(theory Int_ArraysEx :written_by {Cesare Tinelli} :date {12/04/05} :updated {30/01/09} :history { 30/01/09 removed erroneous :assoc attribute for binary minus } :sorts (Int Array) :notes "The (unsupported) annotations of the function/predicate symbols have the following meaning: attribute | possible value | meaning ------------------------------------------------------- :assoc // the symbol is associative :comm // the symbol is commutative :unit a constant c c is the symbol's left and right unit :trans // the symbol is transitive :refl // the symbol is reflexive :irref // the symbol is irreflexive :antisym // the symbol is antisymmetric " :funs ((0 Int) (1 Int) (~ Int Int) ; unary minus (- Int Int Int) ; binary minus (+ Int Int Int :assoc :comm :unit {0}) (* Int Int Int :assoc :comm :unit {1}) (select Array Int Int) (store Array Int Int Array) ) :preds ((<= Int Int :refl :trans :antisym) (< Int Int :trans :irref) (>= Int Int :refl :trans :antisym) (> Int Int :trans :irref) ) :definition "This is a theory of functional arrays with extensionality with integer indeces and elements. It can be formally defined as the union of the SMT-LIB theory Int and the variant of the SMT-LIB theory ArraysEx under the signature morphism that maps both the sorts Index and Element of ArraysEx to the sort Int, and leaves every other symbol unchanged. " :notes "If for i=1,2, T_i is an SMT-LIB theory with sorts S_i, function symbols F_i, predicate symbols P_i, and axioms A_i, by \"union\" of T_1 and T_2 we mean the theory T with sorts S_1 U S_2, function symbols F_1 U F_2, predicate symbols P_1 U P_2, and axioms A_1 U A_2 (where U stands for set theoretic union). The theory T is a well-defined SMT-LIB theory whenever S_1, S_2, F_1, F_2, P_1, P_2 are all pairwise disjoin, as is the case for the component theories considered here. " )