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Function type
Type
| context | $X, Y$ … type |
| context | $\Gamma$ … context |
| rule | ${\large\frac{\Gamma,\,x\ :\ X\ \vdash\ y\ :\ Y}{\Gamma\ \vdash\ \lambda x.\,y\ :\ X\to Y}}$ (lambda abstraction) |
| rule | ${\large\frac{\Gamma\ \vdash\ f\ :\ X\to Y\hspace{1cm}\Gamma\ \vdash\ x\ :\ X}{\Gamma\ \vdash\ f\,x\ :\ Y}}$ (function application) |
Discussion
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
$\Gamma,\,x\ :\ X\ \vdash\ y\ :\ Y$
as
$(\Gamma,\,(x\ :\ X))\ \vdash\ (y\ :\ Y)$
Parents
Element of
