The revised logic PPLAMBDA A reference manual
Lawrence Charles Paulson · CL Technical Reports · 2021
PPLAMBDA is the logic used in the Cambridge LCF proof assistant. It allows Natural Deduction proofs about computation, in Scott’s theory of partial orderings. The logic’s syntax, axioms, primitive inference rules, derived inference rules and standard lemmas are described as are the LCF functions for building and taking apart PPLAMBDA formulas. PPLAMBDA’s rule of fixed-point induction admits a wide class of inductions, particularly where flat or finite types are involved. The user can express and prove these type properties in PPLAMBDA. The induction rule accepts a list of theorems, stating type properties to consider when deciding to admit an induction.