Abstract Good tools can bring mechanical verification to programs written in mainstream functional languages. We use hs-to-coq translate significant portions of Haskell’s containers library into Coq, and verify it against specifications that we derive from a variety sources including type class laws, the library’s test suite, interfaces Coq’s standard library. Our work shows is feasible mature,...

Let G be a monoid that acts on topological space X by homeomorphisms such there is point x0∈X with GU=X for each neighbourhood U of x0. A subset said to G-bounded if x0 finite F A⊆FU. We prove metrizable and separable G-space X, the bounded subsets are completely determined any dense subspace. also obtain sufficient conditions locally G-bounded, which apply groups. Thereby, we extend some previ...

p$^\dagger$q is a C++ accelerated Python library designed to generate equations for many-body quantum chemistry methods and realize proof-of-concept implementations of these rapid prototyping. Central this simple interface define strings second-quantized creation annihilation operators bring normal order with respect either the true vacuum state or Fermi vacuum. Tensor contractions over fully-c...

We prove that the Bloch space coincides with the space BMOA in the tube over the spherical cone of R.3; this extends a well-known onedimensional result. Introduction. Let Q be a symmetric Siegel domain of type II contained in Cn. Let V denote the Lebesgue measure in fi and H{Q) the space of holomorphic (or analytic) functions in fi. When n = 1 and fi = tt+ = {z £ C: Imz > 0}, a Bloch function i...

φ f (x) =   f (x)− f (x0) x−x0 , x , x0 f ′(x0), x = x0. Now, by the differentiability of f at x0, we have lim x→x0 x∈X\{x0 } φ f (x) = lim x→x0 x∈X\{x0 } f (x) − f (x0) x − x0 = f (x0) = φ f (x0). This proves that φ f is continuous at x0. Moreover, (1.1) holds for all x ∈ X by definition of φ f . ((1.1) is clearly true when x , x0. When x = x0, both sides of (1.1) are zero.) Therefore (ii) ...

Let R=K[G] be a group ring of G over field K. It is known that if amenable then R satisfies the Ore condition: for any a,b∈R there exist u,v∈R such au = bv, where u≠0 or v≠0. also true groups non-zero solution exists finite system linear equations R, number unknowns exceeds equations. Recently Bartholdi proved converse. As consequence this theorem, Kielak R. Thompson’s F and only it condition. ...