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A TwoLevel Approach towards Lean ProofChecking
, 1996
"... We present a simple and effective methodology for equational reasoning in proof checkers. The method is based on a twolevel approach distinguishing between syntax and semantics of mathematical theories. The method is very general and can be carried out in any type system with inductive and oracle t ..."
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Cited by 16 (4 self)
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We present a simple and effective methodology for equational reasoning in proof checkers. The method is based on a twolevel approach distinguishing between syntax and semantics of mathematical theories. The method is very general and can be carried out in any type system with inductive and oracle types. The potential of our twolevel approach is illustrated by some examples developed in Lego.
Extending a lambdacalculus with Explicit Substitution which Preserves Strong Normalisation into a Confluent Calculus on Open Terms
, 1993
"... The last fifteen years have seen an explosion in work on explicit substitution, most of which is done in the style of the oecalculus. In (Kamareddine & R'ios, 1995a), we extended the calculus with explicit substitutions by turning de Bruijn's metaoperators into objectoperators offering a style o ..."
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Cited by 7 (0 self)
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The last fifteen years have seen an explosion in work on explicit substitution, most of which is done in the style of the oecalculus. In (Kamareddine & R'ios, 1995a), we extended the calculus with explicit substitutions by turning de Bruijn's metaoperators into objectoperators offering a style of explicit substitution that differs from that of oe. The resulting calculus, s, remains as close as possible to the calculus from an intuitive point of view and, while preserving strong normalisation (Kamareddine & R'ios, 1995a), is extended in this paper to a confluent calculus on open terms: the secaculus. Since the establishment of these results, another calculus, i, came into being in (Mu~noz Hurtado, 1996) which preserves strong normalisation and is itself confluent on open terms. However, we believe that se still deserves attention because, while offering a new style to work with explicit substitutions, it is able to simulate one step of classical fireduction, whereas i is not. To ...
Weak and Strong Beta Normalisations in Typed λCalculi
 In: Proc. of the 3 rd International Conference on Typed Lambda Calculus and Applications, TLCA'97
, 1997
"... . We present a technique to study relations between weak and strong finormalisations in various typed calculi. We first introduce a translation which translates a term into a Iterm, and show that a term is strongly finormalisable if and only if its translation is weakly finormalisable. We t ..."
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Cited by 4 (1 self)
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. We present a technique to study relations between weak and strong finormalisations in various typed calculi. We first introduce a translation which translates a term into a Iterm, and show that a term is strongly finormalisable if and only if its translation is weakly finormalisable. We then prove that the translation preserves typability of terms in various typed calculi. This enables us to establish the equivalence between weak and strong finormalisations in these typed calculi. This translation can deal with Curry typing as well as Church typing, strengthening some recent closely related results. This may bring some insights into answering whether weak and strong finormalisations in all pure type systems are equivalent. 1 Introduction In various typed calculi, one of the most interesting and important properties on terms is how they can be fireduced to finormal forms. A term M is said to be weakly finormalisable (WN fi (M )) if it can be fireduced to a fin...
Globalization of Confluent Partial Actions on Topological and Metric Spaces
, 2004
"... We generalize Exel’s notion of partial group action to monoids. For partial monoid actions that can be defined by means of suitably wellbehaved systems of generators and relations, we employ classical rewriting theory in order to describe the universal induced global action on an extended set. This ..."
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Cited by 4 (0 self)
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We generalize Exel’s notion of partial group action to monoids. For partial monoid actions that can be defined by means of suitably wellbehaved systems of generators and relations, we employ classical rewriting theory in order to describe the universal induced global action on an extended set. This universal action can be lifted to the setting of topological spaces and continuous maps, as well as to that of metric spaces and nonexpansive maps. Wellknown constructions such as Shimrat’s homogeneous extension are special cases of this construction. We investigate various properties of the arising spaces in relation to the original space; in particular, we prove embedding theorems and preservation properties concerning separation axioms and dimension. These results imply that every normal (metric) space can be embedded into a normal (metrically) ultrahomogeneous space of the same dimension and cardinality.
Weak and Strong Beta Normalisations in Typed λCalculi
 IN: PROC. OF THE 3 RD INTERNATIONAL CONFERENCE ON TYPED LAMBDA CALCULUS AND APPLICATIONS, TLCA'97
, 1997
"... We present a technique to study relations between weak and strong finormalisations in various typed calculi. We first introduce a translation which translates a λterm into a λIterm, and show that a λterm is strongly finormalisable if and only if its translation is weakly finormalisable. We t ..."
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We present a technique to study relations between weak and strong finormalisations in various typed calculi. We first introduce a translation which translates a λterm into a λIterm, and show that a λterm is strongly finormalisable if and only if its translation is weakly finormalisable. We then prove that the translation preserves typability of λterms in various typed λcalculi. This enables us to establish the equivalence between weak and strong finormalisations in these typed λcalculi. This translation can deal with Curry typing as well as Church typing, strengthening some recent closely related results. This may bring some insights into answering whether weak and strong finormalisations in all pure type systems are equivalent.