Merge pull request #79 from JuliaDiffEq/hg/fix/constant

Refactor Constant representation

Author: ChrisRackauckas

README.md

@@ -147,16 +147,12 @@ In this section we define the core pieces of the IR and what they mean.
 
 ### Variables
 
-The simplest piece of the IR is the `Variable`. The `Variable` is the
+The most fundamental part of the IR is the `Variable`. The `Variable` is the
 context-aware single variable of the IR. Its fields are described as follows:
 
 - `name`: the name of the `Variable`. Note that this is not necessarily
   the same as the name of the Julia variable. But this symbol itself is considered
   the core identifier of the `Variable` in the sense of equality.
-- `value`: the value of the `Variable`. The meaning of the value can be
-  interpreted differently for different systems, but in most cases it's tied to
-  whatever value information would be required for the system to be well-defined
-  such as the initial condition of a differential equation.
 - `value_type`: the type that the values have to be. It's disconnected
   from the `value` because in many cases the `value` may not be able to be
   specified in advance even when we may already know the type. This can be used
@@ -179,6 +175,10 @@ context-aware single variable of the IR. Its fields are described as follows:
 - `context`: this is an open field for DSLs to carry along more context
   in the variables, but is not used in the systems themselves.
 
+### Constants
+
+`Constant` is a simple wrapper type to store numerical Julia constants.
+
 ### Operations
 
 Operations are the basic composition of variables and puts together the pieces

src/ModelingToolkit.jl

@@ -16,8 +16,8 @@ include("domains.jl")
 include("variables.jl")
 
 Base.promote_rule(::Type{T},::Type{T2}) where {T<:Number,T2<:Expression} = Expression
-Base.one(::Type{T}) where T<:Expression = Constant(1)
-Base.zero(::Type{T}) where T<:Expression = Constant(0)
+Base.zero(::Type{<:Expression}) = Constant(0)
+Base.one(::Type{<:Expression}) = Constant(1)
 Base.convert(::Type{Variable},x::Int64) = Constant(x)
 
 function caclulate_jacobian end

src/differentials.jl

@@ -16,7 +16,7 @@ function (D::Differential)(x::Variable)
 end
 Base.:(==)(D1::Differential, D2::Differential) = D1.order == D2.order && D1.x == D2.x
 
-Variable(x::Variable, D::Differential) = Variable(x.name,x.value,x.value_type,
+Variable(x::Variable, D::Differential) = Variable(x.name,x.value_type,
                 x.subtype,D,x.dependents,x.description,x.flow,x.domain,
                 x.size,x.context)
 
@@ -31,7 +31,7 @@ function expand_derivatives(O::Operation)
 
     return O
 end
-expand_derivatives(x::Variable) = x
+expand_derivatives(x) = x
 
 # Don't specialize on the function here
 function Derivative(O::Operation,idx)

src/operations.jl

@@ -8,12 +8,12 @@ end
 function Base.:(==)(x::Operation,y::Operation)
     x.op == y.op && length(x.args) == length(y.args) && all(isequal.(x.args,y.args))
 end
-Base.:(==)(x::Operation,y::Number) = false
-Base.:(==)(x::Number,y::Operation) = false
-Base.:(==)(x::Operation,y::Nothing) = false
-Base.:(==)(x::Nothing,y::Operation) = false
-Base.:(==)(x::Variable,y::Operation) = false
-Base.:(==)(x::Operation,y::Variable) = false
+Base.:(==)(::Operation, ::Number   ) = false
+Base.:(==)(::Number   , ::Operation) = false
+Base.:(==)(::Operation, ::Variable ) = false
+Base.:(==)(::Variable , ::Operation) = false
+Base.:(==)(::Operation, ::Constant ) = false
+Base.:(==)(::Constant , ::Operation) = false
 
 Base.convert(::Type{Expr}, O::Operation) =
     build_expr(:call, Any[Symbol(O.op); convert.(Expr, O.args)])
@@ -36,8 +36,7 @@ function find_replace!(O::Operation,x::Variable,y::Expression)
 end
 
 # For inv
-Base.convert(::Type{Operation},x::Int) = Operation(identity,Expression[Constant(x)])
-Base.convert(::Type{Operation},x::Bool) = Operation(identity,Expression[Constant(x)])
-Base.convert(::Type{Operation},x::Variable) = Operation(identity,Expression[x])
-Operation(x) = convert(Operation,x)
-Operation(x::Operation) = x
+Base.convert(::Type{Operation}, x::Number) = Operation(identity, Expression[Constant(x)])
+Base.convert(::Type{Operation}, x::Operation) = x
+Base.convert(::Type{Operation}, x::Expression) = Operation(identity, Expression[x])
+Operation(x) = convert(Operation, x)

src/simplify.jl

@@ -1,4 +1,4 @@
-function simplify_constants(O::Operation, shorten_tree = true)
+function simplify_constants(O::Operation, shorten_tree)
     while true
         O′ = _simplify_constants(O, shorten_tree)
         if is_operation(O′)
@@ -8,10 +8,13 @@ function simplify_constants(O::Operation, shorten_tree = true)
         O = O′
     end
 end
+simplify_constants(x, shorten_tree) = x
+simplify_constants(x) = simplify_constants(x, true)
+
 
 const AC_OPERATORS = (*, +)
 
-function _simplify_constants(O, shorten_tree = true)
+function _simplify_constants(O::Operation, shorten_tree)
     # Tree shrinking
     if shorten_tree && O.op ∈ AC_OPERATORS
         # Flatten tree
@@ -67,7 +70,7 @@ function _simplify_constants(O, shorten_tree = true)
 
     return O
 end
-simplify_constants(x::Variable, y=false) = x
-_simplify_constants(x::Variable, y=false) = x
+_simplify_constants(x, shorten_tree) = x
+_simplify_constants(x) = _simplify_constants(x, true)
 
 export simplify_constants

src/systems/diffeqs/first_order_transform.jl

@@ -1,13 +1,12 @@
 function lower_varname(var::Variable, naming_scheme; lower=false)
     D = var.diff
-    D == nothing && return var
+    D === nothing && return var
     order = lower ? D.order-1 : D.order
     lower_varname(var.name, D.x, order, var.subtype, naming_scheme)
 end
 function lower_varname(sym::Symbol, idv, order::Int, subtype::Symbol, naming_scheme)
-    order == 0 && return Variable(sym, subtype)
-    name = Symbol(String(sym)*naming_scheme*String(idv.name)^order)
-    Variable(name, subtype=subtype)
+    name = order == 0 ? sym : Symbol(sym, naming_scheme, string(idv.name)^order)
+    return Variable(name, subtype=subtype)
 end
 
 function ode_order_lowering(sys::DiffEqSystem; kwargs...)

src/utils.jl

@@ -33,7 +33,7 @@ end
 
 toexpr(ex) = MacroTools.postwalk(x -> isa(x, Expression) ? convert(Expr, x) : x, ex)
 
-is_constant(x::Variable) = x.subtype === :Constant
+is_constant(::Constant) = true
 is_constant(::Any) = false
 
 is_operation(::Operation) = true

src/variables.jl

@@ -1,6 +1,5 @@
 mutable struct Variable <: Expression
     name::Symbol
-    value
     value_type::DataType
     subtype::Symbol
     diff::Union{Function,Nothing}  # FIXME
@@ -13,26 +12,23 @@ mutable struct Variable <: Expression
 end
 
 Variable(name,
-         value = nothing,
-         value_type = typeof(value);
+         value_type = Any;
          subtype::Symbol=:Variable,
          dependents::Vector{Variable} = Variable[],
          flow::Bool = false,
          description::String = "",
          domain = Reals(),
          size = nothing,
          context = nothing) =
-         Variable(name,value,value_type,subtype,nothing,
+         Variable(name,value_type,subtype,nothing,
                   dependents,description,flow,domain,size,context)
 Variable(name,args...;kwargs...) = Variable(name,args...;subtype=:Variable,kwargs...)
 
-Variable(name,x::Variable) = Variable(name,x.value,x.value_type,
+Variable(name,x::Variable) = Variable(name,x.value_type,
                 x.subtype,D,x.dependents,x.description,x.flow,x.domain,
                 x.size,x.context)
 
 Parameter(name,args...;kwargs...) = Variable(name,args...;subtype=:Parameter,kwargs...)
-Constant(value::Number) = Variable(Symbol(value),value,typeof(value);subtype=:Constant)
-Constant(name,args...;kwargs...) = Variable(name,args...;subtype=:Constant,kwargs...)
 IndependentVariable(name,args...;kwargs...) = Variable(name,args...;subtype=:IndependentVariable,kwargs...)
 
 function DependentVariable(name,args...;dependents = [],kwargs...)
@@ -64,53 +60,38 @@ export Variable,Parameter,Constant,DependentVariable,IndependentVariable,JumpVar
        @Var, @DVar, @IVar, @Param, @Const
 
 
-Base.get(x::Variable) = x.value
+struct Constant <: Expression
+    value::Number
+end
+Base.get(c::Constant) = c.value
+
 
-Base.iszero(::Expression) = false
-Base.iszero(c::Variable) = get(c) isa Number && iszero(get(c))
-Base.isone(::Expression) = false
-Base.isone(c::Variable) = get(c) isa Number && isone(get(c))
+Base.iszero(ex::Expression) = isa(ex, Constant) && iszero(ex.value)
+Base.isone(ex::Expression)  = isa(ex, Constant) && isone(ex.value)
 
 
 # Variables use isequal for equality since == is an Operation
-function Base.:(==)(x::Variable,y::Variable)
-    x.name == y.name && x.subtype == y.subtype && x.value == y.value &&
+function Base.:(==)(x::Variable, y::Variable)
+    x.name == y.name && x.subtype == y.subtype &&
     x.value_type == y.value_type && x.diff == y.diff
 end
-
-function Base.:(==)(x::Variable,y::Number)
-    x == Constant(y)
-end
-
-function Base.:(==)(x::Number,y::Variable)
-    Constant(x) == y
-end
+Base.:(==)(::Variable, ::Number) = false
+Base.:(==)(::Number, ::Variable) = false
+Base.:(==)(::Variable, ::Constant) = false
+Base.:(==)(::Constant, ::Variable) = false
+Base.:(==)(c::Constant, n::Number) = c.value == n
+Base.:(==)(n::Number, c::Constant) = c.value == n
+Base.:(==)(a::Constant, b::Constant) = a.value == b.value
 
 function Base.convert(::Type{Expr}, x::Variable)
-    if x.subtype == :Constant
-        return x.value
-    elseif x.diff == nothing
-        return :($(x.name))
-    else
-        return :($(Symbol("$(x.name)_$(x.diff.x.name)")))
-    end
+    x.diff === nothing && return x.name
+    return Symbol("$(x.name)_$(x.diff.x.name)")
 end
+Base.convert(::Type{Expr}, c::Constant) = c.value
 
-function Base.show(io::IO, A::Variable)
-    if A.subtype == :Constant
-        print(io,"Constant($(A.value))")
-    else
-        str = "$(A.subtype)($(A.name))"
-        if A.value != nothing
-            str *= ", value = " * string(A.value)
-        end
-
-        if A.diff != nothing
-            str *= ", diff = " * string(A.diff)
-        end
-
-        print(io,str)
-    end
+function Base.show(io::IO, x::Variable)
+    print(io, x.subtype, '(', x.name, ')')
+    x.diff === nothing || print(io, ", diff = ", x.diff)
 end
 
 extract_idv(eq) = eq.args[1].diff.x
@@ -159,45 +140,29 @@ function _parse_vars(macroname, fun, x)
     # begin
     #     x
     #     y
-    #     z = exp(2)
+    #     z
     # end
     x = flatten_expr!(x)
     for _var in x
         iscall = typeof(_var) <: Expr && _var.head == :call
         issym    = _var isa Symbol
-        isassign = issym ? false : _var.head == :(=)
-        @assert iscall || issym || isassign "@$macroname expects a tuple of expressions!\nE.g. `@$macroname x y z=1`"
-        if iscall || issym
-            if iscall
-                dependents = :([$(_var.args[2:end]...)])
-                var = _var.args[1]
-            else
-                dependents = Variable[]
-                var = _var
-            end
-            lhs = var
-            push!(lhss, lhs)
-            expr = :( $lhs = $fun( Symbol($(String(lhs))) ,
-                      dependents = $dependents))
-        end
-        if isassign
-            iscall = typeof(_var.args[1]) <: Expr && _var.args[1].head == :call
-            if iscall
-                dependents = :([$(_var.args[1].args[2:end]...)])
-                lhs = _var.args[1].args[1]
-            else
-                dependents = Variable[]
-                lhs = _var.args[1]
-            end
-            rhs = _var.args[2]
-            push!(lhss, lhs)
-            expr = :( $lhs = $fun( Symbol($(String(lhs))) , $rhs,
-                      dependents = $dependents))
+        @assert iscall || issym "@$macroname expects a tuple of expressions!\nE.g. `@$macroname x y z`"
+
+        if iscall
+            dependents = :([$(_var.args[2:end]...)])
+            lhs = _var.args[1]
+        else
+            dependents = Variable[]
+            lhs = _var
         end
+
+        push!(lhss, lhs)
+        expr = :( $lhs = $fun( Symbol($(String(lhs))) ,
+                  dependents = $dependents))
         push!(ex.args, expr)
     end
-    push!(ex.args, Expr(:tuple, lhss...))
-    ex
+    push!(ex.args, build_expr(:tuple, lhss))
+    return ex
 end
 
 for funs in ((:DVar, :DependentVariable), (:IVar, :IndependentVariable),

test/basic_variables_and_operations.jl

@@ -10,11 +10,11 @@ using Test
 @Const c=0
 
 # Default values
-p = Parameter(:p, 1)
-u = DependentVariable(:u, [1], dependents = [t])
+p = Parameter(:p)
+u = DependentVariable(:u, dependents = [t])
 
-s = JumpVariable(:s,3,dependents=[t])
-n = NoiseVariable(:n,dependents=[t])
+s = JumpVariable(:s, dependents=[t])
+n = NoiseVariable(:n, dependents=[t])
 
 σ*(y-x)
 D(x)

test/derivatives.jl

@@ -11,7 +11,7 @@ expand_derivatives(dsin)
 
 @test expand_derivatives(dsin) == cos(t)
 dcsch = D(csch(t))
-@test expand_derivatives(dcsch) == simplify_constants(Operation(coth(t)*csch(t)*-1))
+@test expand_derivatives(dcsch) == simplify_constants(coth(t) * csch(t) * -1)
 
 # Chain rule
 dsinsin = D(sin(sin(t)))