Introduction and elimination, left and right

Functional programming language design has been shaped by the framework of natural deduction, in which constructs are divided into introduction and elimination rules for producers values. In sequent calculus-based languages, left replace (right) provide a dedicated sublanguage consumers this paper, we present analyze wider space languages encompasses four kinds rules: Introduction elimination, both right. We influence rule choice on program structure argue that having all enriches programmer’s modularity arsenal. particular, identify ways adhering to principle ”the follows data“ show they correspond possible choices rules. also propose bi-expressibility guide validate connective. Finally, deepen well-known dualities between different connectives means proof/refutation duality.