{"responseHeader":{"status":0,"QTime":6,"params":{"q":"{!q.op=AND}id:\"102026\"","hl":"true","hl.simple.post":"","hl.fragsize":"5000","fq":"!embargo_tdt:[NOW TO *]","hl.fl":"ocr_t","hl.method":"unified","wt":"json","hl.simple.pre":""}},"response":{"numFound":1,"start":0,"docs":[{"file_name_t":"Mishra-Static_Inference.pdf","thumb_s":"/a3/66/a3666e8d6f2bef371469608cf0b7589f4984b4e4.jpg","oldid_t":"compsci 10139","setname_s":"ir_computersa","restricted_i":0,"format_t":"application/pdf","modified_tdt":"2016-05-25T00:00:00Z","file_s":"/aa/0a/aa0a9257c20fdd40011069565b467197af817b8d.pdf","title_t":"Page 52","ocr_t":"40 2.3.4 Collecting Interpretation Finally, we compare our constructions with those of [14] and [49]. In Section 2.1 some specific differences were pointed out. We note that our con struction is developed in a nonstandard fashion and limited to a restricted set of abstraction maps. Traditionally abstract interpretations of a standard interpretation are formulated as abstractions of the \"collecting interpretation\" - the natural lifting of the standard semantics to the powerdomain (or powerset) of the underlying domain (or set). The traditional setting has the advantage that interpretations can easily be compared (see Cousots' lattice of abstract interpretations). Attempting to develop a \"collecting interpretation\" for applicative programs involves carrying out a general powerdomain construction over arbitrary domains. In [48] it was suggested that the Plotkin powerdomain yields an appropriate collecting semantics for flat domains. However, the Plotkin powerdomain is restricted to modelling bounded indeterminacy [4] which implies that only selected subsets (convex) of the underlying domain are permissible and that in particular all infinite sets contain .1... This lack of expressive power sharply constrains the class of inference schemes that can be described in such a framework. For example, even simple inference schemes that involve representing infinite sets of values in the original domain by single values in the abstract domain (e .g., analysing integer valued applicative programs on the four point domain {POS, NEG. ZERO . ...L}) cannot be expressed in this framework. Hence the Plotkin powerdomain is not suitable for specifying the collecting semantics. In [49], the inadequacy of the Plotkin powerdomain was recognized. and the collecting semantics for a restricted class of domains (domains with finite ascending chains - fdcpos) developed. The construction remedied the problems with the inadequate express1ve power of the Plotkin construction as described above. However, the identification of sets with their convex closure carried over","id":102026,"created_tdt":"2016-05-25T00:00:00Z","parent_i":102129,"_version_":1679953745247469571}]},"highlighting":{"102026":{"ocr_t":[]}}}