Rust Implementation of Ladder-Types (parsing, unification, rewriting, etc)
In order to implement complex datastructures and algorithms, usually many layers of abstraction are built ontop of each other. 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 the semantics of objects of that type, high-level types are ambiguous in regard to their concrete syntactical representation or memory layout. However for compositions to be type-safe, compatibility of concrete represenations must be ensured.
For example in the unix shell, many different tools & utilities coexist. Depending on the application domain, each of them will potentially make use of different representational forms for the same abstract concepts. E.g. for the concept 'natural number', many representations do exist, 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".
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
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() );
}