Abstracting Definitional Interpreters

by   David Darais, et al.

In this functional pearl, we examine the use of definitional interpreters as a basis for abstract interpretation of higher-order programming languages. As it turns out, definitional interpreters, especially those written in monadic style, can provide a nice basis for a wide variety of collecting semantics, abstract interpretations, symbolic executions, and their intermixings. But the real insight of this story is a replaying of an insight from Reynold's landmark paper, Definitional Interpreters for Higher-Order Programming Languages, in which he observes definitional interpreters enable the defined-language to inherit properties of the defining-language. We show the same holds true for definitional abstract interpreters. Remarkably, we observe that abstract definitional interpreters can inherit the so-called "pushdown control flow" property, wherein function calls and returns are precisely matched in the abstract semantics, simply by virtue of the function call mechanism of the defining-language. The first approaches to achieve this property for higher-order languages appeared within the last ten years, and have since been the subject of many papers. These approaches start from a state-machine semantics and uniformly involve significant technical engineering to recover the precision of pushdown control flow. In contrast, starting from a definitional interpreter, the pushdown control flow property is inherent in the meta-language and requires no further technical mechanism to achieve.


page 1

page 2

page 3

page 4


Topos Semantics for a Higher-Order Temporal Logic of Actions

TLA is a popular temporal logic for writing stuttering-invariant specifi...

Game Semantics: Easy as Pi

Game semantics has proven to be a robust method to give compositional se...

Skeletal Semantics and their Interpretations

Many meta-languages have been proposed for writing rule-based operationa...

Automating the Functional Correspondence between Higher-Order Evaluators and Abstract Machines

The functional correspondence is a manual derivation technique transform...

Pushdown flow analysis with abstract garbage collection

In the static analysis of functional programs, pushdown flow analysis an...

Dynamic Symbolic Execution of Higher-Order Functions

The effectiveness of concolic testing deteriorates as the size of progra...

A Domain-Theoretic Approach to Statistical Programming Languages

We give a domain-theoretic semantics to a statistical programming langua...

Code Repositories


A Haskell transliteration of the paper Abstracting Definitional Interpreters

view repo