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Functional Programming in Sublinear Space
"... Abstract. We consider the problem of functional programming with data in external memory, in particular as it appears in sublinear space computation. Writing programs with sublinear space usage often requires one to use special implementation techniques for otherwise easy tasks, e.g. one cannot comp ..."
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Cited by 4 (2 self)
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Abstract. We consider the problem of functional programming with data in external memory, in particular as it appears in sublinear space computation. Writing programs with sublinear space usage often requires one to use special implementation techniques for otherwise easy tasks, e.g. one cannot compose functions directly for lack of space for the intermediate result, but must instead compute and recompute small parts of the intermediate result on demand. In this paper, we study how the implementation of such techniques can be supported by functional programming languages. Our approach is based on modelling computation by interaction using the Int construction of Joyal, Street & Verity. We derive functional programming constructs from the structure obtained by applying the Int construction to a term model of a given functional language. The thus derived functional language is formulated by means of a type system inspired Baillot & Teruiās Dual Light Affine Logic. We assess its expressiveness by showing that it captures LOGSPACE. 1
Int Construction and Semibiproducts
, 2009
"... We study a relationship between the Int construction of Joyal et al. and a weakening of biproducts called semibiproducts. We then provide an application of geometry of interaction interpretation for the multiplicative additive linear logic (MALL for short) of Girard. We consider not biproducts but s ..."
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Cited by 1 (0 self)
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We study a relationship between the Int construction of Joyal et al. and a weakening of biproducts called semibiproducts. We then provide an application of geometry of interaction interpretation for the multiplicative additive linear logic (MALL for short) of Girard. We consider not biproducts but semibiproducts because in general the Int construction does not preserve biproducts. We show that Int construction is left biadjoint to the forgetful functor from the 2category of compact closed categories with semibiproducts to the 2category of traced symmetric monoidal categories with semibiproducts. We then illustrate a traced distributive symmetric monoidal category with biproducts B(Pfn) and relate the interpretation of MALL in Int(B(Pfn)) to token machines defined over weighted MALL proofs.
A quantum double construction in Rel
, 2010
"... We study bialgebras in the compact closed category Rel of sets and binary relations. Various monoidal categories with extra structure arise as the categories of (co)modules of ..."
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We study bialgebras in the compact closed category Rel of sets and binary relations. Various monoidal categories with extra structure arise as the categories of (co)modules of