Expand description
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);
}
}
Macros
Structs
false
.[T] U
(left) or [T] [V] ...
(right).[f] [g] a
.true
.Enums
Traits
Functions
f
and g
.