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That is, all the expressions we obtain from a given sequent have the same associated partial order.
It is a set of vectors of pairs, each pair consisting of a sequent and (possibly) a reducibility candidate.
However, in this case there is only one sort of sequent and, consequently, it is possible to have nested contexts.
A sequent is a pair (, a) consisting of an environment and a pseudoterm.
The operational semantics of this class of languages is given via a sequent-calculi presentation of the corresponding fragment of linear logic.
We associate with every sequent a quintuple of natural numbers.
The correspondence between sequent calculus derivations and natural deduction derivations is, however, not a one-one map, which causes some syntactic technicalities.
Such a sequent is not an axiom unless a formula in that matches the facts in exists.
In the present paper we define a sequent calculus associated to a linear functor in such a way that any linear functor provides a model.
In this section we present two formulations of linear logic: a one-sided sequent calculus and a two-sided sequent calculus.
All the work cited above uses the formalism of linear sequent calculus.
The sequent can be seen as part of the verification condition which is generated during type-checking.
Suppose now that in the sequent we have that and denote sets of occurrences of formulas.
In the meantime, sequent calculi provide a powerful organization of the knowledge specified through the formulae of the logic language taken into consideration.
The denotational interpretation of a sequent calculus proof is, as usual, defined by induction.
