Quasi-interpretation Synthesis by Decomposition : An application to higher-order programs

International audienceQuasi-interpretations have shown their interest to deal with resource analysis of first order functional programs. There are at least two reasons to study the question of modularity of quasi-interpretations. Firstly, modularity allows to decrease the complexity of the quasi-inter\-pretation search algorithms. Secondly, modularity allows to increase the intentionality of the quasi-interpretation method, that is the number of captured programs. In particular, we take advantage of modularity conditions to extend smoothly quasi-interpretations to higher order programs. In this paper, we study the modularity of quasi-interpretations through the notions of constructor-sharing and hierarchical unions. We show that in the case of constructor-sharing and hierarchical unions, the existence of quasi-interpretations is no longer a modular property. However, we can still certify the complexity of programs

Principal Typing for Lambda Calculus in Elementary Affine Logic.

2ElementaryAffineLogic(EAL)isavariantofLinearLogiccharacterizingthecomputa- tional power of the elementary bounded Turing machines. The EAL Type Inference problem is the problem of automatically assigning to terms of -calculus EAL formulas as types. This problem, re- stricted to the propositional fragment of EAL, is proved to be decidable, and an algorithm is shown, building, for every -term, either a negative answer or a finite set of type schemata, from which all and only its typings can be derived, through suitable operations.reservedmixedCOPPOLA Paolo; RONCHI DELLA ROCCA SimonaCoppola, Paolo; RONCHI DELLA ROCCA, Simon