Tests for rewrite hellper

docs/src/manual/derivatives.md

@@ -13,6 +13,7 @@ the differentials down to basic one-variable expressions.
 ```@docs
 Differential
 expand_derivatives
+is_derivative
 ```
 
 !!! note

docs/src/manual/expression_manipulation.md

@@ -28,4 +28,7 @@ Symbolics.diff2term
 Symbolics.solve_for
 Symbolics.degree
 Symbolics.coeff
+Symbolics.replace
+Symbolics.occursin
+Symbolics.filterchildren
 ```

src/Symbolics.jl

@@ -50,6 +50,7 @@ import MacroTools: splitdef, combinedef, postwalk, striplines
 include("wrapper-types.jl")
 
 include("num.jl")
+include("rewrite-helpers.jl")
 include("complex.jl")
 
 """
@@ -96,7 +97,7 @@ using DiffRules, SpecialFunctions, NaNMath
 
 using SparseArrays
 
-export Differential, expand_derivatives
+export Differential, expand_derivatives, is_derivative
 
 include("diff.jl")
 

src/rewrite-helpers.jl

@@ -0,0 +1,134 @@
+"""
+    replace(expr::Symbolic, rules...)
+Walk the expression and replace subexpressions according to `rules`. `rules`
+could be rules constructed with `@rule`, a function, or a pair where the
+left hand side is matched with equality (using `isequal`) and is replaced by the right hand side.
+
+Rules will be applied left-to-right simultaneously,
+so only one pattern will be applied to any subexpression,
+and the patterns will only be applied to the input text,
+not the replacements.
+
+Set `fixpoint = true` to repeatedly apply rules until no
+change to the expression remains to be made.
+"""
+function Base.replace(expr::Num, r::Pair, rules::Pair...)
+    _replace(unwrap(expr), r, rules...)
+end
+
+# Fix ambiguity
+function Base.replace(expr::Num, rules...)
+    _replace(unwrap(expr), rules...)
+end
+
+function Base.replace(expr::Symbolic, rules...)
+    _replace(unwrap(expr), rules...)
+end
+
+function Base.replace(expr::Symbolic, r::Pair, rules::Pair...)
+    _replace(expr, r, rules...)
+end
+
+function _replace(expr::Symbolic, rules...; fixpoint=false)
+    rs = map(r -> r isa Pair ? (x -> isequal(x, r[1]) ? r[2] : nothing) : r, rules)
+    R = Prewalk(Chain(rs))
+    if fixpoint
+        Fixpoint(R)(expr)
+    else
+        R(expr)
+    end
+end
+
+"""
+    occursin(c, x)
+Returns true if any part of `x` fufills the condition given in c. c can be a function or an expression.
+If it is a function, returns true if x is true for any part of x. If c is an expression, returns
+true if x contains c.
+
+Examples:
+```julia
+@syms x y
+Symbolics.occursin(x, log(x) + x + 1) # returns `true`.
+Symbolics.occursin(x, log(y) + y + 1) # returns `false`.
+```
+
+```julia
+@variables t X(t)
+D = Differential(t)
+Symbolics.occursin(Symbolics.is_derivative, X + D(X) + D(X^2)) # returns `true`.
+```
+"""
+function Base.occursin(r::Function, y::Union{Num, Symbolic})
+    _occursin(r, y)
+end
+
+Base.occursin(r::Num, y::Num) = occursin(unwrap(r), unwrap(y))
+Base.occursin(r::Num, y::Symbolic) = occursin(unwrap(r), unwrap(y))
+
+function _occursin(r, y)
+    y = unwrap(y)
+    if r isa Function
+        if r(y)
+            return true
+        end
+    end
+
+    if istree(y)
+        return r(operation(y)) ||
+                any(y->_occursin(r, y), arguments(y))
+    else
+        return false
+    end
+end
+
+"""
+filterchildren(c, x)
+Returns all parts of `x` that fufills the condition given in c. c can be a function or an expression.
+If it is a function, returns everything for which the function is `true`. If c is an expression, returns
+all expressions that matches it.
+
+Examples:
+```julia
+@syms x
+Symbolics.filterchildren(x, log(x) + x + 1)
+```
+returns `[x, x]`
+
+```julia
+@variables t X(t)
+D = Differential(t)
+Symbolics.filterchildren(Symbolics.is_derivative, X + D(X) + D(X^2))
+```
+returns `[Differential(t)(X(t)^2), Differential(t)(X(t))]`
+"""
+filterchildren(r, y) = filterchildren!(r, y, [])
+
+function filterchildren!(r::Any, y, acc)
+    y = unwrap(y)
+    r = unwrap(r)
+    if isequal(r, y)
+        push!(acc, y)
+        return acc
+    elseif r isa Function
+        if r(y)
+            push!(acc, y)
+            return acc
+        end
+    end
+
+    if istree(y)
+        if isequal(r, operation(y))
+            push!(acc, operation(y))
+        elseif r isa Function && r(operation(y))
+            push!(acc, operation(y))
+        end
+        foreach(c->filterchildren!(r, c, acc),
+                arguments(y))
+        return acc
+    end
+end
+
+module RewriteHelpers
+import Symbolics: filterchildren, unwrap
+export replace, occursin, filterchildren, unwrap
+end

test/diff.jl

@@ -348,3 +348,26 @@ let
     @test isequal(expand_derivatives(Differential(t)(im*t)), im)
     @test isequal(expand_derivatives(Differential(t)(t^2 + im*t)), 2t + im)
 end
+
+
+# Check `is_derivative` function
+let
+    @variables t X(t) Y(t)
+    @syms a b
+    D = Differential(t)
+    my_f(x, y) = x^3 + 2y
+
+    # Single expressions.
+    @test !Symbolics.is_derivative(Symbolics.unwrap(D))
+    @test !Symbolics.is_derivative(Symbolics.unwrap(t))
+    @test !Symbolics.is_derivative(Symbolics.unwrap(X))
+    @test !Symbolics.is_derivative(Symbolics.unwrap(a))
+    @test !Symbolics.is_derivative(Symbolics.unwrap(1))
+
+    # Composite expressions.
+    @test Symbolics.is_derivative(Symbolics.unwrap(D(X)))
+    @test !Symbolics.is_derivative(Symbolics.unwrap(D(X) + 3))
+    @test Symbolics.is_derivative(Symbolics.unwrap(D(X + 2a*Y)))
+    @test !Symbolics.is_derivative(Symbolics.unwrap(D(X) + D(Y)))
+    @test !Symbolics.is_derivative(Symbolics.unwrap(my_f(X, D(Y))))
+end

test/rewrite_helpers.jl

@@ -0,0 +1,102 @@
+
+# Fetch packages.
+using Symbolics
+using Symbolics.RewriteHelpers
+using Test 
+
+@variables t X(t) Y(t) Z(t)
+@syms a b
+D = Differential(t)
+my_f(x, y) = x^3 + 2y
+
+# Check replace function.
+let
+    @test isequal(replace(X + X + X, X =>1), 3)
+    @test isequal(replace(X + X + X, Y => 1), 3X)
+    @test isequal(replace(X + X + X, X => Y), 3Y)
+    @test isequal(replace(X + Y^2 - Z, Y^2 => Z), X)
+end
+
+# Test occursin function.
+let
+    ex1 = 2X^a - log(b + my_f(Y,Y)) - 3
+    ex2 = X^(Y^(Z-a)) +log(log(log(b)))
+    ex3 = sin(X) + sin(Y) + a*a*a*(1-X)
+    ex4 = exp(a)/(pi*a) + D(Y) + D(my_f(1,Z))
+    ex5 = a + 5b^2
+
+    # Test for variables.
+    @test occursin(X, ex1)
+    @test occursin(X, ex2)
+    @test occursin(X, ex3)
+    @test !occursin(X, ex4)
+    @test occursin(Y, ex1)
+    @test occursin(Y, ex2)
+    @test occursin(Y, ex3)
+    @test occursin(Y, ex4)
+    @test !occursin(Z, ex1)
+    @test occursin(Z, ex2)
+    @test !occursin(Z, ex3)
+    @test occursin(Z, ex4)
+
+    # Test for variables.
+    @test_broken occursin(a, ex1)
+    @test_broken occursin(a, ex2)
+    @test_broken occursin(a, ex3)
+    @test_broken occursin(a, ex4)
+    @test occursin(a, ex5)
+    @test_broken occursin(b, ex1)
+    @test_broken occursin(b, ex2)
+    @test !occursin(b, ex3)
+    @test !occursin(b, ex4)
+    @test occursin(b, ex5)
+
+    # Test for function.
+    @test !occursin(is_derivative, ex1)
+    @test !occursin(is_derivative, ex2)
+    @test !occursin(is_derivative, ex3)
+    @test occursin(is_derivative, ex4)
+end
+
+# Check filterchildren function.
+let 
+    ex1 = 2X^a - log(b + my_f(Y,Y)) - 3
+    ex2 = X^(Y^(Z-a)) +log(log(log(b)))
+    ex3 = sin(X) + sin(Y) + a*a*a*(1-X)
+    ex4 = exp(a)/(pi*a) + D(Y) + D(my_f(1,Z))
+    ex5 = a + 5b^2
+
+    # Test for variables.
+    @test isequal(filterchildren(X, ex1), [X])
+    @test isequal(filterchildren(X, ex2), [X])
+    @test isequal(filterchildren(X, ex3), [X, X])
+    @test isequal(filterchildren(X, ex4), [])
+    @test isequal(filterchildren(Y, ex1), [Y, Y])
+    @test isequal(filterchildren(Y, ex2), [Y])
+    @test isequal(filterchildren(Y, ex3), [Y])
+    @test isequal(filterchildren(Y, ex4), [Y])
+    @test isequal(filterchildren(Z, ex1), [])
+    @test isequal(filterchildren(Z, ex2), [Z])
+    @test isequal(filterchildren(Z, ex3), [])
+    @test isequal(filterchildren(Z, ex4), [Z])
+
+    # Test for variables.
+
+    @test isequal(filterchildren(a, ex1), [a])
+    @test isequal(filterchildren(a, ex2), [a])
+    @test isequal(filterchildren(a, ex3), [a])
+    @test isequal(filterchildren(a, ex4), [a, a])
+    @test isequal(filterchildren(a, ex5), [a])
+    @test isequal(filterchildren(b, ex1), [b])
+    @test isequal(filterchildren(b, ex2), [b])
+    @test isequal(filterchildren(b, ex3), [])
+    @test isequal(filterchildren(b, ex4), [])
+    @test isequal(filterchildren(b, ex5), [b])
+
+    # Test for function.
+    @test isequal(filterchildren(is_derivative, ex1), [])
+    @test isequal(filterchildren(is_derivative, ex2), [])
+    @test isequal(filterchildren(is_derivative, ex3), [])
+    @test isequal(filterchildren(is_derivative, ex4), [D(Y), D(my_f(1,Z))])
+end
+

test/runtests.jl

@@ -39,6 +39,7 @@ if GROUP == "All" || GROUP == "Core"
     @safetestset "Build Function Test" begin include("build_function.jl") end
     @safetestset "Build Function Array Test" begin include("build_function_arrayofarray.jl") end
     @safetestset "Build Function Array Test Named Tuples" begin include("build_function_arrayofarray_named_tuples.jl") end
+    @safetestset "Rewrite Helper Function Test" begin include("rewrite_helpers.jl") end
     VERSION >= v"1.9" && @safetestset "Build Targets Test" begin include("build_targets.jl") end
     @safetestset "Latexify Test" begin include("latexify.jl") end
     @safetestset "Domain Test" begin include("domains.jl") end