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https://github.com/rybla/escaigne
A programming language for defining integer sequences.
https://github.com/rybla/escaigne
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A programming language for defining integer sequences.
- Host: GitHub
- URL: https://github.com/rybla/escaigne
- Owner: rybla
- License: bsd-3-clause
- Created: 2019-09-15T23:36:18.000Z (about 5 years ago)
- Default Branch: master
- Last Pushed: 2019-09-16T02:18:43.000Z (about 5 years ago)
- Last Synced: 2024-03-07T06:44:03.129Z (8 months ago)
- Language: Haskell
- Size: 6.84 KB
- Stars: 0
- Watchers: 1
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- Changelog: ChangeLog.md
- License: LICENSE
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README
# Escaigne
A programming language for defining integer sequences.
## Language
Each _Escaigne_ program defines exactly one integer sequence, using the following grammar:
```
«program» ::=
Begin Head. «header» End Head.
Begin Prelude. «statements» End Prelude.
Begin Generator. «expression» End Generator.
«header» ::=
| Title: «string».
| Author: «string».
| Description: «string».
| «name»: «string»
«statement» ::=
| Value «name» := «expression».
| Function «name» «parameters» := «expression».
| Symbolic Value «name».
| Symbolic Function «name» «integer».
| Symbolic Operation «name».
| Table «name».
«expression» ::=
| «value»
| ( «parameters» => «expression» )
| ( «expression» «arguments» )
| ( value «name» := «expression» ; «expression» )
| ( function «name» «parameters» := «expression» ; «expression» )
| ( «name» [ «expression» ] )
«parameters» ::= «name» «name» ... «name»
«arguments» ::= «name» «name» ... «name»
«value» ::=
| «integer»
| «boolean»
| «string»
| «name»
```
The **Head** contains a set of headers which provide metadata about the file and program.
The **Prelude** contains a set of definitions that may be used elsewhere in the Prelude and also in the Generator.
The **Generator** contains a single expression that is expected to be a function that takes a single parameter, `n`, and evaluates to the `n`th term in the sequence it represents.
Note that the grammar is purposely kept very sparse. For example, simple operations are not included. That is because all strings, other than `.`, `;`, `(`, `)`, and keywords, can be used in `«name»`. Of course, many useful operations and functions will be defined in standard libraries.
### Statements
`Value n := e` binds `n` to `e`.
`Function f x1 ... xn := e` binds `f` to a function with parameters `x1, ..., xn` and evaluates to `e`.
`Symbolic Value n` and `Symbolic Function f #` bind their names to the appropriate type of value, which is marked as symbolic. A symbolic value cannot be reduced, and persists in the output. Symbolic values are automatically assumed to extend equality, but no other properties. Symbolic values are useful for forcing a certain representations - making explicit kinds of abstractions about the output sequence.
`Table t` declares a new table that can store values. Notably, these values persist during the evaluation of the generator over many entries of the sequence. This construct is useful for taking advantage of a dynamic-programming approach to computing some sequences (e.g. the Fibbonacci sequence).
## Application
Escaigne is used to provide a simple representation of integer sequences for online reference. This is useful because it allows for efficient generation of sequences on the fly, given a specification of how many entries to count out to.