lib-laddertypes

Rust Implementation of Ladder-Types (parsing, unification, rewriting, etc)

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Ladder Types

In order to implement complex datastructures and algorithms, usually many layers of abstraction are built ontop of each other, and consequently higher-level data types are encoded into lower-level data types, forming a chain of embeddings from concept to `rock bottom' of byte streams. While a high-level type makes claims about an objects semantics, it is ambiguous in regard to its concrete syntactical representation or memory layout. However these concrete representational forms must be compatible for type-safe compositions.

For example in the unix shell, many different tools & utilities exist concurrently and depending on the application domain, each will potentially make use of different representational forms. Abstract concepts like 'natural number' could exist in many representational forms, e.g. with variation over radices, endianness, digit encoding etc.

Intuitively, ladder types provide a way to distinguish between multiple concrete representations of the same abstract / conceptual type, by capturing the represented-as of layered data formats in the structure of type-terms. Formally, we introduce a new type constructor, called the ladder type, written T1 ~ T2, where T1 and T2 are types. The type-term T1 ~ T2 then expresses the abstract type of T1 being represented in terms of the concrete type T2, which can be read by "T1 represented as T2".

Example

The following type describes a colon-separated sequence of timepoints, each represented as unix-timestamp written as decimal number in big-endian, encoded as UTF-8 string.

<Seq Timepoint
     ~<TimeSince UnixEpoch>
     ~<Duration Seconds>
     ~ℕ
     ~<PosInt 10 BigEndian>
     ~<Seq <Digit 10>~Char>>
~<SepSeq Char ':'>
~<Seq Char>
~UTF-8
~<Seq Byte>

An object that fits the format described by this type could look like this:

1696093021:1696093039:1528324679:1539892301:1638141920:1688010253

How to use this crate

use laddertypes::*;

fn main() {
    let mut dict = TypeDict::new();

    let t1 = dict.parse("<A B~X C>").expect("couldnt parse typeterm");
    let t2 = dict.parse("<<A B~X> C>").expect("couldnt parse typeterm");

    assert_eq!( t1.clone().curry(), t2 );
    assert_eq!( t1, t2.clone().decurry() );
}

License

GPLv3