Implementing a Simple Unification Algorithm in Rust

This challenge involves implementing a basic unification algorithm in Rust. Unification is a fundamental operation in logic programming and symbolic computation, used to determine if two terms can be made equal by substituting variables. This exercise will help you understand recursive data structures, pattern matching, and mutable state management in Rust.

Problem Description

Your task is to write a Rust function unify that takes two terms and attempts to unify them. Unification should return a mapping of variable names to terms if successful, indicating how the variables need to be substituted to make the terms equal. If unification fails, it should indicate failure.

The terms can be of the following types:

1. Variables: Represented by a string (e.g., "x", "y").
2. Constants: Represented by a string (e.g., "a", "b", "foo").
3. Structures: Consist of a functor (a string, e.g., "cons", "node") and a list of arguments, where each argument is itself a term.

The unification process should adhere to the following rules:

• If two variables are the same, they unify.
• If a variable is different from another variable, they unify, and the first variable is bound to the second.
• If a variable is unified with a constant or a structure, the variable is bound to that constant or structure.
• If a constant is unified with a different constant, unification fails.
• If a structure is unified with a different functor or a different number of arguments, unification fails.
• If two structures have the same functor and the same number of arguments, their respective arguments are unified recursively.
• Occurs Check: If a variable is being unified with a term that contains that same variable, unification fails (to prevent infinite structures).

The function should return an Option<HashMap<String, Term>>, where Some(map) indicates successful unification and map contains the bindings, and None indicates failure. The HashMap keys will be variable names, and values will be the terms they are bound to.

You'll need to define your own Term enum to represent variables, constants, and structures.

Examples

Example 1:

Term 1: Variable("x")
Term 2: Constant("a")

Output: Some({"x": Constant("a")})
Explanation: The variable "x" is bound to the constant "a".

Example 2:

Term 1: Structure("f", vec![Variable("x"), Constant("b")])
Term 2: Structure("f", vec![Constant("a"), Variable("y")])

Output: Some({"x": Constant("a"), "y": Constant("b")})
Explanation: First, "x" is unified with "a", so x = a. Then, "b" is unified with "y", so y = b. The functor "f" and number of arguments match.

Example 3:

Term 1: Variable("x")
Term 2: Structure("g", vec![Variable("x")])

Output: None
Explanation: This is an "occurs check" failure. The variable "x" is being unified with a term that contains "x".

Example 4:

Term 1: Structure("h", vec![Constant("c")])
Term 2: Structure("h", vec![Constant("d")])

Output: None
Explanation: The arguments Constant("c") and Constant("d") do not unify.

Example 5:

Term 1: Variable("z")
Term 2: Variable("z")

Output: Some({})
Explanation: Two identical variables unify without any new bindings needed.

Example 6:

Term 1: Structure("foo", vec![Variable("a")])
Term 2: Structure("bar", vec![Constant("b")])

Output: None
Explanation: The functors "foo" and "bar" do not match.

Constraints

• The maximum depth of nested structures is not explicitly limited, but you should aim for a solution that handles reasonable recursion.
• Variable names and functor names are alphanumeric strings.
• The number of arguments in a structure is at least 0.
• Performance should be reasonable for typical use cases, avoiding exponential complexity if possible through efficient variable lookup and substitution.

Notes

• You will need to define a Term enum. Consider using #[derive(Debug, Clone, PartialEq, Eq)] for convenience.
• When unifying a variable with another term, you will need to manage a mapping of variable names to their bound terms. This mapping can grow as unification proceeds.
• The HashMap in the output should contain only the new bindings established during this specific unify call. If a variable is already bound, and the unification is consistent with that binding, no new entry for that variable should be added. However, if a variable is unbound and gets bound, it should be added.
• The occurs check is crucial. You'll need a way to detect if a variable appears within a term being unified with it.
• Consider how to handle substitutions: if you encounter a variable that is already bound, you should unify with its bound value.