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Program analysis

Program analysis allows us to ask questions about and analyze the behavior of computer programs. Analyzing this behavior allows us to (eventually) answer subtle but powerful questions such as, will this use more than 8 GB of RAM? Does this present a user interface? We perform program analysis statically—that is, without executing the program.

We’re able to compute the following end results using evaluation:

  1. Import graph: graph representing all dependencies (imports, requires, etc.)
  2. Call graph: a control flow graph that represents calling relationships (ie., how one particular function calls other functions). This information is often vital for debugging purposes and determining where code is failing.
  3. Control flow graph: representation of all paths that might be traversed through a program during its execution.

Abstract interpretation

To do program analysis, we implement an approach based on the paper Abstracting Definitional Interpreters, which we've extended to work with our à la carte representation of syntaxes. This allows us to build a library of interpreters that do different things, but are written with the same evaluation semantics. This approach offers several advantages; we can define one evaluator and get different behaviors out of it (via type-directed polymorphism).

We employ three types of interpretation: concrete semantics, abstract semantics and type-checking.

  1. Under concrete semantics, we are precise; we only compute the result of code that is called. This allows us to see exactly what happens when we run our program. For example, if we expect to return a boolean value and our results differ, we’ll throw an error (which is sub-optimal because in a language like Ruby, a lot of objects that are not booleans could be used as booleans).
  2. Under abstract semantics, we are exhaustive; we compute the result of all possible permutations. This is how we compute call graphs. Under abstract semantics, we don’t know if something is going to be true or false, so we take both branches—non-deterministically producing both using the <|> operator which represents choice, building a union of possibilities.
  3. Under type-checking semantics, we verify that the type of a syntactic construct (ex., an object of type Int) matches what is expected when it is used. This helps us check type errors, emulating compile-time static type checking.

Evaluation

The Evaluatable class defines the necessary interface for a term to be evaluated. While a default definition of eval is given, instances with computational content must implement eval to perform their small-step operational semantics. Evaluation gives us a way to capture what it means to interpret the syntax data types we create using the Assignment stage. The evaluation algebra also handles each syntax without caring about any language-specific implementation. We do this by cascading polymorphic functions using the Evaluatable type class.

We have yet to finish implementing Evaluatable instances for the various à la carte syntaxes. Doing so requires knowledge of the type and value evaluation semantics of a particular syntax and familiarity with the functions for interacting with the environment and store.

Implementing Evaluatable instances

The following is a brief guide to working with the definitional interpreters and implementing instances of Evaluatable for the various pieces of syntax. Semantil.Util defines a series of language-specific wrapper functions for working in ghci to do evaluation.

Helpers:

  • parseFile: parses one file.
  • evaluateLanguageProject: takes a list of files and evaluates them usually under concrete semantics.
  • callGraphLanguageProject: uses the same mechanism for evaluating, but uses abstract semantics.
  • typeCheckLanguageFile: allows us to evaluate under type checking semantics.

Creating good abstractions

When adding Evaluatable instances, we may notice that certain language-specific syntaxes share semantics sufficiently enough to be consolidated into a language-agnostic data type (and resultantly, have one Evaluatable instance). Other times—it may be the opposite case where there is not enough overlap in evaluation semantics and therefore requires decoupling. Reasoning through the right abstractions is a big part of determining how to write these Evaluatable instances.

Effects

To perform these computations, we need effects. An effect is something a piece of code does which isn’t strictly encapsulated in its return value. Outside of taking inputs and returning outputs, programs must capture state in memory by read or write, throw exceptions, fail to terminate, or terminate non-deterministically, etc. These outcomes are known as effects. An an example, consider the JS function:

function square(x) {
  return x * x;
}

This is pure because it performs no effects, whereas the similar function:

  console.log("squaring x: " + x);
  return x * x;
}

computes the same result value but additionally performs an effect (logging). Effects provide convenient access to powerful and efficient capabilities of the machine such as interrupts, stateful memory, the file system, and the monitor.

We compute effects non-deterministically.

Potential use-cases

  • Dead code analysis: reduce potential surface area (security vulnerabilities). Less code to maintain is always a good thing. Good examples in most IDEs.
  • Symbolic - allows us to do symbolic execution. https://prepack.io/
  • Caching - a way to guarantee that an analysis will terminate. allows us to write a type checker. abstracting variables to their types. Instead of potentially infinite series of integers, you can represent as Int (finitization of values)
  • Collecting - allows us to have greater precision in other analyses (more useful internally)
  • Tracing and reachable state - useful for debugging (it's verbose).
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