[ home
| schedule
| assignments
| projects
| resources
| handouts
| overview
| links
]
# 15-815 Automated Theorem Proving

# Lecture 12: Residuating Equality

We have addressed conjunctive non-determinism by solving subgoals
in an arbitrary order, and disjunctive non-determinism by backtracking,
capping the depth to which to search. Universal non-determinism
corresponds to picking a new parameter name, which is a form of
don't care non-determinism (the parameter name does not matter, as
long as it is new).

This leaves *existential non-determinism*, that is, the
choice of picking a term *t* in the right rule for the existential
and the left rule for the universal quantifier. We show how this
choice can be postponed by a general technique of *residuation*.
Later we show how the residual equality goals can be solved by unification,
and how this can be interleaved with the search process. At that point
we will have the first full implementation of a theorem prover for
intuitionistic logic.

### Reading

- Handout 9 on
*Residuating
Equality* (also availabe in PDF
format).

### Key Concepts

- Existential non-determinism
- Residuation
- Unification logic
- Computation staging

### Links

[ home
| schedule
| assignments
| projects
| resources
| handouts
| overview
| links
]

Frank Pfenning
fp@cs