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update demo
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mortberg committed Oct 22, 2016
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Expand Up @@ -18,7 +18,7 @@ Makoto Takeya.
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
Expand All @@ -45,21 +45,21 @@ not : bool -> bool = split


{-
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
-----------------------------------------------
|- PathP P a b Type

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