Initial

BidirTT/Examples.lean

@@ -0,0 +1,72 @@
+import BidirTT.Syntax
+
+namespace BidirTT.Examples
+
+open BidirTT
+
+def idTy : Raw :=
+  .pi "A" (.univ 0) (.pi "_" (.var "A") (.var "A"))
+
+def idTm : Raw :=
+  .lam "A" (.lam "x" (.var "x"))
+
+def idAnn : Raw := .ann idTm idTy
+
+def constTy : Raw :=
+  .pi "A" (.univ 0) (.pi "B" (.univ 0)
+    (.pi "_" (.var "A") (.pi "_" (.var "B") (.var "A"))))
+
+def constTm : Raw :=
+  .lam "A" (.lam "B" (.lam "x" (.lam "_" (.var "x"))))
+
+def constAnn : Raw := .ann constTm constTy
+
+def swapTy : Raw :=
+  .pi "A" (.univ 0) (.pi "B" (.univ 0)
+    (.pi "_" (.sig "_" (.var "A") (.var "B"))
+             (.sig "_" (.var "B") (.var "A"))))
+
+def swapTm : Raw :=
+  .lam "A" (.lam "B" (.lam "p"
+    (.pair (.snd (.var "p")) (.fst (.var "p")))))
+
+def swapAnn : Raw := .ann swapTm swapTy
+
+def depPairTy : Raw :=
+  .sig "A" (.univ 2) (.var "A")
+
+def depPairTm : Raw :=
+  .pair
+    (.univ 1)
+    (.pi "_" (.univ 0) (.univ 0))
+
+def depPairAnn : Raw := .ann depPairTm depPairTy
+
+def fstDepPair : Raw := .fst depPairAnn
+
+def sndDepPair : Raw := .snd depPairAnn
+
+def omegaTy : Raw :=
+  .pi "A" (.univ 0) (.var "A")
+
+def omegaTm : Raw :=
+  .lam "x" (.app (.var "x") (.var "x"))
+
+def omegaAnn : Raw := .ann omegaTm omegaTy
+
+def unknownVar : Raw := .var "nope"
+
+def pairMismatch : Raw :=
+  .ann (.pair (.univ 1) (.univ 1))
+       (.sig "A" (.univ 2) (.var "A"))
+
+def badFst : Raw := .fst (.univ 0)
+
+def letUniverse : Raw :=
+  .ann
+    (.letE "A" (.univ 1) (.pi "_" (.univ 0) (.univ 0)) (.var "A"))
+    (.univ 1)
+
+def univ0 : Raw := .univ 0
+
+end BidirTT.Examples