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Call-by-value, call-by-name, and strong normalization for the classical sequent calculus
  • S. Lengrand
  • Computer Science, Mathematics
  • Electron. Notes Theor. Comput. Sci.
  • 1 December 2003
TLDR
We present a typed calculus λξ isomorphic to the implicational fragment of the classical sequent calculus LK. Expand
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LJQ: A Strongly Focused Calculus for Intuitionistic Logic
TLDR
LJQ is a focused sequent calculus for intuitionistic logic, with a simple restriction on the first premisss of the usual left introduction rule for implication. Expand
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  • 10
  • PDF
Non-idempotent intersection types and strong normalisation
TLDR
We present a typing system with non-idempotent intersection types, typing a term syntax covering three different calculi: the pure {\lambda}-calculus, the calculus with explicit substitutions, contractions and weakenings {\lambda)lxr, and a filter model based on filters of intersection types. Expand
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Resource operators for lambda-calculus
TLDR
We present a simple term calculus with an explicit control of erasure and duplication of substitutions, enjoying a sound and complete correspondence with the intuitionistic fragment of Linear Logic's proof-nets. Expand
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Intersection types for explicit substitutions
TLDR
We present a new system of intersection types for a composition-free calculus of explicit substitutions with a rule for garbage collection, and show that it characterizes those terms which are strongly normalizing. Expand
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Extending the Explicit Substitution Paradigm
TLDR
We present a simple term language with explicit operators for erasure, duplication and substitution enjoying a sound and complete correspondence with the intuitionistic fragment of Linear Logic's Proof Nets. Expand
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  • 3
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Call-by-Value λ-calculus and LJQ
LJQ is a focused sequent calculus for intuitionistic logic, with a simple restriction on the first premiss of the usual left introduction rule for implication. In a previous paper we discussed itsExpand
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  • 3
  • PDF
Complexity of Strongly Normalising λ-Terms via Non-idempotent Intersection Types
TLDR
We present a typing system for the λ-calculus, with nonidempotent intersection types. Expand
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  • 2
  • PDF
Resource operators for λ-calculus
TLDR
We present a simple term calculus with an explicit control of erasure and duplication of substitutions, enjoying a sound and complete correspondence with the intuitionistic fragment of Linear Logic's proof-nets. Expand
  • 21
  • 2
  • PDF
The Language chi: Circuits, Computations and Classical Logic
TLDR
We present the syntax and reduction rules for χ, an untyped language that is well suited to describe structures which we call “circuits” and which are made of parts that are connected by wires. Expand
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