Re: EE Student, Edit, Proposal Masters, Help (concepts of functional programming, symbolic programming and MATLAB)

From: John Creighton (JohnCreighton__at_hotmail.com)
Date: 03/14/05

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    Date: 13 Mar 2005 16:42:20 -0800

    Jens Axel Søgaard <usenet@soegaard.net> wrote in message news:<4231b555$0$246$edfadb0f@dread12.news.tele.dk>...
    > John Creighton wrote:
    >
    > > Lisp has since been
    > > expanded to include many programming paradigms and is now known as
    > > Common Lisp (CLisp). Although, Common Lisp is no longer a pure
    > > functional language some functional programming language lisp dialects
    > > have been created (e.g. Scheme).
    >
    > Scheme support the paradigm of functional programming very well,
    > but is also impure.

    I think I will put Scheme on my list of things to read about. I have
    been reading a tutorial on Haskell
    http://www.isi.edu/~hdaume/htut/
     and a primmer on Lisp.
    http://mypage.iu.edu/~colallen/lp/node11.html
     I have not seen a lot of the concepts in the Lisp tutorial that I
    have been reading about in Haskel turorial. Perhaps this is just
    because the Haskel tutorial is much more thorough.

    > > In a pure functional (e.g. Haskell) languages such as Haskell [39]
    > > assignment is not allowed
    After some reading I guess I should use the word reassignment. In
    Haskell, you can define symbols to represent functions and parts of
    expressions using the Let statement. It is called something different
    when something does not have a consistent value like reading from the
    keyboard. I am not yet clear on these concepts.
    >> in order to eliminate side effects.
    > > Alternatively monads are used to solve problems such as exception
    > > handling which is difficult to do without assignment.=20
    >
    > Are you saying that it is difficult for the user of Haskell or the
    > implementor of haskell to implement exceptions? Or perhaps you
    > are talking about exceptional situations rather than "traditional"
    > exceptions.

    I think I concluded to much from reading the first of the paper at:
    http://homepages.inf.ed.ac.uk/wadler/papers/marktoberdorf/marktoberdorf.pdf
    "Say I write an evaluator in a pure functional language.
    { To add error handling to it, I need to modify each recursive call to
    check
    for and handle errors appropriately. Had I used an impure language
    with
    exceptions, no such restructuring would be needed.
    { To add a count of operations performed to it, I need to modify each
    recursive
    call to pass around such counts appropriately. Had I used an impure
    language
    with a global variable that could be incremented, no such
    restructuring would
    be needed.
    { To add an execution trace to it, I need to modify each recursive
    call to
    pass around such traces appropriately. Had I used an impure language
    that
    performed output as a side e_ect, no such restructuring would be
    needed."
    I will wait until I finish the tutorial on Haskell before I read the
    paper with the above quote.

    > > This is not
    > > necessary in Maple because Maple is not a pure functional language. In
    > > Maple assignment can be done as in a procedural style:
    > > x:=3D2
    > > x:=3Dx+1
    >
    > Perhaps you mean "imperative style" rather than "procedural style"?
    > (Since you don't define any procedures nor call them in the example)
    Maybe this is right but for some reason people seem to separate
    languages as object oriented, functional and procedural. Is imperative
    a relatively new way of describing languages. I wonder when it was
    first introduced.

    > > Variables can represent many kinds of data structures.=20
    > > A data structure that can be evaluated is known as an expression.=20
    >
    > Variables are bound to values. How do you define data structure?
    I'll take a crack this. A data structure definition describes the
    operations by which data can be accessed for all instances of the data
    structure. A group of data that can be accessed in this fashion is
    considered an instance of the data structure. For instance an array
    can be accessed though indices and the data of a tree can be accessed
    though the operations get root, get left node, get right node. Thus
    from this perspective an assignment chain could be considered a data
    structure that could be accessed though the operations eval(x,n).
    Where x is a member of the assignment chain and n is the level of
    evaluation.
    > > The symbolic package for MATLAB performs symbolic operations by
    > > storing symbolic expressions as objects. MATLAB manipulates
    > > expressions by: passing the expression to the Maple kernel and then
    > > storing the resulting string in a field of a symbolic object [7].=20
    >
    > What is a symbolic object?
    In MATLAB a symbolic object is an object with one field which contains
    a symbolic expression in a string representation. To make this behave
    similarly to a symbolic variable in Maple many operations are
    overridden including +, -, / *. Many overridden functions and all
    operations are performed via the Maple Kernal.
    > > However, there is a size limitation on the size of a symbolic
    > > variables that can be used within the symbolic package.
    >
    > What is the size of a variable?
    General Size is thought of as a memory requirement. But it could also
    include measures like the number of elements. Since the memory space
    of a MATLAB symbolic object depends on the amount of characters needed
    to make up the symbolic expression, the number of characters in the
    symbolic object is a reasonable measure of its size.
    > --=20
    > Jens Axel S=F8gaard

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