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Weak Normalization for the SimplyTyped LambdaCalculus in Twelf (Extended Abstract)
 In Logical Frameworks and Metalanguages (LFM 04), IJCAR
, 2004
"... Andreas Abel Department of Computer Science, Chalmers University of Technology Rannvagen 6, SWE41296 Goteborg, Sweden Abstract. Weak normalization for the simplytyped calculus is proven in Twelf, an implementation of the Edinburgh Logical Framework. Since due to prooftheoretical restrict ..."
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Andreas Abel Department of Computer Science, Chalmers University of Technology Rannvagen 6, SWE41296 Goteborg, Sweden Abstract. Weak normalization for the simplytyped calculus is proven in Twelf, an implementation of the Edinburgh Logical Framework. Since due to prooftheoretical restrictions Twelf Tait's computability method does not seem to be directly usable, a combinatorical proof is adapted and formalized instead.
Fixed points of type constructors and primitive recursion
 Computer Science Logic, 18th International Workshop, CSL 2004, 13th Annual Conference of the EACSL, Karpacz, Poland, September 2024, 2004, Proceedings, volume 3210 of Lecture Notes in Computer Science
, 2004
"... Our contribution to CSL 04 [AM04] contains a little error, which is easily corrected by 2 elementary editing steps (replacing one character and deleting another). Definition of wellformed contexts (fifth page). Typing contexts should, in contrast to kinding contexts, only contain type variable decla ..."
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Cited by 7 (3 self)
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Our contribution to CSL 04 [AM04] contains a little error, which is easily corrected by 2 elementary editing steps (replacing one character and deleting another). Definition of wellformed contexts (fifth page). Typing contexts should, in contrast to kinding contexts, only contain type variable declarations without variance information. Hence, the second rule is too liberal; we must insist on p = ◦. The corrected set of rules is then: ⋄ cxt ∆ cxt ∆, X ◦κ cxt ∆ cxt ∆ ⊢ A: ∗ ∆, x:A cxt Definition of welltyped terms (immediately following). Since wellformed typing contexts ∆ contain no variance information, hence ◦ ∆ = ∆, we might drop the “◦ ” in the instantiation rule (fifth rule). The new set of rules is consequently, (x:A) ∈ ∆ ∆ cxt ∆ ⊢ x: A ∆, X ◦κ ⊢ t: A ∆ ⊢ t: ∀X κ. A ∆, x:A ⊢ t: B ∆ ⊢ λx.t: A → B ∆ ⊢ t: ∀X κ. A ∆ ⊢ F: κ
On Zucker's isomorphism for LJ and its extension to Pure Type Systems
, 2003
"... It is shown how the sequent calculus LJ can be embedded into a simple extension of the calculus by generalized applications, called J. The reduction rules of cut elimination and normalization can be precisely correlated, if explicit substitutions are added to J. The resulting system J2 is prove ..."
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It is shown how the sequent calculus LJ can be embedded into a simple extension of the calculus by generalized applications, called J. The reduction rules of cut elimination and normalization can be precisely correlated, if explicit substitutions are added to J. The resulting system J2 is proved strongly normalizing, thus showing strong normalization for Gentzen's cut elimination steps. This re nes previous results by Zucker, Pottinger and Herbelin on the isomorphism between natural deduction and sequent calculus.