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By Ron K. (ed.) Cytron

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X , then we say that C is a small constructor kind (or just a small constructor when there is no ambiguity) and denote it as small(C). ACM Transactions on Programming Languages and Systems, Vol. 27, No. 1, January 2005. A Type System for Certified Binaries • 41 Our inductive definitions reside in Kind, whereas a small constructor does not make universal quantification over objects of type Kind. Therefore, an inductive definition with small constructors is a predicative definition. While dealing with impredicative inductive definitions, we must forbid projections on universes equal to or bigger than the one inhabited by the definition.

2001. An expressive, scalable type theory for certified code. Tech. Rep. , Pittsburgh, Pa. , AND MORRISETT, G. 1999. Typed memory management in a calculus of capabilities. In Proceedings of the 26th ACM Symposium on Principles of Programming Languages. ACM , New York, 262–275. CRARY, K. AND WEIRICH, S. 1999. Flexible type analysis. In Proceedings of the 1999 ACM SIGPLAN International Conference on Functional Programming. ACM, New York, 233–248. CRARY, K. AND WEIRICH, S. 2000. Resource bound certification.

REFERENCES ALTENKIRCH, T. 1993. Constructions, inductive types and strong normalization. D. dissertation. University of Edinburgh, UK. APPEL, A. W. AND FELTEN, E. W. 2001. Models for security policies in proof-carrying code. Tech. Rep. J. APPEL, A. W. AND FELTY, A. P. 2000. A semantic model of types and machine instructions for proof-carrying code. In Proceedings of the 27th ACM Symposium on Principles of Programming Languages. ACM, New York, pp. 243–253. BARENDREGT, H. P. 1991. Lambda calculi with types.

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ACM transactions on programming languages and systems (January) by Ron K. (ed.) Cytron

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