1. Error Example - 65/4; ! Toplevel input: ! 65/4; ! ^^ ! Type clash: expression of type ! int ! cannot have type ! real

2. Currying Example Difference with left binding functions Difference with left binding functions –exp x y-1  (exp x y) -1 –exp x (y-1) - fun exp x y = if (y=0) then 1 else x * (exp x (y-1)); > val exp = fn : int -> int -> int

3. Type Examples fun cast (n:int) = n; fun cast (n:int) = n; fun cast n = n : int; fun cast n = n : int; fun cast n = n+”abc”; fun cast n = n+”abc”; fun cast (n:int) = n+”abc”; fun cast (n:int) = n+”abc”;

4. Polymorphic Functions - fun id x = x; > val id = fn : 'a -> 'a - fun cond c x y = if c then x else y; > val cond = fn : bool -> 'a -> 'a -> 'a

5. the Let Function - fun prodSum x y = (x+y) * (x+y); > val prodSum = fn : int -> int -> int - fun prodSum x y = let val sumXY = x + y val sumXY = x + yin sumXY * sumXY sumXY * sumXY end ; end ; > val prodSum = fn : int -> int -> int > val prodSum = fn : int -> int -> int

6. Tuple Extraction - let val (u,v) = incBoth (3,5) inu end; end; > val it = 4 : int

7. The Map Function - fun map f inpList = case inpList of [] => [] | (h::t) => (f h) :: (map f t) ; > val map = fn : ('a -> 'b) -> 'a list -> 'b list

8. The Filter Function - fun filter condition inpList = case inpList of [] => [] | (h::t) => if (condition h) then h :: (filter condition t) else filter condition t ; > val filter = fn : ('a -> bool) -> 'a list -> 'a list

9. Programming in ML By Drew Wyborski

10. Data Type/Operators Operators and types similar to C++/Java Operators and types similar to C++/Java –int, string, bool and real remain the same –Operators have slight differences Additional Boolean types are included showing the rational/logical basis Additional Boolean types are included showing the rational/logical basis –andalso & orelse

11. Syntax Input is placed into user’s implementation Input is placed into user’s implementation Machine responds with result of expression Machine responds with result of expression Specified layout for entry and output Specified layout for entry and output –3 + 4; –val it = 7 : int If an error is made in entry, the machine responds with an appropriate error If an error is made in entry, the machine responds with an appropriate errorerror The unit data type The unit data type

12. Definitions Global constants Global constants –val PI = 3.4; –Help increase readability Functions Functions –fun succ n = n+1; –val succ = fn : int  int –Differences in calling compared to imperative Extensions Extensions –if…then…else functions –Multiple input/output functions

13. Currying An extension of function writing An extension of function writing Special ability of functional language Special ability of functional language Left binding Left binding Partial evaluation (aka “currying”) Partial evaluation (aka “currying”) Example Example Example

14. “Side-effect Free” Programming The interaction of functions in ML The interaction of functions in ML The use of referential-transparency occurs through the elimination of some imperative-type features: The use of referential-transparency occurs through the elimination of some imperative-type features: –Global variables –Assignments –Value-result parameters –Pointers Advantages in readability and modification in small components or functions Advantages in readability and modification in small components or functions Victims of elimination of side-effects Victims of elimination of side-effects

15. Exceptions to Referential Transparency Input/Output devices Input/Output devices –Something outside the program is changed –The functions have type that returns unit Functions because the result must be expressed outside the interpreter Functions because the result must be expressed outside the interpreter The print function The print function print “Hello there \n”; Hello there > value it = ( ) : unit

16. Basic Syntactical Notes There is the option for expression sequencing There is the option for expression sequencing The use of sequencing leads to the loss of previous expressions unless they have the rare side-effect (most likely “print”) The use of sequencing leads to the loss of previous expressions unless they have the rare side-effect (most likely “print”) Comments are important as in any other language Comments are important as in any other language –Denoted through the use of (* … *)

17. Type Inference Strength of ML that helps offset loss of imperative functions Strength of ML that helps offset loss of imperative functions Ability to declare or not declare data type Ability to declare or not declare data type –Encouraged to do so for documentation –Similar notation to what we’ve already seen –Allow us to make the implementer operate correctly –Help to clear up possible error messages error messageserror messages

18. Polymorphism ML exhibits a strong amount of polymorphism ML exhibits a strong amount of polymorphism –Exists in function calls and data typing –Gives us the ability to openly code for many different data types –Can create data variables Some common polymorphic functions Some common polymorphic functionscommon polymorphic functionscommon polymorphic functions Different notation associated with polymorphic functions Different notation associated with polymorphic functions Different notation Different notation

19. Higher-Order Functions Used to compact functions together Used to compact functions together Useful to extend an already defined function Useful to extend an already defined function Helps add levels of abstraction Helps add levels of abstraction Another example of the polymorphism present in ML Another example of the polymorphism present in ML

20. Function Extension We are able to define some “local variables” through the use of the let function We are able to define some “local variables” through the use of the let functionthe let functionthe let function –This allows us to temporarily assign a value of something to be used later in the expression –It is only good for the part of the statement enclosed in let expression –Cannot use the let expression to try and mimic imperative assignment statements We can also use functions in this statement We can also use functions in this statement

21. Function Extension There are some good guidelines that are almost universal in writing longer functions in ML: There are some good guidelines that are almost universal in writing longer functions in ML: –Name the function and parameters on line 1 –Indent the body of the function like you would in Java or C++ –Include the terminating end; portion on its own line at the end

22. Tuples Consist of pieces of data grouped together in parenthesis Consist of pieces of data grouped together in parenthesis –(3,4) or (“abc”,1) or (true,”abc”,87.4) We can use tuples across functions just like any other data type We can use tuples across functions just like any other data type To extract individual pieces of data from the tuple we utilize the let function To extract individual pieces of data from the tuple we utilize the let functionutilize

23. Records Similar to tuples except with names for the components Similar to tuples except with names for the components Enclosed in a set of brackets with field=value components inside for definition Enclosed in a set of brackets with field=value components inside for definition They are then accessed through the use of the # function and then the field name They are then accessed through the use of the # function and then the field name

24. Lists Lists are created through the construction of data values between brackets of the same type Lists are created through the construction of data values between brackets of the same type –[1,2,3] or [“ab”,”cd”,”ef”] Things can be appended using :: Things can be appended using :: –5 :: [1,2,3]  [5,1,2,3] : int list Concatenation is done using the @ symbol Concatenation is done using the @ symbol –[1,2,3] @ [4,5,6]  [1,2,3,4,5,6] : int list When using functions with lists we use the case operator When using functions with lists we use the case operator –This provides us with operations for an empty list as well as one with data in it –We split the list into the head value and the tail to use for recursion so we can process the full list

25. List Iteration Can be used to replace the for loop function from imperative languages Can be used to replace the for loop function from imperative languages The map function The map function –Iterates down the list by applying the specified function to the head –The tail then recurses on itself using map again –Example Example The filter function The filter function –Eliminates the values that don’t match the input function –Operates the same way as map except eliminates those without a positive bool value from the given function –Example Example

26. User-defined Types Enumerated Types Enumerated Types –datatype Food = Burger | Chicken | Hot Dog; Custom data types Custom data types datatype Stats Rebounds of int | Point of int | Fouls of int; –val StatsThisGame = [Rebounds 4, Point 12, Fouls 3, Rebounds]; Can be applied over many ways and used in functions for various purposes Can be applied over many ways and used in functions for various purposes