Sentence examples for explicit calculus from inspiring English sources

The 'implicit' suggests that the explicit calculus expression of this governing equation is difficult to derive and not required.

The proof follows from an explicit calculus with respect to the N-adapted frame (Equation 19) and N-adapted coframe (Equation 20) in Equation 50 (equivalently, in Equation 51) and re-grouping of the components as to distinguish the z- and v-components (Equation 53) for g AB = g a ' a ', h ab Open image in new window.The set of metric d-connections.

The λσ-calculus is a concrete λ-calculus of explicit substitutions, designed for reasoning about implementations of λ-calculi.

On the other hand, despite the circularity of impredicative definitions, which is made so explicit in Takeuti's calculus, no paradoxes have been found yet in second-order Arithmetic.

By applying the results of fractional calculus an explicit equation is derived to express non-integer moments as a function of any arbitrary number of integer moments.

A new calculus of explicit substitutions for higher-order abstract syntax is introduced, allowing a high-level description of variable binding in object languages while also providing substitutions as explicit programmer-manipulable data objects.

While these constructions, and the associated graph reductions bear striking similarity with lambda calculus with explicit substitutions, as first remarked by Di Cosmo & Kesner (1997), they are too similar to the corresponding sequent calculus rules: the parallelization effect so elegant for MLL does not properly carry on here, and the graph reduction rules involve boxes and are not local.

To move closer to actual implementations, which use environments rather than actual substitutions, we then represent methods as closures and we present three new semantic artifacts for a version of Abadi and Cardelli's calculus with explicit substitutions: a reduction semantics, an environment-based abstract machine, and a natural semantics (i.e., an interpreter) with environments.

In order to simplify the proof and give an intuitive understanding of the encoding, we design an intermediate language: the π-Calculus with Explicit Substitutions and Channels, which is a syntactic extension of the π-calculus with a specific operational semantics.

The reduction rules extend the 'vanilla' lambda-calculus in a simple and modular way and preserve the look and feel of a standard lambda-calculus with explicit substitutions.

In this paper we present the Network Conscious π-calculus ( NCPi), a proper extension of the π-calculus with an explicit notion of network: network links and nodes are represented as names, in full analogy with ordinary π-calculus names, and observations are routing paths through which data is transported.