The 𝜆𝜇𝜇˜-calculus introduces logical connectives and explores their connection to a simplified sequent calculus. The sequent calculus involves sequents consisting of multisets of formulas, including two conjunctions that align with strict and lazy pairs in Core. The introduction rules define how complex formulas are used in derivations without appearing in premises. In this framework, the Cut rule is noted for disrupting the subformula property, and the cut-elimination property is essential for establishing connections to the Curry-Howard correspondence.
In the classical sequent calculus, both the premises and the conclusion of a derivation rule consist of sequents Γ ⊢ Δ, where Γ and Δ are multisets of formulas.
The only rule which destroys the subformula property in sequent calculus is the Cut rule, which can be eliminated to show that a calculus enjoys the cut-elimination property.
#lambda-calculus #sequent-calculus #logical-connectives #cut-elimination #curry-howard-correspondence
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