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Expressions (without order of operations)

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Quinn Dougherty 2022-03-28 19:51:14 -04:00
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spec/src/main.tex
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\usepackage[backend=biber, hyperref=true, citestyle=authoryear]{biblatex}
\addbibresource{biblio.bib}
\title{Squiggle-alpha specification v0.0.1 (INTERNAL)}
\title{Squiggle $\alpha$-v0.0.1 Specification (INTERNAL)}
\author{Quinn Dougherty}
\date{April 2022}

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spec/src/syntax.tex
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\begin{document}
\section{Syntax}\label{section:syntax}
At a high level, we will first be slightly dishonest because the different types of distributions make the story more intricate. Details about assignment and arithmetic on floats will follow eventually, but I want to sketch out a theory of combining distributions, first.
Details about assignment and arithmetic on floats will follow eventually, but I want to sketch out a theory of combining distributions, first.
Abstractly, you can think of Squiggle as containing two types
\begin{grammar}
<type> ::= <GenericDist> \alt \texttt{float}
\end{grammar}\label{gram:type}
\subsection{THE FOLLOWING IS HERE FOR TEMPLATE SO I DON'T FORGET HOW TO BNF IN LATEX. }
In regex notation, we provide the following means of describing literals as well as the specification of the constants T and F.
\begin{center}
\begin{tabular}{c c c}
\texttt{var} & ::= & [a-z][a-zA-Z0-9]* \\
\texttt{int} & ::= & "-"? [0-9]+ \\
\texttt{byte} & ::= & "0x" [0-9a-fA-F] \\
\texttt{bytestring} & ::= & "0x" [0-9a-fA-F]+ \\
\texttt{text} & ::= & <too tough to get latex to compile it lol> \\
\texttt{bool} & ::= & [TF] \\
\texttt{unit} & ::= & [()]
\end{tabular}
\end{center}
\label{tab:atomsregex}
Where \texttt{float} is ordinary IEEE754 floating point numbers, and $\langle \textit{GenericDist} \rangle$ is as follows
\begin{grammar}
<builtin> ::=
"AddInteger" \alt "SubtractInteger" \alt "MultiplyInteger"
\alt "DivideInteger" \alt "QuotientInteger" \alt "RemainderInteger"
\alt "ModInteger" \alt "EqualsInteger" \alt "LessThanInteger"
\alt "LessThanEqualsInteger" \alt "AppendByteString"
\alt "ConsByteString" \alt "SliceByteString" \alt "LengthByteString"
\alt "IndexByteString" \alt "EqualsByteString" \alt "LessThanByteString"
\alt "LessThanEqualsByteString" \alt "Sha2_256" \alt "Sha3_256" \alt "Blake2b_256"
\alt "VerifySignature" \alt "AppendString" \alt "EqualsString"
\alt "EncodeUtf8" \alt "DecodeUtf8" \alt "IfThenElse" \alt "ChooseUnit"
\alt "MkCons" \alt "HeadList" \alt "TailList" \alt "NullList"
\alt "ChooseData" \alt "ConstrData" \alt "MapData" \alt "ListData"
\alt "IData" \alt "BData" \alt "UnConstrData" \alt "UnMapData"
\alt "EqualsData" \alt "MkPairData" \alt "MkNilData" \alt "MkNilPairData"
<GenericDist> ::= <PointSetDist> \alt \texttt{SampleSet} \alt <Symbolic>
<PointSetDist> ::= <Mixed> \alt <Continuous> \alt <Discrete>
<Symbolic> ::= \texttt{Normal} \alt \texttt{LogNormal} \alt \texttt{Triangular} \alt \texttt{Beta} \alt \texttt{Uniform} \alt \texttt{Float} \alt \texttt{Exponential} \alt \texttt{Cauchy}
\end{grammar}
From a grammatical perspective \texttt{SampleSet} and all of the alternatives of $\langle \textit{Symbolic} \rangle$ are \textit{black boxes}. They needn't be discussed from this point of view.
Finally, most of the magic happens in $\langle \textit{Expression} \rangle$
\begin{grammar}
<Expression> ::= <GenericDist> \alt \texttt{float} \alt <Expression> + <Expression> \alt <Expression> * <Expression> \alt <Expression> .+ <Expression> \alt <Expression> .* <Expression>
\end{grammar}
TODO: split this up into multiple declarations such that order of operations is captured/described.
\end{document}