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Linear Recursive Functions
"... With the recent trend of analysing the process of computation through the linear logic looking glass, it is well understood that the ability to copy and erase data is essential in order to obtain a Turingcomplete computation model. However, erasing and copying do not need to be explicitly included ..."
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With the recent trend of analysing the process of computation through the linear logic looking glass, it is well understood that the ability to copy and erase data is essential in order to obtain a Turingcomplete computation model. However, erasing and copying do not need to be explicitly included in Turingcomplete computation models: in this paper we show that the class of partial recursive functions that are syntactically linear (that is, partial recursive functions where no argument is erased or copied) is Turingcomplete.
HigherOrder and Symbolic Computation manuscript No. (will be inserted by the editor) Linearity and Iterator Types for Gödel’s System T
"... Abstract System LI is a linear λcalculus with numbers and an iterator, which, although imposing linearity restrictions on terms, has all the computational power of Gödel’s System T. System LI owes its power to two features: the use of a closed reduction strategy (which permits the construction of a ..."
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Abstract System LI is a linear λcalculus with numbers and an iterator, which, although imposing linearity restrictions on terms, has all the computational power of Gödel’s System T. System LI owes its power to two features: the use of a closed reduction strategy (which permits the construction of an iterator on an open function, but only iterates the function after it becomes closed), and the use of a liberal typing rule for iterators based on iterative types. In this paper, we study these new types, and show how they relate to intersection types. We also give a sound and complete type reconstruction algorithm for System LI.
Minimality in a Linear Calculus with Iteration Abstract
"... System L is a linear version of Gödel’s System T, where the λcalculus is replaced with a linear calculus; or alternatively a linear λcalculus enriched with some constructs including an iterator. There is thus at the same time in this system a lot of freedom in reduction and a lot of information ab ..."
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System L is a linear version of Gödel’s System T, where the λcalculus is replaced with a linear calculus; or alternatively a linear λcalculus enriched with some constructs including an iterator. There is thus at the same time in this system a lot of freedom in reduction and a lot of information about resources, which makes it an ideal framework to start a fresh attempt at studying reduction strategies in λcalculi. In particular, we show that callbyneed, the standard strategy of functional languages, can be defined directly and effectively in System L, and can be shown minimal among weak strategies. 1