Differences
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function_type [2014/09/17 23:10] nikolaj |
function_type [2014/09/17 23:12] nikolaj |
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| Note that from the wikis perspective, the described type theory is an object language and in it, the context $\Gamma$ is a list of judgements, alla '$a:A$'. That's not to be confused with the context of the meta language (blue boxes) where we also use the notations '$a$...$A$' or '$a\in A$'. | Note that from the wikis perspective, the described type theory is an object language and in it, the context $\Gamma$ is a list of judgements, alla '$a:A$'. That's not to be confused with the context of the meta language (blue boxes) where we also use the notations '$a$...$A$' or '$a\in A$'. | ||
| - | Parse | + | Parse ${\large\frac{\Gamma,\,x\ :\ X\ \vdash\ y\ :\ Y}{\Gamma\ \vdash\ \lambda x.\,y\ :\ X\to Y}}$ as ${\large\frac{(\Gamma,\,(x\ :\ X))\ \vdash\ (y\ :\ Y)}{\Gamma\ \vdash\ ((\lambda x.\,y)\ :\ (X\to Y))}}$. |
| - | + | ||
| - | $\Gamma,\,x\ :\ X\ \vdash\ y\ :\ Y$ | + | |
| - | + | ||
| - | as | + | |
| - | + | ||
| - | $(\Gamma,\,(x\ :\ X))\ \vdash\ (y\ :\ Y)$ | + | |
| ==== Parents ==== | ==== Parents ==== | ||
| === Element of === | === Element of === | ||
| [[Type]] | [[Type]] | ||
