diff --git a/src/jit/JIT.jl b/src/jit/JIT.jl
index 3283005a..2f30bb0c 100644
--- a/src/jit/JIT.jl
+++ b/src/jit/JIT.jl
@@ -1,5 +1,8 @@
 module JIT
 
+include("shapes.jl")
+include("inplace.jl")
 include("trace.jl")
+include("lib.jl")
 
 end
diff --git a/src/jit/inplace.jl b/src/jit/inplace.jl
new file mode 100644
index 00000000..cf87b102
--- /dev/null
+++ b/src/jit/inplace.jl
@@ -0,0 +1,11 @@
+mutable struct Cached{F,A}
+  f::F
+  buffer::A
+end
+
+function (c::Cached)(args...)
+  sh = shape(c.f, shape(args)...)
+  bytes(sh) > length(c.buffer) && (c.buffer = similar(c.buffer, bytes(sh)))
+  y = restructure(sh, c.buffer)
+  inplace!(c.f, y, args...)
+end
diff --git a/src/jit/lib.jl b/src/jit/lib.jl
new file mode 100644
index 00000000..cc89fa00
--- /dev/null
+++ b/src/jit/lib.jl
@@ -0,0 +1,9 @@
+# Primitive definitions
+
+inplace!(::typeof(*), C::AbstractArray, A::AbstractMatrix, B::AbstractArray) =
+  A_mul_B!(C, A, B)
+
+shape(::typeof(broadcast), f, xs...) =
+  Shape{eltype(xs[1])}(Base.Broadcast.broadcast_shape(size.(xs)...)...)
+
+inplace!(::typeof(broadcast), y, f, xs...) = broadcast!(f, y, xs...)
diff --git a/src/jit/shapes.jl b/src/jit/shapes.jl
new file mode 100644
index 00000000..bd6f4993
--- /dev/null
+++ b/src/jit/shapes.jl
@@ -0,0 +1,37 @@
+struct Shape{T,N}
+  dims::NTuple{N,Int}
+end
+
+VecShape{T} = Shape{T,1}
+MatShape{T} = Shape{T,2}
+
+Shape{T}(dims::Vararg{Integer,N}) where {T,N} = Shape{T,N}(dims)
+
+Base.size(s::Shape) = s.dims
+Base.size(s::Shape, n) = s.dims[n]
+Base.length(s::Shape) = prod(s.dims)
+Base.eltype(s::Shape{T}) where T = T
+
+Base.sizeof(s::Shape{T}) where T = sizeof(T)*prod(size(s))
+
+function Base.show(io::IO, s::Shape{T}) where T
+  print(io, "Shape{$T}(")
+  join(io, s.dims, ", ")
+  print(io, ")")
+end
+
+shape(x) = typeof(x)
+shape(x::Shape) = x
+shape(x::Tuple) = shape.(x)
+shape(x::AbstractArray) = Shape{eltype(x)}(size(x)...)
+
+bytes(s::Shape) = sizeof(s)
+bytes(x::Tuple) = sum(bytes.(x))
+
+# Recover structure from byte buffers
+# Make sure to hold on to the parent buffer for the lifetime of the data.
+
+function restructure(sh::Shape{T}, buf::Vector{UInt8}) where T
+  buf = unsafe_wrap(Array, pointer(buf), sizeof(sh))
+  reshape(reinterpret(T, buf), size(sh))
+end