  We present a polymorphic type system for lambda calculus ensuring that
well-typed programs can be executed in polynomial space: dual light affine
logic with booleans (DLALB).
  To build DLALB we start from DLAL (which has a simple type language with a
linear and an intuitionistic type arrow, as well as one modality) which
characterizes FPTIME functions. In order to extend its expressiveness we add
two boolean constants and a conditional constructor in the same way as with the
system STAB.
  We show that the value of a well-typed term can be computed by an alternating
machine in polynomial time, thus such a term represents a program of PSPACE
(given that PSPACE = APTIME).
  We also prove that all polynomial space decision functions can be represented
in DLALB.
  Therefore DLALB characterizes PSPACE predicates.
