Static analysis of multi-staged programs via unstaging translation

Abstract

Static analysis of multi-staged programs is challenging because the basic assumption of conventional static analysis no longer holds: the program text itself is no longer a fixed static entity, but rather a dynamically constructed value. This article presents a semanticpreserving translation of multi-staged call-by-value programs into unstaged programs and a static analysis framework based on this translation. The translation is semantic-preserving in that every small-step reduction of a multi-staged program is simulated by the evaluation of its unstaged version. Thanks to this translation we can analyze multi-staged programs with existing static analysis techniques that have been developed for conventional unstaged programs: we first apply the unstaging translation, then we apply conventional static analysis to the unstaged version, and finally we cast the analysis results back in terms of the original staged program. Our translation handles staging constructs that have been evolved to be useful in practice (typified in Lisp's quasi-quotation): open code as values, unrestricted operations on references and intentional variable-capturing substitutions. This article omits references for which we refer the reader to our companion technical report.

A practical theory of language-integrated query

“…Here we generalise T-LINQ to support a form of open quotation, and we show how this form may be simulated by closed quotation. Choi et al (2011) give a similar result. Our formalisation of open quotation is not as powerful as that found in systems such as MetaML or Ur, but the translation is suggestive of why closed quotation may be adequate for dealing with cases (such as composition of queries or dynamic generation of queries) that one may previously have thought required open quotation.…”

Optimization by runtime specialization for sparse matrix-vector multiplication

“…The area of program specialization -also called code generation, partial evaluation, or staging -has been quite heavily studied, especially with respect to language features, such as type-checking, that promote simplicity and safety of specialization [13,30,32]. Work in this area specifically addressing highperformance for realistic applications includes work on marshalling [7,14] and on code-optimizing transformations [15].…”

“…Request permissions from permissions@acm.org. GPCE, '14, September 15-16, 2014 Program specialization is a well-studied area [13,30,32]. Research has produced many examples of programs, in many problem domains, that have been optimized by specialization.…”

Effective quotation

“…Reasoning about multi-stage programs is a well-known hard problem. Choi et al [6] present translations from staged to unstaged programs that employ similar ideas to our translations, particularly hoisting pl-code out of dbcode in the − translation. Inoue and Taha [18] present techniques for reasoning about call-by-value multi-stage programs.…”