Certificates for Incremental Type Checking

The central topic of this thesis is the study of algorithms for type checking, both from the programming language and from the proof-theoretic point of view. A type checking algorithm takes a program or a proof, represented as a syntactical object, and checks its validity with respect to a specification or a statement. It is a central piece of compilers and proof assistants. We postulate that since type checkers are at the interface between proof theory and program theory, their study can let these two fields mutually enrich each other. We argue by two main instances: first, starting from the problem of proof reuse, we develop an incremental type checker; secondly, starting from a type checking program, we evidence a novel correspondence between natural deduction and the sequent calculus.

A SMO inhibitor drug reduces the progenitor cell's maintenance in the Drosophila hematopoietic organ: a novel model to study Chronic Myelogenous Leukemia relapse

The chronic myeloid leukemia complexity and the difficulties of disease eradication have recently led to the development of drugs which, together with the inhibitors of TK, could eliminate leukemia stem cells preventing the occurrence of relapses in patients undergoing transplantation. The Hedgehog (Hh) signaling pathway positively regulates the self-renewal and the maintenance of leukemic stem cells and not, and this function is evolutionarily conserved. Using Drosophila as a model, we studied the efficacy of the SMO inhibitor drug that inhibit the human protein Smoothened (SMO). SMO is a crucial component in the signal transduction of Hh and its blockade in mammals leads to a reduction in the disease induction. Here we show that administration of the SMO inhibitor to animals has a specific effect directed against the Drosophila ortholog protein, causing loss of quiescence and hematopoietic precursors mobilization. The SMO inhibitor induces in L3 larvae the appearance of melanotic nodules generated as response by Drosophila immune system to the increase of its hemocytes. The same phenotype is induced even by the dsRNA:SMO specific expression in hematopoietic precursors of the lymph gland. The drug action is also confirmed at cellular level. The study of molecular markers has allowed us to demonstrate that SMO inhibitor leads to a reduction of the quiescent precursors and to an increase of the differentiated cells. Moreover administering the inhibitor to heterozygous for a null allele of Smo, we observe a significant increase in the phenotype penetrance compared to administration to wild type animals. This helps to confirm the specific effect of the drug itself. These data taken together indicate that the study of inhibitors of Smo in Drosophila can represent a useful way to dissect their action mechanism at the molecular-genetic level in order to collect information applicable to the studies of the disease in humans.