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Functional Languages

Functional Languages. A function is an “association of a certain object from one set (the range) with each object from another set (the domain)

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Functional Languages

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  1. Functional Languages • A function is an “association of a certain object from one set (the range) with each object from another set (the domain) • A function is an expression and its associated values, where the expression provides a method or rule for making the association between domain and range values.

  2. Functional languages • Ways of expressing functions • Age(Amalia) = 7 • (Age Amalia) • (age Amalia 7) • function / applicative • Functions are single valued – for each domain value there is exactly one associated range value.

  3. Functional Languages • Distinguishing Features • Programs are a composition of functions • Functions are supported as first-class objects • Functions can be arguments to other functions • There are relatively few side effects • Simple semantics • Recursive control prevalent

  4. Functional Languages • LISP • Typeless • Primary data structure is the list • Scheme – a dialog of LISP • typeless • ML = Meta Language • Strongly typed • APL – not purely functional • Primary data structure is the array • FP

  5. Relations vs Functions • Relation is • Ordered association of elements of ten listed as a tuple • Function • Given an ordered tuple (argument list of elements) returns a value • Composition of functions example (+ (* w x) ( - y z))

  6. First Order Functions • A function is first-order if it takes individuals as arguments and returns an individual value • Numbers • Strings • Records • Etc. • An individual is a function of order 0

  7. Side Effects • A function (f x y z) is said to have a side effect if x,y, and/or z change in the calling environment during application of the function. • GetData (x,y,z) • (GetData Getx Gety Getz) • A function defined with all value parameters, and where no assignments are made to global variables, has no side effects.

  8. Clean Semantics • Language means what it says • Language is not ambiguous • Results of a program can be verified

  9. LISP – a functional language • History • First major AI workshop • summer 1956 – at Dartmouth • John McCarthy – late 50’s – MIT • Kleene’s - recursive function theory • Alonzo Church’s – lambda calculus • IBM 704 • few primitives • Punched cards • Good for AI areas of • Robotics & knowledge engineering • Standardization attempt: Common LISP

  10. Knowledge Engineering • Expert Systems • Public knowledge • Textbooks • Private knowledge • Heuristics (rules of thumb) • Examples • DENDRAL – data analysis • MACYSYMA – symbolic calculus • EXPERT – medical • MYCIN – infectious disease diagnosis & prescription

  11. LISP – a functional language • McCarthy’s original LISP – 6 functions cons, cond, car, cdr, eq, atom • Today’s LISP – many more functions • Arithmetic • Input • Output

  12. LISP – a functional language • Simple Data Type • Atom • Number • Use built in hardware for integer & real arithmetic • String • Structured Data Type • List • Cam be empty () • Can contain an ordered list

  13. LISP – a functional language • LISP manages pointers for you • ordinary Lisp lists are singly linked lists • When dealing with recursion • Need a base case (stopping case) • Need a recursive case • Common Lisp provides macros for push and pop (xlisp doesn’t)

  14. LISP – a functional language • (setf pair (cons ‘a ‘b)) • returns the dotted pair (A.B) • (A.B) is a two part data structure • A is the car of the cons • B is the cdr of the cons

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