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Type substitution.

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Daniel Hillerström
2020-01-23 17:27:59 +00:00
parent 874b9182ad
commit b2a2ca4bc4
1 changed files with 22 additions and 3 deletions
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thesis.tex
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@@ -745,14 +745,33 @@ defined as follows.
\[ \[
\begin{eqs} \begin{eqs}
-[-/-] &:& \TypeCat \times \TypeCat \times \TyVarCat \to \TypeCat\\ -[-/-] &:& \TypeCat \times \TypeCat \times \TyVarCat \to \TypeCat\\
(A \to C)[B/\alpha] &\defas& A[B/\alpha] \to C[B/\alpha]\\ (A \eff E)[B/\beta] &\defas& A[B/\beta] \eff E[B/\beta]\\
(A \to C)[B/\beta] &\defas& A[B/\beta] \to C[B/\beta]\\
(\forall \alpha^K.C)[B/\beta] &\defas& \begin{cases}
\forall \alpha^K.C & \text{if } \alpha = \beta\\
\forall \alpha^K.C[B/\beta] & \text{otherwise}
\end{cases}\\
\alpha[B/\beta] &\defas& \begin{cases} \alpha[B/\beta] &\defas& \begin{cases}
B & \text{if } \alpha = \beta\\ B & \text{if } \alpha = \beta\\
\alpha & \text{otherwise} \alpha & \text{otherwise}
\end{cases} \end{cases}\\
\Record{R}[B/\beta] &\defas& \Record{R[B/\beta]}\\
{[R]}[B/\beta] &\defas& [R[B/\beta]]\\
\{R\}[B/\beta] &\defas& \{R[B/\beta]\}\\
\cdot[B/\beta] &\defas& \cdot\\
\rho[B/\beta] &\defas& \begin{cases}
B & \text{if } \rho = \beta\\
\rho & \text{otherwise}
\end{cases}\\
(\ell : P;R)[B/\beta] &\defas& (\ell : P[B/\beta]; R[B/\beta])\\
\theta[B/\beta] &\defas& \begin{cases}
B & \text{if } \rho = \beta\\
\theta & \text{otherwise}
\end{cases}\\
\Abs[B/\beta] &\defas& \Abs\\
\Pre{A}[B/beta] &\defas& \Pre{A[B/\beta]}
\end{eqs} \end{eqs}
\] \]
\dhil{Complete the implementation\dots}
% %
The \tylab{Split} rule handles typing of record destructing. When The \tylab{Split} rule handles typing of record destructing. When
splitting a record term $V$ on some label $\ell$ binding it to $x$ and splitting a record term $V$ on some label $\ell$ binding it to $x$ and