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Michael Sippel 2024-09-23 23:06:05 +02:00
parent 10cd2f9bc9
commit ae9e451bf3
14 changed files with 621 additions and 55 deletions
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2
beamer/lc-beamer/Makefile
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@ -9,7 +9,7 @@ EXAMPLE_PDF = example.pdf
CACHE_DIR := $(shell pwd)/.latex-cache
COMPILE_TEX := latexmk -lualatex -output-directory="$(CACHE_DIR)"
COMPILE_TEX := latexmk -lualatex -latexoption="-shell-escape" -output-directory="$(CACHE_DIR)"
.PHONY: install uninstall example all clean

346
beamer/lc-beamer/example.tex
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@ -6,6 +6,16 @@
\usepackage[dvipsnames]{xcolor}
\usepackage{mathpartir}
\usepackage{stmaryrd}
%\usepackage{minted}
%\usemintedstyle{tango}
\usepackage{listings}% http://ctan.org/pkg/listings
\lstset{
basicstyle=\ttfamily,
mathescape
}
\newcommand{\metavariable}[1]{\textcolor{teal}{#1}}
\newcommand{\typeterminal}[1]{\textcolor{brown}{#1}}
@ -28,9 +38,11 @@
\titlepage
\end{frame}
\begin{frame}
\frametitle{Type Systems}
\framesubtitle{Tension between Safety and Flexibility}
\framesubtitle{Safety <> Flexibility}
\begin{itemize}
\item<1-> Goal: eliminate undefined behaviour,
@ -47,46 +59,213 @@
\end{itemize}
\end{frame}
\begin{frame}{How to get fast code?}
\framesubtitle{Requirements for a type system}
\begin{frame}[t, fragile]{Type Systems}
\framesubtitle{Safety <> Flexibility}
\begin{lstlisting}
/* this is an angle in degrees */
double hue = 156.4;
\end{lstlisting}
\end{frame}
\begin{frame}{Performance Checklist}
\framesubtitle{(singlethreaded)}
\begin{enumerate}
\item<1-> algorithmic
\begin{itemize}
\item<1-> algorithmic optimization
\begin{itemize}
\item see which methods are used most frequently
\item switch structures to reduce complexity there
\item choose appropriate data structures\\
(reduce complexity in frequent cases)
\item identify special cases
\end{itemize}
\item<2-> optimize implementation detail:
\item<2-> implementation detail:
\begin{itemize}
\item remove indirection
\item bottleneck? memory!\\
(plenty of Main-memory, but FAST memory is scarce\\
\(\rightarrow\) improve cache \& bus efficiency with compact representations)
\item optimize memory bottleneck
\begin{itemize}
\item<3-> Balance De-/Encode Overhead
vs. Fetch-Overhead
\item improve cache \& bus efficiency with compact representations
\item<3-> Synchronize locality in access order and memory layout.
(elements accessed in succession shall be close in memory,
AoS vs SoA)
\item<4-> Synchronize locality in access order and memory layout.
-> elements accessed in succession shall be close in memory.
(e.g. AoS vs SoA)
\item<4-> \(\rightarrow\) De-/Encode Overhead
vs. Fetch-Overhead,\\
account for machine specific cache-sizes
\end{itemize}
\item
\item<5-> accounting for machine specific cache-sizes
\item<6-> accounting for SIMD instructions
\item<6-> use SIMD instructions
\item<7-> interfacing with kernels running on accelerator devices
\end{itemize}
\end{enumerate}
\end{frame}
\begin{frame}[t, fragile]{Example - Image Processing}
\begin{lstlisting}
image-read :: FilePath -> [Color]
image-write :: FilePath -> [Color] -> ()
image-mix :: $\mathbb{R}$ -> [Color] -> [Color] -> [Color]
image-saturate :: $\mathbb{R}$ -> [Color] -> [Color]
let im1 = image-read "in1.png"
let im2 = image-read "in2.png"
let im3 = image-mix 0.5
im1
(image-saturate 0.8 im2)
image-write "out.png" im3
\end{lstlisting}
\end{frame}
\begin{frame}{Example - Image Processing}
\framesubtitle{More Types}
\begin{itemize}
\item \texttt{ColorRGBu8}
\item \texttt{ColorRGBf32}
\item \texttt{ColorHSVu8}
\item \texttt{ColorHSVf32}
\end{itemize}
\end{itemize}
\end{frame}
\begin{frame}[t, fragile]{Example - Image Processing}
\framesubtitle{More Types}
\begin{lstlisting}
image-read :: FilePath -> [ColorRGBu8]
image-write :: FilePath -> [ColorRGBu8] -> ()
image-mix :: f32 -> [ColorRGBf32] -> [ColorRGBf32] -> [ColorRGBf32]
image-saturate:: f32->[ColorHSVf32]->[ColorHSVf32]
let im1 = image-read "in1.png"
let im2 = image-read "in2.png"
let im3 = image-mix 0.5
im1
(image-saturate 0.8 im2)
image-write "out.png" im3
\end{lstlisting}
\end{frame}
\begin{frame}[t, fragile]{Example - Image Processing}
\framesubtitle{AoS vs SoA}
\begin{verbatim}
[cacheline][cacheline][cacheline]
\end{verbatim}
\begin{verbatim}
[RGBRGBRG][BRGBRGBR][GBRGBRGB]
\end{verbatim}
\begin{verbatim}
[HSVHSVHS][VHSVHSVH][SVHSVHSV]
\end{verbatim}
\begin{verbatim}
[HHHHHHHH][SSSSSSSS][VVVVVVVV]
\end{verbatim}
\end{frame}
\begin{frame}{Abstract Concept - Multiple Representations}
\framesubtitle{Requirements for a type system}
\framesubtitle{OpenGL Image Formats}
\begin{itemize}
\item
\item \texttt{GL\_R3\_G3\_B2}
\item \texttt{GL\_RGB10\_A2}
\item \texttt{GL\_R11F\_G11F\_B10F}
\item \texttt{GL\_SRGB8\_ALPHA8}
\item \ldots
\end{itemize}
\end{frame}
\begin{frame}{Sea of Types}
\centering
\includegraphics[width=0.5\textwidth]{sea-of-types/target/sea-of-types-0-bytes.png}
\end{frame}
\begin{frame}{Sea of Types}
\centering
\includegraphics[width=0.5\textwidth]{sea-of-types/target/sea-of-types-1-ieee754.png}
\end{frame}
\begin{frame}{Sea of Types}
\centering
\includegraphics[height=0.5\textheight]{sea-of-types/target/sea-of-types-2-real.png}
\end{frame}
\begin{frame}{Sea of Types}
\centering
\includegraphics[height=0.5\textheight]{sea-of-types/target/sea-of-types-3-real.png}
\end{frame}
\begin{frame}{Sea of Types}
\centering
\includegraphics[height=0.8\textheight]{sea-of-types/target/sea-of-types-4-degrees.png}
\end{frame}
\begin{frame}{Sea of Types}
\centering
\includegraphics[height=0.8\textheight]{sea-of-types/target/sea-of-types-5-turns.png}
\end{frame}
\begin{frame}{Sea of Types}
\centering
\includegraphics[height=0.8\textheight]{sea-of-types/target/sea-of-types-6-radians.png}
\end{frame}
\begin{frame}{Sea of Types}
\centering
\includegraphics[height=0.8\textheight]{sea-of-types/target/sea-of-types-7-angle.png}
\end{frame}
\begin{frame}{Sea of Types}
\centering
\includegraphics[height=0.8\textheight]{sea-of-types/target/sea-of-types-8-hue.png}
\end{frame}
\begin{frame}{Sea of Types}
\centering
\includegraphics[height=0.8\textheight]{sea-of-types/target/sea-of-types-9-u8.png}
\end{frame}
\begin{frame}{Sea of Types}
\centering
\includegraphics[width=\textwidth]{sea-of-types/target/sea-of-types-10-u8.png}
\end{frame}
\begin{frame}{Solutions (I): Traits / Typeclasses / Interfaces}
\begin{itemize}
\item todo
\end{itemize}
\end{frame}
\begin{frame}{Solutions (II): Wrapper structs / newtype}
\begin{itemize}
\item todo
\end{itemize}
\end{frame}
\begin{frame}{Coercions: (In-)Coherence with Transitivity}
\begin{itemize}
\item<1-> Common example: coerce \texttt{Int -> Real}
@ -114,15 +293,16 @@
\end{itemize}
\end{frame}
\begin{frame}{Sea of Types}
\includegraphics[width=\textwidth]{sot-int.png}
\end{frame}
\begin{frame}{Sea of Types}
\includegraphics[width=\textwidth]{sot-json.png}
\begin{frame}{Related Work}
\begin{itemize}
\item TODO
\item cite
\item some
\item stuff
\end{itemize}
\end{frame}
\begin{frame}{Ladder Types}
\begin{block}{Intuition}
Encode "represented-as" relation into type terms
@ -142,6 +322,38 @@
\)\end{example}
\end{frame}
\begin{frame}{Morphisms}
\begin{block}{Intuition}
Transform between semantically equivalent representations of the same abstract concept
\end{block}
\begin{block}{Type}
\( \tau \sim \tau_1 \rightarrow_\text{morph} \tau \sim \tau_2 \)
\end{block}
\begin{example}\(
Angle \sim Degrees \sim \mathbb{R}
\rightarrow_\text{morph}
Angle \sim Radians \sim \mathbb{R}
\)\end{example}
\end{frame}
\begin{frame}{Morphisms}
\framesubtitle{Coherence}
\begin{block}{Coherence Condition}
Assume\\
\(\metavariable{m_\sigma} : \typeterminal{\metavariable{\sigma} \sim \metavariable{\sigma_1} \rightarrow_\text{morph} \metavariable{\sigma} \sim \metavariable{\sigma_2}}\)\\
\(\metavariable{m_\tau} : \typeterminal{\metavariable{\tau} \sim \metavariable{\tau_1} \rightarrow_\text{morph} \metavariable{\tau} \sim \metavariable{\tau_2}}\)\\
\(\metavariable{f_1} : \typeterminal{\metavariable{\sigma} \sim \metavariable{\sigma_1} \rightarrow \metavariable{\tau} \sim \metavariable{\tau_1} }\)\\
\(\metavariable{f_2} : \typeterminal{\metavariable{\sigma} \sim \metavariable{\sigma_2} \rightarrow \metavariable{\tau} \sim \metavariable{\tau_2} }\)\\
then it holds that:\\
\(\forall x:\typeterminal{\metavariable{\sigma}\sim\metavariable{\sigma_1}},\quad
\metavariable{m_\tau}(\metavariable{f_1} x) = \metavariable{f_2} (\metavariable{m_\sigma} x) \)
\end{block}
\end{frame}
\begin{frame}{Extending System F}
\small
\begin{grammar}
@ -238,10 +450,10 @@ $$\\$$
}{Descension}
\end{grammar}
\end{frame}
\begin{frame}{Morphism Graph}
\begin{definition}[Morphism Paths]
@ -278,8 +490,8 @@ $$\\$$
\end{definition}
\end{frame}
\begin{frame}{Morphism Graph}
\begin{frame}{Morphism Graph}
\begin{example}[Morphism Graph]
\begin{mathpar}
\small
@ -290,12 +502,11 @@ $$\\$$
\}.
\end{mathpar}
\end{example}
\end{frame}
\begin{frame}{Morphism Graph}
\begin{frame}{Morphism Graph}
\begin{example}[Morphism Graph]
Then ..
\small
@ -305,23 +516,9 @@ Then ..
\item \(\Gamma \vdash \typeterminal{\langle\text{Seq }\text{Angle}\sim\text{Degrees}\sim\mathbb{R}\rangle} \leadsto \typeterminal{\langle\text{Seq }\text{Angle}\sim\text{Radians}\sim\mathbb{R}\rangle}\) (by \textsc{M-MapSeq})
\end{itemize}
\end{example}
\end{frame}
\begin{frame}{Typing}
\begin{definition}[Typing Relation]
\begin{mathpar}
\inferrule[T-App]{
\Gamma \vdash \metavariable{f} : \metavariable{\sigma} \typeterminal{\rightarrow} \metavariable{\tau}\\
\Gamma \vdash \metavariable{a} : \metavariable{\sigma'}\\
\Gamma \vdash \metavariable{\sigma'} \leadsto \metavariable{\sigma}
}{
\Gamma \vdash (\metavariable{f} \quad \metavariable{a}) : \metavariable{\tau}
}
\end{mathpar}
\end{definition}
\end{frame}
\begin{frame}{Translation}
\begin{definition}[Morphism Translation]
@ -382,8 +579,46 @@ Then ..
\end{definition}
\end{frame}
\begin{frame}{Translation}
\begin{frame}{Translation}
\begin{example}[Morphism Translation]
\begin{mathpar}
\small
\Big{\llbracket}
\inferrule[M-Chain]{
\ldots
}{
\Gamma \vdash \typeterminal{\langle\text{Seq}\quad\text{Angle}\sim\text{Degrees}\sim\mathbb{R}\rangle}\\
\leadsto \typeterminal{\langle\text{Seq}\quad\text{Angle}\sim\text{Radians}\sim\mathbb{R}\rangle}
}
\Big{\rrbracket} =
\exprterminal{\lambda \text{xs}:\typeterminal{\langle\text{Seq}\quad \text{Angle}\sim\text{Degrees}\sim\mathbb{R} \rangle}}
\newline
\exprterminal{\mapsto (map \text{ }(\lambda \text{x}:\metavariable{\tau} \mapsto \text{turns-to-radians } (\text{degrees-to-turns } x)) \text{ } xs) }
\end{mathpar}
\end{example}
\end{frame}
\begin{frame}{Typing}
\begin{definition}[Typing Relation]
\begin{mathpar}
\inferrule[T-App]{
\Gamma \vdash \metavariable{f} : \metavariable{\sigma} \typeterminal{\rightarrow} \metavariable{\tau}\\
\Gamma \vdash \metavariable{a} : \metavariable{\sigma'}\\
\Gamma \vdash \metavariable{\sigma'} \leadsto \metavariable{\sigma}
}{
\Gamma \vdash (\metavariable{f} \quad \metavariable{a}) : \metavariable{\tau}
}
\end{mathpar}
\end{definition}
\end{frame}
\begin{frame}{Translation}
\begin{definition}[Expression Translation]
Translates a type-derivation tree into a fully expanded expression
@ -424,8 +659,10 @@ D :: \Gamma \vdash \metavariable{e} : \metavariable{\tau}\\
\end{lemma}
\end{frame}
\begin{frame}{Soundness}
\begin{frame}{Soundness}
\begin{theorem}[Preservation]
\begin{mathpar} \forall \Gamma, \metavariable{e}, \metavariable{\tau},\\
D :: \Gamma \vdash \metavariable{e} : \metavariable{\tau}\\
@ -436,19 +673,26 @@ D :: \Gamma \vdash \metavariable{e} : \metavariable{\tau}\\
\end{frame}
\begin{frame}{Soundness}
\begin{theorem}[Progress]
\begin{mathpar} \forall \Gamma, \metavariable{e}, \metavariable{\tau},\\
D :: \Gamma \vdash \metavariable{e} : \metavariable{\tau}\\
\Rightarrow \llbracket D \rrbracket \text{ is a value} \\ \vee \\
\Rightarrow \llbracket D \rrbracket \text{ is a value} \\ \vee
\exists \metavariable{e'} . \llbracket D \rrbracket \rightarrow_{eval} \metavariable{e'} \\
\end{mathpar}
\end{theorem}
\end{frame}
\begin{frame}{Summary}
todo
\end{frame}
\end{document}

8
beamer/lc-beamer/sea-of-types/makefile Normal file
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@ -0,0 +1,8 @@
TARGETS=$(shell find -name '*.dot' | sed -E 's~\.dot~\.png~')
all: $(TARGETS)
%.png: %.dot
dot -Tpng $< -o target/$@

6
beamer/lc-beamer/sea-of-types/sea-of-types-0-bytes.dot Normal file
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@ -0,0 +1,6 @@
digraph SeaOfTypes {
Byte4 [label="[Byte; 4]", fontsize=24, shape=plaintext];
}

9
beamer/lc-beamer/sea-of-types/sea-of-types-1-ieee754.dot Normal file
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@ -0,0 +1,9 @@
digraph SeaOfTypes {
Byte4 [label="[Byte; 4]", fontsize=24, shape=plaintext];
IEEE754single [label="IEEE-754.single", fontsize=24, shape=plaintext];
IEEE754single -> Byte4
}

69
beamer/lc-beamer/sea-of-types/sea-of-types-10-u8.dot Normal file
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@ -0,0 +1,69 @@
digraph SeaOfTypes {
Byte1 [label="[Byte; 1]", fontsize=10, shape=plaintext, color=lightgrey];
Byte4 [label="[Byte; 4]", fontsize=10, shape=plaintext, color=lightgrey];
Byte8 [label="[Byte; 8]", fontsize=10, shape=plaintext, color=lightgrey];
IEEE754single [label="IEEE-754.single", fontsize=10, shape=plaintext, color=lightgrey];
IEEE754double [label="IEEE-754.double", fontsize=10, shape=plaintext, color=lightgrey];
Real [label="ℝ", fontsize=20, shape=plaintext];
Degrees [label="Degrees", fontsize=18, shape=plaintext];
Turns [label="Turns", fontsize=18, shape=plaintext];
Radians [label="Radians", fontsize=18, shape=plaintext];
Angle [label="Angle", fontsize=20, shape=plaintext];
RealUnit [label="ℝ_[0,1]", fontsize=24, shape=plaintext];
HSV [label="HSV", fontsize=20, shape=plaintext];
U8 [label="machine.UInt8", fontsize=18, shape=plaintext];
Z256 [label="ℤ_256", fontsize=20, shape=plaintext];
Real360 [label="ℝ_[0,360)", fontsize=18, shape=plaintext];
Real1 [label="ℝ_[0,1)", fontsize=18, shape=plaintext];
Real2pi [label="ℝ_[0,2π)", fontsize=18, shape=plaintext];
QuantizedLinear [label="<QuantizedLinear[0,1] 256>", fontsize=20, shape=plaintext];
QuantizedLinear1 [label="<QuantizedLinear[0,1) 256>", fontsize=20, shape=plaintext];
QuantizedLinear360 [label="<QuantizedLinear[0,360) 256>", fontsize=20, shape=plaintext];
QuantizedLinear2pi [label="<QuantizedLinear[0,2π) 256>", fontsize=20, shape=plaintext];
IEEE754single -> Byte4
IEEE754double -> Byte8
Real -> IEEE754single
Real -> IEEE754double
Real360 -> Real
Real1 -> Real
Real2pi -> Real
Real360 -> QuantizedLinear360
Real1 -> QuantizedLinear1
Real2pi -> QuantizedLinear2pi
Degrees -> Real360
Turns -> Real1
Radians -> Real2pi
RealUnit -> Real
RealUnit -> QuantizedLinear
QuantizedLinear -> Z256
QuantizedLinear1 -> Z256
QuantizedLinear360 -> Z256
QuantizedLinear2pi -> Z256
Z256 -> U8
U8 -> Byte1
Angle -> Degrees
Angle -> Turns
Angle -> Radians
HSV -> Angle [label="hue"]
HSV -> RealUnit [label="saturation"]
HSV -> RealUnit [label="value"]
}

11
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@ -0,0 +1,11 @@
digraph SeaOfTypes {
Byte4 [label="[Byte; 4]", fontsize=24, shape=plaintext];
IEEE754single [label="IEEE-754.single", fontsize=24, shape=plaintext];
Real [label="ℝ", fontsize=28, shape=plaintext];
IEEE754single -> Byte4
Real -> IEEE754single
}

20
beamer/lc-beamer/sea-of-types/sea-of-types-3-real.dot Normal file
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@ -0,0 +1,20 @@
digraph SeaOfTypes {
Byte4 [label="[Byte; 4]", fontsize=24, shape=plaintext];
Byte8 [label="[Byte; 8]", fontsize=24, shape=plaintext];
IEEE754single [label="IEEE-754.single", fontsize=24, shape=plaintext];
IEEE754double [label="IEEE-754.double", fontsize=24, shape=plaintext];
Real [label="ℝ", fontsize=28, shape=plaintext];
IEEE754single -> Byte4
IEEE754double -> Byte8
Real -> IEEE754single
Real -> IEEE754double
}

24
beamer/lc-beamer/sea-of-types/sea-of-types-4-degrees.dot Normal file
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@ -0,0 +1,24 @@
digraph SeaOfTypes {
Byte4 [label="[Byte; 4]", fontsize=12, shape=plaintext, color=lightgrey];
Byte8 [label="[Byte; 8]", fontsize=12, shape=plaintext, color=lightgrey];
IEEE754single [label="IEEE-754.single", fontsize=12, shape=plaintext, color=lightgrey];
IEEE754double [label="IEEE-754.double", fontsize=12, shape=plaintext, color=lightgrey];
Real [label="ℝ", fontsize=28, shape=plaintext];
Degrees [label="Degrees", fontsize=24, shape=plaintext];
IEEE754single -> Byte4
IEEE754double -> Byte8
Real -> IEEE754single
Real -> IEEE754double
Degrees -> Real
}

25
beamer/lc-beamer/sea-of-types/sea-of-types-5-turns.dot Normal file
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@ -0,0 +1,25 @@
digraph SeaOfTypes {
Byte4 [label="[Byte; 4]", fontsize=12, shape=plaintext, color=lightgrey];
Byte8 [label="[Byte; 8]", fontsize=12, shape=plaintext, color=lightgrey];
IEEE754single [label="IEEE-754.single", fontsize=12, shape=plaintext, color=lightgrey];
IEEE754double [label="IEEE-754.double", fontsize=12, shape=plaintext, color=lightgrey];
Real [label="ℝ", fontsize=28, shape=plaintext];
Degrees [label="Degrees", fontsize=24, shape=plaintext];
Turns [label="Turns", fontsize=24, shape=plaintext];
IEEE754single -> Byte4
IEEE754double -> Byte8
Real -> IEEE754single
Real -> IEEE754double
Degrees -> Real
Turns -> Real
}

27
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@ -0,0 +1,27 @@
digraph SeaOfTypes {
Byte4 [label="[Byte; 4]", fontsize=12, shape=plaintext, color=lightgrey];
Byte8 [label="[Byte; 8]", fontsize=12, shape=plaintext, color=lightgrey];
IEEE754single [label="IEEE-754.single", fontsize=12, shape=plaintext, color=lightgrey];
IEEE754double [label="IEEE-754.double", fontsize=12, shape=plaintext, color=lightgrey];
Real [label="ℝ", fontsize=28, shape=plaintext];
Degrees [label="Degrees", fontsize=24, shape=plaintext];
Turns [label="Turns", fontsize=24, shape=plaintext];
Radians [label="Radians", fontsize=24, shape=plaintext];
IEEE754single -> Byte4
IEEE754double -> Byte8
Real -> IEEE754single
Real -> IEEE754double
Degrees -> Real
Turns -> Real
Radians -> Real
}

33
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@ -0,0 +1,33 @@
digraph SeaOfTypes {
Byte4 [label="[Byte; 4]", fontsize=10, shape=plaintext, color=lightgrey];
Byte8 [label="[Byte; 8]", fontsize=10, shape=plaintext, color=lightgrey];
IEEE754single [label="IEEE-754.single", fontsize=10, shape=plaintext, color=lightgrey];
IEEE754double [label="IEEE-754.double", fontsize=10, shape=plaintext, color=lightgrey];
Real [label="ℝ", fontsize=24, shape=plaintext];
Degrees [label="Degrees", fontsize=20, shape=plaintext];
Turns [label="Turns", fontsize=20, shape=plaintext];
Radians [label="Radians", fontsize=20, shape=plaintext];
Angle [label="Angle", fontsize=24, shape=plaintext, color=brown];
IEEE754single -> Byte4
IEEE754double -> Byte8
Real -> IEEE754single
Real -> IEEE754double
Degrees -> Real
Turns -> Real
Radians -> Real
Angle -> Degrees
Angle -> Turns
Angle -> Radians
}

40
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@ -0,0 +1,40 @@
digraph SeaOfTypes {
Byte4 [label="[Byte; 4]", fontsize=10, shape=plaintext, color=lightgrey];
Byte8 [label="[Byte; 8]", fontsize=10, shape=plaintext, color=lightgrey];
IEEE754single [label="IEEE-754.single", fontsize=10, shape=plaintext, color=lightgrey];
IEEE754double [label="IEEE-754.double", fontsize=10, shape=plaintext, color=lightgrey];
Real [label="ℝ", fontsize=20, shape=plaintext];
Degrees [label="Degrees", fontsize=18, shape=plaintext];
Turns [label="Turns", fontsize=18, shape=plaintext];
Radians [label="Radians", fontsize=18, shape=plaintext];
Angle [label="Angle", fontsize=20, shape=plaintext];
RealUnit [label="ℝ_[0,1]", fontsize=24, shape=plaintext];
HSV [label="HSV", fontsize=24, shape=plaintext];
IEEE754single -> Byte4
IEEE754double -> Byte8
Real -> IEEE754single
Real -> IEEE754double
Degrees -> Real
Turns -> Real
Radians -> Real
RealUnit -> Real
Angle -> Degrees
Angle -> Turns
Angle -> Radians
HSV -> Angle [label="hue", textcolor=blue]
HSV -> RealUnit [label="saturation", textcolor=blue]
HSV -> RealUnit [label="value", textcolor=blue]
}

50
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@ -0,0 +1,50 @@
digraph SeaOfTypes {
Byte1 [label="[Byte; 1]", fontsize=10, shape=plaintext, color=lightgrey];
Byte4 [label="[Byte; 4]", fontsize=10, shape=plaintext, color=lightgrey];
Byte8 [label="[Byte; 8]", fontsize=10, shape=plaintext, color=lightgrey];
IEEE754single [label="IEEE-754.single", fontsize=10, shape=plaintext, color=lightgrey];
IEEE754double [label="IEEE-754.double", fontsize=10, shape=plaintext, color=lightgrey];
Real [label="ℝ", fontsize=20, shape=plaintext];
Degrees [label="Degrees", fontsize=18, shape=plaintext];
Turns [label="Turns", fontsize=18, shape=plaintext];
Radians [label="Radians", fontsize=18, shape=plaintext];
Angle [label="Angle", fontsize=20, shape=plaintext];
RealUnit [label="ℝ_[0,1]", fontsize=24, shape=plaintext];
HSV [label="HSV", fontsize=20, shape=plaintext];
U8 [label="machine.UInt8", fontsize=18, shape=plaintext];
Z256 [label="ℤ_256", fontsize=20, shape=plaintext];
QuantizedLinear [label="<QuantizedLinear[0,1] 256>", fontsize=20, shape=plaintext];
IEEE754single -> Byte4
IEEE754double -> Byte8
Real -> IEEE754single
Real -> IEEE754double
Degrees -> Real
Turns -> Real
Radians -> Real
RealUnit -> Real
RealUnit -> QuantizedLinear
QuantizedLinear -> Z256
Z256 -> U8
U8 -> Byte1
Angle -> Degrees
Angle -> Turns
Angle -> Radians
HSV -> Angle [label="hue"]
HSV -> RealUnit [label="saturation"]
HSV -> RealUnit [label="value"]
}