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Relational Reasoning about Contexts
 HIGHER ORDER OPERATIONAL TECHNIQUES IN SEMANTICS, PUBLICATIONS OF THE NEWTON INSTITUTE
, 1998
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From Settheoretic Coinduction to Coalgebraic Coinduction: some results, some problems
, 1999
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Using synthetic domain theory to prove operational properties of a polymorphic programming language based on strictness
 Manuscript
"... We present a simple and workable axiomatization of domain theory within intuitionistic set theory, in which predomains are (special) sets, and domains are algebras for a simple equational theory. We use the axioms to construct a relationally parametric settheoretic model for a compact but powerful ..."
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Cited by 12 (3 self)
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We present a simple and workable axiomatization of domain theory within intuitionistic set theory, in which predomains are (special) sets, and domains are algebras for a simple equational theory. We use the axioms to construct a relationally parametric settheoretic model for a compact but powerful polymorphic programming language, given by a novel extension of intuitionistic linear type theory based on strictness. By applying the model, we establish the fundamental operational properties of the language. 1.
Operational domain theory and topology of a sequential language
 In Proceedings of the 20th Annual IEEE Symposium on Logic In Computer Science
, 2005
"... A number of authors have exported domaintheoretic techniques from denotational semantics to the operational study of contextual equivalence and order. We further develop this, and, moreover, we additionally export topological techniques. In particular, we work with an operational notion of compact ..."
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A number of authors have exported domaintheoretic techniques from denotational semantics to the operational study of contextual equivalence and order. We further develop this, and, moreover, we additionally export topological techniques. In particular, we work with an operational notion of compact set and show that total programs with values on certain types are uniformly continuous on compact sets of total elements. We apply this and other conclusions to prove the correctness of nontrivial programs that manipulate infinite data. What is interesting is that the development applies to sequential programming languages, in addition to languages with parallel features. 1
Congruence of bisimulation in a nondeterministic callbyneed lambda calculus
 Electron. Notes Theor. Comput. Sci
, 2005
"... We present a callbyneed λcalculus λND with an erratic nondeterministic operator pick and a nonrecursive let. A definition of a bisimulation is given, which has to be based on a further calculus named λ≈, since the näıve bisimulation definition is useless. The main result is that bisimulation i ..."
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We present a callbyneed λcalculus λND with an erratic nondeterministic operator pick and a nonrecursive let. A definition of a bisimulation is given, which has to be based on a further calculus named λ≈, since the näıve bisimulation definition is useless. The main result is that bisimulation in λ ≈ is a congruence and contained in the contextual equivalence. The proof is a nontrivial extension of Howe’s method. This might be a step towards defining useful bisimulation relations and proving them to be congruences in calculi that extend the λNDcalculus.
Themes in Final Semantics
 Dipartimento di Informatica, Università di
, 1998
"... C'era una volta un re seduto in canap`e, che disse alla regina raccontami una storia. La regina cominci`o: "C'era una volta un re seduto in canap`e ..."
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C'era una volta un re seduto in canap`e, che disse alla regina raccontami una storia. La regina cominci`o: &quot;C'era una volta un re seduto in canap`e
Coinductive Characterizations of Applicative Structures
 MATH. STRUCTURES IN COMP. SCI. 9(4):403–435
, 1998
"... We discuss new ways of characterizing, as maximal fixed points of monotone operators, observational congruences on terms and, more in general, equivalences on applicative structures. These characterizations naturally induce new forms of coinduction principles, for reasoning on program equivalences, ..."
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We discuss new ways of characterizing, as maximal fixed points of monotone operators, observational congruences on terms and, more in general, equivalences on applicative structures. These characterizations naturally induce new forms of coinduction principles, for reasoning on program equivalences, which are not based on Abramsky's applicative bisimulation. We discuss in particular, what we call, the cartesian coinduction principle, which arises when we exploit the elementary observation that functional behaviours can be expressed as cartesian graphs. Using the paradigm of final semantics, the soundness of this principle over an applicative structure can be expressed easily by saying that the applicative structure can be construed as a strongly extensional coalgebra for the functor (P( \Theta )) \Phi (P( \Theta )). In this paper, we present two general methods for showing the soundenss of this principle. The first applies to approximable applicative structures. Many c.p.o. models in...
Relating stepindexed logical relations and bisimulations
, 2009
"... Operational logical relations and bisimulations are two particularly successful syntactic techniques for reasoning about program equivalence. Although both techniques seem to have common intuitions, their basis is on different mathematical principles: induction for the former, and coinduction for t ..."
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Operational logical relations and bisimulations are two particularly successful syntactic techniques for reasoning about program equivalence. Although both techniques seem to have common intuitions, their basis is on different mathematical principles: induction for the former, and coinduction for the latter. The intuitive understanding of the two techniques seems more common, but their mathematical connection more ambitious, when each is combined with stepbased reasoning, such as in the case of AppelMcAllesterAhmed stepindexed (SI) logical relations [5, 4] and KoutavasWand (KW) bisimulations [12, 11]. In this paper we give an alternative formulation of a SI logical relation in the style of AppelMcAllesterAhmed. We derive this from a definition that is parametric on the indexing scheme by requiring it to satisfy the desirable properties of a SI logical relation. We then argue that SI logical relations and KW bisimulations approximate the same relation each in a distinct way. Finally we prove a somewhat surprising commutation theorem between unions and intersections that may be used as a new proof technique. 1
This document in subdirectoryRS/97/24/ Relational Reasoning about Contexts ∗
, 909
"... See back inner page for a list of recent BRICS Report Series publications. Copies may be obtained by contacting: BRICS ..."
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See back inner page for a list of recent BRICS Report Series publications. Copies may be obtained by contacting: BRICS
A Theory of Inductive Definitions With αequivalence: Semantics, Implementation, Programming Language.
"... This document was compiled from L ATEX source on 10 August 2000. Copies will be printed, bound, and submitted for the title of PhD in Mathematics from Cambridge University, England. Other copies will be passed to those interested. Those interested are invited to write to me at Trinity College, Camb ..."
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This document was compiled from L ATEX source on 10 August 2000. Copies will be printed, bound, and submitted for the title of PhD in Mathematics from Cambridge University, England. Other copies will be passed to those interested. Those interested are invited to write to me at Trinity College, Cambridge, or email m.j.gabbay@dpmms.cam.ac.uk. I remind the reader that my examiners may well suggest corrections to this document so it need not necessarily be the final version of my thesis. If the reader is wondering, DPMMS stands for the “Department of Pure Maths