Assignment 5

Due Monday October 4

1. Define an appropriate notion of proof term and extend the implementation of unification shown in class to a certifying theorem prover for unification logic.
2. Define a notion of valid substitution in the presence of parameter restrictions on existential variables.
3. Define composition for substitutions.
4. Prove the main properties of composition:
   1. If substitutions s1 and s2 are valid, so is their composition s1 o s2
   2. t[s1 o s2] = (t[s1])[s2]