## A Semantic Model of Reference Counting and its Abstraction (1986)

Venue: | In Proceedings ACM Conference on Lisp and Functional Programming |

Citations: | 66 - 0 self |

### BibTeX

@INPROCEEDINGS{Hudak86asemantic,

author = {Paul Hudak},

title = {A Semantic Model of Reference Counting and its Abstraction},

booktitle = {In Proceedings ACM Conference on Lisp and Functional Programming},

year = {1986},

pages = {351--363}

}

### Years of Citing Articles

### OpenURL

### Abstract

Interpretation of Reference Counting The semantics presented thus far is exact, and thus evaluating a particular reference count may not terminate, any more than a program in the standard semantics would. For use by a compiler we must choose a suitable abstraction (i.e., approximation) that will guarantee termination yet still provide useful information about the true reference counts. For us a suitable abstraction is one in which the inferred reference count is at least as great as the true one; i.e., we wish to err on the side of thinking there are more pointers to an object than there actually are. In this section we methodically develop such an abstraction in which: (1) the base domains are abstracted to powersets of finite approximations, (2) the primitive functions are abstracted similarly, (3) an abstract interpretation is thus induced on R p and R, and finally (4) a collecting interpretation of expressions is developed. 4.1 Preliminaries To set up things to come, we first gi...

### Citations

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Abstract interpretation: A unified lattice model for static analysis of programs by construction or approximation of fixpoints
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- 1977
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474 |
Denotational Semantics: The Scott-Strachey Approach to Programming Language Theory
- STOY
- 1977
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Citation Context ...d variable environment with no store suffices. 1 That is, (strictf) is a function just like f but that returns ? if applied to any argument that is ?. It is similar to Stoy's use of the same function =-=[12]-=-. 2 These terms have traditionally been used to describe parameter-passing mechanisms in procedure calls, but here we attribute the term to the objects themselves. 3 To see that a reference count oper... |

103 |
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Citation Context ...ction that any element selected from the array must be considered as a likely candidate for the subarray. Reasoning about the structure of such composite objects is more difficult; Jones and Muchnick =-=[7] provide s-=-uch a treatment for lists. 6 The original "challenge" to solve this problem functionally and efficiently was posed in January 1985 by Daniel Friedman. 17 It is interesting to note that since... |

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Citation Context ...ing [6, 8, 11]. A special case of this situation arises in the construction of semantics-directed compilers, where knowing sharing properties of store arguments is crucial to generating efficient code=-=[10]. Other op-=-timizations include eliminating reference count operations determined to be extraneous, performing "compile-time garbage collection" of objects whose extent can be determined statically[1], ... |

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Shifting garbage collection overhead to compile time
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Citation Context ...e[10]. Other optimizations include eliminating reference count operations determined to be extraneous, performing "compile-time garbage collection" of objects whose extent can be determined =-=statically[1]-=-, stack-allocating instead of heap-allocating activation records, and reusing activation records in tail-recursive calls. In this paper we present a precise semantic model of reference counting for an... |

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The Aggregate Update Problem in Functional Programming Systems. Pages 300–313 of
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Citation Context ...anguages supporting aggregate data structures that are updated "functionally," where knowing that an aggregate has only one reference allows the update to be done destructively rather than b=-=y copying [6, 8, 11]-=-. A special case of this situation arises in the construction of semantics-directed compilers, where knowing sharing properties of store arguments is crucial to generating efficient code[10]. Other op... |

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An empirical study of list structure in Lisp
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Citation Context ...a reference count ever exceeds maxrc, it "jumps" to infinity and "sticks" there, never to decrease again. 3 Justification for using this domain comes from empirical studies (at lea=-=st of Lisp programs [2]-=-) that indicate that objects are generally not shared very much, so that choosing a suitably high value for maxrc will give fairly accurate results most of the time. As with Rc, Src is a flat domain. ... |

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Collecting interpretations of expressions
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- 1991
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Citation Context ..."collects" all possible values that each expression might have during program execution. 5 The general theory of such an interpretation is beyond the scope of this paper; more details may be=-= found in [5]-=-. For our purposes the following discussion suffices: We will write a recursive set equation for RC(lab) whose least fixpoint (i.e., smallest set) has the general 5 Our use of the term collecting inte... |

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The global storage needs of a subcomputation
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Citation Context ... can be inferred via abstract reference counting as described here, or by a more direct (but perhaps less general) analysis as described in [10]. It is also related to the pebbling games described in =-=[9]-=-. 8 Extensions There are several extensions to the analysis that should be straightforward, such as adding constants that may be pass-by-reference (i.e., that are initially allocated in the store), an... |

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Verifying the safe use of destructive operations in applicative programs
- Schwarz
- 1978
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Citation Context ...anguages supporting aggregate data structures that are updated "functionally," where knowing that an aggregate has only one reference allows the update to be done destructively rather than b=-=y copying [6, 8, 11]-=-. A special case of this situation arises in the construction of semantics-directed compilers, where knowing sharing properties of store arguments is crucial to generating efficient code[10]. Other op... |