plots = "~1.33.0"
PlutoUI = "~0.7.48"
"""
# ╔═╡ 00000000-0000-0000-0000-000000000002
PLUTO_MANIFEST_TOML_CONTENTS = """
# This file is machine-generated - editing it directly is not advised
[[AbstractFFTs]]
deps = ["ChainRulesCore", "LinearAlgebra"]
git-tree-sha1 = "69f7020bd72f069c219b5e8c236c1fa90d2cb409"
uuid = "621f4979-c628-5d54-868e-fcf4e3e8185c"
version = "1.2.1"
[[AbstractPlutoDingetjes]]
deps = ["Pkg"]
git-tree-sha1 = "8eaf9f1b4921132a4cff3f36a1d9ba923b14a481"
uuid = "6e696c72-6542-2067-7265-42206c756150"
version = "1.1.4"
[[Adapt]]
deps = ["LinearAlgebra"]
git-tree-sha1 = "195c5505521008abea5aee4f96930717958eac6f"
uuid = "79e6a3ab-5dfb-504d-930d-738a2a938a0e"
version = "3.4.0"
[[ArgTools]]
uuid = "0dad84c5-d112-42e6-8d28-ef12dabb789f"
version = "1.1.1"
[[ArnoldiMethod]]
deps = ["LinearAlgebra", "Random", "StaticArrays"]
git-tree-sha1 = "62e51b39331de8911e4a7ff6f5aaf38a5f4cc0ae"
uuid = "ec485272-7323-5ecc-a04f-4719b315124d"
version = "0.2.0"
[[Artifacts]]
uuid = "56f22d72-fd6d-98f1-02f0-08ddc0907c33"
[[AxisAlgorithms]]
deps = ["LinearAlgebra", "Random", "SparseArrays", "WoodburyMatrices"]
git-tree-sha1 = "66771c8d21c8ff5e3a93379480a2307ac36863f7"
uuid = "13072b0f-2c55-5437-9ae7-d433b7a33950"
version = "1.0.1"
[[AxisArrays]]
deps = ["Dates", "IntervalSets", "IterTools", "RangeArrays"]
git-tree-sha1 = "1dd4d9f5beebac0c03446918741b1a03dc5e5788"
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[[Base64]]
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[[Bzip2_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "19a35467a82e236ff51bc17a3a44b69ef35185a2"
uuid = "6e34b625-4abd-537c-b88f-471c36dfa7a0"
version = "1.0.8+0"
[[CEnum]]
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[[Cairo_jll]]
deps = ["Artifacts", "Bzip2_jll", "CompilerSupportLibraries_jll", "Fontconfig_jll", "FreeType2_jll", "Glib_jll", "JLLWrappers", "LZO_jll", "Libdl", "Pixman_jll", "Pkg", "Xorg_libXext_jll", "Xorg_libXrender_jll", "Zlib_jll", "libpng_jll"]
git-tree-sha1 = "4b859a208b2397a7a623a03449e4636bdb17bcf2"
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[[CatIndices]]
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[[ChainRulesCore]]
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[[ChangesOfVariables]]
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[[Clustering]]
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git-tree-sha1 = "64df3da1d2a26f4de23871cd1b6482bb68092bd5"
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[[CodecZlib]]
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[[ColorSchemes]]
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version = "3.19.0"
[[ColorTypes]]
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[[ColorVectorSpace]]
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[[Colors]]
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[[Compat]]
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[[CompilerSupportLibraries_jll]]
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[[CoordinateTransformations]]
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[[DataStructures]]
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git-tree-sha1 = "d1fff3a548102f48987a52a2e0d114fa97d730f0"
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[[Distances]]
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[[FFMPEG_jll]]
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git-tree-sha1 = "74faea50c1d007c85837327f6775bea60b5492dd"
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[[TOML]]
deps = ["Dates"]
uuid = "fa267f1f-6049-4f14-aa54-33bafae1ed76"
version = "1.0.0"
[[Tar]]
deps = ["ArgTools", "SHA"]
uuid = "a4e569a6-e804-4fa4-b0f3-eef7a1d5b13e"
version = "1.10.1"
[[TensorCore]]
deps = ["LinearAlgebra"]
git-tree-sha1 = "1feb45f88d133a655e001435632f019a9a1bcdb6"
uuid = "62fd8b95-f654-4bbd-a8a5-9c27f68ccd50"
version = "0.1.1"
[[Test]]
deps = ["InteractiveUtils", "Logging", "Random", "Serialization"]
uuid = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
[[TiffImages]]
deps = ["ColorTypes", "DataStructures", "DocStringExtensions", "FileIO", "FixedPointNumbers", "IndirectArrays", "Inflate", "Mmap", "OffsetArrays", "PkgVersion", "ProgressMeter", "UUIDs"]
git-tree-sha1 = "70e6d2da9210371c927176cb7a56d41ef1260db7"
uuid = "731e570b-9d59-4bfa-96dc-6df516fadf69"
version = "0.6.1"
[[TiledIteration]]
deps = ["OffsetArrays"]
git-tree-sha1 = "5683455224ba92ef59db72d10690690f4a8dc297"
uuid = "06e1c1a7-607b-532d-9fad-de7d9aa2abac"
version = "0.3.1"
[[TranscodingStreams]]
deps = ["Random", "Test"]
git-tree-sha1 = "8a75929dcd3c38611db2f8d08546decb514fcadf"
uuid = "3bb67fe8-82b1-5028-8e26-92a6c54297fa"
version = "0.9.9"
[[Tricks]]
git-tree-sha1 = "6bac775f2d42a611cdfcd1fb217ee719630c4175"
uuid = "410a4b4d-49e4-4fbc-ab6d-cb71b17b3775"
version = "0.1.6"
[[URIs]]
git-tree-sha1 = "e59ecc5a41b000fa94423a578d29290c7266fc10"
uuid = "5c2747f8-b7ea-4ff2-ba2e-563bfd36b1d4"
version = "1.4.0"
[[UUIDs]]
deps = ["Random", "SHA"]
uuid = "cf7118a7-6976-5b1a-9a39-7adc72f591a4"
[[UnPack]]
git-tree-sha1 = "387c1f73762231e86e0c9c5443ce3b4a0a9a0c2b"
uuid = "3a884ed6-31ef-47d7-9d2a-63182c4928ed"
version = "1.0.2"
[[Unicode]]
uuid = "4ec0a83e-493e-50e2-b9ac-8f72acf5a8f5"
[[UnicodeFun]]
deps = ["REPL"]
git-tree-sha1 = "53915e50200959667e78a92a418594b428dffddf"
uuid = "1cfade01-22cf-5700-b092-accc4b62d6e1"
version = "0.4.1"
[[Unzip]]
git-tree-sha1 = "ca0969166a028236229f63514992fc073799bb78"
uuid = "41fe7b60-77ed-43a1-b4f0-825fd5a5650d"
version = "0.2.0"
[[Wayland_jll]]
deps = ["Artifacts", "Expat_jll", "JLLWrappers", "Libdl", "Libffi_jll", "Pkg", "XML2_jll"]
git-tree-sha1 = "3e61f0b86f90dacb0bc0e73a0c5a83f6a8636e23"
uuid = "a2964d1f-97da-50d4-b82a-358c7fce9d89"
version = "1.19.0+0"
[[Wayland_protocols_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "4528479aa01ee1b3b4cd0e6faef0e04cf16466da"
uuid = "2381bf8a-dfd0-557d-9999-79630e7b1b91"
version = "1.25.0+0"
[[WoodburyMatrices]]
deps = ["LinearAlgebra", "SparseArrays"]
git-tree-sha1 = "de67fa59e33ad156a590055375a30b23c40299d3"
uuid = "efce3f68-66dc-5838-9240-27a6d6f5f9b6"
version = "0.5.5"
[[XML2_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Libiconv_jll", "Pkg", "Zlib_jll"]
git-tree-sha1 = "58443b63fb7e465a8a7210828c91c08b92132dff"
uuid = "02c8fc9c-b97f-50b9-bbe4-9be30ff0a78a"
version = "2.9.14+0"
[[XSLT_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Libgcrypt_jll", "Libgpg_error_jll", "Libiconv_jll", "Pkg", "XML2_jll", "Zlib_jll"]
git-tree-sha1 = "91844873c4085240b95e795f692c4cec4d805f8a"
uuid = "aed1982a-8fda-507f-9586-7b0439959a61"
version = "1.1.34+0"
[[Xorg_libX11_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libxcb_jll", "Xorg_xtrans_jll"]
git-tree-sha1 = "5be649d550f3f4b95308bf0183b82e2582876527"
uuid = "4f6342f7-b3d2-589e-9d20-edeb45f2b2bc"
version = "1.6.9+4"
[[Xorg_libXau_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "4e490d5c960c314f33885790ed410ff3a94ce67e"
uuid = "0c0b7dd1-d40b-584c-a123-a41640f87eec"
version = "1.0.9+4"
[[Xorg_libXcursor_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXfixes_jll", "Xorg_libXrender_jll"]
git-tree-sha1 = "12e0eb3bc634fa2080c1c37fccf56f7c22989afd"
uuid = "935fb764-8cf2-53bf-bb30-45bb1f8bf724"
version = "1.2.0+4"
[[Xorg_libXdmcp_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "4fe47bd2247248125c428978740e18a681372dd4"
uuid = "a3789734-cfe1-5b06-b2d0-1dd0d9d62d05"
version = "1.1.3+4"
[[Xorg_libXext_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
git-tree-sha1 = "b7c0aa8c376b31e4852b360222848637f481f8c3"
uuid = "1082639a-0dae-5f34-9b06-72781eeb8cb3"
version = "1.3.4+4"
[[Xorg_libXfixes_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
git-tree-sha1 = "0e0dc7431e7a0587559f9294aeec269471c991a4"
uuid = "d091e8ba-531a-589c-9de9-94069b037ed8"
version = "5.0.3+4"
[[Xorg_libXi_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll", "Xorg_libXfixes_jll"]
git-tree-sha1 = "89b52bc2160aadc84d707093930ef0bffa641246"
uuid = "a51aa0fd-4e3c-5386-b890-e753decda492"
version = "1.7.10+4"
[[Xorg_libXinerama_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll"]
git-tree-sha1 = "26be8b1c342929259317d8b9f7b53bf2bb73b123"
uuid = "d1454406-59df-5ea1-beac-c340f2130bc3"
version = "1.1.4+4"
[[Xorg_libXrandr_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libXext_jll", "Xorg_libXrender_jll"]
git-tree-sha1 = "34cea83cb726fb58f325887bf0612c6b3fb17631"
uuid = "ec84b674-ba8e-5d96-8ba1-2a689ba10484"
version = "1.5.2+4"
[[Xorg_libXrender_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
git-tree-sha1 = "19560f30fd49f4d4efbe7002a1037f8c43d43b96"
uuid = "ea2f1a96-1ddc-540d-b46f-429655e07cfa"
version = "0.9.10+4"
[[Xorg_libpthread_stubs_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "6783737e45d3c59a4a4c4091f5f88cdcf0908cbb"
uuid = "14d82f49-176c-5ed1-bb49-ad3f5cbd8c74"
version = "0.1.0+3"
[[Xorg_libxcb_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "XSLT_jll", "Xorg_libXau_jll", "Xorg_libXdmcp_jll", "Xorg_libpthread_stubs_jll"]
git-tree-sha1 = "daf17f441228e7a3833846cd048892861cff16d6"
uuid = "c7cfdc94-dc32-55de-ac96-5a1b8d977c5b"
version = "1.13.0+3"
[[Xorg_libxkbfile_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libX11_jll"]
git-tree-sha1 = "926af861744212db0eb001d9e40b5d16292080b2"
uuid = "cc61e674-0454-545c-8b26-ed2c68acab7a"
version = "1.1.0+4"
[[Xorg_xcb_util_image_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "0fab0a40349ba1cba2c1da699243396ff8e94b97"
uuid = "12413925-8142-5f55-bb0e-6d7ca50bb09b"
version = "0.4.0+1"
[[Xorg_xcb_util_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libxcb_jll"]
git-tree-sha1 = "e7fd7b2881fa2eaa72717420894d3938177862d1"
uuid = "2def613f-5ad1-5310-b15b-b15d46f528f5"
version = "0.4.0+1"
[[Xorg_xcb_util_keysyms_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "d1151e2c45a544f32441a567d1690e701ec89b00"
uuid = "975044d2-76e6-5fbe-bf08-97ce7c6574c7"
version = "0.4.0+1"
[[Xorg_xcb_util_renderutil_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "dfd7a8f38d4613b6a575253b3174dd991ca6183e"
uuid = "0d47668e-0667-5a69-a72c-f761630bfb7e"
version = "0.3.9+1"
[[Xorg_xcb_util_wm_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xcb_util_jll"]
git-tree-sha1 = "e78d10aab01a4a154142c5006ed44fd9e8e31b67"
uuid = "c22f9ab0-d5fe-5066-847c-f4bb1cd4e361"
version = "0.4.1+1"
[[Xorg_xkbcomp_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_libxkbfile_jll"]
git-tree-sha1 = "4bcbf660f6c2e714f87e960a171b119d06ee163b"
uuid = "35661453-b289-5fab-8a00-3d9160c6a3a4"
version = "1.4.2+4"
[[Xorg_xkeyboard_config_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Xorg_xkbcomp_jll"]
git-tree-sha1 = "5c8424f8a67c3f2209646d4425f3d415fee5931d"
uuid = "33bec58e-1273-512f-9401-5d533626f822"
version = "2.27.0+4"
[[Xorg_xtrans_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "79c31e7844f6ecf779705fbc12146eb190b7d845"
uuid = "c5fb5394-a638-5e4d-96e5-b29de1b5cf10"
version = "1.4.0+3"
[[Zlib_jll]]
deps = ["Libdl"]
uuid = "83775a58-1f1d-513f-b197-d71354ab007a"
version = "1.2.12+3"
[[Zstd_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "e45044cd873ded54b6a5bac0eb5c971392cf1927"
uuid = "3161d3a3-bdf6-5164-811a-617609db77b4"
version = "1.5.2+0"
[[libaom_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "3a2ea60308f0996d26f1e5354e10c24e9ef905d4"
uuid = "a4ae2306-e953-59d6-aa16-d00cac43593b"
version = "3.4.0+0"
[[libass_jll]]
deps = ["Artifacts", "Bzip2_jll", "FreeType2_jll", "FriBidi_jll", "HarfBuzz_jll", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
git-tree-sha1 = "5982a94fcba20f02f42ace44b9894ee2b140fe47"
uuid = "0ac62f75-1d6f-5e53-bd7c-93b484bb37c0"
version = "0.15.1+0"
[[libblastrampoline_jll]]
deps = ["Artifacts", "Libdl", "OpenBLAS_jll"]
uuid = "8e850b90-86db-534c-a0d3-1478176c7d93"
version = "5.1.1+0"
[[libfdk_aac_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "daacc84a041563f965be61859a36e17c4e4fcd55"
uuid = "f638f0a6-7fb0-5443-88ba-1cc74229b280"
version = "2.0.2+0"
[[libpng_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Zlib_jll"]
git-tree-sha1 = "94d180a6d2b5e55e447e2d27a29ed04fe79eb30c"
uuid = "b53b4c65-9356-5827-b1ea-8c7a1a84506f"
version = "1.6.38+0"
[[libsixel_jll]]
deps = ["Artifacts", "JLLWrappers", "JpegTurbo_jll", "Libdl", "Pkg", "libpng_jll"]
git-tree-sha1 = "d4f63314c8aa1e48cd22aa0c17ed76cd1ae48c3c"
uuid = "075b6546-f08a-558a-be8f-8157d0f608a5"
version = "1.10.3+0"
[[libvorbis_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Ogg_jll", "Pkg"]
git-tree-sha1 = "b910cb81ef3fe6e78bf6acee440bda86fd6ae00c"
uuid = "f27f6e37-5d2b-51aa-960f-b287f2bc3b7a"
version = "1.3.7+1"
[[nghttp2_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d"
version = "1.48.0+0"
[[p7zip_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0"
version = "17.4.0+0"
[[x264_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "4fea590b89e6ec504593146bf8b988b2c00922b2"
uuid = "1270edf5-f2f9-52d2-97e9-ab00b5d0237a"
version = "2021.5.5+0"
[[x265_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
git-tree-sha1 = "ee567a171cce03570d77ad3a43e90218e38937a9"
uuid = "dfaa095f-4041-5dcd-9319-2fabd8486b76"
version = "3.5.0+0"
[[xkbcommon_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Wayland_jll", "Wayland_protocols_jll", "Xorg_libxcb_jll", "Xorg_xkeyboard_config_jll"]
git-tree-sha1 = "9ebfc140cc56e8c2156a15ceac2f0302e327ac0a"
uuid = "d8fb68d0-12a3-5cfd-a85a-d49703b185fd"
version = "1.4.1+0"
"""
# ╔═╡ Cell order:
# ╠═71b53b98-8038-11eb-0ea5-d953294e9f35
# ╟─938107f0-80ee-11eb-18cf-775802c43c2f
# ╟─eb043a90-8102-11eb-3b78-d590a23c83f4
# ╟─5994117c-8102-11eb-1b05-671b7cf87a7e
# ╟─b2c90407-ca04-4f96-a640-d197be02d155
# ╟─b4558306-804a-11eb-2719-5fd37c6fa281
# ╟─bc631086-804a-11eb-216e-c955e2115f55
# ╟─d1c851ee-80d5-11eb-1ce4-357dfb1e638e
# ╟─7191b674-80dc-11eb-24b3-518de83f465a
# ╟─5dd22d0e-80d6-11eb-0541-d77668309f6c
# ╟─92605063-f0f6-4619-8a0a-e4b18e4c6f88
# ╠═75d6f388-d057-4d8f-bb5f-78b757dacb41
# ╠═fdfa9f4f-35ea-4578-8fd1-358aaf3eac23
# ╠═b086bb69-7194-4fb3-95fb-2403761468fd
# ╟─4e4d333e-8102-11eb-0ba1-0f0183d0d3c2
# ╟─0f0e7456-8104-11eb-1d90-e9f0009e8789
# ╟─4f969032-80e9-11eb-1ada-d1aa64960967
# ╟─28f18aa2-8104-11eb-0c01-dbd14c760ecf
# ╟─37ebfa3e-80e5-11eb-166c-4ff3471ab12d
# ╟─84bb1f5c-80e5-11eb-0e55-83068948870c
# ╟─d0eb5a08-149b-40e8-9fbe-14ace325e335
# ╟─a307eafd-056d-47ca-a7ab-b6438960355e
# ╟─e5367534-80e5-11eb-341d-7b3e6ca4f111
# ╟─4d81a6f4-8104-11eb-1f06-5bb7a56c8406
# ╟─d9265982-80ed-11eb-3a5f-27712a23506b
# ╟─ba4acb08-8104-11eb-1771-15bc5d8076fd
# ╟─163bf8fe-80d0-11eb-2066-75439a533513
# ╟─4e8c8052-8102-11eb-3e9f-01494b525ba0
# ╠═bfa04a82-80d8-11eb-277a-f74429b09870
# ╠═f30776b8-abe9-4b9d-b60a-65e8c31c8480
# ╠═59b6694f-e851-42e3-ae53-d826bd6b7792
# ╠═e04331b8-8331-4c7e-bf62-83e3b55206df
# ╠═4f72bfb4-b6b5-4824-81d6-acbf30b44c56
# ╟─00000000-0000-0000-0000-000000000001
# ╟─00000000-0000-0000-0000-000000000002
ExpressionExplorer.can_be_function_wrapped is not scope aware so it thinks that this creates a global function:
julia> Pluto.ExpressionExplorer.can_be_function_wrapped(quote
let
rectangle(w, h, x, y) = Shape(x .+ [0,w,w,0], y .+ [0,0,h,h])
rectangle(1, 2, 3, 4)
end
end)
false
