Natural deduction and coherence for non-symmetric linearly distributive categories.
Natural deduction and sequent typed lambda calculus.
Normal Form Theorem for Systems of Sequents
Normalisation of the theory of Cartesian closed categories and conservativity of extensions of
Normalisation of the Theory T of Cartesian Closed Categories and Conservativity of Extensions T[x] of T
Using an inductive definition of normal terms of the theory of Cartesian Closed Categories with a given graph of distinguished morphisms, we give a reduction free proof of the decidability of this theory. This inductive definition enables us to show via functional completeness that extensions of such a theory by new constants (“indeterminates”) are conservative.
Normalization as a consequence of cut elimination