-
Notifications
You must be signed in to change notification settings - Fork 0
/
lojban-fanva-ctaipe.lagda
237 lines (178 loc) · 8.48 KB
/
lojban-fanva-ctaipe.lagda
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
\documentclass{article}
\usepackage{ar}
\usepackage[bw]{agda}
\usepackage{ifsym}
\usepackage{amsthm}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{parskip}
\usepackage{mathabx}
\usepackage{unicode-math}
\usepackage{newunicodechar}
\newtheorem{thm}{Theorem}
\renewcommand\abstractname{le me'oi .abstract.}
\newunicodechar{∷}{\ensuremath{\mathnormal\Colon}}
\newunicodechar{ℕ}{\ensuremath{\mathbb{N}}}
\newunicodechar{∘}{\ensuremath{\mathnormal{\circ}}}
\newunicodechar{∀}{\ensuremath{\mathnormal\forall}}
\newunicodechar{⊤}{\ensuremath{\mathnormal{\top}}}
\newunicodechar{λ}{\ensuremath{\mathnormal{\lambda}}}
\newunicodechar{→}{\ensuremath{\mathnormal{\rightarrow}}}
\newunicodechar{⦃}{\ensuremath{\mathnormal{\lbrace\!\lbrace}}}
\newunicodechar{⦄}{\ensuremath{\mathnormal{\rbrace\!\rbrace}}}
\newunicodechar{ₗ}{\ensuremath{\mathnormal{_l}}}
\newunicodechar{ₛ}{\ensuremath{\mathnormal{_s}}}
\newunicodechar{ᵥ}{\ensuremath{\mathnormal{_v}}}
\newunicodechar{∸}{\ensuremath{\mathnormal\dotdiv}}
\newunicodechar{∧}{\ensuremath{\mathnormal{\land}}}
\newunicodechar{≡}{\ensuremath{\mathnormal\equiv}}
\newunicodechar{ᵇ}{\ensuremath{\mathnormal{^\mathrm{b}}}}
\newunicodechar{≟}{\ensuremath{\mathnormal{\stackrel{?}{=}}}}
\newunicodechar{≤}{\ensuremath{\mathnormal{\leq}}}
\newcommand\Sym\AgdaSymbol
\newcommand\D\AgdaDatatype
\newcommand\F\AgdaFunction
\newcommand\B\AgdaBound
\title{le ctaipe be le su'u la .varik.\ cu te selneimau fi lo nu la .varik.\ cu fanva fi le glibau fo la .lojban.\ / The Proof of that VARIK Prefers that VARIK Translates to English and from Lojban}
\author{la .varik.\ .VALefor.}
\begin{document}
\maketitle
\begin{abstract}
\noindent
\paragraph{la .lojban.}
ni'o vasru le velcki be le ctaipe be le su'u la .varik.\ cu te selneimau fi lo nu la .varik.\ cu fanva fi le glibau fo la .lojban.\ kei lo nu la .varik.\ cu cusku bau le glibau jenai cu fanva fi le glibau fo la .lojban.
\paragraph{English}
The thing contains the definition of the proof of that VARIK prefers (over that VARIK uses English and does-not translate to English and from Lojban) that VARIK translates to English and from Lojban.
\end{abstract}
\section{le torveki / The Summary}
\subsection{le me'oi .disclaimer.}
\paragraph{la .lojban.}
ni'o pilno la'oi .\texttt{subsection}.\ jenai la'oi .\texttt{paragraph}.\ ki'u le su'u le tcita be lo se ctaipe cu smimlu lo tcita be lo jufmei
\paragraph{English}
That (labels of proofs resemble labels of paragraphs) justifies using \texttt{subsection} and not \texttt{paragraph}.
\subsection{la .lojban.}
ni'o la .varik.\ cu te selneimau fi ko'a goi lo nu vo'a fanva fi le glibau fo la .lojban.\ kei fe ko'e goi lo nu vo'a cusku bau le glibau jenai cu fanva fi le glibau fo la .lojban.\ kei ni'i le su'u\ldots
\begin{itemize}
\item ga je ko'a zmadu ko'e le ka ce'u frili vo'a kei je le ka vo'a nelci lo jalge be ce'u gi
\item ro da zo'u ro de zo'u ga janai da de selneimau vo'a gi da zmadu de le ka ce'u frili vo'a kei je le ka vo'a nelci lo jalge be ce'u
\end{itemize}
\subsection{English}
\begin{thm}
VARIK prefers (over that VARIK uses English and does-not translate to English and from Lojban) that VARIK translates to English and from Lojban.
\end{thm}
\begin{proof}
${}$
$F$ is some event of that VARIK translates to English and from Lojban.
$N$ is some event of that (VARIK uses English and does-not translate to English and from Lojban).
For all $A$, for all $B$, if VARIK finds that the ease of $A$ exceeds the ease of $B$, then if the extent (of that VARIK likes the result of $A$) exceeds the extent (of that VARIK likes the result of $B$), then VARIK prefers (over $B$) $A$.
VARIK finds that the ease of $F$ exceeds the ease of $N$.
The extent (of that VARIK likes the result of $F$) exceeds the extent of that VARIK likes the result of $N$.
Therefore, VARIK prefers (over $N$) $F$.
\end{proof}
\section{le co'e ja jicmu / The Basic}
\subsection{la'oi .\AgdaPostulate{Prenu}.}
\paragraph{la .lojban.}
ni'o ro da zo'u da ctaipe la'oi .\AgdaPostulate{Prenu}.\ jo cu prenu
\paragraph{English}
For all $A$, \AgdaPostulate{Prenu} is the type of $A$ iff $A$ is a prenu.
\begin{code}
postulate Prenu : Set
\end{code}
\subsection{la'oi .\AgdaPostulate{Fasnu}.}
\paragraph{la .lojban.}
ni'o ro da zo'u da ctaipe la'oi .\AgdaPostulate{Fasnu}.\ jo cu fasnu
\paragraph{English}
For all $A$, \AgdaPostulate{Fasnu} is the type of $A$ iff $A$ is an event.
\begin{code}
postulate Fasnu : Set
\end{code}
\subsection{la'oi .\AgdaPostulate{Selkai}.}
\paragraph{la .lojban.}
ni'o ro da zo'u da ctaipe la'oi .\AgdaPostulate{Selkai}.\ jo cu se ckaji
\paragraph{English}
For all $A$, \AgdaPostulate{Selkai}\ is the type of $A$ iff $A$ is a property/quality/whatever.
\begin{code}
postulate Selkai : Set
\end{code}
\subsection{la'o zoi.\ \AgdaPostulate{zmadu-fa}\ .zoi.}
\paragraph{la .lojban.}
ni'o ga jo ctaipe la'o zoi.\ \AgdaPostulate{zmadu-fa} \B a \B b \B c\ .zoi.\ gi la'o zoi.\ \B a\ .zoi.\ zmadu la'o zoi.\ \B b\ .zoi.\ la'o zoi.\ \B c\ .zoi.
\paragraph{English}
\newcommand\epdisp{exhibits/possesses/displays}
A proof of \AgdaPostulate{zmadu-fa} \B a \B b \B c\ exists iff the extent (of that \B a\ \epdisp\ \B c) exceeds the extent of that \B b \epdisp\ \B c.
\begin{code}
postulate zmadu-fa : ∀ {a b} → {A : Set a} → {B : Set b}
→ A → B → Selkai → Set
\end{code}
\section{le selkai / The Properties, Qualities, or Whatever}
\subsection{la'o zoi.\ \AgdaPostulate{la-kafrilis}\ .zoi.}
\newcommand\propglis{is a property/quality/whatever which is expressed/displayed by}
\paragraph{la .lojban.}
ni'o la'o zoi.\ \AgdaPostulate{la-kafrilis}\ .zoi.\ ka ce'u frili la .varik.
\paragraph{English}
For all $A$, \AgdaPostulate{la-kafrilis} \propglis\ $A$ iff VARIK finds that $A$ is easy.
\begin{code}
postulate la-kafrilis : Selkai
\end{code}
\subsection{la'o zoi.\ \AgdaPostulate{la-kajalneis}\ .zoi.}
\paragraph{la .lojban.}
ni'o la'o zoi.\ \AgdaPostulate{la-kajalneis}\ .zoi.\ ka la .varik.\ cu nelci lo jalge be ce'u
\paragraph{English}
For all $A$, \AgdaPostulate{la-kajalneis} \propglis\ $A$ iff VARIK likes the result of $A$.
\begin{code}
postulate la-kajalneis : Selkai
\end{code}
\subsection{la'o zoi.\ \AgdaPostulate{la-kaselneis}\ .zoi.}
\paragraph{la .lojban.}
ni'o la'o zoi.\ \AgdaPostulate{la-kaselneis}\ .zoi.\ ka ce'u selnei la .varik.
\paragraph{English}
For all $A$, \AgdaPostulate{la-kaselneis} \propglis\ $A$ iff VARIK likes $A$.
\begin{code}
postulate la-kaselneis : Selkai
\end{code}
\section{le fasnu / The Events}
\newcommand\cmene{\AgdaPostulate{la-nufanvas}}
\subsection{la'o zoi.\ \cmene\ .zoi.}
\paragraph{la .lojban.}
ni'o la'o zoi.\ \cmene\ .zoi.\ nu la .varik.\ cu fanva fi le glibau fo la .lojban.
\paragraph{English}
\cmene\ is an event of that VARIK translates to English and from Lojban.
\begin{code}
postulate la-nufanvas : Fasnu
\end{code}
\renewcommand\cmene{\AgdaPostulate{la-nunafanvas}}
\subsection{la'o zoi.\ \cmene\ .zoi.}
\paragraph{la .lojban.}
ni'o la'o zoi.\ \cmene\ .zoi.\ nu la .varik.\ cu baupli le glibau jenai cu fanva fi le glibau fo la .lojban.
\paragraph{English}
\cmene\ is an event of that VARIK uses English and does-not translate to English and from Lojban.
\begin{code}
postulate la-nunafanvas : Fasnu
\end{code}
\section{la .\AgdaPostulate{frijalnei-fa}.}
\paragraph{la .lojban.}
ni'o ro da zo'u ro de zo'u da zmadu de le ka ce'u selnei la .varik.\ kei janai ke le ka ce'u frili la .varik.\ kei je le ka la .varik.\ cu nelci lo jalge be ce'u
\paragraph{English}
For all $A$, for all $B$, if VARIK finds that the ease of $A$ exceeds the ease of $B$, then if the extent (of that VARIK likes the result of $A$) exceeds the extent of that VARIK likes the result of $B$, then VARIK prefers (over $B$) $A$.
\begin{code}
postulate
frijalnei-fa : ∀ {a b} → {A : Set a} → {B : Set b}
→ {x : A} → {z : B}
→ zmadu-fa x z la-kafrilis
→ zmadu-fa x z la-kajalneis
→ zmadu-fa x z la-kaselneis
\end{code}
\section{le ctaipe be le su'u selneimau / The Proof of the Preference}
\paragraph{la .lojban.}
ni'o la .varik.\ na jinvi le du'u sarcu fa lo nu ciksi bau la .lojban.
\paragraph{English}
VARIK does-not find that necessary is that VARIK provides English definitions.
\begin{code}
la-fanvynelcis : zmadu-fa la-nufanvas la-nunafanvas la-kaselneis
la-fanvynelcis = frijalnei-fa la-fanvyfrilis la-fanvyjalges
where
postulate
la-fanvyfrilis : zmadu-fa la-nufanvas la-nunafanvas la-kafrilis
la-fanvyjalges : zmadu-fa la-nufanvas la-nunafanvas la-kajalneis
\end{code}
\end{document}