D composed of:
BS also called the base structure(DSj ) j ∈ J of trees also called ∀ j ∈ J, there is a relationship Rj that associates
each node of DSj with a subset of BS ; for each leaf of DSj
this subset must be non empty. if' for boolean conditions and add for
the addition of a new element at the end of a Map. A Map a b is a
structure of elements of type b indexed by element of type a.
From the signature of if' we learn that the function takes
three arguments, the first argument being a Boolean value. if'
True is a two arguments function that evaluates its first argument (the second argument will never be evaluated), while if' False is a two arguments function that evaluates its second argument (the first argument will never be evaluated).
addTag function tries to add a tag to a structure, if the addition
does not imply overlapping then the modified structure is returned, else a
pair of structures is returned: the first structure is the original one
except that every instances of the added tag have been
transfered to the second structure. In a similar way, the $delTag$ function
removes the instance of a given tag from a selected interval and may imply
overlapping thus the type signature.
addText and delText functions.
moveTag is the main function offered to the user for reacting to the automatic
restructuring, it allows him to move all the instances of a tag from one
structure to another. The function may fail if it introduces
overlapping hierarchies.
…suppose I awake in the morning before my wife, and that afterwards she wakes up and inquires, "What sort of a day is it?" This is a sign, whose Object, as expressed, is the weather at that time, but whose Dynamical Object is the impression which I have presumably derived from peeping between the window-curtains. Whose Interpretant, as expressed, is the quality of the weather, but whose Dynamical Interpretant, is my answering her question. But beyond that, there is a third Interpretant. The Immediate Interpretant is what the Question expresses, all that it immediately expresses, which I have imperfectly restated above. The Dynamical Interpretant is the actual effect that it has upon me, its interpreter. But the Significance of it, the Ultimate, or Final, Interpretant is her purpose in asking it, what effect its answer will have as to her plans for the ensuing day. I reply, let us suppose: "It is a stormy day." Here is another sign. Its Immediate Object is the notion of the present weather so far as this is common to her mind and mine - not the character of it, but the identity of it. The Dynamical Object is the identity of the actual or Real meteorological conditions at the moment. The Immediate Interpretant is the schema in her imagination, i.e. the vague Image or what there is in common to the different Images of a stormy day. The Dynamical Interpretant is the disappointment or whatever actual effect it at once has upon her. The Final Interpretant is the sum of the Lessons of the reply, Moral, Scientific, etc.
By a sign I mean any thing which is in any way, direct or indirect, so influenced by any thing (which I term its object) and which in turn influence a mind that this mind is thereby influenced by the Object ; and I term that which is called forth in the mind the Interpretant of the sign.