lf-class

Lecture 3: Higher-Order Abstract Syntax

Code

Lecture plan

• OL: Simply-typed lambda calculus (syntax and typing)
• Encoding: syntax and typing
• LF type theory: lambda; adequacy for HOAS
• Encoding: %blocks and %worlds
• OL: Step rules (weak head reduction)
• Encoding: step rules; preserv proof

Exercises

• Add LF encodings for product types and pairs with a “split” elimination form. Extend the relevant judgments and proofs. (See code file for exact inference rules.)
• Create an intrinsic encoding of STLC, where expression syntax is indexed by the type of the expression. Declare blocks and worlds for every type family.
• In class, we talked about how adequacy with HOAS depends on LF functions not being allowed to case-analyze their arguments. What goes wrong if we allow this? Construct an example, if you can.

Further reading

• The STLC example is also a tutorial on the Twelf Wiki.
• Robert Harper and Daniel Licata. Mechanizing Metatheory in a Logical Framework (2007).