expressions

Expressions and Formulae a la carte.

This package is aimed at providing means of fixing a first-order language and declaring sorted expressions and formulae, the types ensure the declared expressions fall within the language.

This package pre-defines the common logical symbols for conjunction, disjunction, negation, and universal and existential quantification as well as some specific non-logical symbols such as equality, addition of linear integer arithmetic, and other. Common languages such as Lia and ALia (standard linear integer arithmetic and linear integer arithmetic with arrays) come included.

An example of a formula declaration:

-- Let's state that zero is successor to no integer (while this would be
-- true for non-negative integers, stated this way it is clearly false, but
-- it still is a well-formed first-order statement)

forall [var "x" :: Var 'IntegralSort] (cnst 0 ./=. var "x" .+. cnst 1) :: Lia 'BooleanSort

Let's see what declarations the library rejects:

(var "x" :: Lia 'BooleanSort) .=. (var "y" :: Lia 'IntegralSort)
(var "x" :: Lia 'BooleanSort) .=. (var "y" :: ALia 'BooleanSort)
forall [var "x" :: Var 'IntegralSort] true :: QFLia 'BooleanSort