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Build, augment and destroy. Universally
 In Asian Symposium on Programming Languages, Proceedings
, 2004
"... Abstract. We give a semantic footing to the fold/build syntax of programming with inductive types, covering shortcut deforestation, based on a universal property. Specifically, we give a semantics for inductive types based on limits of algebra structure forgetting functors and show that it is equiva ..."
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Abstract. We give a semantic footing to the fold/build syntax of programming with inductive types, covering shortcut deforestation, based on a universal property. Specifically, we give a semantics for inductive types based on limits of algebra structure forgetting functors and show that it is equivalent to the usual initial algebra semantics. We also give a similar semantic account of the augment generalization of build and of the unfold/destroy syntax of coinductive types. 1
Logical reasoning about programming of mathematical machines
 Acta Electrotechnica et Informatica
"... We always start the solving of a problem with the formulation of its theoretical foundations. If we would like to use mathematical machines (computers) in problem solving, we need to formalize its theoretical foundations as logical reasoning because the programs should really prove the correctness o ..."
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We always start the solving of a problem with the formulation of its theoretical foundations. If we would like to use mathematical machines (computers) in problem solving, we need to formalize its theoretical foundations as logical reasoning because the programs should really prove the correctness of their results. In our paper we present central ideas of our approach regarding programming as logical reasoning. Our first idea is that the theory in which we reason is the type theory starting with basic types. Our second idea is that the running program is actually a proof in the theory above formulated as the intuitionistic linear version of Gentzen’s calculus. We show that such a synthesis of categorical and linear logic forms a theoretical foundations of programming for mathematical machines.