% 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}}
}