Interface for symbolic terms
Author JuliaSymbolics
22 Stars
Updated Last
8 Months Ago
Started In
May 2021


This package contains definitions for common functions that are useful for symbolic expression manipulation. Its purpose is to provide a shared interface between various symbolic programming Julia packages, for example SymbolicUtils.jl, Symbolics.jl and Metatheory.jl.


You should define the following methods for an expression tree type T with symbol types S to work with TermInterface.jl, and therefore with SymbolicUtils.jl and Metatheory.jl.

istree(x::T) or istree(x::Type{T})

Check if x represents an expression tree. If returns true, it will be assumed that operation(::T) and arguments(::T) methods are defined. Definining these three should allow use of SymbolicUtils.simplify on custom types. Optionally symtype(x) can be defined to return the expected type of the symbolic expression.


If x is a term as defined by istree(x), exprhead(x) must return a symbol, corresponding to the head of the Expr most similar to the term x. If x represents a function call, for example, the exprhead is :call. If x represents an indexing operation, such as arr[i], then exprhead is :ref. Note that exprhead is different from operation and both functions should be defined correctly in order to let other packages provide code generation and pattern matching features.


Returns the head (a function object) performed by an expression tree. Called only if istree(::T) is true. Part of the API required for simplify to work. Other required methods are arguments and istree


Returns the arguments (a Vector) for an expression tree. Called only if istree(x) is true. Part of the API required for simplify to work. Other required methods are operation and istree

In addition, the methods for Base.hash and Base.isequal should also be implemented by the types for the purposes of substitution and equality matching respectively.

similarterm(t::MyType, f, args, symtype=T; metadata=nothing, exprhead=exprhead(t))

Or similarterm(t::Type{MyType}, f, args, symtype=T; metadata=nothing, exprhead=:call).

Construct a new term with the operation f and arguments args, the term should be similar to t in type. if t is a SymbolicUtils.Term object a new Term is created with the same symtype as t. If not, the result is computed as f(args...). Defining this method for your term type will reduce any performance loss in performing f(args...) (esp. the splatting, and redundant type computation). T is the symtype of the output term. You can use SymbolicUtils.promote_symtype to infer this type. The exprhead keyword argument is useful when creating Exprs.



If x is a term satisfying istree(x) and your term type T orovides and optimized implementation for storing the arguments, this function can be used to retrieve the arguments when the order of arguments does not matter but the speed of the operation does. Defaults to arguments(x).


The supposed type of values in the domain of x. Tracing tools can use this type to pick the right method to run or analyse code.

This defaults to typeof(x) if x is numeric, or Any otherwise. For the types defined in this SymbolicUtils.jl, namely T<:Symbolic{S} it is S.

Define this for your symbolic types if you want SymbolicUtils.simplify to apply rules specific to numbers (such as commutativity of multiplication). Or such rules that may be implemented in the future.

Required Packages

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