Abstract. Datatypes freely generated by their constructors are well supported in mainstream proof assistants. Algebraic specification languages offer more ex-pressive datatypes on axiomatic means: nonfree datatypes generated from con-structors modulo equations. We have implemented an Isabelle/HOL package for nonfree datatypes, without compromising foundations. The use of the package, and its nonfree iterator in particular, is illustrated with examples: bags, polynomi-als and λ-terms modulo α-equivalence. The many-sorted metatheory of nonfree datatypes is formalized as an ordinary Isabelle theory and is animated by the package into user-specified instances. HOL lacks a type of types, so we employ an ad hoc construction of a universe embedding the relevant parameter types. 1

Abstract. This paper describes the integration of Squolem, Quantified Boolean Formulas (QBF) solver, with the interactive theorem prover HOL Light. Squolem generates certificates of validity which are based on witness functions. The certificates are checked in HOL Light by con-structing proofs based on these certificates. The presented approach al-lows HOL Light users to prove larger valid QBF problems than before and provides correctness checking of Squolem’s outputs based on the LCF approach. An error in Squolem was discovered thanks to the integration. Experiments show that the feasibility of the integration is very sensitive to implementation of HOL Light and used inferences. This resulted in improvements in HOL Light’s inference system. 1