Interfacing with Metatheory.jl

This section is for Julia package developers who may want to use the rule rewriting systems on their own expression types.

Defining the interface

Metatheory.jl matchers can match any Julia object that implements an interface to traverse it as a tree. The interface in question, is defined in the TermInterface.jl package. Its purpose is to provide a shared interface between various symbolic programming Julia packages. In particular, you should define methods from TermInterface.jl for an expression tree type T with symbol types S to work with SymbolicUtils.jl You can read the documentation of TermInterface.jl on the Github repository.

Concrete example

using Metatheory, TermInterface, Test
using Metatheory.EGraphs

We first define our custom expression type in MyExpr: It behaves like Expr, but it adds some extra fields.

struct MyExpr
  head::Any
  args::Vector{Any}
  foo::String # additional metadata
end
MyExpr(head, args) = MyExpr(head, args, "")
MyExpr(head) = MyExpr(head, [])

Main.var"ex-custom_types".MyExpr

We also need to define equality for our expression.

function Base.:(==)(a::MyExpr, b::MyExpr)
  a.head == b.head && a.args == b.args && a.foo == b.foo
end

Overriding TermInterface` methods

First, we need to discern when an expression is a leaf or a tree node. We can do it by overriding istree.

TermInterface.istree(::MyExpr) = true

The operation function tells us what's the node's represented operation.

TermInterface.operation(e::MyExpr) = e.head

arguments tells the system how to extract the children nodes.

TermInterface.arguments(e::MyExpr) = e.args

A particular function is exprhead. It is used to bridge our custom MyExpr type, together with the Expr functionality that is used in Metatheory rule syntax. In this example we say that all expressions of type MyExpr, can be represented (and matched against) by a pattern that is represented by a :call Expr.

TermInterface.exprhead(::MyExpr) = :call

While for common usage you will always define exprhead it to be :call, there are some cases where you would like to match your expression types against more complex patterns, for example, to match an expression x against an a[b] kind of pattern, you would need to inform the system that exprhead(x) is :ref, because

ex = :(a[b])
(ex.head, ex.args)

(:ref, Any[:a, :b])

metadata should return the extra metadata. If you have many fields, i suggest using a NamedTuple.

TermInterface.metadata(e::MyExpr) = e.foo

Additionally, you can override EGraphs.preprocess on your custom expression to pre-process any expression before insertion in the E-Graph. In this example, we always uppercase the foo::String field of MyExpr.

EGraphs.preprocess(e::MyExpr) = MyExpr(e.head, e.args, uppercase(e.foo))

TermInterface provides a very important function called similarterm. It is used to create a term that is in the same closure of types of x. Given an existing term x, it is used to instruct Metatheory how to recompose a similar expression, given a head (the result of operation), some children (given by arguments) and additionally, metadata and exprehead, in case you are recomposing an Expr.

function TermInterface.similarterm(x::MyExpr, head, args; metadata = nothing, exprhead = :call)
  MyExpr(head, args, isnothing(metadata) ? "" : metadata)
end

Since similarterm works by making a new term similar to an existing term x, in the e-graphs system, there won't be enough information such as a 'reference' object. Only the type of the object is known. This extra function adds a bit of verbosity, due to compatibility with SymbolicUtils.jl

function EGraphs.egraph_reconstruct_expression(::Type{MyExpr}, op, args; metadata = nothing, exprhead = nothing)
  MyExpr(op, args, (isnothing(metadata) ? () : metadata))
end

Theory Example

Note that terms in the RHS will inherit the type of terms in the LHS.

t = @theory a begin
  f(z(2), a) --> f(a)
end

1-element Vector{RewriteRule}:
 f(z(2), ~a) --> f(~a)

Let's create an example expression and e-graph

hcall = MyExpr(:h, [4], "hello")
ex = MyExpr(:f, [MyExpr(:z, [2]), hcall])
g = EGraph(ex; keepmeta = true)

EGraph(IntDisjointSet([-1, -1, -1, -1, -1], Base.RefValue{Bool}(true)), Dict{Int64, EClass}(5 => EClass 5 ([ENode(call, f, Main.var"ex-custom_types".MyExpr, [2, 4])], ), 4 => EClass 4 ([ENode(call, h, Main.var"ex-custom_types".MyExpr, [3])], ), 2 => EClass 2 ([ENode(call, z, Main.var"ex-custom_types".MyExpr, [1])], ), 3 => EClass 3 ([4], ), 1 => EClass 1 ([2], )), Dict{AbstractENode, Int64}(4 => 3, 2 => 1, ENode(call, f, Main.var"ex-custom_types".MyExpr, [2, 4]) => 5, ENode(call, z, Main.var"ex-custom_types".MyExpr, [1]) => 2, ENode(call, h, Main.var"ex-custom_types".MyExpr, [3]) => 4), Int64[], 5, Dict{Union{Function, Symbol}, Union{Function, Symbol}}(:metadata_analysis => :metadata_analysis), Dict{Any, Vector{Int64}}(:f => [5], 4 => [3], 2 => [1], :h => [4], :z => [2]), Expr, Dict{Tuple{Any, Int64}, Type}(), 5, 0, false, Base.ImmutableDict{Int64, Tuple{Int64, Int64}}[], Tuple{Int64, Int64}[], ReentrantLock(nothing, 0x00000000, 0x00, Base.GenericCondition{Base.Threads.SpinLock}(Base.IntrusiveLinkedList{Task}(nothing, nothing), Base.Threads.SpinLock(0)), (8, 140126206070464, 165)))

We use settermtype! on an existing e-graph to inform the system about the default type of expressions that we want newly added expressions to have.

settermtype!(g, MyExpr)

Main.var"ex-custom_types".MyExpr

Now let's test that it works.

saturate!(g, t)
expected = MyExpr(:f, [MyExpr(:h, [4], "HELLO")], "")
extracted = extract!(g, astsize)
@test expected == extracted

Test Passed

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