Mini-TT is a variant Martin-Löf type theory with data
types. cubiclaltt extends Mini-TT with:
- o Name abstraction and application
+ o Path types
o Compositions
o Equivalences can be transformed into equalities
o Some higher inductive types
{-
- Identity types, names and formulas
+ Path types, names and formulas
--------------------------------------------------------------------------
-An element in ID A B is a line in the universe connecting A and B:
+An element in PATH A B is a line in the universe connecting A and B:
|- A Type |- B Type
------------------------------
- |- ID A B Type
+ |- PATH A B Type
PathP is heterogeneous equality:
- |- P : ID A B |- a : A |- b : B
+ |- P : PATH A B |- a : A |- b : B
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|- PathP P a b Type