Equational synonyms

We look at denotational semantics, using sets and functions, the substitution lemma and equational theory.

It is proved using a direct axiomatization of Kleisli categories of equational lifting monads.

Our framework allows equational reasoning of non-deterministic functions, even tho it is possible to specify non-determinism.

- (i.) The statement of problems in equational form should precede the solution of equations.

In quantitative judgments we may think x = y, or, as Boolero oses x = v ° p p y = - ° y, or, as Jevons proposes, x = xy, or, as Venn proposes, x which is not y=o; and equational symbolic logic is useful whenever we think in this quantitative way.