symbolicgraph

Symbolicgraph is a concept used to represent symbolic information as a graph. It is not a single standard data format but a family of representations in which expressions, constraints, or formulas are encoded as nodes and edges. Nodes denote symbols such as variables, constants, or operators, while edges indicate operands or relational structure. The graph-based form supports sharing of subexpressions, enabling memory-efficient storage and enabling common subexpression elimination during evaluation and rewriting.

A common instantiation is the term graph, where a node labeled by a function symbol connects to its argument nodes. Such graphs can be directed and may be acyclic, though some designs allow cycles to model recursive definitions or fixed-point computations. Graphs can be augmented with types or attributes to capture additional information about symbols and relations. Graph rewriting, driven by pattern-matching rules, provides a mechanism for transforming symbolic graphs, supporting algebraic simplification, solving equations, or executing proof steps.

Variants of symbolic graphs include hypergraphs, which can represent multi-arity relations more naturally, and attributed graphs, which attach metadata to nodes and edges. Constraint graphs and knowledge graphs are also used in related contexts to encode logical constraints and symbolic knowledge within a graph framework.

Applications span symbolic algebra systems, automated reasoning and theorem proving, model checking, symbolic execution in program analysis, and certain forms of knowledge representation. Benefits include compact representation and efficient sharing, while challenges involve the complexity of pattern matching, potential graph growth during rewriting, and interoperability with traditional term-based representations. See also term graph, graph rewriting, symbolic computation, and expression trees.