By Dominique Bolignano (auth.), Sandrine Blazy, Christine Paulin-Mohring, David Pichardie (eds.)
This booklet constitutes the refereed court cases of the 4th overseas convention on Interactive Theorem Proving, ITP 2013, held in Rennes, France, in July 2013. The 26 standard complete papers provided including 7 tough diamond papers, three invited talks, and a pair of invited tutorials have been conscientiously reviewed and chosen from sixty six submissions. The papers are geared up in topical sections comparable to application verfication, safeguard, formalization of arithmetic and theorem prover development.
Read Online or Download Interactive Theorem Proving: 4th International Conference, ITP 2013, Rennes, France, July 22-26, 2013. Proceedings PDF
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Additional info for Interactive Theorem Proving: 4th International Conference, ITP 2013, Rennes, France, July 22-26, 2013. Proceedings
Sample text
Z hd-red proj It goes without saying that the first premise of (3) composes with the fst-order rule, given that both sides have the same head constant *. z) that unifies with (t1 ∗ t2 ) by the fst-order rule. It is now clear that type inference can make sense of a comparison by the == infix notation of any nested pairs of objects, as soon as their types are equipped Canonical Structures for the Working Coq User 27 with registered equality structures, and that this could be made to work for other type constructors like list, option, etc.
The reason why the _Pack constructor has been named this way becomes clear in the next section, where we implement a smarter constructor Pack to ease the declaration of canonical instances. 28 ✞ A. Mahboubi and E. Tassi Unfortunately we have not yet fulfilled our goals completely: Module theory. Fail Check ∀ (leq : type) (n m : obj leq), n <= m → n <= m → n == m. 44". *) ✆ The error message is better explained in the following graph where the nodes are types and the edges represent the inheritance relation.
The automatic provers are given prefixes φ1 , . . , φm of the selected n facts. The order of the facts—the estimated relevance—is exploited by some provers to guide the search. Although Sledgehammer’s default time limit is 30 s, the automatic provers are invoked repeatedly for shorter time periods, with different options and different number of facts m ≤ n; for example, SPASS is given as few as 50 facts in some slices and as many as 1000 in others. Excluding some facts restricts the search space, helping the prover find deeper proofs within the allotted time, but it also makes fewer proofs possible.