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21 lines
2 KiB
TeX
21 lines
2 KiB
TeX
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\section{Names, Values and States}
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\begin{table}[t]
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\begin{tabular}{cccl}
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denotation & instances & definition & comments \\
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\hline
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$\mathscr X$ & $x,\,y,\,z,\,\dots$ & & variables \\
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$\mathscr T$ & $\llang{C},\,\llang{D},\,\dots$ & & tags (constructors) \\
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$\Sigma$ & $\sigma$ & $\mathscr X\to\mathscr V$ & bindings (a partial map from variables to values) \\
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$\Sigma_{\mathscr X}$ & $\inbr{\sigma,\,S}$ & $2^{\mathscr X}\times\Sigma$ & local scope (a set of variable and bindings) \\
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$St$ & $\inbr{\sigma_g,\,ss}$ & $\Sigma\times\Sigma^*_{\mathscr X}$ & state (global bindings and a stack of local scopes) \\
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$\mathscr L$ & $l$ & & locations \\
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$M$ & $\mu$ & $\mathscr L\to\mathscr C$ & abstract memory (a partial map from locations to composite values) \\
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$\mathscr V$ & $v$ & $\mathbb Z\uplus \mathscr L$ & values (integer values or locations) \\
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$\mathscr C$ & & $Arr\uplus Sexp \uplus Clo$ & composite values (arrays, S-expressions or closures) \\
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$Arr$ & & $\mathbb N\times (\mathbb N\to\mathscr V)$ & arrays (length and element function) \\
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$Sexp$ & & $\mathscr T \times Arr$ & S-expressions (tag and array of subvalues) \\
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$Clo$ & & $\mathscr X \times \Sigma^*_{\mathscr X}$ & closures (function name and a stack of local scopes)
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\end{tabular}
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\end{table}
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