Delving Simplicity Part Ⅲ: Building Data Types

The language's foundation lies in its type system and a core set of computational combinators introduced earlier, raising questions about its practicality for real-world applications. By starting with the Boolean type and using computational combinators, Boolean logic operators such as and, or, not, and xor can be constructed, demonstrating Simplicity's capability to handle logical operations.

Further advancements include the development of bit adders like the half-adder and full-adder, which are essential for arithmetic operations in digital logic. These adders showcase how Simplicity can perform arithmetic by manipulating bits through combinations of logical operations. The language's ability to create vectors and iterate or fold functions over these vectors introduces a method for operating on fixed-length sequences of data, enabling more complex data manipulations.

The concept of multi-bit words extends the utility of Simplicity into handling integers of arbitrary size, facilitating the definition of arithmetic operations on larger scales, such as addition and subtraction across multi-bit integers. This capability is critical for implementing cryptographic functions within the language, exemplified by the recursive definition of SHA-256's block compression function. The formal verification of such cryptographic implementations within Simplicity assures their correctness.

Option types and variable length buffers introduce flexibility in handling data that may not conform to strict size constraints, allowing for operations on potentially undefined values and collections of varying sizes, respectively. These constructs enable the creation of more adaptable and robust programs.

Despite the initial impression of Simplicity's limited expressiveness due to its minimalistic design, the language demonstrates considerable depth and flexibility. It supports the development of practical functionalities, including cryptographic operations and complex data structures, within its constrained system. The use of higher-level languages, such as SimplicityHL, is anticipated to simplify the programming process, translating more intuitive code into Simplicity's low-level expressions. The introduction of jets, optimized implementations for common functions, signifies an important optimization strategy, maintaining the language's adherence to formal specifications while improving efficiency.

As the discussion transitions towards handling side-effects and interacting with transaction data, it becomes evident that Simplicity is designed to evolve beyond pure computations. This evolution addresses the practical requirements of blockchain programming, indicating a comprehensive approach to developing secure, efficient, and verifiable smart contracts and blockchain applications.