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-<h1>The Formal System λδ (\lambda\delta)<br>
-</h1>
-<h2>Towards the unification of terms, types, environments and contexts</h2>
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- <li>Foreword</li>
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- <li><a href="news.html">News</a></li>
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- <li><a href="documentation.html">Papers</a></li>
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- <h3 style="text-align: right;">Foreword <img style="width: 37px; height: 37px;" alt="[Butterfly]" title="Butterfly" src="images/b9.png"></h3>
-The formal system λδ
-(\lambda\delta) is a typed lambda calculus that pursues the static and
-dynamic unification of terms, types, environments and contexts while
-enjoying a well-conceived theory, which includes the commonly
-desired properties.<br>
- <br>
-λδ takes some features from the calculi of the Automath family and
-some from the pure type systems, but it differs from both in that it
-does not include the Π construction while it provides for an
-abbreviation mechanism at the level of terms.<br>
- <br>
-λδ features explicit type annotations, which are borrowed from
-realistic type checker implementations and with which type checking is
-reduced to type inference.<br>
- <br>
-The reduction steps of λδ include β-contraction, δ-expansion,
-ζ-contraction and θ-swap. On the other hand,
-η-contraction is not included.<br>
- <br>
-The theory of λδ includes important properties such as the
-confluence of reduction, the correctness of types, the
-uniqueness of types up to conversion, the subject reduction of the type
-assignment, the strong normalization of the typed terms. The
-decidability of type inference and of type checking come as corollaries.<br>
- <br>
-λδ features uniformly dependent types and a predicative abstraction
-mechanism, so the calculus can serve as a formal specification language
-for the type theories that need a predicative foundation. λδ is
-expected to have the expressive power of λ→.<br>
- <br>
-λδ comes in several versions listed in the following table, which
-includes the major milestones:<br>
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