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dependent_type_theory [2014/11/18 22:00] nikolaj |
dependent_type_theory [2015/01/08 01:14] ben don't insult the parser |
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| - | ===== Dependent type theory ===== | + | ===== Dependent type theory ===== |
| ==== Framework ==== | ==== Framework ==== | ||
| We want dependent types together with type constructors | We want dependent types together with type constructors | ||
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| * $\to$ can be taken as $\Pi$ when the quantified expression is constant, $A\to B:=\Pi_{x:A}B$ | * $\to$ can be taken as $\Pi$ when the quantified expression is constant, $A\to B:=\Pi_{x:A}B$ | ||
| - | * $\times$ can be taken as $\Sigma$ when the quantified expression is constant $A\to B:=\Sigma_{x:A}B$ | + | * $\times$ can be taken as $\Sigma$ when the quantified expression is constant $A\times B:=\Sigma_{x:A}B$ |
| * $+$ can be taken as $\Sigma$ over ${\bf 2}$, here we need an if-construction | * $+$ can be taken as $\Sigma$ over ${\bf 2}$, here we need an if-construction | ||
