The vectorial λ-calculus
نویسندگان
چکیده
We describe a type system for the linear-algebraic λ-calculus. The type system accounts for the linear-algebraic aspects of this extension of λ-calculus: it is able to statically describe the linear combinations of terms that will be obtained when reducing the programs. This gives rise to an original type theory where types, in the same way as terms, can be superposed into linear combinations. We prove that the resulting typed λ-calculus is strongly normalising and features weak subject reduction. Finally, we show how to naturally encode matrices and vectors in this typed calculus.
منابع مشابه
Call-by-value, call-by-name and the vectorial behaviour of the algebraic \lambda-calculus
We examine the relationship between the algebraic λ-calculus, a fragment of the differential λ-calculus and the linear-algebraic λ-calculus, a candidate λ-calculus for quantum computation. Both calculi are algebraic: each one is equipped with an additive and a scalarmultiplicative structure, and their set of terms is closed under linear combinations. However, the two languages were built using ...
متن کاملOn modal mu-calculus in S5 and applications
We show that the vectorial μ-calculus model checking problem over arbitrary graphs reduces to the vectorial, existential μ-calculus model checking problem over S5 graphs. We also draw some consequences of this fact. Moreover, we give a proof that satisfiability of μ-calculus in S5 is NP -complete, and by using S5 graphs we give a new proof that the satisfiability problem of the existential μ-ca...
متن کاملFabio Fioravanti ( Ed . ) CILC 2011 26 th Italian Conference on Computational Logic
We show that the vectorial μ-calculus model checking problem over arbitrary graphs reduces to the vectorial, existential μ-calculus model checking problem over S5 graphs. We also draw some consequences of this fact. Moreover, we give a proof that satisfiability of μ-calculus in S5 is NP -complete, and by using S5 graphs we give a new proof that the satisfiability problem of the existential μ-ca...
متن کاملScalar and Vectorial mu-calculus with Atoms
We study an extension of modal mu-calculus to sets with atoms and we study its basic properties. Model checking is decidable on orbit-finite structures, and a correspondence to parity games holds. On the other hand, satisfiability becomes undecidable. We also show expressive limitations of atom-enriched mu-calculi, and explain how their expressive power depends on the structure of atoms used, a...
متن کاملA multi-domain spectral method for scalar and vectorial Poisson equations with non-compact sources
We present a spectral method for solving elliptic equations which arise in general relativity, namely three-dimensional scalar Poisson equations, as well as generalized vectorial Poisson equations of the type ∆ ~ N + λ~ ∇(~ ∇ · ~ N) = ~ S with λ 6= −1. The source can extend in all the Euclidean space R, provided it decays at least as r−3 (scalar case) or r−4 (vectorial case). A multi-domain app...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Inf. Comput.
دوره 254 شماره
صفحات -
تاریخ انتشار 2017