lf-class

Lecture 2: LF Type Theory

Code

Lecture plan

• LF type theory (minus lambda)
• Datatype encodings and (informal) adequacy

Exercises

• Come up with a second proof that (node (node leaf leaf) (node leaf leaf)) is balanced.
• Come up with both an extrinsic and intrinsic encoding for AVL trees. Show that the extrinsic encoding is not adequate, and that the intrinsic one is.
• Exercise (bonus): can you describe a type theory that “stratifies” the levels of [syntax, judgments, theorems], all of which LF uses dependent functions to represent? What would the advantages/disadvantages be?

Further reading

• A Framework for Defining Logics, Harper, Honsell, and Plotkin. The original LF paper.
• Computation and Deduction Chapter 3 (Formalization in a Logical Framework)
• Church and Curry: Combining Intrinsic and Extrinsic Typing, by Frank Pfenning