The semantics of procedures and parameters were formalized by Hoare  in terms of axioms and rules of inference. Igarashi et al.  reformulated Hoare's system. This paper extends their rule of inference for procedure calls to allow
actual variable parameters to occur in actual value parameters;
the body of a procedure to contain global variables that do not occur in assignment positions;
post-conditions and “internal” assertions of a procedure to refer to the initial values of variable parameters.
None of these are allowed in Hoare's system or the system of Igarashi, London and Luckham. An attractive feature of these extensions is that they do not increase the complexity of the rules of inference.