# iris

Small (toy) dependently typed core w. a bidirectional typechecker. It takes a named raw syntax, checks and elaborates it into a de Bruijn core and evaluates terms into semantic values, quotes them back for diagnostics and uses conversion checking to compare normal forms. The current kernel has explicit universe levels `U0`, `U1`, `U2`, dependent function and pair types, projections, annotations, and `let`

One of the checked examples is:

```lean
def depPairTy : Raw :=
  .sig "A" (.univ 2) (.var "A")

def depPairTm : Raw :=
  .pair
    (.univ 1)
    (.pi "_" (.univ 0) (.univ 0))
```

which elaborates to a pair whose first component is the type `U1` and whose second component inhabits it