Path-Iter

A cocategory enumeration library based on path semantics

Implementation based on paper Cocategory Enumeration.

For an introduction to Path Semantics, see this paper.

Sub-types in Path Semantics

In normal Path Semantics, one uses normal paths in theorem proving. Normal paths is a derivation from functions with sub-types.

This library focuses on sub-types, not on the more general case of normal paths.

A sub-type in Path Semantics is written in this form:

x : [f] a

Where x is some input, f is a function and a is the output of f.

This library is for enumerating such sub-types efficiently.

Example: AND

The path! macro is used to write in the standard notation of Path Semantics. It constructs a type using Path that implements IntoIterator:

use path_iter::*;

fn main() {
    for a in path!([And] true) {
        // Prints `(true, true)`
        println!("{:?}", a);
    }
}

It prints (true, true) because that is the only input value to And which produces true as output.

Example: AND 2

You can decide the output value at runtime:

use path_iter::*;

fn main() {
    for &b in &[false, true] {
        for a in path!([And] b) {
            println!("{:?}", a);
        }
        println!("");
    }
}

This prints:

(false, false)
(false, true)
(true, false)

(true, true)

Example: AND-NOT

You can chain path sub-types together:

use path_iter::*;

fn main() {
    for a in path!([And] [Not] true) {
        println!("{:?}", a);
    }
}

Example: Partial Application

Partial application is a technique where a function reduces to another function when calling it with fewer arguments than the signature.

For example, And(true) reduces to Idb.

use path_iter::*;

fn main() {
   for a in path!([And(true)] true) {
        println!("{:?}", a);
    }
}

This should not be confused with function currying, which is extensionally equal to partial application, but captures the underlying function in a closure.

The path! macro expands to partial application automatically, but it is very limited. Outside the macro path! or for complex cases, one must use PApp::papp.

Example: AND 3

The standard notation for composing paths is not very friendly with Rust macros. Therefore, one can use a single bracket [] with functions separated by commas:

use path_iter::*;

fn main() {
    for a in path!([((And, And), (And, And)), (And, And), And] true) {
        println!("{:?}", a);
    }
}