Logic Primitives Library

This project is an implementation of a library for mathematical and logical operations using combinatory logic. It provides a set of templates and utilities for constructing complex functions using recursive, combinatorial, and functional programming principles.

Features

• Combinators: Implements standard combinators such as Z, N, S, U, and R for building mathematical logic.
• Recursive Formulas: Provides recursive definitions for arithmetic operations like addition, subtraction, multiplication, division, and modulus.
• Fast Arithmetic Operations: Includes optimized (fast) versions of operations for improved runtime performance of more complex operations.
• Boolean Logic: Constructs logical operations such as cast to boolean, negation, boolean folds, and all type of comparisons.
• Prime Number Utilities:
  • Check if a number is prime.
  • Count primes.
  • Retrieve the nth prime.
• Stack Implementation:
  • Create stacks.
  • Append elements.
  • Peek at the top element.
  • Pop elements.
  • Check if the stack is empty.

Code Structure

Core Types

• Natural: A type alias for int, representing natural numbers.

Combinators

• Z: Always returns 0.
• N: Increments a value by 1.
• U<K, N>: Projection combinator for selecting the K-th argument from N arguments.
• S<G, Fs...>: Super combinator for applying functions in sequence.
• R<F, G>: Recursive combinator for defining functions with base and recursive cases.

Recursive Functions

• Arithmetic:
  • add: Addition.
  • sub: Subtraction.
  • mul: Multiplication.
  • power: Exponentiation.
• Comparisons:
  • eq: Equality.
  • leq: Less than or equal.
  • geq: Greater than or equal.
  • greater: Greater than.
  • less: Less than.
• Division and Modulus:
  • divide: Integer division.
  • mod: Modulus.

Boolean Logic

• return_yes and return_no: Boolean constants.
• negate: Logical NOT.
• or_fold and and_fold: Logical OR and AND.

Prime Utilities

• is_complex: Check if a number is complex.
• is_prime: Check if a number is prime.
• prime_count: Count primes up to a given number.
• get_prime_by_index: Get the nth prime number.

Stack Interface

• create_stack: Create an empty stack.
• append: Append elements to a stack.
• peek: Retrieve the top element of a stack.
• pop: Remove the top element of a stack.
• empty: Check if the stack is empty.

Usage

Basic Arithmetic

apply<add>(3, 4); // Returns 7

Prime Checking

apply<fast::is_prime>(7); // Returns true

Stack Operations

Natural stack = apply<create_stack>();
stack = apply<append>(stack, 5);
Natural top = apply<peek>(stack); // Returns 5
stack = apply<pop>(stack);
bool stack_is_empty = apply<empty>(stack); // Returns true

Build

Clone the repository:

git clone git@github.com:IPodtsepko/logic-primitives.git
cd logic-primitives

Install dependencies (e.g., GoogleTest as a submodule):

git submodule update --init --recursive

Build the project using CMake:

mkdir build && cd build
cmake ..
make

Run tests:

./tests