progress on my updates to section 2
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Jeremy Siek
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2 changed files with 135 additions and 2 deletions
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@ -284,3 +284,93 @@
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year={1994},
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publisher={San Diego: Academic Press, c1987-}
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}
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@article{Abadi-1991,
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Author = {Abadi, M. and Cardelli, L. and Curien, P.-L. and Levy, J.-J.},
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Journal = {Journal of Functional Programming},
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Number = {4},
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Pages = {375-416},
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Title = {Explicit Substitutions},
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Volume = {1},
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Year = {1991}}
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@book{Barendregt-1984,
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Author = {H.P. Barendregt},
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Publisher = {Elsevier},
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Series = {Studies in Logic},
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Title = {The Lambda Calculus},
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Volume = {103},
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Year = {1984}}
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@inproceedings{Schafer-Tebbi-Smolka-2015,
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Author = {Steven Sch{\"{a}}fer and Tobias Tebbi and Gert Smolka},
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Booktitle = {Interactive Theorem Proving - 6th International Conference},
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Month = {August},
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Pages = {359--374},
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Publisher = {Springer},
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Series = {ITP},
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Title = {Autosubst: Reasoning with de Bruijn Terms and Parallel Substitutions},
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Year = {2015}}
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@techreport{Pfenning-1992,
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Address = {Pittsburgh, PA, USA},
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Author = {Pfenning, Frank},
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Institution = {Carnegie Mellon University},
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Number = {CMU-CS-92-186},
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Title = {A Proof of the Church-Rosser Theorem and Its Representation in a Logical Framework},
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Year = {1992}}
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@article{Siek-2017,
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Author = {Jeremy G. Siek},
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Journal = {CoRR},
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Number = {4},
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Title = {Revisiting Elementary Denotational Semantics},
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Volume = {abs/1707.03762},
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Year = {2017}}
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@article{Scott-1976,
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Author = {Dana Scott},
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Journal = {SIAM Journal on Computing},
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Number = {3},
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Pages = {522-587},
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Title = {Data Types as Lattices},
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Volume = {5},
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Year = {1976}}
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@article{Engeler-1981,
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Author = {Engeler, Erwin},
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Journal = {algebra universalis},
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Month = {Dec},
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Number = {1},
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Pages = {389--392},
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Title = {Algebras and combinators},
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Volume = {13},
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Year = {1981}}
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@article{Plotkin-1993,
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Author = {Gordon D. Plotkin},
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Journal = {Theoretical Computer Science},
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Number = {1},
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Pages = {351 - 409},
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Title = {Set-theoretical and other elementary models of the λ-calculus},
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Volume = {121},
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Year = {1993}}
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@article{Barendregt-1983,
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Author = {Henk Barendregt and Mario Coppo and Mariangiola Dezani-Ciancaglini},
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Journal = {Journal of Symbolic Logic},
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Month = {12},
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Number = {4},
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Pages = {931-940},
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Title = {A filter lambda model and the completeness of type assignment},
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Volume = {48},
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Year = {1983}}
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@ -18,7 +18,7 @@
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\author[adr1]{Wen Kokke}
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\ead{wen.kokke@ed.ac.uk}
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\author[adr2]{Jeremy Siek}
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\author[adr2]{Jeremy G. Siek}
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\ead{jsiek@indiana.edu}
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\author[adr1]{Philip Wadler\corref{cor1}}
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\ead{wadler@inf.ed.ac.uk}
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@ -287,6 +287,49 @@ with full normalisation (including reduction under lambda terms). Emphasis
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is put on the correspondence between the structure of a term and
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evidence that it is in normal form.
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\paragraph{Substitution: in the untyped lambda calculus}
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Delves deeper into the properties of simultaneous substitution,
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establishing the equations of the $\sigma$ algebra of
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\citet{Abadi-1991}. These equations enable a straightforward proof of
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the Substitution Lemma~\citep{Barendregt-1984}, which is needed in the
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next chapter.
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\paragraph{Confluence: of the untyped lambda calculus}
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Presents a proof of the Church-Rosser theorem based on the classic
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idea of parallel reduction due to Tait and Martin-L\"of. The proof in
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Agda is streamlined by the use of ideas from
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\citet{Schafer-Tebbi-Smolka-2015} and \citet{Pfenning-1992}.
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\paragraph{Big-step: evaluation for call-by-name}
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Introduces the notion of big-step evaluation to develop a
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deterministic call-by-name reduction strategy. The main result of this
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chapter is a proof that big-step evaluation implies the existence of a
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reduction sequence that terminates with a lambda abstraction.
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\subsection*{Part III, Denotational Semantics}
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\paragraph{Denotational: semantics of the untyped lambda calculus}
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The early denotational semantics of the lambda calculus based on graph
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models~\citep{Scott-1976,Engeler-1981,Plotkin-1993} and filter
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models~\citep{Barendregt-1983} were particularly simple and elegant.
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This chapter presents such a semantics in a big-step style that is
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approachable to readers familiar with operational semantics.
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\paragraph{Compositional: the denotational semantics is compositional}
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TODO
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\paragraph{Soundness: of reduction with respect to denotational semantics}
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TODO
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\paragraph{Adequacy: of denotational semantics with respect to reduction}
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TODO
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\paragraph{Contextual Equivalence: is implied by denotational equality}
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TODO
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\subsection*{Discussion}
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PLFA and SF differ in several particulars. PLFA begins with a computationally
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