Execution Time of Lambda-Terms via Non Uniform Semantics and Intersection Types
نویسنده
چکیده
The relational semantics for Linear Logic induces a semantics for the type free Lambda Calculus. This one is built on non-idempotent intersection types. We give a principal typing property for this type system.We then prove that the size of the derivations is closely related to the execution time of lambda-terms in a particular environment machine, Krivine’s machine.
منابع مشابه
Intersection Types for Normalization and Verification
One of the basic principles in typed lambda calculi is that typable lambda terms are normalizable. Since the converse direction does not hold for simply typed lambda calculus, people have been studying its extensions. This gave birth to the intersection type systems, that exactly characterize various classes of lambda terms, such as strongly/weakly normalizable terms and solvable ones (see e.g....
متن کاملExecution Time of lambda-Terms via Denotational Semantics and Intersection Types
This paper presents a work whose aim is to obtain information on execution time of λ-terms by semantic means. By execution time, we mean the number of steps in a computational model. As in [Ehrhard and Regnier 2006], the computational model considered in this paper will be Krivine’s machine, a more realistic model than β-reduction. Indeed, Krivine’s machine implements (weak) head linear reducti...
متن کاملNon uniform (hyper/multi)coherence spaces
In (hyper)coherence semantics, proofs/terms are cliques in (hyper)graphs. Intuitively, vertices represent results of computations and the edge relation witnesses the ability of being assembled into a same piece of data or a same (strongly) stable function, at arrow types. In (hyper)coherence semantics, the argument of a (strongly) stable functional is always a (strongly) stable function. As a c...
متن کاملIntersection Types for the λμ-Calculus
We introduce an intersection type system for the pure λμ-calculus, which is invariant under subject reduction and expansion. The system is obtained by describing Streicher and Reus’s denotational model of continuations in the category of omega-algebraic lattices via Abramsky’s domain logic approach. This provides at the same time an interpretation of the type system and a proof of the completen...
متن کاملExecution Time of λ-Terms via Denotational Semantics and Intersection Types
This paper presents a work whose aim is to obtain information on execution time of λ-terms by semantic means. By execution time, we mean the number of steps in a computational model. As in [Ehrhard and Regnier 2006], the computational model considered in this paper will be Krivine’s machine, a more realistic model than β-reduction. Indeed, Krivine’s machine implements (weak) head linear reducti...
متن کامل