| F. Nielson and H. R. Nielson. Layered predicates. In Proceedings of the |
....to hold. For more complex situations the formulation of has a type may have to be defined coinductively [42] in which case also the proof of the subject reduction result may need to exploit coinduction (e.g. 30] and the notions of Kripke relations and Kripke logical relations (see e.g. [28]) may be useful when using a denotational semantics [26] We refer to [3, 39, 40, 45] for a number of applications of these techniques. The inference algorithm. The development of a syntactically sound and complete inference algorithm may be based on the ideas in [20, 41] The simplest approach is ....
.... di#culty is to show how this can be obtained from W(#, e) S, #, #) or W(#, e) S, #, #, C) The solution is to formally define when one typing is an instance of another; the notion of lazy instance [9] is very useful here and in more complex scenarios Kripke logical relations (see e.g. [28]) may be needed [1] The proofs are often challenging and often require developing extensive techniques for normalising deductions made in the inference system so as to control the use of non syntax directed rules. For su#ciently complex scenarios syntactic completeness may fail or may be open ....
F. Nielson and H. R. Nielson. Layered predicates. In Proc. REX'92 workshop on Semantics --- foundations and applications, volume 666 of Lecture Notes in Computer Science, pages 425--456. Springer, 1993.
....soundness are mostly standard. For operational semantics the statement of correctness may be a subject reduction result and the method of proof may bene t from the use of co induction; when the use of denotational semantics is possible one may bene t from the use of Kripke logical relations[64]. iii) Algorithmic techniques often involve the generation of constraint systems in a program independent representation. Sometimes e cient techniques developed for ow based analyses can be used to solve the constraint problems; in other cases the problems take the form of semi uni cation ....
F Nielson and H.R. Nielson. Layered Predicates. In Proc. REX'92 workshop on \Semantics|foundations and applications", pages 425-456, Springer Lecture Notes in Computer Science 666, 1993.
....ie 0 ; oe 0 SO 0 (ae; oe) for O 0 = range(ae) obj(ie 0 ) Proof. Overall the proof is by induction on the shape of ae hie; oei hie 0 ; oe 0 i. However, to deal with the case of bind we use a stronger induction hypothesis using the notion of Kripke logical relations [3]: For all O: C; ae; oe) j= Sigma ( m i = i i=1: n ] iff hm i i=1: n i 2 C( C; ae; oe) j= Sigma (bind ae 1 in it 2 2 ) iff ae 1 R ae ( C; ae; oe) j= Sigma it 2 2 C( 2) C( ae R ae iff 8x 2 dom(ae) dom(ae) 8[m i = i i=1: n ] ae(x) ....
F. Nielson and H. R. Nielson. Layered predicates. In Proc. REX'92 workshop on Semantics --- foundations and applications, volume 666 of Lecture Notes in Computer Science, pages 425--456. Springer, 1993.
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F. Nielson and H. R. Nielson, "Layered predicates," in REX'92 workshop "Semantics - foundations and applications", vol. 666 of Lecture Notes in Computer Science, pp. 425-456, Springer-Verlag, 1992. [DART-131].
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F. Nielson and H. R. Nielson. Layered predicates. In Proceedings of the
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