منابع مشابه
Ornaments in practice, higher-order ornaments
6 Syntactic ornaments in the binary language 21 6.1 From ornaments to projection . . . . . . . . . . . . . . . . . . . . . . . . . . 24 6.2 Syntax of the binary language . . . . . . . . . . . . . . . . . . . . . . . . . . 25 6.3 Projection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 6.4 Datatype environment . . . . . . . . . . . . . . . . . . . . . . . . . . ....
متن کاملProgramming with ornaments
Dependently typed programming advocates the use of various indexed versions of the same shape of data, but the formal relationship among these structurally similar datatypes usually needs to be established manually and tediously. Ornaments have been proposed as a formal mechanism to manage the relationships between such datatype variants. In this paper, we conduct a case study under an ornament...
متن کاملThe essence of ornaments
Functional programmers from all horizons strive to use, and sometimes abuse, their favorite type system in order to capture the invariants of their programs. A widely-used tool in that trade consists in defining finely-indexed datatypes. Operationally, these types classify the programmer’s data, following the ML tradition. Logically, these types enforce the program invariants in a novel manner....
متن کاملBeautiful Interpolants
We describe a compositional approach to Craig interpolation based on the heuristic that simpler proofs of special cases are more likely to generalize. The method produces simple interpolants because it is able to summarize a large set of cases using one relatively simple fact. In particular, we present a method for finding such simple facts in the theory of linear rational arithmetic. This make...
متن کاملHyperbolization of Euclidean Ornaments
In this article we outline a method that automatically transforms an Euclidean ornament into a hyperbolic one. The necessary steps are pattern recognition, symmetry detection, extraction of a Euclidean fundamental region, conformal deformation to a hyperbolic fundamental region and tessellation of the hyperbolic plane with this patch. Each of these steps has its own mathematical subtleties that...
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ژورنال
عنوان ژورنال: Scientific American
سال: 1876
ISSN: 0036-8733
DOI: 10.1038/scientificamerican02121876-109asupp