[−][src]Crate path_iter
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
path | Syntax sugar for a path sub-type. |
Structs
And | Logical AND. |
Comp | Function composition. |
Eqb | Logical EQ. |
False1 | A boolean unary function that returns |
Fstb | Returns the first argument of a boolean binary function. |
Idb | Returns the argument of a boolean unary function. |
Item | Used to wrap value types to avoid impl collisions. |
Not | Logical NOT. |
Or | Logical OR. |
Path | Stores a path sub-type |
PathIter | Iterates over a path composition, e.g. |
ProductIter | Iterates over a product of two iterator generators. |
Sndb | Returns the second argument of a boolean binary function. |
True1 | A boolean unary function that returns |
Xor | Logical XOR. |
Enums
Either | Used to lift iterator generators into a sum type. |
EitherIter | Iterates over two the sum type of two iterators. |
Traits
HigherIntoIterator | Implemented by iterator generators. |
PApp | Implemented for partial application. |