An introduction to deciding higher order matching
Higher-order unification is the problem given an equation
t = u containing free variables
is there a solution substitution theta such that
t theta and u theta have the same normal form?
The terms t and u belong to the simply typed lambda calculus
and the same normal form is with respect to beta eta-equivalence.
Higher order matching is the particular instance when the term
u is closed; can t be pattern matched to u?
Although higher order unification is undecidable,
higher order matching was conjectured to be decidable
by Huet in the 1970s.
In the talk I will describe a proof of decidability
that is based on a game theoretic analysis of
beta-reduction which is essentially game semantics.
Besides the use of games to understand beta-reduction,
I also emphasise how tree automata can recognise
terms of simply typed lambda calculus.