Safety Analysis versus Type Inference

Abstract

Safety analysis is an algorithm for determining if a term in the untyped lambda calculus with constants is safe, i.e., if it does not cause an error during evaluation. This ambition is also shared by algorithms for type inference. Safety analysis and type inference are based on rather different perspectives, however. Safety analysis is based on closure analysis, whereas type inference attempts to assign a type to all subterms.In this paper we prove that safety analysis is sound, relative to both a strict and a lazy operational semantics, and superior to type inference, in the sense that it accepts strictly more safe lambda terms.The latter result may indicate the relative potentials of static program analyses based on respectively closure analysis and type inference.

Type safety analysis for Dart

“…We express our analysis using set constraints on a collection of type variables [15,19]. For a given program component to be analyzed, we allocate a type variable for each program variable x, denoted x , and similarly for each non-variable expression e and class field or method N.f and N.m, respectively.…”

“…As can be seen, we use only simple subset constraints and conditional constraints (X ⊆ Y ∩ Z represents two constraints, X ⊆ Y and X ⊆ Z). The least solution to the constraints can be found using standard fixpoint algorithms [15,19,25].…”

“…The purpose of our program analysis is not to automatically add type annotations to programs, but to infer the dataflow through non-annotated code and statically check for potential type errors. Using the terminology of Palsberg and Schwartzbach [19], this is a safety analysis, not a type inference. We believe such an analysis may be useful for programmers who wish to gain confidence in their code, in the spirit of gradual typing [21].…”

Lightweight closure conversion

“…currence [Sestoft 1991], α-converting a program so that each binding occurrence is unique, and using the binding variable as a token [Palsberg and Schwartzbach 1995]. In both cited works, only occurrences of procedures are specified.…”

“…Ayers [1993] used similar techniques to compute a highly optimized version of 0CFA. Palsberg and Schwartzbach [1995] use a constraint-based closure analysis similar to ours to support safety analysis. Stefanescu and Zhou [1994] have formulated a generalized closure analysis framework using abstract interpretation that can handle both mono-and polyvariance.…”