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A Semantic Proof of Polytime Soundness of Light Affine Logic
"... Abstract. We define a denotational semantics for Light Affine Logic (LAL) which has the property that denotations of functions are polynomial time computable by construction of the model. This gives a new proof of polytimesoundness of LAL which is considerably simpler than the standard proof based ..."
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Abstract. We define a denotational semantics for Light Affine Logic (LAL) which has the property that denotations of functions are polynomial time computable by construction of the model. This gives a new proof of polytimesoundness of LAL which is considerably simpler than the standard proof based on proof nets and also is entirely semantical in nature. The model construction uses a new instance of a resource monoid; a general method for interpreting variations of linear logic with complexity restrictions introduced earlier by the authors. 1
Quantitative Models and Implicit Complexity
, 2005
"... We give new proofs of soundness (all representable functions on base types lies in certain complexity classes) for Elementary Affine Logic, LFPL (a language for polytime computation close to realistic functional programming introduced by one of us), Light Affine Logic and Soft Affine Logic. The proo ..."
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We give new proofs of soundness (all representable functions on base types lies in certain complexity classes) for Elementary Affine Logic, LFPL (a language for polytime computation close to realistic functional programming introduced by one of us), Light Affine Logic and Soft Affine Logic. The proofs are based on a common semantical framework which is merely instantiated in four different ways. The framework consists of an innovative modification of realizability which allows us to use resourcebounded computations as realisers as opposed to including all Turing computable functions as is usually the case in realizability constructions. For example, all realisers in the model for LFPL are polynomially bounded computations whence soundness holds by construction of the model. The work then lies in being able to interpret all the required constructs in the model. While being the first entirely semantical proof of polytime soundness for light logics, our proof also provides a notable simplification of the original already semantical proof of polytime soundness for LFPL. A new result made possible by the semantic framework is the addition of polymorphism and a modality to LFPL thus allowing for an internal definition of inductive datatypes. 1