unify functions and models in autodiff

src/rt/code.jl

@@ -1,22 +1,14 @@
 function forward_temporaries(body, ∇s)
   exs = union((common(body, ∇) for ∇ in values(∇s))...)
-  filter!(ex -> !@capture(value(ex), self._), exs)
+  filter!(ex -> !(@capture(value(ex), self._) || isconstant(ex)), exs)
   [ex=>symbol("temp", i) for (i, ex) in enumerate(exs)]
 end
 
-resolve_calls(ex) = ex
-
-function resolve_calls(ex::Expr)
-  @capture(ex, f_(a__)) ?
-    Expr(:call, eval(current_module(), f), map(resolve_calls, a)...) :
-    Expr(ex.head, map(resolve_calls, ex.args))
-end
-
 function process_func(ex, params)
   @capture(shortdef(ex), (args__,) -> body_)
-  body = il(graphm(resolve_calls(body)))
+  body = il(graphm(body))
   body = map(x -> x in params ? :(self.$x) : x, body)
-  ∇ = ∇graph(body, @flow(∇))
+  ∇ = invert(body, @flow(∇))
   return args, body, ∇
 end
 
@@ -74,11 +66,10 @@ function process_type(ex)
   args, body, ∇s = process_func(funcs[1], params)
   @assert length(args) == 1
   temps = forward_temporaries(body, ∇s)
-  ∇s
   quote
     $(build_type(T, params, collect(values(temps))))
     (self::$T)($(args...),) = $(syntax(build_forward(body, temps)))
-    back!(self::$T, ∇) = $(syntax(build_backward(∇s, args[1], params, temps)))
+    back!(self::$T, ∇, $(args...)) = $(syntax(build_backward(∇s, args[1], params, temps)))
     $(build_update(T, params))
   end |> longdef |> MacroTools.flatten
 end

src/rt/diff.jl

@@ -2,29 +2,30 @@ import Flow: isconstant, il, dl, cse, prewalk, graphm, syntax, @v
 
 vertex(a...) = IVertex{Any}(a...)
 
-∇graph(f, ∇, a) = (@v(∇ .* ∇₁(f)(a)),)
+# Special case a couple of operators to clean up output code
+const symbolic = Dict()
 
-∇graph(::typeof(+), ∇, a...) = (∇ for _ in a)
+symbolic[:+] = (Δ, args...) -> map(_->Δ, args)
 
-∇graph(::typeof(-), ∇, a, b) = ∇, @v(-∇)
+function ∇v(v::Vertex, Δ)
+  haskey(symbolic, value(v)) && return symbolic[value(v)](Δ, inputs(v)...)
+  Δ = vertex(:back!, vertex(value(v)), Δ, inputs(v)...)
+  map(i -> @flow(getindex($Δ, $i)), 1:Flow.nin(v))
+end
 
-∇graph(::typeof(*), ∇, a, b) = map(x->@v(∇ * transpose(x)), (b, a))
-
-function ∇graph(v::IVertex, ∇, out = d())
+function invert(v::IVertex, Δ, out = d())
   if isconstant(v)
     @assert !haskey(out, value(v))
-    out[value(v)] = il(∇)
+    out[value(v)] = il(Δ)
   else
-    ∇′s = ∇graph(value(v), ∇, inputs(v)...)
-    for (v′, ∇′) in zip(inputs(v), ∇′s)
-      ∇graph(v′, ∇′, out)
+    Δ′s = ∇v(v, Δ)
+    for (v′, Δ′) in zip(inputs(v), Δ′s)
+      invert(v′, Δ′, out)
     end
   end
   return out
 end
 
-macro derive(ex)
-  ∇s = ∇graph(il(graphm(resolve_calls(ex))), @flow(∇))
-  v = vertex(Flow.Do(), (@v(Flow.Assign(Symbol("∇", k))(v)) for (k, v) in ∇s)...)
-  Expr(:quote, @> v cse syntax prettify)
-end
+back!(::typeof(+), Δ, args...) = map(_ -> Δ, args)
+
+back!(::typeof(*), Δ, a, b) = Δ*b', Δ*a'