tame/design/tpl/glossary.tex

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% The TAME Programming Language glossary
%
% Copyright (C) 2021 Ryan Specialty Group, LLC.
%
% Licensed under the Creative Commons Attribution-ShareAlike 4.0
% International License.
%%
\makeglossaries
\newacronym{tamer}{\textsc{Tamer}}{\tame{} in Rust}
\newglossaryentry{classification}
{
name={classification},
description={TODO}
}
\newglossaryentry{free variable}
{
name={free variable},
description={a variable that is not a \gls{bound variable}}
}
\newglossaryentry{bound variable}
{
name={bound variable},
description={}
}
\newglossaryentry{predicate}
{
name={predicate},
description={}
}
\newglossaryentry{boolean}
{
name={boolean},
description={a value of \gls{true} or \gls{false}},
symbol={\Bool},
}
\newglossaryentry{true}
{
name={true},
description={boolean value representing ``true''},
symbol={\true},
}
\newglossaryentry{false}
{
name={false},
description={boolean value representing ``false''},
symbol={\false},
}
\newglossaryentry{conjunction}
{
name={conjunction},
description={logical conjunction (``and'')},
symbol={\ensuremath{\logand}},
}
\newglossaryentry{disjunction}
{
name={disjunction},
description={logical disjunction (``or'')},
symbol={\ensuremath{\logor}},
}
\newglossaryentry{cardinality}
{
name={cardinality},
description={number of elements in some set~$S$},
symbol={\ensuremath{|S|}}
}
\newglossaryentry{family}
{
name={family},
description={a set sharing the same \gls{index set}},
symbol={\ensuremath{\{A_j\}_{j\in J}}}
}
\newglossaryentry{index set}
{
name={index set},
description={a set whose members index members of another set; see also
\gls{family}},
}
\newglossaryentry{castable}
{
name={castable},
description={type $A$ is castable to type $B$ if there exists some
\gls{surjective} function $A\rightarrow B$}
}
\newglossaryentry{surjective}
{
name={surjective},
description={$\forall y\in Y : \exists x\in X : f(x) = y$},
}
\newglossaryentry{equivalent}
{
name={equivalent},
description={an equivalence relation is a reflexive, symmetric, and
transitive binary operation},
}
\newglossaryentry{logical equivalence}
{
name={logical equivalence},
description={$p$ and $q$ are logically equivalent ($p\equiv q$) \gls{iff}
both $q$ and~$p$ are~\true or both are~\false},
symbol={\ensuremath{\equiv}},
}
\newglossaryentry{logical implication}
{
name={logical implication},
description={},
symbol={\ensuremath{\implies}},
}
\newglossaryentry{iff}
{
name={iff},
description={if and only if},
symbol={\ensuremath{\iff}},
}
\newglossaryentry{forall}
{
name={universal quantification},
description={expresses a predicate that must be satisfied for every
element in a \gls{domain}},
symbol={\ensuremath{\forall}},
}
\newglossaryentry{exists}
{
name={existential quantification},
description={expresses a predicate that must be satisfied for some
element in a \gls{domain}},
symbol={\ensuremath{\exists}},
}
\newglossaryentry{domain}
{
name={domain of discourse},
description={set of elements over which variables of interest may range},
symbol={\ensuremath{\mathbb{D}}},
}
\newglossaryentry{integer}
{
name={integer},
description={set of all integers},
symbol={\ensuremath{\mathbb{Z}}},
}
\newglossaryentry{empty set}
{
name={empty set},
description={set of zero elements},
symbol={\ensuremath{\emptyset}}
}