\[\begin{split}\newcommand{\as}{\kw{as}}
\newcommand{\Assum}[3]{\kw{Assum}(#1)(#2:#3)}
\newcommand{\case}{\kw{case}}
\newcommand{\cons}{\textsf{cons}}
\newcommand{\consf}{\textsf{consf}}
\newcommand{\Def}[4]{\kw{Def}(#1)(#2:=#3:#4)}
\newcommand{\emptyf}{\textsf{emptyf}}
\newcommand{\End}{\kw{End}}
\newcommand{\kwend}{\kw{end}}
\newcommand{\even}{\textsf{even}}
\newcommand{\evenO}{\textsf{even}_\textsf{O}}
\newcommand{\evenS}{\textsf{even}_\textsf{S}}
\newcommand{\Fix}{\kw{Fix}}
\newcommand{\fix}{\kw{fix}}
\newcommand{\for}{\textsf{for}}
\newcommand{\forest}{\textsf{forest}}
\newcommand{\Functor}{\kw{Functor}}
\newcommand{\In}{\kw{in}}
\newcommand{\Ind}[4]{\kw{Ind}[#2](#3:=#4)}
\newcommand{\ind}[3]{\kw{Ind}~[#1]\left(#2\mathrm{~:=~}#3\right)}
\newcommand{\Indp}[5]{\kw{Ind}_{#5}(#1)[#2](#3:=#4)}
\newcommand{\Indpstr}[6]{\kw{Ind}_{#5}(#1)[#2](#3:=#4)/{#6}}
\newcommand{\injective}{\kw{injective}}
\newcommand{\kw}[1]{\textsf{#1}}
\newcommand{\length}{\textsf{length}}
\newcommand{\letin}[3]{\kw{let}~#1:=#2~\kw{in}~#3}
\newcommand{\List}{\textsf{list}}
\newcommand{\lra}{\longrightarrow}
\newcommand{\Match}{\kw{match}}
\newcommand{\Mod}[3]{{\kw{Mod}}({#1}:{#2}\,\zeroone{:={#3}})}
\newcommand{\ModA}[2]{{\kw{ModA}}({#1}=={#2})}
\newcommand{\ModS}[2]{{\kw{Mod}}({#1}:{#2})}
\newcommand{\ModType}[2]{{\kw{ModType}}({#1}:={#2})}
\newcommand{\mto}{.\;}
\newcommand{\nat}{\textsf{nat}}
\newcommand{\Nil}{\textsf{nil}}
\newcommand{\nilhl}{\textsf{nil\_hl}}
\newcommand{\nO}{\textsf{O}}
\newcommand{\node}{\textsf{node}}
\newcommand{\nS}{\textsf{S}}
\newcommand{\odd}{\textsf{odd}}
\newcommand{\oddS}{\textsf{odd}_\textsf{S}}
\newcommand{\ovl}[1]{\overline{#1}}
\newcommand{\Pair}{\textsf{pair}}
\newcommand{\plus}{\mathsf{plus}}
\newcommand{\SProp}{\textsf{SProp}}
\newcommand{\Prop}{\textsf{Prop}}
\newcommand{\return}{\kw{return}}
\newcommand{\Set}{\textsf{Set}}
\newcommand{\Sort}{\mathcal{S}}
\newcommand{\Str}{\textsf{Stream}}
\newcommand{\Struct}{\kw{Struct}}
\newcommand{\subst}[3]{#1\{#2/#3\}}
\newcommand{\tl}{\textsf{tl}}
\newcommand{\tree}{\textsf{tree}}
\newcommand{\trii}{\triangleright_\iota}
\newcommand{\Type}{\textsf{Type}}
\newcommand{\WEV}[3]{\mbox{$#1[] \vdash #2 \lra #3$}}
\newcommand{\WEVT}[3]{\mbox{$#1[] \vdash #2 \lra$}\\ \mbox{$ #3$}}
\newcommand{\WF}[2]{{\mathcal{W\!F}}(#1)[#2]}
\newcommand{\WFE}[1]{\WF{E}{#1}}
\newcommand{\WFT}[2]{#1[] \vdash {\mathcal{W\!F}}(#2)}
\newcommand{\WFTWOLINES}[2]{{\mathcal{W\!F}}\begin{array}{l}(#1)\\\mbox{}[{#2}]\end{array}}
\newcommand{\with}{\kw{with}}
\newcommand{\WS}[3]{#1[] \vdash #2 <: #3}
\newcommand{\WSE}[2]{\WS{E}{#1}{#2}}
\newcommand{\WT}[4]{#1[#2] \vdash #3 : #4}
\newcommand{\WTE}[3]{\WT{E}{#1}{#2}{#3}}
\newcommand{\WTEG}[2]{\WTE{\Gamma}{#1}{#2}}
\newcommand{\WTM}[3]{\WT{#1}{}{#2}{#3}}
\newcommand{\zeroone}[1]{[{#1}]}
\end{split}\]
Libraries and plugins¶
Coq is distributed with a standard library and a set of internal plugins (most of which provide tactics that have already been presented in Writing proofs). This chapter presents this standard library and some of these internal plugins which provide features that are not tactics.
In addition, Coq has a rich ecosystem of external libraries and plugins. These libraries and plugins can be browsed online through the Coq Package Index and installed with the opam package manager.