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Computational Interpretations of Linear Logic
 Theoretical Computer Science
, 1993
"... We study Girard's Linear Logic from the point of view of giving a concrete computational interpretation of the logic, based on the CurryHoward isomorphism. In the case of Intuitionistic Linear Logic, this leads to a refinement of the lambda calculus, giving finer control over order of evaluati ..."
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We study Girard's Linear Logic from the point of view of giving a concrete computational interpretation of the logic, based on the CurryHoward isomorphism. In the case of Intuitionistic Linear Logic, this leads to a refinement of the lambda calculus, giving finer control over order of evaluation and storage allocation, while maintaining the logical content of programs as proofs, and computation as cutelimination.
weak
, 1996
"... A natural deduction system NDIL described here admits normalization and has subformula property. It has standard axioms A ⊢ A, ⊢ 1, standard introduction and elimination rules for &, − ◦ (linear implication), ⊕ and quantifiers. The rules for ⊗ are now standard too. Structural rules are (implic ..."
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A natural deduction system NDIL described here admits normalization and has subformula property. It has standard axioms A ⊢ A, ⊢ 1, standard introduction and elimination rules for &, − ◦ (linear implication), ⊕ and quantifiers. The rules for ⊗ are now standard too. Structural rules are (implicit) permutation plus contraction and weakening for mformulas. The rules for! use an idea of D. Prawitz. By a mformula we mean 1, any formula beginning with!, and any expression < Γ>!A, whereΓisa list of formulas and mformulas, and A is a formula. Derivable objects are sequents Γ ⊢ A where Γ is a multiset of formulas and mformulas, and A is a formula. The rules for!, weakening and contraction are as follows: Γ ⊢!A