Elements of functional programming
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The document describes a small functional programming language called Little Quilt that manipulates geometric objects. Little Quilt includes basic values like squares and operations like turning and sewing squares together. It then discusses types in functional programming including basic types, product types, list types, and operations on types. The document also covers function declarations and applications, recursive functions, approaches to expression evaluation, type checking, and overloading.
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TYPES: VALUES AND OPERATIONS
• Lists of Elements:
•A list is a finite-length sequence of elements
•Type A list consists of all lists of elements, where each
element belongs to type A.
•Example:
•int list consists of all lists of integers
•[1,2,3] is a list of three integers 1, 2, and 3.
•[“red”, “white”, “blue”] is a list of three strings](https://image.slidesharecdn.com/elementsoffunctionalprogramming-150613130343-lva1-app6891/85/Elements-of-functional-programming-9-320.jpg)
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Elements of functional programming
- 1. 1 Elements of Functional Programming
- 2. 2 A LITTLE LANGUAGE OF EXPRESSIONS •The little language ----Little QuiltLittle Quilt: •small enough to permit a short description •different enough to require description •representative enough to make description worthwhile • Constructs in Little Quilt are expressions denoting geometric objects call quilts:quilts:
- 3. 3 A LITTLE LANGUAGE OF EXPRESSIONS •What Does Little Quilt Manipulate? •Little Quilt manipulates geometric objects with height, width and texture • Basic Value and Operations: •The two primitive objects in the language are the square piece. The earliest programming languages began with only integers and reals
- 4. 4 A LITTLE LANGUAGE OF EXPRESSIONS •The operation are specified by the following rules: •A quilt is one of the primitive piece, or •It is formed by turning a quilt clockwise 90°, or •it is formed by sewing a quilt to the right of another quilt of equal height. •Nothing else is a quilt.
- 5. 5 A LITTLE LANGUAGE OF EXPRESSIONS • Constants: • Names for basic values: the pieces be called aa and bb •Names of operations: the operations be called turnturn and sewsew. (like the picture on the previous slide) •now that we have chosen the built-in object and operations (a,b, turn, sew) expressions can be formed •<expression>::=a | b | turn(<expression>) • | sew (<expression>,<expression>)
- 6. 6 TYPES: VALUES AND OPERATIONS • A typetype consists of a set of elements called valuesvalues together with a set of function called operationsoperations. •<type-expression>::=<type-name> | <type-expression> <type-expression> | <type-expression>*<type-expression> |<type-expression> list •A type expression can be a type name, or it can denote a function, product, or list type. (operations are ->, * and list)
- 7. 7 TYPES: VALUES AND OPERATIONS • Basic Types: •A type is basic if its values are atomic •the values are treated as whole elements, with no internal structure. •Example: the boolean values in the set { true, false} •Operations on Basic Values: • The only operation defined for all basic types is a comparison for equality (have no internal structure)
- 8. 8 TYPES: VALUES AND OPERATIONS • Products of Types: The product A*B consists of ordered pairs written as (a, b) •Operations on Pairs •A pair is constructed from a and b by writing (a, b) •Associated with pairs are operations called projectionprojection functionsfunctions to extract the first and second elements from a pair •Projection functionsProjection functions can be defined: •fun first(x,y) = x; •fun second( x, y)=y;
- 9. 9 TYPES: VALUES AND OPERATIONS • Lists of Elements: •A list is a finite-length sequence of elements •Type A list consists of all lists of elements, where each element belongs to type A. •Example: •int list consists of all lists of integers •[1,2,3] is a list of three integers 1, 2, and 3. •[“red”, “white”, “blue”] is a list of three strings
- 10. 10 TYPES: VALUES AND OPERATIONS •Operations on Lists •List-manipulation programs must be prepared to construct and inspect lists of any length. •Operations on list from ML: •null(x) True if x is the empty list, false otherwise. •hd(x) The first or head element of list x. •tl(x) The tail or rest of the list after the first element is removed. •a::x Construct a list with head a and tail x. Cons operator
- 11. 11 TYPES: VALUES AND OPERATIONS •Types in ML Predeclared basic types of ML. Type Name Values Operations _____________________________________________________ boolean bool true,false =,<>,… integer int …,-1,0,1,2,… =,<>,<,+,*,div,mod,… real real …,0.0,…,3.14,.. =,<>,<,+,*,/,… string string “foo”,””quoted”” =,<>,… _____________________________________________________ •New basic types can be defined as needed by a datatype declaration •Example: datatype direction = ne | se |sw| nw;
- 12. 12 FUNCTION DECLARATIONS • Functions as Algorithms A function declaration has three parts: •The name of the declared function •The parameters of the function •A rule for computing a result from the parameters
- 13. 13 FUNCTION DECLARATIONS • Syntax of Function Declarations and Applications •The basic syntax for function declarations is fun <name><formal-parameter> = <body> •<name> is the function name •<formal-parameter> is a parameter name •<body> is an expression to be evaluated •fun successor n = n +1; •fun successor (n)= n +1; () are optional
- 14. 14 FUNCTION DECLARATIONS • The use of a function within an expression is called an applicationapplication of the function. •Prefix notation is the rule for the application of declared function •<name><actual-parameter> •<name> is the function name •<actual-parameter> is an expression corresponding to the parameter name in the declaration of the function •Example: successor(2+3)
- 15. 15 FUNCTION DECLARATIONS • Recursive Functions -- A function f is recursive if its body contains an application of f. •Example1: •Function len counts the number of elements in a list •fun len(x)= if null(x) then 0 else 1 + len(tl(x))
- 16. 16 Approaches to Expression Evaluation •Innermost Evaluation •Outermost Evaluation •Selective Evaluation •Evaluation of Recursive Functions •Short-Circuit Evaluation
- 17. 17 Type Checking Type Inference: •Wherever possible ,ML infers the type of an expression.An error is reported if the type of an expression cannot be inferred. •If E and F have type int then E+F also has type int . •In general, If f is a function of type A -->B , and a has type A, then f(a) has type B.
- 18. 18 Type Names and Type Equivalence Two type expressions are said to be structurally equivalent if and only if they are equivalent under the following rules: 1. A type name is structurally equivalent to itself. 2. Two type expressions are structurally equivalent if they are formed by applying the same type constructor to structurally equivalent types. 3. After a type declaration, type n = T ,the type name n is structurally equivalent to T .
- 19. 19 Overloading:Multiple Meanings A symbol is said to be overloaded if it has different meanings in different contexts.Family operator symbols like + and * are overloaded. e.g. 2+2 here + is of type int 2.5+3.6 here + is of type real. ML cannot resolve overloading in fun add(x,y) = x+y ; Explicit types can be used to resolve overloading. fun add(x,y): int =x+y ;
- 20. PRESENTED BY SAJJAD ALI P M CS –B ,34 20
- 21. THANK YOU!! 21