EXAMPLES.md

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Tests

Simple expressions

Haskell	LaTeX	pdf
𝑎 + 𝑏 * 𝑐	a+b{\cdot}c
𝐴 * 𝐵 + 𝐶	A{\cdot}B+C
(𝑎 + 𝑏) * 𝑐	\left(a+b\right){\cdot}c
(𝑎 + 𝑏) / (𝑥 - 𝑦)	\frac{a+b}{x-y}
(𝑎 + 𝑏)**(𝑥 - 𝑦)	\left(a+b\right)^{x-y}
(𝑝/𝑞)**γ	\left(\frac{p}{q}\right)^{\gamma{}}
abs(𝑝/𝑞)**ξ	\left|\frac{p}{q}\right|^{\xi{}}
𝑎**𝑏**𝑐	a^{b^{c}}
(𝑎**𝑏)**𝑐	\left(a^{b}\right)^{c}
sin (sin 𝑥)	\sin{\left(\sin{x}\right)}
(𝑖⩵0,3)∑ 𝑖	\sum_{i=0}^{3} i
matrix[[ 0,1] ,[-1,0]]	\begin{pmatrix}0&1\\ -1&0\end{pmatrix}

Number literals

Haskell	LaTeX	pdf
25697325	25697325
4.718	4.718
1e-3	1{\cdot}10^{ -3}
257.35e9	2.5735{\cdot}10^{11}
-5.1e-8	-5.1{\cdot}10^{ -8}
7/13	\frac{7}{13}
-(1/2)	-\frac{1}{2}

Operators

Arithmetic

Haskell	LaTeX	pdf
𝑎 + 𝑏	a+b
𝑎 - 𝑏	a-b
𝑎 * 𝑏	a{\cdot}b
𝑎<⍪>𝑏	\left\langle{a,b}\right\rangle
𝑎 × 𝑏	a\times{}b
𝑎 ± 𝑏	a\pm{}b
𝑎 ∓ 𝑏	a\mp{}b
𝑎 ⊕ 𝑏	a\oplus{}b
𝑎 ⊗ 𝑏	a\otimes{}b

Sub/superscripts

Haskell	LaTeX	pdf
𝑎◞𝑏	a_{b}
𝑎◞◝(𝑏,𝑐)	a_{b}^{c}
ψ◞"Foo"	\psi{}_{\mathrm{Foo}}
ψ◞𝐹‸𝑜‸𝑜	\psi{}_{Foo}
𝑓◝(3☽"")☾𝑥	f^{\left(3\right)}\left(x\right)

Function application and definition

Haskell	LaTeX	pdf
𝑓☾𝑥	f\left(x\right)
𝑓☾(𝑔☾𝑥)	f\left(g\left(x\right)\right)
𝑓☾(𝑥⍪𝑦)	f\left(x,y\right)
𝓕☾φ☾𝑥	\mathcal{F}\left(\varphi{}\right)\left(x\right)
(𝑓∘𝑔)☽𝑥	\left(f\circ{}g\right)x
(𝑓∘𝑔)☽(𝑥*𝑦)	\left(f\circ{}g\right)\left(x{\cdot}y\right)
𝑓∘𝑔☾𝑥	f\circ{}g\left(x\right)
𝑓 ÷ (ℤ-→ℝ)	f:\mathbb{Z}\to{}\mathbb{R}
𝑓☾𝑥 ÷= 𝑥+π	f\left(x\right){:=}x+\pi{}

Logical

Haskell	LaTeX	pdf
𝑝 ∨ 𝑞	p\vee{}q
𝑝 ∧ 𝑞	p\wedge{}q
𝑝==>𝑞	p\Longrightarrow{}q
𝑝<==𝑞	p\Longleftarrow{}q
𝑝<=>𝑞	p\Longleftrightarrow{}q
𝑝==>𝑞==>𝑟	p\Longrightarrow{}q\Longrightarrow{}r
cases[(1, "Today"), (2, "Else")]	\begin{cases}1&\text{Today}\\2&\text{Else}\end{cases}

Relations

Haskell	LaTeX	pdf
𝑎 ⩵ 𝑏	a=b
𝑎 ≥ 𝑐	a\geq{}c
𝑎 ⪪ ρ	a<\rho{}
𝑥 ⩵ 𝑦 ⩵ 𝑧	x=y=z
𝑠 ⊂ 𝑡 ⊆ 𝑢	s\subset{}t\subseteq{}u
ℎ ≈ 𝑔 ∼ 𝑓 ≃ 𝑒 ≅ 𝑑	h\approx{}g\sim{}f\simeq{}e\cong{}d
𝑝 ∈ ℚ ⊂ ℝ	p\in{}\mathbb{Q}\subset{}\mathbb{R}
𝐮 ⟂ (vec%$>𝑣) ∥ (underline%$>𝑤)	\mathbf{u}\perp{}\vec{v}\parallel{}\underline{w}

Calculus

Integration

Haskell	LaTeX	pdf
(-1,1)∫d 𝑥 (𝑥**2)	\int\limits_{ -1}^{1}\mathrm{d}x\ {}x^{2}
ω◞∫d 𝑥 (exp $ -(𝑥**2))	\int_{\omega{}}\!\!\!\mathrm{d}x\ {}\exp{\left( -x^{2}\right)}
(0,1)∫d 𝑥 ((0,1)∫d 𝑦 (𝑥*𝑦))	\int\limits_{0}^{1}\mathrm{d}x\ {}\int\limits_{0}^{1}\mathrm{d}y\ {}\left(x{\cdot}y\right)

Algebraic manipulation

Haskell	LaTeX	pdf
𝑎 + 𝑏 + 𝑐 &~~! [𝑏 ⩵ 𝑦]	a+b+c=a+y+c
𝑎 + 𝑏 + 𝑐 &~~! [𝑏+𝑐 ⩵ 𝑐+𝑏, 𝑎+𝑐 ⩵ ξ]	a+b+c=\xi{}+b
𝑎 - 𝑏 &~~! [𝑏 ⩵ 𝑦] &~~! [𝑎 ⩵ 𝑧]	a-b=a-y=z-y
𝑥 + 𝑦 & continueExpr (⩵) (&~: 𝑦 :=: 𝑥*(1+𝑥)) & continueExpr (⩵) (&~: 𝑥 :=: 2◝𝑝)	x+y=x+x{\cdot}\left(1+x\right)=2^{p}+2^{p}{\cdot}\left(1+2^{p}\right)

Juxtaposition

Haskell	LaTeX	pdf
𝑚 + 𝑝‸𝑞‸𝑟	m+pqr
𝑚 + 𝑝‸(2+𝑞)‸𝑟	m+p\left(2+q\right)r
𝑚 + (𝑝␣𝑞␣𝑟)	m+\left(p\ {}q\ {}r\right)
𝑚 + (𝑝␣2+𝑞␣𝑟)	m+\left(p\ {}2+q\ {}r\right)
𝑚 + (𝑝<>𝑞<>𝑟)	m+pqr
𝑚 + (𝑝<>(2+𝑞)<>𝑟)	m+\left(p2+qr\right)
𝑚 * ((1+2)<>(3+4))	m{\cdot}\left(1+23+4\right)

Set-builders

Haskell	LaTeX	pdf
set(3⍪4⍪5)	\left\{3,4,5\right\}
setCompr (𝑥◝2) (𝑥∈ℕ)	\left\{x^{2}\middle|x\in{}\mathbb{N}\right\}
setCompr (𝑥/𝑦) (𝑥∈ℤ⍪ 𝑦∈ℕ⍪ 𝑦⪫0)	\left\{\frac{x}{y}\middle|x\in{}\mathbb{Z},y\in{}\mathbb{N},y>0\right\}
setCompr (𝑥⍪𝑦) (𝑥∈ℤ⍪ 𝑦∈ℝ)	\left\{\left(x,y\right)\middle|x\in{}\mathbb{Z},y\in{}\mathbb{R}\right\}

Stylised symbols

Haskell	LaTeX	pdf
𝓐<>𝔅<>𝔥<>𝐏<>𝐳	\mathcal{A}\mathfrak{B}\mathfrak{h}\mathbf{P}\mathbf{z}

Misc

Haskell	LaTeX	pdf
3*𝑧 - 1	3{\cdot}z-1
𝑎-𝑏+𝑐	a-b+c
(𝑥/2)|◞◝(𝑥⩵0,1)	\left.\frac{x}{2}\right|_{x=0}^{1}
𝑏 + (𝑥/2) ╰─┬─╯"fraction"	b+\underbrace{\frac{x}{2}}_{\mathrm{fraction}}
3 - 1 &~~! [ ㄒ-ㄗ ⩵ -(ㄗ-ㄒ) ]	3-1= -\left(1-3\right)
𝑎 ∗ 𝑏	a\ast{}b
𝑎 ⋆ 𝑏	a\star{}b