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.

path_type

Syntax sugar for the type of a path sub-type.

Structs

Add

Addition.

AddRangeIter

Iterates over numbers that adds up to some range.

And

Logical AND.

Eqb

Logical EQ.

False1

A boolean unary function that returns false.

Fstb

Returns the first argument of a boolean binary function.

Id

Identity function.

Idb

Returns the argument of a boolean unary function.

Imply

Logical IMPLY.

Neg

Negation.

Not

Logical NOT.

Or

Logical OR.

Path

Stores a path sub-type with either [T] U (left) or [T] [V] ... (right).

PathIter

Iterates over a path composition, e.g. [f] [g] a.

ProductIter

Iterates over a product of two iterator generators.

Sndb

Returns the second argument of a boolean binary function.

Square

Square.

SquareRangeIter

Iterates over numbers that squares up to some range.

True1

A boolean unary function that returns true.

Xor

Logical XOR.

Enums

Either

Used to lift iterator generators into a sum type.

EitherIter

Iterates over two the sum type of two iterators.

Empty

A type that is impossible to construct.

Traits

HigherIntoIterator

Implemented by iterator generators.

PApp

Implemented for partial application.

Functions

item

Constructs an item.

path

Construct a path composition.

pullback

Gets the pullback of two maps f and g.

Type Definitions

Item

Used to make end of path disambiguous from path composition.

PathComp

Represents a path composition.

PathEnd

Represents a terminal path [T] U.