Homotopy Type Theory
Heyting algebra > history (Rev #2)
Contents
Definition
A Heyting algebra is a distributive lattice $(L, \leq, \bot, \vee, \top, \wedge)$ with

a function $\implies: L \times L to L$

a family of dependent terms
$a:L, b:L \vdash (b \to a) \wedge a \leq b$

a family of dependent terms
$a:L, b:L \vdash a \leq b \to (a \wedge b)$
representing the carteisan closed condition for the lattice.
See also
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