regular logic



Type theory

natural deduction metalanguage, practical foundations

  1. type formation rule
  2. term introduction rule
  3. term elimination rule
  4. computation rule


syntax object language


logiccategory theorytype theory
falseinitial objectempty type
proofgeneralized elementprogram
cut rulecomposition of classifying morphisms / pullback of display mapssubstitution
cut elimination for implicationcounit for hom-tensor adjunctionbeta reduction
introduction rule for implicationunit for hom-tensor adjunctioneta conversion
logical conjunctionproductproduct type
implicationinternal homfunction type
negationinternal hom into initial objectfunction type into empty type
universal quantificationdependent productdependent product type
equivalencepath space objectidentity type
equivalence classquotientquotient type
inductioncolimitinductive type, W-type, M-type
higher inductionhigher colimithigher inductive type
coinductionlimitcoinductive type
setinternal 0-groupoidBishop set/setoid
universeobject classifiertype of types
proof netstring diagramquantum circuit
synthetic mathematicsdomain specific embedded programming language

homotopy levels




Regular logic is the internal logic of regular categories. Its logical operations consist only of truth, conjunction, and existential quantification, which makes it a superset of finite-limit logic and a subset of coherent logic and geometric logic.


Last revised on December 18, 2018 at 03:06:08. See the history of this page for a list of all contributions to it.