rewrite helpers module

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")
 
 """

src/rewrite-helpers.jl

@@ -0,0 +1,85 @@
+"""
+    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 _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
+# Fix ambiguity
+function Base.replace(expr::Num, r::Pair, rules::Pair...)
+    _replace(unwrap(expr), r, rules...)
+end
+
+function Base.replace(expr::Num, rules...)
+    _replace(unwrap(expr), rules...)
+end
+
+function Base.replace(expr::Symbolic, r, rules...)
+    _replace(expr, r, rules)
+end
+
+
+Base.occursin(x::Num, y::Num) = occursin(unwrap(x), unwrap(y))
+@wrapped function Base.occursin(r::Any, y::Real)
+    y = unwrap(y)
+    if isequal(r, y)
+        return true
+    elseif 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
+
+function filterchildren!(r::Any, y::Union{Num, Symbolic}, acc)
+    y = unwrap(y)
+    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 r(operation(y))
+            push!(acc, y)
+        end
+        foreach(c->filterchildren!(r, c, acc),
+                arguments(y))
+        return acc
+    end
+end
+
+filterchildren(r, y) = filterchildren!(r, y, [])
+
+module RewriteHelpers
+import Symbolics: is_derivative, filterchildren, unwrap
+export replace, occursin, is_derivative,
+       filterchildren, unwrap
+end