<!--Version 1.21 from 21\ Feb\ 2024@Copyright 
    --><!--
   ++++++++++++++++++++++++++++++
    The DTD of Core SBML 
   ++++++++++++++++++++++++++++++ --><!-- 
      Joachim Niehren, 
    Inria Center of the University of Lille,
    BioComputing Team, France
   --><!--@Copyright 
    -->
 <!--
    +++++++++++ Section ++++++++++++++
    Version and Sources
    +++++++++++++++++++++++++++++++ --><!--
      
      Version   from  . 
    --> <!--
      
      The documentation  of the schema of Core SBML shown here is
	      created from the same source as
	      the DTD  of Core SBML itself.
    --> <!--
    +++++++++++ Section ++++++++++++++
    Core SBML Networks
    +++++++++++++++++++++++++++++++ --><!--
      
      A Core SBML network represents a reaction network
      with a set of algebraic and differential equations possibly
      with delays.
    --> 
    <!--  - - - - - - - - - - - - - -  - - - - - - - - - - - - - - - -
    Introduction
     - - - - - - - - - - - - - -  - - - - - - - - - - - - - - - - -  -->
         <!--
      
	Core SBML has an XML syntax, so it is composed
	from XML elements. Any network of Core SBML
	contains a set of variable and
	reaction elements. Species are
	special types of variables. Each reaction has
	linear combination of reactants and
	a linear combination of products. Reactants
	and products must always be variables
	of type species. A reaction
	also has a set of modifiers, which are variables
	of any type.
      --> 
         <!--
      
	Each reactions has a kinetic expression, which
	is a  arithmetic expressions that is build from the variables
	and the usual arithmetic functions. Furthermore, kinetic
	expressions  may use macros for subexpresssions that
	are defined by expression
	elements. They may also contain application of
	arithmetic functions that are defined by
	the network's function elements.
      --> 
         <!--
      
	Any Core SBML network can be drawn as a graph that
	is  bipartite.  The  variable elements yield
	the variable nodes, while the reaction
	elements constitute its reaction nodes
	of the graph of a network,
	Variable nodes are drawn as circles and
	reaction nodes as  boxes, following the
	usual notions coming from Petri nets.
	The reactants, products, and modifiers
	define the
	edges of the network's graph. The edge
	go from the nodes of reactants and modifiers to
	the nodes of reactions and from the nodes
	of  reactions to the nodes of products. 
      --> 
         <!--
      
	Any Core SBML network contains a set of event elements
	that describe possible changes of the values of variables
	controlled by differential equations.
	Finally, it may also contain comment
	and edgecluster elements that serve to
	represent the edges of the network's graph
	in a clustered manner.
      --> 
      
    <!--  - - - - - - - - - - - - - -  - - - - - - - - - - - - - - - -
    Network Elements
     - - - - - - - - - - - - - -  - - - - - - - - - - - - - - - - -  -->
         <!--
      
	In summary, any network element
	has the following content:
      --> 
         
	<!ELEMENT network (( variable |
               reaction | expression | function | event |
               comment | edgecluster )*) >
      
         <!--
      
	The attributes of a network are not required since
	mostly of administrative or graphicla character
	and unrelated to its semantics.
      --> 
         
	<!ATTLIST network
               id      CDATA        #IMPLIED
	       name    CDATA      #IMPLIED
	       biomodels CDATA  #IMPLIED
	       version CDATA      #IMPLIED
	       csbml-version CDATA #IMPLIED 
	       kind    CDATA      #IMPLIED
	       scale   CDATA      #IMPLIED>
      
         <!--
       Any network may have an identifier, a kind, and a scale for its graph.--> 
          <!-- @id  the identifier is relevant when referencing to the networks entities within LaTeX -->

          <!-- @scale  the scale is a positive real number      that permits to  scale      the x-axis and y-axis simultaneously -->

          <!-- @kind  is an identifier which serves for     debugging purposes -->

      
    <!--  - - - - - - - - - - - - - -  - - - - - - - - - - - - - - - -
    Variable Types
     - - - - - - - - - - - - - -  - - - - - - - - - - - - - - - - -  -->
         <!--
      
	Each variable must have
	an attribute @type which  may
	have one of  four possible values:
      --> 
         <!--  ° 
               species,
	 ° 
               algebraic,
	 ° 
               differential, or
	 ° 
               control
            -->
         <!--
      
	Only variables of type species may be used as reactants
	or products of reactions, while any type of variables may
	be used in the kinetic expressions or as modifier of the reaction. Furthermore,
	variablesof type  control do not lead to any
	variable node in the graph, in contrast to the three other
	types of variables.
      --> 
         <!--
      
	Semantically, each  variable defines a signal or
	equivalently a  trajectory, i.e., a real-valued function from the
	positive reals.  The type of a variable declares how its signal
	is defined by the network. 
      --> 
         <!--
      
	The signal of a species variable is specified by the reactions
	of the networks: The reactions define a system of
	differential equations, one for each species variable
	an equality for the derivation. The signal of a species
	variable is a solution of the differential equations.
      --> 
         <!--
      
	For any algebraic variable the signal is defined by
	some algebraic equation that is explictely given
	by the network. The signal of a differential variable
	is given a differential equation that is explictely
	given by the network. A control variable
	is constant except that its value may be
	changed by events.	Since directed by
	differential equations, the values of
	all nonalgebraic variables can also be
	updated by events.
      --> 
      <!--
    +++++++++++ Section ++++++++++++++
    Identified  Objects
    +++++++++++++++++++++++++++++++ --><!--
      
    All variable, reaction, and
    expression elements are objects with unique
    identifiers and may have pretty names.
    --> 
	  <!ENTITY % object "
                 id               CDATA     #REQUIRED
	         latex-look   CDATA    #IMPLIED
	         comment     CDATA    #IMPLIED
          ">
	 <!-- id  the unique identifier of the object. The
	symbols "-" and "+" are the only non alpha numeric symbols
	allowed
	in identifiers.
	 -->
 <!-- latex-look  the pretty name of the object. It
	is allowed to contain arbitarary symbols. In many
	tools, these pretty names will be interpreted by latex, so
	they better contain valid latex sequences.
	 -->
 <!-- @comment  a latex comment -->
<!--
    +++++++++++ Section ++++++++++++++
    Graphical Entities
    +++++++++++++++++++++++++++++++ --><!--
      
      The variable elements of Core SBML networks
      are identified objects that contain information about where
      to place the corresponding graph nodes.
    --> 
    <!--  - - - - - - - - - - - - - -  - - - - - - - - - - - - - - - -
    Graph Nodes
     - - - - - - - - - - - - - -  - - - - - - - - - - - - - - - - -  -->
         <!--
      
	  The graph of a reaction network has nodes for variables
	  of type different than  control,
	  reactions, and edge clusters. 
	--> 
         
	  <!ENTITY % node " %object;
	         x                CDATA     #IMPLIED
	         y                CDATA     #IMPLIED
	         aux               CDATA    #IMPLIED 
	         epsilon          CDATA    #IMPLIED 
          ">
	
         <!--
      
	Graph nodes may be given x-y coordinates for their layout in the
	graph.
	--> 
          <!-- @x  position coordinate at x-axis -->

          <!-- @y  position coordinate at y-axis -->

         <!--
      Constraints--> 
         <!--  °   the value of @x must be castable to xs:float
	   °   the value of @y must be castable to xs:float
	  -->
         <!--
      
	  The nodes of variables are called variable nodes.
	  Recall that all variables but those of type
	  control are mapped to variable
	  nodes. So also the variables of types
	  algebraic
	  and differential.
	--> 
         
	  <!ENTITY % variable-node " %node;
	         initial              CDATA      #IMPLIED
	         initial-expression   CDATA      #IMPLIED
	         essential         CDATA         #IMPLIED
	  ">
	
         <!--
       Note that either of @inital or
	@inital-expression
	must be present.  The otherwise optional
	attributes of variable nodes have the following meaning:
	--> 
          <!-- @initial    a real number for the initial value of the variable.
	 -->

          <!-- @initial-expression    the identifier of an initial
	expression that specifies the initial value. 
	 -->

          <!-- @essential    if present, the circle around the species' node will be drawn in red.  It indicates that the presence of the species is
        essential for a    network to work properly.
	 -->

      
    <!--  - - - - - - - - - - - - - -  - - - - - - - - - - - - - - - -
    Copies of variable-nodes
     - - - - - - - - - - - - - -  - - - - - - - - - - - - - - - - -  -->
         <!--
      
	  Each variable node may have a set of copies, which are drawn as 
	  nodes with dashed circles. All nodes for the same variable are
	  linked by a splitpoint which also is drawn as a node (but
	  does not need any identifier). 
	  Logically, it doesn't matter whether a variable node
	  is linked to a reaction node or one of its copies.
	--> 
         
	  <!ENTITY % copies "((copy+,splitpoint,comment?)?,comment*)">
	  <!ELEMENT copy        (#PCDATA) >
	  <!ATTLIST copy        %node;   >
	  <!ELEMENT splitpoint  (#PCDATA) >
	  <!ATTLIST splitpoint
	         x           CDATA     #IMPLIED
                 y           CDATA     #IMPLIED
                 comment    CDATA     #IMPLIED >
	
         <!--
      
	  So copies can be used in any positon where species nodes
	  can be used.
	--> 
      <!--
    +++++++++++ Section ++++++++++++++
    Arithmetic and Boolean Expressions
    +++++++++++++++++++++++++++++++ -->
    <!--  - - - - - - - - - - - - - -  - - - - - - - - - - - - - - - -
    Arithmetic Expressions
     - - - - - - - - - - - - - -  - - - - - - - - - - - - - - - - -  -->
         <!--
      
	Real numbers or signals are refered to by the following elements.
	There are constant elements, references
	to variables var, references to
	expression macros expr,
	and references to a reaction's speed,
	that is to its kinetic-expression.
      --> 
         
	<!ENTITY % number-reference "constant | var | expr | speed">

	<!ELEMENT constant  (#PCDATA)>
	<!ATTLIST constant 
              id	   CDATA     #IMPLIED 
	      value     CDATA     #IMPLIED >

	<!ELEMENT speed  (#PCDATA)>
	<!ATTLIST speed
	      reaction    CDATA     #REQUIRED >

	<!ELEMENT expr  (#PCDATA) >
	<!ATTLIST expr
	      id          CDATA    #REQUIRED  >

	<!ELEMENT var  (#PCDATA)>
	<!ATTLIST var
	      type         CDATA     #IMPLIED
              id	      CDATA     #IMPLIED >
      
         <!--
       An arithmetic expression may define a real number,
      but in most cases, it defines a signal, i.e. a real-valued function.
      The atomic expressions are the references above. There are 
      applications of built-in arithmetic functions mult,
      power, etc.
      The built-in functions  are named as usual
      (as standarized by MathML). However, compared
      to MathML; they are applied with a
s      simplified syntax without
      using any apply elements everywhere.
      Apply elements a reserved for the
      application of user
      defined functions.
      --> 
         
	<!ENTITY % expression "
               %number-reference; |
               plus|minus|times|divide|
	       power|log|
	       sin|cos|tan|cot|
	       sinh|cosh|tanh|coth|
	       ceiling|floor|
	       delay|time|
	       ifthenelse|
  	       apply             ">

	<!ELEMENT times  (%expression;)*>
	<!ELEMENT plus  (%expression;)*>
	<!ELEMENT divide  ((%expression;),(%expression;))>
	<!ELEMENT minus ((%expression;),(%expression;)?)>

	<!ELEMENT power ((%expression;),(%expression;))>
	<!ELEMENT log ((%expression;),(%expression;))>

	<!ELEMENT sin (%expression;)>
	<!ELEMENT cos (%expression;)>
	<!ELEMENT tan (%expression;)>
	<!ELEMENT cot (%expression;)>

	<!ELEMENT sinh (%expression;)>
	<!ELEMENT cosh (%expression;)>
	<!ELEMENT tanh (%expression;)>
	<!ELEMENT coth (%expression;)>
	
	<!ELEMENT ceiling (%expression;)>
	<!ELEMENT floor (%expression;)>
      
         <!--
       Beside of the usual building operators from MathML, there
      are the following more specific operators:
      --> 
         <!--  ° 
               time for the identity function
	 ° 
               delay for delays in differential equations
	 ° 
               ifthenelse for conditionals
	 ° 
               apply for applying function defined in the network
	  itself (rather than being built-in in MathML).
	-->
         
	<!ELEMENT time  (#PCDATA)>
	<!ELEMENT delay ((%expression;),(%expression;))>
	<!ELEMENT apply  ((%expression;)*)>
	<!ATTLIST apply
	       fun             CDATA     #REQUIRED
	       latex-look  CDATA     #IMPLIED >
      
         <!--
      
	Arithmetic expressions subsume conditionals ifthenelse
	that permit to define piecewise functions. They contain boolean
	expressions as conditions.
      --> 
      
    <!--  - - - - - - - - - - - - - -  - - - - - - - - - - - - - - - -
    Boolean Expressions
     - - - - - - - - - - - - - -  - - - - - - - - - - - - - - - - -  -->
         <!--
      
	Boolean expressions can be used to compare 
	real numbers for equality or ordering. Furthermore,
	Boolean expressions are closed under the boolean operators.
      --> 
         
	<!ENTITY % boolexpression "eq | lt  |  leq | and | or | not |  true "> 
	
	<!ELEMENT eq  ((%expression;),(%expression;))>
	<!ELEMENT lt   ((%expression;),(%expression;))>
	<!ELEMENT leq ((%expression;),(%expression;))>
	<!ELEMENT and ((%boolexpression;)*)>
	<!ELEMENT or ((%boolexpression;)*)>
	<!ELEMENT not (%boolexpression;)>
	<!ELEMENT true (#PCDATA) >

	<!ELEMENT ifthenelse ((%boolexpression;),(%expression;),(%expression;))>
      
      <!--
    +++++++++++ Section ++++++++++++++
    Top-Level Network Elements
    +++++++++++++++++++++++++++++++ --><!--
      
	A Core SMBL  network may contain the following
	children element on top-level.
      --> 
    <!--  - - - - - - - - - - - - - -  - - - - - - - - - - - - - - - -
    Variables
     - - - - - - - - - - - - - -  - - - - - - - - - - - - - - - - -  -->
         <!--
      
	Variable elements must contain one kinetic-expression and a set of
	copies.
      --> 
         
	<!ELEMENT variable (kinetic-expression?, %copies;)   >
	<!ATTLIST variable %variable-node;
	       type         CDATA #IMPLIED
	       compartment  CDATA #IMPLIED
	       concentration CDATA #IMPLIED>
      
         <!--
      
	A kinetic expression may and must be present only if @type="differential"
         --> 
          <!-- @type   the type of a variable 
      must be either of species,
      algebraic, differential
      or control.
       -->

          <!-- @compartment  
	variables of type species may have a compartment.
       -->

          <!-- @concentration   the concentration of a variable of
      type species  with a compartment
      is given by its concentration variable.
       -->

      
    <!--  - - - - - - - - - - - - - -  - - - - - - - - - - - - - - - -
    Expression Macros
     - - - - - - - - - - - - - -  - - - - - - - - - - - - - - - - -  -->
         <!--
       An expression element  defines a macro
      for some arithmetic expression: --> 
         
	<!ELEMENT expression (%expression;)>
	<!ATTLIST expression %node; >
      
      
    <!--  - - - - - - - - - - - - - -  - - - - - - - - - - - - - - - -
    Function Definitions
     - - - - - - - - - - - - - -  - - - - - - - - - - - - - - - - -  -->
         <!--
      
	Function definitions have a sequence of lambda bound variables
	for the function's formal arguments.
      --> 
         
	<!ELEMENT function (lambda)>
	<!ATTLIST function
            id	      CDATA     #REQUIRED
            latex-look  CDATA     #IMPLIED >
	
	<!ELEMENT lambda ((bvar | %expression;)*)>
	
	<!ELEMENT bvar  (#PCDATA)>
	<!ATTLIST bvar 
               id	      CDATA     #IMPLIED >
      
      
    <!--  - - - - - - - - - - - - - -  - - - - - - - - - - - - - - - -
    Reactions
     - - - - - - - - - - - - - -  - - - - - - - - - - - - - - - - -  -->
         <!--
       The kinetic law of a reaction is given by an arithmetic expression.
      --> 
         
	<!ELEMENT kinetic-expression (%expression;)>
	<!ATTLIST kinetic-expression 
	     angle      CDATA     #IMPLIED >
      
         <!--
       A reaction may have four kinds of
      modifiers that are represented by the following elements;
      --> 
         
	<!ENTITY % modifier " modifier|inhibitor|activator|accelerator ">
      
          <!-- modifier  a general modifier of the reaction -->

          <!-- accelerator  an accelerator speeds up the reaction -->

          <!-- activator  an activator is an accelerator necessary to apply the reaction -->

          <!-- inhibitor  an inhibitor slows down the reaction -->

         <!--
       A reaction has a kinetics and a set of complements, which
      are products, reactant, or modifiers.--> 
         
	<!ENTITY % complement "%modifier; | reactant | product  ">
      
         <!--
      
	The content of a reaction element has the following form:
      --> 
         
	<!ELEMENT reaction  ((comment)*,(((kinetic-expression))?,(expression|%complement;)*))>
	<!ATTLIST reaction %node;
	    type         CDATA     #IMPLIED
	    candidate    CDATA    #IMPLIED  >
      
         <!--
      
	The expresssion in a reaction a macros that are local to the
	reaction's definition. They can be used to represent local
	parameters of SBML reactions.
      --> 
         <!--
       A reaction is drawn as a boxed node. The fill-color of the
      box indicates whether the reaction is a candidate for knockout.
      --> 
          <!-- candidate  the presence of this attribute means that the reaction         is a candidate for knockout. -->

      
    <!--  - - - - - - - - - - - - - -  - - - - - - - - - - - - - - - -
    Events
     - - - - - - - - - - - - - -  - - - - - - - - - - - - - - - - -  -->
         <!--
       An event has a trigger condition and a set of updates: --> 
         
	<!ELEMENT event (condition, (update)*)>
	<!ATTLIST event 
            id	      CDATA     #IMPLIED  >
	
      
         <!--
       A trigger condition is a conjunction of equations and inequations --> 
         
	<!ELEMENT condition (%boolexpression;)>
	<!ATTLIST condition >
      
         <!--
       we can update the values of variable of type species,
      differential, and control, so all types but algebraic variables.
      --> 
         
	<!ELEMENT update (var, (%expression;))>
	<!ATTLIST update >
        
      
      
    <!--  - - - - - - - - - - - - - -  - - - - - - - - - - - - - - - -
    Edge Clusters
     - - - - - - - - - - - - - -  - - - - - - - - - - - - - - - - -  -->
         <!--
      
	Edge clusters introduce extra nodes that permit to cluster
	edges between variables and reactions for nicer graph
	presentation.
      --> 
         
	<!ELEMENT edgecluster (source*)>
      
         <!--
       a source of an edge cluster is a species, a 
      copy of species, or an edge-cluster that has an outgoing edge
      pointing to it 

      'edgecluster':       a node that clusters edges from several sources.
      --> 
         
	<!ATTLIST edgecluster %node;
	    type       CDATA     #REQUIRED>
      
         <!--
       the type of an edge cluster is the type of edges that point to it. Only edges of
      the same type can be clustered.  
      --> 
          <!-- type  thie value is one of the 6 types of reaction
      complements (see entity @complement below)
       -->

      <!--
    +++++++++++ Section ++++++++++++++
    Reaction Complements
    +++++++++++++++++++++++++++++++ --><!--
       We next specify the contents of reaction complements which are
reactants, products and modifiers.
   --> 
    <!--  - - - - - - - - - - - - - -  - - - - - - - - - - - - - - - -
    References to Species
     - - - - - - - - - - - - - -  - - - - - - - - - - - - - - - - -  -->
         <!--
       Each reaction complement give refererence to some species
      variable. Also the source of an edgecluster must contain a reference 
      to a species variable.  --> 
         
	<!ENTITY % species-reference "	  
	       spec        CDATA     #IMPLIED
	       copy        CDATA     #IMPLIED
	       edgecluster CDATA     #IMPLIED" >
      
         <!--
        The values of these attributes give references to one or many species:--> 
          <!-- @spec  identifier of a species -->

          <!-- @copy  Identifier of a copy of that species -->

          <!-- @edgecluster  reference to one or many species -->

         <!--
      Constraints:--> 
         <!--  °  Either  @spec  or @edgecluster
	must be present
	 °  the attribute @copy is optional in the case where @spec is present.
	 °  in this case, there must be some species $species with 
	$species/@id=@spec and  $species/copy/@id=@copy
            -->
         
	<!ELEMENT source (#PCDATA) >
	<!ATTLIST source %species-reference; >
      
      
    <!--  - - - - - - - - - - - - - -  - - - - - - - - - - - - - - - -
    Reactants and Products
     - - - - - - - - - - - - - -  - - - - - - - - - - - - - - - - -  -->
         <!--
      
      There are two main reaction complements 
      are reactant and product elements. --> 
         
	<!ENTITY % reaction-complement "%species-reference;
              stoichiometry CDATA   #IMPLIED" >
	
	<!ELEMENT reactant      (#PCDATA) >
	<!ATTLIST reactant       %reaction-complement; >
	<!ELEMENT product       (#PCDATA) >
	<!ATTLIST product       %reaction-complement; >
      
      
    <!--  - - - - - - - - - - - - - -  - - - - - - - - - - - - - - - -
    Modifiers
     - - - - - - - - - - - - - -  - - - - - - - - - - - - - - - - -  -->
         <!--
      
	  Reactions may have four kinds of modifiers: 
	  (generic) modifiers, inhibitors, activator, and
	  accelerators.
	  None of these intervenes in the formal semantics,
	  but they are all relevant for the graphical representation
	  of a reaction network.
      --> 
         
	<!ELEMENT modifier   (#PCDATA) >
	<!ATTLIST modifier    %species-reference; >
	<!ELEMENT inhibitor   (#PCDATA) >
	<!ATTLIST inhibitor    %species-reference; >
	<!ELEMENT activator   (#PCDATA) >
	<!ATTLIST activator    %species-reference; >
	<!ELEMENT accelerator   (#PCDATA) >
	<!ATTLIST accelerator %species-reference; >
      
      
    <!--  - - - - - - - - - - - - - -  - - - - - - - - - - - - - - - -
    Comments
     - - - - - - - - - - - - - -  - - - - - - - - - - - - - - - - -  -->
         <!--
       Comments are given in latex format --> 
         
	<!ELEMENT comment      (#PCDATA)>

	<!ATTLIST comment 
            latex	      CDATA     #IMPLIED 
            experiment   CDATA     #IMPLIED
  	    prediction     CDATA     #IMPLIED >