What is "K"?
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If you’ve been around Pi Squared for a while, or even read any of our blog posts, there’s one thing you might be curious about, which is K. It’s a recurring topic, and for good reason—K is at the heart of what we do. In this guide, we’ll break it down for you.
The K framework is a semantics-based approach to language design and implementation. Instead of manually building tools like interpreters or verifiers for each programming language, K allows developers to define a language formally and extract a full set of tools automatically.
As illustrated below in Figure 1, with just a formal specification of a language’s syntax and semantics, K can produce a parser, an interpreter, and a symbolic deductive verifier, among other tools. This means that once a language is defined in K, you don’t need to write separate execution tools—it’s all derived from the semantics.
At Pi Squared we depend on K’s abilities to achieve the following:
To define any programming language formally and generate correct-by-construction interpreters.
To automatically generate efficient execution models for blockchain-based computation.
To ensure that smart contracts and blockchain applications behave as expected—no hidden compiler bugs, no unforeseen behavior.
This is the foundation for making blockchain programming truly verifiable, correct, and performant.
In K, a definition of a language consists of three main components:
Concrete syntax: A conventional BNF grammar that defines the structure of valid programs in the language.
Execution state (configuration): A representation of the state maintained by a program during execution.
Operational semantics: A set of rewrite rules that define how the program's state changes over time.
K uses rewrite rules to define execution in a precise way. A rewrite rule takes an initial configuration and transforms it into a new configuration based on predefined logic, ensuring that program execution follows the formal semantics.
A core feature of K is its ability to generate a language-agnostic interpreter. Given a K definition of a language, K automatically generates an interpreter that can execute any program written in that language.
Initially, K was designed to interpret programs using a language-generic tool, which essentially would run an interpreter inside another interpreter. However, generic interpretation can introduce additional overhead compared to language-specific execution.
As such, the current version of K builds on LLVM-K, which leverages LLVM IR to compile K into efficient native code. By generating a native interpreter, LLVM-K eliminates the extra layer of interpretation, significantly improving performance.
K is scalable and has been used to formalize multiple real-world programming languages, including , , , , , , and , making it suitable for both research and commercial applications.
