By Colin Stirling (auth.), Frank Pfenning (eds.)
This ebook constitutes the refereed lawsuits of the twenty first foreign convention on computerized Deduction, CADE-21, held in Bremen, Germany, in July 2007.
The 28 revised complete papers and six process descriptions awarded have been rigorously reviewed and chosen from sixty four submissions. All present elements of computerized deduction are addressed, starting from theoretical and methodological matters to presentation and assessment of theorem provers and logical reasoning platforms. The papers are geared up in topical sections on higher-order good judgment, description good judgment, intuitionistic common sense, satisfiability modulo theories, induction, rewriting, and polymorphism, first-order common sense, version checking and verification, termination, in addition to tableaux and first-order systems.
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Additional resources for Automated Deduction – CADE-21: 21st International Conference on Automated Deduction Bremen, Germany, July 17-20, 2007 Proceedings
Simpliﬁcation of Let-expressions. It is often useful both for clariﬁcation and for eﬃciency, to reduce expressions such as let v1 = v2 in e[v1 ] to e[v2 ] by expanding the aliasing of variables. Rule atom let supports such reduction; obviously it is a special case of inline expansion. g. closure conversion). Rule useless let is for eliminating unused variable/function deﬁnitions. It requires that x does not appear free in e2 (thus the execution of expression e1 is unnecessary). [atom let] let x = atom v in e[x] ←→ e[v] [ﬂatten let] let x = (let y = e1 in e2 [y]) in e3 [x, y] ←→ let y = e1 in let x = e2 [y] in e3 [x, y] [useless let] let x = e1 in e2 ←→ e2 Constant Folding.
Our compiler adopts the caller-save convention, so every function call is assumed to destroy the values of all registers. Therefore, we need to, as implemented in the caller save rule, save the values of all registers that are live at that point. In addition, as we allocate the two branches of a conditional expression separately, a variable may be assigned diﬀerent registers by the branches. This will contradict the convention that a variable should be assigned only one register. In this case, we will early spill it through the spill if rule.
The essence of our approach is: for each rewriting step, a theorem that establishes the equality of the original program and result of the transformation is given as by-product (we call this technique compilation by proof ). Proof producing compilation has already been investigated in a prototype hardware compiler , which synthesizes Verilog netlists, and a software compiler , which produces ARM code, from ﬁrst-order HOL functions. In the software compiler, the core intermediate languages and the target language are imperative languages with syntax and operational semantics explicitly deﬁned.