1. The K summarizer

[PL, K] Last update: 8/4/2022, 3:15:07 PM

The vision of the current K framework is that it is a unifying formal semantics framework for all programming languages. Given any programming language L, we can define its formal semantics in K, from which all the language tools (like a parser, an interpreter, a deductive verifier, a model checker, etc.) of L will be automatically generated. This way, we only need to implement language tools generically, once and for all, and then instantiate them by a formal programming language semantics.

The K Summarizer pushes the above idea even further. It allows us to extract from a given language semantics LL and a given program PP in that language, a new semantics LPL_P that is the K semantics of the program PP in language LL. In other words, LPL_P is how we would implement the same program PP directly in K if we didn't have LL. The key idea is to summarize statically all possible known (symbolic) behaviors of program PP and leave for runtime only what cannot be inferred statically. The result of that is a control-flow graph of the program PP, where all the basic blocks (i.e., straight-line executions/code) are pre-computed and decisions only need to be made at certain choice points such as conditional statements, while-loops, etc.

Compared to the original semantics of LL, the new semantics LPL_P is much simpler. Indeed, the entire C semantics can have thousands of semantic rules but the semantics of the following C program sum.c that computes the sum from 1 to the input n

while(n >= 0) {
  s += n;

can be implemented using the following two rules:

    rule <k> while(n >= 0) { s += n; n-- } => .K </k>
         <state> s |-> S,
                 n |-> N
      requires  notBool N >=Int 0
    rule <k> while(n >= 0) { s += n; n-- } => while(n >= 0) { s += n; n-- } </k>
         <state> s |-> (S => S +Int N),
                 n |-> (N => N -Int 1)
      requires  N >=Int 0

If we only care about the </state> cell, we can simplify the configurations even further and have the entire semantics of sum.c implemented in one rule:

rule <n, sum> => <n -Int 1, sum +Int n> requires n >Int 0

At a high level, the new semantics LPL_P implements the control-flow graph of PP where each edge is an all-path reachability rule that summarizes a basic block. When branching occurs, we may split the state on the branch condition and continue execution from there.

This generalizes what compilers do, and also the classic "partial evaluation" approach, where a compiler is seen as a partial evaluation of an interpreter with the program (but not program input). The critical insight in our context is to do this at the level of a formal semantics, instead of a particular ad-hoc implementation of an interpreter.

The K summarize is currently under active development. At this point it is an umbrella project for three different things (all important):

  1. A web interface for the K prover and for K symbolic execution that allows visualizing K executions and manipulating them.
  2. A new interactive approach to using the K prover, where we expose a command-line tool that brings us some light interactivity to the K prover.
  3. The semantics-based compilation (SBC) project [link], which has the goal that we stated above to take a programming language LL, a program PP in that language, and produce a new programming language LPL_P for that one program.

For anyone who wants to learn more about the K summarize we recommend the 3-hour K summarizer workshop recording where we covered the history, the current status, the theoretical foundation, and the future plans about the project.


[video] The 3-hour K summarizer workshop recording

[related project] Semantic-based compilation


Everett Hildenbrandt [github]

Nishant Rodrigues (nishant2@illinois.edu)

Xiaohong Chen (xc3@illinois.edu)

2. Semantics-based compilation

[PL, Logic, K] Last update: 8/3/2022, 8:21:37 PM

(The following project description is based on an old article Open Problems and Challenges in 2017. See The K Summarizer for the latest development of the project.)

An ideal language framework should allow us to generate compilers from language definitions. Specifically, we hope that soon the K framework will have the capability to take a language semantics and a program in that language, and generate an efficient binary for the program. Conceptually, K already provides the ingredients needed for such a semantics-based compiler. One way to approach the problem is to use symbolic execution on all non-recursive non-iterative program fragments and calculate the mathematical summary of the fragment as a (potentially large) K rule; the left-hand side of that rule will contain the fragment. For example, consider the trivial IMP language and a while loop whose body contains no other while loops. Then we can conceptually replace the while loop body with a new statement, say stmt17093, whose semantics is given with a K rule that symbolically accumulates the semantics of the individual statements that composed stmt17093. We can do the same for all non-loop fragments of code, until we eventually obtain a program containing only while statements whose bodies are special statement constants like stmt17093, each with its own K semantics.

Once the above is achieved, there are two more important components left. One is to translate the while statements into jump statements in the backend language, say LLVM. In the long term, this should be inferred automatically from the K semantics of the while statement. In the short term, we can get the user involved by asking them to provide a translation for the while loop (yes, this is not nice, but hey, getting a compiler for your language is a big deal). The other component is to translate the K rules for statements like stmt17093 into efficient target language code. We believe this is an orthogonal issue, which we want to have efficiently implemented in K anyway, as part of our effort on providing a fast execution engine.


[related project] K summarizer


Everett Hildenbrandt [github]

Nishant Rodrigues (nishant2@illinois.edu)

Xiaohong Chen (xc3@illinois.edu)

3. Specifying medical guidelines in K

[PL, K] Last update: 8/5/2022, 1:21:45 AM

MediK is a K-based domain-specific language (DSL) for expressing medical guidelines as concurrently executing finite state machines (FSMs). Hospitals and medical associations often publish flowchart based Clinical best-Practice Guidelines to codify standard treatment for conditions such as Cardiac Arrest. In MediK, we systematically expresses these guidelines, along with other relevant data, such as the state of the patient's organ systems, and instructions to/from Healthcare Professionals, as FSMs that interact via passing events. Since MediK guidelines are executable, they can be used in a hospital setting as correct-by-construction guidance systems that assist Healthcare Professionals. For example, consider this simple model of a patient's cardiovascular system, and some treatment:

machine CardiovascularSystem {
  init state CardiovascularLoop {
    // Code to execute on entry
    entry(heartRateSensor) {
      // Read sensor data
      if (heartRateSensor.rate < 10) {
        // declare an emergency
        broadcast CardioEmergency;
      goto CardiovascularLoop;
machine Treatment receives CardioEmergency {
  on CardioEmergency do {
    // handle emergency
interface HeartRateSensor {
  var rate;

In the example above, the CardiovascularSystem FSM starts in the state CardiovascularLoop, and uses a reference to a HeartRateSensor FSM to obtain the patient's heart rate. If the obtained heart rate is too low, the CardiovascularSystem FSM broadcasts a CardioEmergency event. Note that the heart rate sensor itself is not implemented in MediK. In medical guidance systems, it is common to interact with various external agents such as sensors and databases. We handle such actors by treating them as FSMs with transition systems external to MediK. In our example, the HeartRateSensor is declared as interface instead of a machine, signifying that the transition system is implemented elsewhere. This allows us to use the existing event passing mechanism to interact with external components.

While K suppports I/O through "stdin" and "stdout" attributes on cells, the I/O mechanism itself is synchronous, as reading from or writing to an I/O cell is blocking, i.e., no other rule can apply until the read or write is complete. Synchronous I/O can be a limitation for languages like MediK, where rules responsible for execution must continue to apply while waiting for I/O to be completed. This necessitates the need for a generic asynchronous I/O mechanism in K that allows rules for I/O to not block the application of other rules.


[project] MediK [link]


Manasvi Saxena [github] (msaxena2@illinois.edu)

4. Modeling hybrid systems in K

[Logic, K] Last update: 8/2/2022, 3:10:56 PM

Hybrid systems are dynamical systems that exhibit both discrete and continuous dynamic behavior. Such systems can both flow (described using differential equations) and jump (often described using discrete automata). Cyber-Physical Systems (CPS), or systems that combine cyber capabilities (computation, communication and control) with physical capabilities are hybrid systems are examples of such systems. In recent years, CPS are increasingly being employed to tackle challenges in domains like medicine, transportation and energy. The use of CPS in safety-critical applications, how- ever, makes their correctness and reliability extremely important.

Research Direction: Modeling Hybrid Automata in Matching Logic

The framework of Hybrid Automata (HA) is widely used to model CPS. The semantics of HA are described in this seminal paper by Henzinger. The research question is: can we capture the semantics of Hybrid Automata in Matching Logic? Such an embedding would be useful, as it would allow us to use the Matching Logic theorem proving infrastructure to reason about CPS. This technical report describes both the problem and some preliminary work we've done towards addressing it.

Research Direction: Embedding Differential Dynamic Logic in Matching Logic

Differential Dynamic Logic is a variant of First Order Dynamic Logic over the domain of Reals that supports specifying and reasoning about hybrid systems. The research question is: can we define an embedding of Differential Dynamic Logic into Matching Logic? dL has specific proof rules for handling differential equations and invariants used to specify continuous components of hybrid systems. Is the proof system of matching logic sufficient to handle such proof rules?


[paper] Formal semantics of hybrid automata TechRep, 2020. [pdf]


Manasvi Saxena (msaxena2@illinois.edu)

5. Intermediate verification languages (IVL) in K

[PL, K] Last update: 8/18/2022, 1:28:52 AM

Many programming languages provide verification tools via translation to the Boogie [link] intermediate verification language (IVL). Boogie provides powerful and efficient tools that allow the development of high-quality, easy-to-use annotation-based verifiers, and allows for modular verification of large software.

However, the translation from the target programming language to Boogie is essentially another compiler for the language, and, besides the additional manpower needed for developing this tranlation, it also introduces scope for divergence between the actual language behaviour, severely reducing the confidence in their correctness.

We believe that a solution to this extra complexity introduced by the translation is to use a semantics-based approach to language development. More specifically, we define the formal semantics of Boogie in K and let K fulfil many of the use cases of Boogie within this semantic-based approach. To achieve that, we need to define the following Boogie-powered features in K:

  • loop invariants and function contracts specified in the programming language's concrete syntax,
  • quantification over expressions,
  • ghost variables,
  • clear and easy-to-read error messages.

The goal of the project is a formal semantics of Boogie in K that supports all the above features.


[project] Boogie semantics in K [github]


Nishant Rodrigues (nishantjr@gmail.com)