By Frank Pfenning

This booklet constitutes the refereed complaints of the twenty first overseas convention on automatic Deduction, CADE-21, held in Bremen, Germany, in July 2007. The 28 revised complete papers and six method descriptions offered have been conscientiously reviewed and chosen from sixty four submissions. All present points of automatic deduction are addressed, starting from theoretical and methodological matters to presentation and review of theorem provers and logical reasoning structures. The papers are geared up in topical sections on higher-order good judgment, description common sense, intuitionistic good judgment, satisfiability modulo theories, induction, rewriting, and polymorphism, first-order common sense, version checking and verification, termination, in addition to tableaux and first-order structures.

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Extra info for Automated deduction -- CADE-21: 21st International Conference on Automated Deduction, Bremen, Germany, July 17-20, 2007 : proceedings

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R ← r and ∀r ∈ Smach ∀m. r m (where Smach is the set of machine registers). , avail e = Smach − {r | ∀w. w ∈ e ∧ r ← w}. x. app is used to mark function applications. Finally, loc (v, l) = l indicates that variable v is allocated to location l (where l = r or m). [assgn reg] [spill] let v = e1 in e2 [v] ←→ let rˆ = e1 in e2 [loc(v, rˆ)] avail e2 = φ let v = e1 in e2 [v, loc(w, r)] ←→ ˆ avail e2 = φ let m ˆ = save r in let r = e1 in e2 [loc(v, r), loc(w, m)] [early spill] let v = e1 in e2 [v, loc(w, r)] ←→ let m ˆ = save r in let v = e1 in e2 [v, loc(w, m)] ˆ avail e2 = φ [restore] e[loc(v, m)] ←→ let vˆ = restore m in e[ˆ v] [caller save] let = app f in e[ , loc(w, r)] ←→ let m ˆ = save r in let = app f in e[ , loc(w, m)] ˆ let = if e1 then e2 [loc(w, r1 )] else e3 [loc(w, r2 )] in e4 [loc(w, r0 )] ←→ [spill if] ˆ else e3 [loc(w, m)] ˆ in let m ˆ = save r0 in let = if e1 then e2 [loc(w, m)] e4 [loc(w, m)] ˆ ¬(r0 = r1 = r2 ) When variable v in expression let v = e1 in e2 [v] is to be assigned a register, the live variables to be considered are just the free variables in e2 excluding v.

Clight, to PowerPC assembly code in the Coq system. The semantics of Clight is completely deterministic and specified as big-step operational semantics. Several intermediate languages are introduced and translations between them are verified. The proof of semantics preservation for the translation proceeds by induction over the Clight evaluation derivation and case analysis on the last evaluation rule used; in contrast, our proofs proceed by verifying the rewrite rules. A purely operational semantics based development is that of Klein and Nipkow [9] which gives a thorough formalization of a Java-like language.

The transformation presented in this section admits only tail recursive programs. ::= r | m | i ::= r | i ::= r | m ::= (e1 , . . , en ) | x opb x | if r opr y then e else e | fid x1 . . xn | let (v1 , . . , vn ) = e in e f ::= fid = λv1 . . λvn . e x y v e register variable, memory variable and integer register variable and integer register and memory variable tuple binary operation conditional function application let definition function definition Fig. 4. Syntax of the Functional Intermediate Language (FIL) For those non-tail recursive programs, we rely on third party translator to turn them into equivalent tail recursion.

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