From: Anders Mörtberg <andersmortberg@gmail.com>
Date: Thu, 7 Jul 2016 10:58:21 +0000 (+0200)
Subject: add a line without any specified points
X-Git-Url: https://git.ak3n.com/?a=commitdiff_plain;h=f04d61385b466d48a979b53eb9f63b3c666f217c;p=cubicaltt.git

add a line without any specified points
---

diff --git a/examples/implicit_point.ctt b/examples/implicit_point.ctt
new file mode 100644
index 0000000..32a78c8
--- /dev/null
+++ b/examples/implicit_point.ctt
@@ -0,0 +1,35 @@
+module implicit_point where
+
+import equiv
+
+data NoPoints =
+  p <i> []
+
+propNoPoints : prop NoPoints = split
+  p @ i -> let rem : (b : NoPoints) -> Id NoPoints (p{NoPoints} @ i) b = split
+    p @ j -> <k> p{NoPoints} @ (i /\ -k) \/ (j /\ k)
+           in rem
+  
+point0 : NoPoints = p{NoPoints} @ 0
+point1 : NoPoints = p{NoPoints} @ 1
+
+p' : Id NoPoints point0 point1 = <i> p{NoPoints} @ i
+
+f1 : NoPoints -> Unit = split
+  p @ i -> tt
+
+f2 : Unit -> NoPoints = split
+  tt -> point0
+
+test : Id U NoPoints Unit =
+  isoId NoPoints Unit f1 f2 rem1 rem2
+    where
+    rem1 : (y : Unit) -> Id Unit (f1 (f2 y)) y = split
+      tt -> <i> tt
+    rem2 : (x : NoPoints) -> Id NoPoints (f2 (f1 x)) x = split
+      p @ i -> <j> p{NoPoints} @ j /\ i
+
+fext (A B : U) (f g : A -> B) (h : (x : A) -> Id B (f x) (g x)) :
+     Id (A -> B) f g = <j> (\(x : A) -> htpy x (p{NoPoints} @ j))
+  where htpy (x : A) : NoPoints -> B = split
+          p @ i -> h x @ i