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A von Neumann language is any of those programming languages that are high-level abstract isomorphic copies of von Neumann architectures. As of 2004, most current programming languages fit into this description, likely as a consequence of the extensive domination of the von Neumann computer architecture during the past 50 years.

The differences between FORTRAN, C, and even Java, although considerable, are ultimately constrained by the fact that all three are based on the programming style of the von Neumann computer (if, for example, Java objects were all executed in parallel with asynchronous message passing and attribute-based declarative addressing, then Java would not be in the group).

The isomorphism between von Neumann programming languages and architectures is in the following manner:

• program variables → computer storage cells
• control statements → computer test-and-jump instructions
• assignment statements → fetching, storing instructions
• expressions → memory reference and arithmetic instructions

Using a metaphor from Backus, assignment statements in von Neumann languages split programming into two worlds: the right side and left side of assignment statements. The right side consists of expressions, an orderly mathematical space with potentially useful algebraic properties: most computation takes place here. The left side consists of statements, a disorderly mathematical space with few useful mathematical properties (structured programming can be seen as a limited heuristic that does apply in this space, though).

Backus claimed that there exists now in computer science a vicious cycle where the long standing emphasis on von Neumann languages has continued the primacy of the von Neumann computer architecture... and our dependency on it has made non-von Neumann languages uneconomical and thus limited their further development: the lack of widely available and effective non-von Neumann languages has deprived computer designers of the motivation and the intellectual foundation necessary to develop new computer architectures.

Some examples of non-von Neumann languages are: APL, FP, FL, J, NGL, ZPL, Mercury, and Plankalkül.