Cardinality

Constraints for constraining sets of real numbers

Cardinality introduces numerically-constrained Double types which are as usable as ordinary Doubles, but safely constrained to a range that is specified in their type.

Features

• introduces Doubles which are constrained to a numeric range, checked at compile time
• intuitive a ~ b syntax for representing a ranged Double
• ordinary Double literals can be used in positions which expect a ranged type
• numeric ranges compose under arithmetic operations
• escape-hatch (called force) for unsafe but easy conversions

Availability Plan

Cardinality has not yet been published. The medium-term plan is to build Cardinality with Fury and to publish it as a source build on Vent. This will enable ordinary users to write and build software which depends on Cardinality.

Subsequently, Cardinality will also be made available as a binary in the Maven Central repository. This will enable users of other build tools to use it.

For the overeager, curious and impatient, see building.

Getting Started

Cardinality provides a representation of numbers which must lie within a certain (closed) range. A range type is written with the infix ~ type operator, between two doubles, for example, -1.0 ~ 1.0 represents a Double which is at least -1.0 and at most 1.0.

Compiletime operations check Double literals for conformance to the claimed bounds, for example:

val x: 0.0 ~ 100.0 = 33.3 // good
val y: 0.0 ~ 1.0 = 2.0    // compile error

Standard arithmetic operations are also implemented on ranged Doubles. Depending on whether the right-hand operand is a statically-unknown Double, a Double singleton literal, or a ranged Double, the result will be typed as precisely as possible. For example, adding 10.0 to an instance of 3.0 ~ 5.0 will produce a result of type, 13.0 ~ 15.0. These operations use typelevel arithmetic to calculate the resultant range of the calculation, and can be composed like other arithmetic functions, with the return type inferred. For example,

var x: 0.0 ~ 1.0 = 0.2
var y: -1.0 ~ 1.0 = 0.2
var z: 1e3 ~ 1e8 = 10000

val result = (x + y*3.0)*z

will infer the type of result to be -2.0e8 ~ 3.0e8 (while its value will be 6000.0.

Forcing values

Unranged Doubles are pervasive in Scala, so a Double#force extension method is provided which can be used (carefully) to convert a Double to an expected ranged type.

Status

Cardinality is classified as embryotic. For reference, Scala One projects are categorized into one of the following five stability levels:

• embryonic: for experimental or demonstrative purposes only, without any guarantees of longevity
• fledgling: of proven utility, seeking contributions, but liable to significant redesigns
• maturescent: major design decisions broady settled, seeking probatory adoption and refinement
• dependable: production-ready, subject to controlled ongoing maintenance and enhancement; tagged as version 1.0.0 or later
• adamantine: proven, reliable and production-ready, with no further breaking changes ever anticipated

Projects at any stability level, even embryonic projects, can still be used, as long as caution is taken to avoid a mismatch between the project's stability level and the required stability and maintainability of your own project.

Cardinality is designed to be small. Its entire source code currently consists of 139 lines of code.

Building

Cardinality will ultimately be built by Fury, when it is published. In the meantime, two possibilities are offered, however they are acknowledged to be fragile, inadequately tested, and unsuitable for anything more than experimentation. They are provided only for the necessity of providing some answer to the question, "how can I try Cardinality?".

1. Copy the sources into your own project

   Read the fury file in the repository root to understand Cardinality's build structure, dependencies and source location; the file format should be short and quite intuitive. Copy the sources into a source directory in your own project, then repeat (recursively) for each of the dependencies.

   The sources are compiled against the latest nightly release of Scala 3. There should be no problem to compile the project together with all of its dependencies in a single compilation.

2. Build with Wrath

   Wrath is a bootstrapping script for building Cardinality and other projects in the absence of a fully-featured build tool. It is designed to read the fury file in the project directory, and produce a collection of JAR files which can be added to a classpath, by compiling the project and all of its dependencies, including the Scala compiler itself.

   Download the latest version of wrath, make it executable, and add it to your path, for example by copying it to /usr/local/bin/.

   Clone this repository inside an empty directory, so that the build can safely make clones of repositories it depends on as peers of cardinality. Run wrath -F in the repository root. This will download and compile the latest version of Scala, as well as all of Cardinality's dependencies.

   If the build was successful, the compiled JAR files can be found in the .wrath/dist directory.

Contributing

Contributors to Cardinality are welcome and encouraged. New contributors may like to look for issues marked beginner.

We suggest that all contributors read the Contributing Guide to make the process of contributing to Cardinality easier.

Please do not contact project maintainers privately with questions unless there is a good reason to keep them private. While it can be tempting to repsond to such questions, private answers cannot be shared with a wider audience, and it can result in duplication of effort.

Author

Cardinality was designed and developed by Jon Pretty, and commercial support and training on all aspects of Scala 3 is available from Propensive OÜ.

Name

The cardinality of a set is the number of elements it contains, while Cardinality controls the size of sets of Doubles.

In general, Scala One project names are always chosen with some rationale, however it is usually frivolous. Each name is chosen for more for its uniqueness and intrigue than its concision or catchiness, and there is no bias towards names with positive or "nice" meanings—since many of the libraries perform some quite unpleasant tasks.

Names should be English words, though many are obscure or archaic, and it should be noted how willingly English adopts foreign words. Names are generally of Greek or Latin origin, and have often arrived in English via a romance language.

Logo

The logo shows the hat typically worn by a cardinal, alluding to the name Cardinality.

License

Cardinality is copyright © 2024 Jon Pretty & Propensive OÜ, and is made available under the Apache 2.0 License.