Computation by interaction for space-bounded functional programming
When programming with sublinear space constraints one often needs to use special implementation techniques even for simple tasks, such as function composition. In this paper, we study how such implementation techniques can be supported in a functional programming language. Our approach is based on m...
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| Abstract | When programming with sublinear space constraints one often needs to use special implementation techniques even for simple tasks, such as function composition. In this paper, we study how such implementation techniques can be supported in a functional programming language. Our approach is based on modelling computation by interaction using the Int construction of Joyal, Street & Verity. We apply this construction to a term model of a first-order programming language and use the resulting structure to derive the functional programming language intml. Intml can be understood as a programming language simplification of Stratified Bounded Affine Logic. We formulate intml by means of a type system inspired by Baillot & Terui's Dual Light Affine Logic. We show that it captures the complexity classes flogspace and nflogspace. We illustrate its expressiveness by showing how typical graph algorithms, such a test for acyclicity in undirected graphs, can be represented. |
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| AbstractList | We consider the problem of supporting sublinear space programming in a functional programming language. 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 core functional language intml is formulated by means of a type system inspired by Baillot & Terui's Dual Light Affine Logic. It can be understood as a programming language simplification of Stratified Bounded Affine Logic. We show that it captures the classes flogspace and nflogspace of the functions computable in deterministic logarithmic space and in non-deterministic logarithmic space, respectively. We illustrate the expressiveness of intml by showing how typical graph algorithms, such a test for acyclicity in undirected graphs, can be represented in it. When programming with sublinear space constraints one often needs to use special implementation techniques even for simple tasks, such as function composition. In this paper, we study how such implementation techniques can be supported in a functional programming language. Our approach is based on modelling computation by interaction using the Int construction of Joyal, Street & Verity. We apply this construction to a term model of a first-order programming language and use the resulting structure to derive the functional programming language intml. Intml can be understood as a programming language simplification of Stratified Bounded Affine Logic. We formulate intml by means of a type system inspired by Baillot & Terui's Dual Light Affine Logic. We show that it captures the complexity classes flogspace and nflogspace. We illustrate its expressiveness by showing how typical graph algorithms, such a test for acyclicity in undirected graphs, can be represented. |
| Author | Schöpp, Ulrich Dal Lago, Ugo |
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| Keywords | Type system Logarithmic space Geometry of interaction Functional programming Implicit computational complexity |
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| Title | Computation by interaction for space-bounded functional programming |
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