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Explicit substitutions calculi with one step Eta-reduction decided explicitly
2009
Logic Journal of the IGPL
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In particular, we show that the explicit definitions of the eta rules coincide with the Eta rule for pure λ-terms and that moreover, their application is decidable in the sense that Eta redices are effectively ...
In this paper constructive Eta rules are proposed for both the λσ-and the λse-calculi of explicit substitutions. ...
One has b[s] = b + s = 0. Then,
by Lemma 4.7, (s • η i
i )
ES Calculi with One Step Eta-reduction Decided Explicitly ...
doi:10.1093/jigpal/jzp027
fatcat:3wsbhxuoqjen7f3msj455ljx2q
Eta-Equivalence in Core Dependent Haskell
2020
Types for Proofs and Programs
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We extend the core semantics for Dependent Haskell with rules for η-equivalence. This semantics is defined by two related calculi, Systems D and DC. ...
Our work builds on and extends the existing metatheory for these systems developed using the Coq proof assistant. ...
One difficulty with η-reduction in this setting is the problem with confluence for Churchstyle calculi. ...
doi:10.4230/lipics.types.2019.7
dblp:conf/types/Kravchuk-Kirilyuk19
fatcat:kjlierzyn5at3ls35xsdzomumm
More Church-Rosser proofs (in Isabelle/HOL)
[chapter]
1996
Lecture Notes in Computer Science
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All proofs are based on a general theory of commutating relations which supports an almost geometric style of con uence proofs. ...
For -reduction, both the standard proof and the variation by Takahashi are given and compared. ...
H o wever, after I had nished my o wn development I found out about the following two formalizations of in -calculi with explicit substitutions. ...
doi:10.1007/3-540-61511-3_125
fatcat:k6rjkyixgzhpvosc5dpqd742li
Second-Order Matching via Explicit Substitutions
[chapter]
2005
Lecture Notes in Computer Science
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In this paper, we will make use of explicit substitutions to facilitate matching: we develop a second-order matching algorithm via the λσ-style of explicit substitutions. ...
The past few years have established the benefit of using explicit substitutions for theorem proving and higher-order unification. ...
We write M → r M to denote one step reduction by one application of rule r. ...
doi:10.1007/978-3-540-32275-7_29
fatcat:bfzqutroerhbtcdgys4mro6yei
Higher-Order Rewriting: Framework, Confluence and Termination
[chapter]
2005
Lecture Notes in Computer Science
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Acknowledgments: This paper would not exist without the pionneering work of Klop on higher-order rewriting and the work I have done myself with my coauthors Femke van Raamsdonk and Albert Rubio, my colleague ...
Mitsuhiro Okada with who I started getting into that subject, and my students Maribel Fernandez, Frederic Blanqui and Daria Walukiewicz who investigated some of these questions within the framework of ...
In both cases, the conventional expression is transformed by the parser into the one with explicit application. ...
doi:10.1007/11601548_14
fatcat:iwdbwyqmbre2bkbza545hxkjfu
Type Destructors
2002
Information and Computation
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We study a variant of System F that integrates and generalizes several existing proposals for calculi with structural typing rules. To the usual type constructors ! ...
We illustrate this by giving elementary presentations of two w ell-known encodings of objects, one based on recursive record types and the other based on existential packages. ...
Moreover, most of the de nition in Section 3.2 is mirrored directly here: Eta-A-Refl is an explicit symmetry rule, while Eta-A-Any through Eta-A-Rec give explicit congruence rules for all the type constructors ...
doi:10.1006/inco.2001.2926
fatcat:alca7rajqrgrhl5g66ygpefpzu
Full Reduction in the Face of Absurdity
[chapter]
2015
Lecture Notes in Computer Science
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Core calculi that model the essence of computations use full reduction semantics to be built on solid grounds. ...
To preserve type soundness, reduction must then be delayed until logical hypotheses on which the computation depends have been proved consistent. ...
We know how to design calculi with explicit uses of logical assumptions and full reduction, or calculi with implicit uses of assumptions and weak reduction. ...
doi:10.1007/978-3-662-46669-8_28
fatcat:yy7nhn76eraapc7w5wzufrgptq
Polymorphism and separation in hoare type theory
2006
Proceedings of the eleventh ACM SIGPLAN international conference on Functional programming - ICFP '06
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Each judgment relates an expression with its one-step reduct. The inference rules of the evaluation judgments are straightforward, so we omit them here. ...
Monadic and hereditary substitutions. The equational theory of HTT is based on the usual beta and eta reductions for the various type constructors. ...
doi:10.1145/1159803.1159812
dblp:conf/icfp/NanevskiMB06
fatcat:2rfoxzsbxba4fncioxrqbxa3hy
Polymorphism and separation in hoare type theory
2006
SIGPLAN notices
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Each judgment relates an expression with its one-step reduct. The inference rules of the evaluation judgments are straightforward, so we omit them here. ...
Monadic and hereditary substitutions. The equational theory of HTT is based on the usual beta and eta reductions for the various type constructors. ...
doi:10.1145/1160074.1159812
fatcat:2xtpzu7l2zckzhketfmhjftdba
Resource operators for λ-calculus
2007
Information and Computation
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We present a simple term calculus with an explicit control of erasure and duplication of substitutions, enjoying a sound and complete correspondence with the intuitionistic fragment of Linear Logic's proof-nets ...
simulation of -reduction and full composition. ...
on the calculus with explicit substitutions to mimic exactly the calculus without explicit substitutions [25] . ...
doi:10.1016/j.ic.2006.08.008
fatcat:3rmvqhcrpjbd3gs24yqzmvgvtm
Separability in the Ambient Logic
2008
Logical Methods in Computer Science
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We also present some (un)decidability results that are related to the above separation properties for AL: the undecidability of _=L on MA and its decidability on the subcalculus. ...
In these calculi, we provide two operational characterisations of _=L: a coinductive one (as a form of bisimilarity) and an inductive one (based on structual properties of processes). ...
Unless explicitely stated, we use P, Q, . . . to range over closed processes in our definitions and results. Substitutions, ranged over with σ, are partial functions from variables to names. ...
doi:10.2168/lmcs-4(3:4)2008
fatcat:5cgoodeasjenbjefxkft2ntbua
Mechanizing the Metatheory of LF
[article]
2010
arXiv
pre-print
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In the process, we identified and resolved a gap in one of the proofs and a small number of minor lacunae in others. ...
However, correct use of LF relies on nontrivial metatheoretic developments such as proofs of correctness of decision procedures for LF's judgments. ...
Benjamin Pierce and Stephanie Weirich have also made helpful comments on drafts of this paper. ...
arXiv:0804.1667v3
fatcat:a372v4ivi5cxhl555b5kamvnzi
Logical foundations for hybrid type-logical grammars
[article]
2020
arXiv
pre-print
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This paper explores proof-theoretic aspects of hybrid type-logical grammars , a logic combining Lambek grammars with lambda grammars. ...
Term labels have been added to the vertices of the graph to make the correspondence with beta-reduction explicit. ...
Finally, the rules in δ ′ 3 are therefore those in δ 3 with possibly a single β reduction removed and with P either identical to P ′ or β-reducible to it in one step. 4 In what follows, we assume that ...
arXiv:2009.10387v1
fatcat:6toldo6dozccnkjjltcjvvibaa
Mechanizing the metatheory of LF
2011
ACM Transactions on Computational Logic
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substitution) by (nominal) primitive recursion, and (3) strong induction principles for datatypes and inductive definitions that build in Barendregt-style renaming conventions. ...
In the process, we identified and resolved a gap in one of the proofs and a small number of minor lacunae in others. ...
Benjamin Pierce and Stephanie Weirich have also made helpful comments on drafts of this paper. ...
doi:10.1145/1877714.1877721
fatcat:asxhcrfavbhrnnm6cvtqpi7nhq
Mechanizing the Metatheory of LF
2008
Logic in Computer Science
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substitution) by (nominal) primitive recursion, and (3) strong induction principles for datatypes and inductive definitions that build in Barendregt-style renaming conventions. ...
In the process, we identified and resolved a gap in one of the proofs and a small number of minor lacunae in others. ...
Benjamin Pierce and Stephanie Weirich have also made helpful comments on drafts of this paper. ...
doi:10.1109/lics.2008.29
dblp:conf/lics/UrbanCB08
fatcat:dtiowrtba5ey7i2cwryfeocdnq
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