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.

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.

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

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

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))

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

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.

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

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

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

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

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

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)

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