J. Hannay. Abstraction Barriers and Refinement in the Polymorphic Lambda Calculus. PhD thesis, Laboratory for Foundations of Computer Science (LFCS), University of Edinburgh (2001). Home/Search Document Not in Database Summary Related Articles |
This paper is cited in the following contexts:
Semantic and Syntactic Approaches to Simulation Relations - Hannay, Katsumata, Sannella (2003) Self-citation (Hannay) (Correct)
.... of taking a syntactic approach, placing the concept of simulation relation in a logical setting and using existential type quantification for data abstraction [MP88] This line of development has been investigated in a string of papers on abstraction barrierobserving simulation relations by Hannay [Han99,Han00,Han01,Han03] based on a logic for parametric polymorphism due to Plotkin and Abadi [PA93] A clear advantage of such an approach is that it is amenable to computer aided reasoning but there are certain compromises forced by the syntactic nature of the framework. We present this background in Sects. 2 4 and ....
....does not give us an f### : ###) such that f###Aa = x f###Bb = y, so we cannot construct our f : to complete the proof. This negative result involving Dfnbl generalises. At higher order, there might not exist any simulation relation in the presence of observational equivalence [Han01]. To exemplify with T [#] above, any candidate R AB has to satisfy : A#A, y : B#B . x (R#R) y a.px = nat b.py, and this includes x and y that do not belong to, or are not expressible by, operations in the respective data types. This, one might argue, is unreasonable. In fact, it is. ....
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J. Hannay. Abstraction Barriers and Refinement in the Polymorphic Lambda Calculus. PhD thesis, Laboratory for Foundations of Computer Science (LFCS), University of Edinburgh (2001).
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