Constructors - Cont. must be distinguished by the number or type of their arguments.

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1 Constructors - Cont. 1 Constructors can be overloaded! must be distinguished by the number or type of their arguments. 2 When no constructor is defined, there is a default constructor with no arguments. You cannot use the default constructor once one has been defined in your program. (bad style!) 3 When declaring a type, it is also possible to define default values for each field: c l a s s P o i n t { double l a t i t u d e = ; double l o n g i t u d e = 0. 0 ; double a l t i t u d e = 0. 0 ; } J.Carette (McMaster) CS/SE 2S03 1 / 22

2 The Semantics of Records To cover records: we need to add a fifth argument to the functions Σ and Θ: the list of constructed types, each type being associated to an ordered pair composed: T (list of fields, list of constructors) J.Carette (McMaster) CS/SE 2S03 2 / 22

3 Define the Σ function for the four operations: type definition, cell allocation, accessing to a field, assigning to a field. Sharing 4.2 Sharing Sharing Suppose that x and y are two variables of type Point, associated with two references r1 and r2 in the environment. In addition, suppose that, in memory, r1 is associated with a reference r3, which itself is associated with a record {latitude = , longitude = 2.208, altitude = 156.0} and r2 with a reference r4, which itself is associated with the record {latitude = 90.0, longitude = 0.0, altitude = 0.0}. So, e = [x = r1, y = r2 ], m = [r1 = r3, r2 = r4, r3 = {latitude = , longitude = 2.208, altitude = 156.0}, r4 = {latitude = 90.0, longitude = 0.0, altitude = 0.0}]. In the first case (sharing), all changes of the cell associated with x automatically change the cell associated with y, and vice versa. 4.2 Sharing Sharing 67 x x x! x x! ! ! y ! y y! y y! ! ! ! x = y (Sharing!) y,lat = x.lat y.long = x.long y.alt = x.alt ! ! ! 0.0 In contrast, if the statements y.latitude = x.latitude; y.longitude = x.longitude; y.altitude = x.altitude; are executed, the resultant mem ! 0.0! =90.0 {latitude 0.0 = , longitude = ory state is [r1 = r3, r2 = r4, r3 90.0! 2.208, altitude = 156.0}, r4 = {latitude = , longitude = 2.208, altitude = 156.0}]. In contrast, if the statements y.latitude = x.latitude; y.longitude = x x! x.longitude; y.altitude = x.altitude; are executed, the resultant memory state is [r1 = r3, r2 = r4, r3 = {latitude = , longitude = 2.208, altitude = 156.0}, r4 = {latitude = , longitude = 2.208, altitude = 156.0}] ! ! 2.208! When the statement y = x; is executed, the value of x is computed, which is the reference r3 and we associate this value with the reference r2. The memory state becomes [r1 = r3, r2 = r3, r3 = {latitude = , longitude = 2.208, altitude = 156.0}, r4 = {latitude = 90.0, longitude = 0.0, altitude = 0.0}]. x y y! ! ! ! If you then assign to the field latitude of the record x: x.latitude = y 23.45; and then output the field latitude of y, you get in the first case, and in the second. We say, in the first case, that the variables x and y share the cell r3. All changes of the cell associated with x automatically change the cell associated with y, and vice versa. J.Carette (McMaster) CS/SE 2S / 22

4 Equality a = new P o i n t ( 1, 2, 3 ) ; b = new P o i n t ( 1, 2, 3 ) ; Two types of equality: Physical. Two records of the same type are physically equivalent (a==b) only when they are identical (share the same cell). Hence, a == b is false. Structural. Two records of the same type are structural equivalent when their field s value are equal. Hence, a and b are structural equivalent. J.Carette (McMaster) CS/SE 2S03 4 / 22

5 Wrapper Types (from Base type to Object type) A wrapper is a type of record with one lone field. c l a s s I n t e g e r { i n t c ; I n t e g e r ( i n t x ) { t h i s. c = x ; } } The Points (allows several variables to share a single value.): 1 Uniformity 2 Sharing J.Carette (McMaster) CS/SE 2S03 5 / 22

6 Wrapper Types - Cont. x! x y! y 5! 5 4! 4 Integer x = new Integer(4); int x = 4; Integer y = new Integer(x.c); int y = x; x.c = 5; x = 5; System.out.println(y.c); System.out.println(y); print 4 print 4 If we replace the second line with Integer y = x then it prints 5 x! 5! y! y J.Carette (McMaster) CS/SE 2S03 6 / 22

7 Wrapper Types - Cont. The following function swaps values of x and y. s t a t i c void swap ( I n t e g e r x, I n t e g e r y ) { i n t temp = x. c ; x. c = y. c ; y. c = temp ; } In java, it is not possible to do so with arguments of type int. The following functions do nothing on x and y. s t a t i c void swp ( i n t x, i n t y ) { i n t temp = x ; x = y ; y = temp ; } J.Carette (McMaster) CS/SE 2S03 7 / 22

8 Wrapper Types - Cont. When we call the function swap(a, b), we create the state: a! a bb! 44! 77! x! x y! and so swapping the contents of x and y will also swap those of a and b. sif a, b are constant (final), and x, y too, then: a a! x! x b! b y! y 44! 7! 7 and swap works too. J.Carette (McMaster) CS/SE 2S03 8 / 22

9 Records in Caml 1 Record Type: t y p e p o i n t = { l a t i t u d e : double ; l o n g i t u d e : double ; a l t i t u d e : double ; } 2 Creating: l e t x = { l a t = ; l o n g i = 0. 0 ; a l t i t u d e = 0. 0 ; } or l e t y = r e f { l a t = ; l o n g i = 0. 0 ; a l t i t u d e = 0. 0 ; } 3 Accessing: x. l a t i t u d e (! y ). l a t i t u d e 4 Assigning: all fields are constant by default! t y p e i n t wrap = { mutable c : i n t } l e t x = { c = r e f 5} x. c < 4 J.Carette (McMaster) CS/SE 2S03 9 / 22

10 Records in C 1 Record Type: s t r u c t P o i n t { double l a t i t u d e ; double l o n g i t u d e ; double a l t i t u d e ; } ; 2 Creating: s t r u c t P o i n t x ; or s t r u c t P o i n t x = { 5. 0, 7. 0, } ; 3 Accessing: x. l a t i t u d e 4 Assigning: all fields are constant by default! x. l a t i t u d e = Call by copy! (the value of x is not a reference associated with a record in memory as it is in Java and Caml!) J.Carette (McMaster) CS/SE 2S03 10 / 22

11 Arrays Array Types: In Java, an array with elements of type T is of type T[ ]. int [ ] t; This adds t, a new reference r to the environment. The default value is null. In java, the box r can only contain null or another reference. Allocation of an Array: To allocate, you create a box large enough: new int [10]; This creates a new reference r pointing to an n-tuple (10-tuple in this case) of default values (0 in this case). The fields are numbered from 0 to n-1. i.e., int [ ] t = new int [10]; env: [t = r] mem: [r = r, r = [0,, 0]]: }{{} 10 J.Carette (McMaster) CS/SE 2S03 11 / 22

12 Arrays - Cont. Accessing: t[k] gives the k th field. Creation: i n t [ ] t1 ; t1 = new i n t [ ] { 1 0, 1 1, 1 2, 1 3, 1 4, 1 5, 1 6, 1 7 } ; i n t [ ] t2 = new i n t [ ] { 2 0, 2 1, 2 2, 2 3, 2 4, 2 5, 2 6, 2 7 } ; char [ ] ca = { J, a, v, a } ; t1[5] 15, t2[5] 25, ca[0] J Assigning: ca [ 0 ] = j ; (Arrays in C and Caml are essentially the same) J.Carette (McMaster) CS/SE 2S03 12 / 22

13 Arrays of Arrays (T [ ])[ ] is an array of arrays. i n t [ ] [ ] t = new i n t [ 2 0 ] [ 1 5 ] ; t[ i }{{} 0 19 ][ j ] }{{} 0 14 J.Carette (McMaster) CS/SE 2S03 13 / 22

14 Arrays of Objects P o i n t [ ] pa = new P o i n t [ 4 ] ; pa# x null# 0.0 null# 0.0 null# 0.0 Usual looping construct: f o r ( i n t i =0; i <pa. l e n g t h ; i ++) {... ( r e f e r to pa [ i ] ) } Better! f o r ( P o i n t p : pa ) {... ( r e f e r to p ) } J.Carette (McMaster) CS/SE 2S03 14 / 22

15 Dynamic Data Types - Recursive Records Example: c l a s s L i s t { i n t hd ; L i s t t l ; } Note: int List is only non-empty lists but List {empty list} (int List) Observe: List is a record and its value is a reference, a reference can be null. So, List {null} (int List) J.Carette (McMaster) CS/SE 2S03 15 / 22

16 Recursive Records - Example L i s t l ; l = new L i s t ( ) ; l. hd = 4 ; l. t l = new L i s t ( ) ; l. t l. hd = 5 ; l. t l. t l = n u l l ; J.Carette (McMaster) CS/SE 2S03 16 / 22

17 Recursive Records - Example - Cont. ll! l! l! 0! 0 44! (1)! (2)! (3)! l! 44! 0! 0 ll! (4)! 44! 05! (5)! J.Carette (McMaster) CS/SE 2S03 17 / 22

18 Recursive Records - Constructor L i s t ( f i n a l i n t x, f i n a l L i s t y ) { t h i s. hd = x ; t h i s. t l = y ; } L i s t l = new L i s t ( 4, new L i s t ( 5, n u l l ) ) ; J.Carette (McMaster) CS/SE 2S03 18 / 22

19 Recursive Definitions and Fixed Point Equations List {null} int List is not a definition but an equation to be solved! How? To construct a solution we proceed by successive approximations: Let i be the number step of approximation and L i the solution at the step i. L 0 = L 1 = {null} (int L 0 ) = {null} L 2 = {null} (int L 1 ) = {null} (int {null}) L 3 = {null} (int L 2 ) = {null} (int {null}) (int (int {null})). List := lim i L i J.Carette (McMaster) CS/SE 2S03 19 / 22

20 Infinite Values The type List contains values that cannot be constructed in a finite number of steps. For example: L i s t l = new L i s t ( ) ; l. hd = 4 ; l. t l = l ; Creates the following list: ll! 44! The following program terminates properly if you apply it to finite lists, but enters an infinite loop if you try to apply it to infinite lists. s t a t i c i n t sum ( f i n a l L i s t l ) { i f ( l == n u l l ) r e t u r n 0 ; r e t u r n l. hd + sum ( l. t l ) ; } J.Carette (McMaster) CS/SE 2S03 20 / 22

21 Type Algebra 0: empty 1: unit +: disjoint some : product X : variable, some types +: disjoint some µx.f (x): least-fixed point, solve x F (x) Bool := false true = A A A A.1 1.A A A + B B + A A.B B.A A.(B + C) A.B + A.C A + (B + C) (A + B) + C J.Carette (McMaster) CS/SE 2S03 21 / 22

22 Type Calculus δ x A δ x 1 = 0 δ x (A + B) = δ x A + δ x B δ x (A. B) = δ x A. δ x B δ x A = type of one context of A. δ x L = L. L. δ x ( 1 1 x ) = ( 1 1 x )2 Solve δ x Y (X ) = Y (X )? Y (X ) = Bag(X ) J.Carette (McMaster) CS/SE 2S03 22 / 22