  An interactive theorem prover, Isabelle, is under development. In LCF, each
inference rule is represented by one function for forwards proof and another (a
tactic) for backwards proof. In Isabelle, each inference rule is represented by
a Horn clause. Resolution gives both forwards and backwards proof, supporting a
large class of logics. Isabelle has been used to prove theorems in
Martin-L\"of's Constructive Type Theory. Quantifiers pose several difficulties:
substitution, bound variables, Skolemization. Isabelle's representation of
logical syntax is the typed lambda-calculus, requiring higher- order
unification. It may have potential for logic programming. Depth-first
subgoaling along inference rules constitutes a higher-order Prolog.
