To Do List ---------- - ~~Add `cast : Pi (A B : Type) (H : A = B) (a : A) : B`, and implement "casting propagation" in the type checker.~~ - ~~Modify the `let` construct to store the type of the value. The idea is to allow `let name : type := value in expr`. The type does not need to be provided by the user. However, the user may want to provide it as a hint for the Lean elaborator.~~ - Refactor the elaborator code. The elaborator will be one of the main data-structures in Lean. The elaborator manager should be shared between different frontends. - ~~Reconsider whether meta-variables should be in `expr` or not. Metavariables (aka holes) are fundamental in our [design](design.md).~~ - ~~Improve Lean pretty printer for Pi's. For example, it produces `Var a : Pi (A : Type) (_ : A), A` instead of `Var a : Pi (A : Type), A -> A`.~~ - Decide what will be the main technique for customizing Lean's behavior. The elaborator manager will have many building blocks that can be put together in many different ways. Possible solutions: - We design our own configuration language. - We use an off-the-shelf embedded language such as [Lua](http://www.lua.org). - We use Lean itself. - Module for reading [OpenTheory](http://www.gilith.com/research/opentheory/) proofs. - Higher-Order unification and matching. - Rewriter (and Rewriter Combinators). - [MCSat](http://leodemoura.github.io/files/fmcad2013.pdf) framework. - Implement independent type checker using a different programming language (e.g., OCaml). - Add `match` construct in `expr`. - Add inductive datatype (families) in the environment. It will be a new kind of object. - Add recursive function definition objects (low priority). It is another new kind of object.