Last Class. Announcements. Lecture Outline. Types. Structural Equivalence. Type Equivalence. Read: Scott, Chapters 7 and 8. T2 y; x = y; n Types

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1 Aoucemets HW9 due today HW10 comig up, will post after class Team assigmet Data abstractio (types) ad cotrol abstractio (parameter passig) Due o Tuesday, November 27 th Last Class Types Type systems Type checkig Type safety Type equivalece Remember, we are ow i the world of vo Neuma laguages usig value model for variables! Fall 18 CSCI 4430, A Milaova/BG Ryder 1 2 Lecture Outlie Type equivalece Types i C Primitive types Composite types Records (Structures i C) Variats (Uios i C) Arrays Poiters 3 Types Read: Scott, Chapters 7 ad 8 4 Type Equivalece Structural Equivalece Two ways of defiig type equivalece Structural equivalece: based o shape Roughly, two types are the same if they cosists of the same compoets, put together i the same way Name equivalece: based o lexical occurrece of the type defiitio Strict ame equivalece T1 x; T2 y; Loose ame equivalece A type ame is structurally equivalet to itself Two types are structurally equivalet if they are formed by applyig the same type costructor to structurally equivalet types (i.e., argumets are structurally equivalet) After type declaratio type = T or typedef T i C, the type ame is structurally equivalet to T Declaratio makes a alias of T. ad T are said to be aliased types 5 6 x = y; Fall 18 CSCI 4430, A Milaova 1

2 Structural Equivalece Example, Pascal-like laguage: type S = array [0..99] of char type T = array [0..99] of char Example, C: typedef struct { it j, it k, it *ptr } cell; typedef struct { it, it m, it *p } elemet; Fall 18 CSCI 4430, A Milaova/BG Ryder This is a type defiitio: a applicatio of the array type costructor 7 Structural Equivalece Show by isomorphism of correspodig type trees Show the type trees of these costructed types Are these types structurally equivalet? struct cell struct elemet { char data; { char c; it a[3]; it a[5]; struct cell *ext; struct elemet *ptr; } } Equivalet types: are field ames part of the struct costructed type? are array bouds part of the array costructed type? Fall 18 CSCI 4430, A Milaova/BG Ryder 8 Name Equivalece Name equivalece Roughly, based o lexical occurrece of type defiitio. A applicatio of a type costructor is a type defiitio. E.g., the red array[1..20] is oe type defiitio ad the blue array[1..20] is a differet type defiitio. type T = array [1..20] of it; x,y: array [1..20] of it; w,z: T; v: T; x ad y are of same type, w, z,v are of same type, but x ad w are of differet types! Questio Name equivalece w,z,v: array [1..20] of it; x,y: array [1..20] of it; Are x ad w of equivalet type accordig to ame equivalece? Aswer: x ad w are of distict types. Fall 18 CSCI 4430, A Milaova/BG Ryder 9 Fall 18 CSCI 4430, A Milaova/BG Ryder 10 Name Equivalece A subtlety arises with aliased types (e.g., type = T, typedef it Age i C) Strict ame equivalece A laguage i which aliased types are cosidered distict, is said to have strict ame equivalece (e.g., it ad Age above would be distict types) Loose ame equivalece A laguage i which aliased types are cosidered equivalet, is said to have loose ame equivalece (e.g., it ad Age would be same) 11 Exercise type cell = // record type type alik = poiter to cell type blik = alik p,q : poiter to cell r : alik s : blik t : poiter to cell u : alik Group p,q,r,s,t ito equiv. classes, accordig to structural equiv., strict ame equiv. ad loose ame equiv. 12 2

3 Example: Type Equivalece i C First, i the Algol family, field ames are part of the record/struct costructed type. E.g., the record types below are NOT eve structurally equivalet type A = record x,y : real ed; type B = record z,w : real ed; Type Equivalece i C Aoymous types are differetiated by iteral (compiler-geerated) type ames struct RecA typedef struct struct { char x; { char x; { char x; it y; it y; it y; } a; } RecB; } c; RecB b; This struct is of type ao1. What variables are of equivalet type accordig to the rules i C? Fall 18 CSCI 4430, A Milaova/BG Ryder 13 Fall 18 CSCI 4430, A Milaova/BG Ryder 14 Type Equivalece i C C uses structural equivalece for everythig, except uios ad structs, for which it uses loose ame equivalece struct A struct B { char x; { char x; it y; it y; } } typedef struct A C; typedef C *P; typedef struct B *Q; typedef struct A *R; typedef it Age; typedef it (*F) (it); Type Equivalece i C struct B { char x; it y; }; typedef struct B A; struct { A a; A *ext; } aa; struct { struct B a; struct B *ext; } bb; struct { struct B a; struct B *ext; } cc; A a; struct B b; a = b; aa = bb; bb = cc; typedef Age (*G) (Age); Which of the above assigmets pass the type checker? Questio Structural equivalece for record types is cosidered a bad idea. Ca you thik of a reaso why? Type Equivalece ad Type Compatibility Questios: e := expressio þ or ý Are e ad expressio of same type? e ad expressio may ot be of equivalet types, but they may be of compatible types. It may be possible to covert the type of expressio to the type of e Fall 18 CSCI 4430, A Milaova 17 Fall 18 CSCI 4430, A Milaova/BG Ryder 18 3

4 Type Coversio Implicit coversio coercio Coversio doe implicitly by the compiler I C, mixed mode umerical operatios I e = expressio if e is a double ad expressio is a it, expressio is implicitly coerced i to a double double d,e; e = d + 2; //2 coerced to 2.0 Type Coversio Explicit coversio Programmer must ackowledge coversio I Pascal, roud ad truc perform explicit coversio roud(s) real to it by roudig truc(s) real to it by trucatig it to double, float to double How about float to it? No. May lose precisio ad thus, caot be coerced! I C, type castig performs explicit coversio freelist *s;... (char *)s; forces s to be cosidered as poitig to a char for the purposes of poiter arithmetic Fall 18 CSCI 4430, A Milaova/BG Ryder 19 Fall 18 CSCI 4430, A Milaova/BG Ryder 20 Lecture Outlie Type equivalece Types i C Primitive types Composite types Records (Structures i C) Variats (Uios i C) Arrays Poiters 21 Poiters: Poiters ad Arrays i C Poiters ad arrays are iteroperable: it ; it *a it b[10]; 1. a = b; 2. = a[3]; 3. = *(a+3); 4. = b[3]; 5. = *(b+3); Fall 18 CSCI 4430, A Milaova/BG Ryder 22 Type Declaratio i C What is the meaig of the followig declaratio i C? Draw the type trees. 1. it *a[] 2. it (*a)[] 3. it (*f)(it) Type Declaratio i C typedef it (*PFB)(); // Type variable PFB: what type? struct parse_table { // Type struct parse_table: what type? char *ame; PFB fuc; }; it fuc1() {... } // Fuctio fuc1: what type? it fuc2() {... } struct parse_table table[] = { // Variable table: what type? {"ame1", &fuc1}, {"ame2", &fuc2} }; PFB fid_p_fuc(char *s) { // Fuctio fid_p_fuc: what type? for (i=0; i<um_fuc; i++) if (strcmp(table[i].ame,s)==0) retur table[i].fuc; retur NULL; } it mai(it argc,char *argv[]) {... } Fall 18 CSCI 4430, A Milaova/BG Ryder 23 Fall 18 CSCI 4430, A Milaova 24 4

5 Type Declaratios i C Exercise Type tree for PFB: poiterto () it Type tree for type of fid_p_fuc: Eglish: a fuctio that takes a poiter to char as argumet, ad returs a poiter to a fuctio that takes void as argumet ad returs it. poiterto char poiterto () it struct _chuk { // Type struct_chuk: what type? char ame[10]; it id; }; struct obstack { // Type struct obstack: what type? struct _chuk *chuk; struct _chuk *(*chukfu)(); void (*freefu) (); }; void chuk_fu(struct obstack *h, void *f) { // Fuctio chuk_fu: what type? h->chukfu = (struct _chuk *(*)()) f; } void free_fu(struct obstack *h, void *f) { // Fuctio free_fu: what type? h->freefu = (void (*)()) f; } it mai() { struct obstack h; chuk_fu(&h,&xmalloc); free_fu(&h,&xfree);... } Fall 18 CSCI 4430, A Milaova 25 Fall 18 CSCI 4430, A Milaova 26 Type Declaratios i C Lecture Outlie poiterto Type tree for type of field chukfu: () poiterto struct _chuk: struct ame: array id: it char Fall 18 CSCI 4430, A Milaova 27 Type equivalece Types i C Primitive types Composite types Records (Structures i C) Variats (Uios i C) Arrays Poiters 28 Primitive Types A small collectio of built-i types iteger, float/real, etc. Desig issues: e.g., boolea Use iteger 0/o-0 vs. true/false? Implemetatio issues: represetatio i the machie Iteger Legth fixed by stadards or implemetatio (portability issues) Multiple legths (C: short, it, log) Sigs Float/real All issues of itegers ad more Composite Types: Record (Struct) Collectio of heterogeeous fields Operatios Selectio through field ames (s.um, p->ext) Assigmet Fall 18 CSCI 4430, A Milaova/BG Ryder Example: structures i C typedef struct cell listcell; struct cell { it um; listcell *ext; } s,t; s.um = 0; s.ext = 0; t = s; 5

6 Record (Struct) Variat (Uio) Defiitio of type. What is part of the type? order ad type of fields (but ot the ame) ame ad type of fields order, ame ad type of fields Implemetatio issues: memory layout Successive memory locatios at offset from first byte. Usually, word-aliged, but sometimes packed typedef struct { char ame[10]; it age; } Perso; Perso p; 4 bytes/32 bits ame holes Allow a collectio of alterative fields; oly oe alterative is valid durig executio Fortra: equivalece Algol68 ad C: uios Pascal: variat records Problem: how ca we assure type-safety? Pascal ad C are ot type-safe Algol68 is type-safe! Uses ru-time checks Usually alteratives use same storage Mutually exclusive value access age Fall 18 CSCI 4430, A Milaova/BG Ryder 31 Fall 18 CSCI 4430, A Milaova/BG Ryder 32 Variats (Uios) Example: uios i C uio data { it k; char c; } d1,d2; Operatios Selectio through field ames, Assigmet: d1.k = 3; d2 = d1; d2.c = b ; What about type safety? if (>0) d1.k=5 else d1.c= a ; d1.k << 2 // What is the problem? 33 Pascal s Variat Record program mai(iput,output); type paytype = (salaried,hourly); var employee : record id : iteger; Type tag dept: iteger; age : iteger; case payclass: paytype of salaried: (mothlyrate : real; startdate : iteger); hourly: (rateperhour : real; reghours : iteger; overtime : iteger); ed; begi employee.id:=001234; employee.dept:=12; employee.age:=38; employee.payclass:=hourly; employee.rateperhour:=2.75; employee.reghours:=40; employee.overtime:=3; writel(employee.rateperhour, employee.reghours, employee.overtime); {this should bomb as there is o mothlyrate because payclass=hourly} writel(employee.mothlyrate); Output: E Fall 18 CSCI 4430, A Milaova/BG Ryder E Pascal Variat Record type paytype = (salaried,hourly); var employee : record id : iteger; dept: iteger; age : iteger; case payclass: paytype of salaried:( mothlyrate : real; startdate : iteger); hourly: ( rateperhour : real; reghours : iteger; overtime : iteger); ed; employee.payclass:=salaried; employee.mothlyrate:=575.0; employee.startdate:=13085; {this should bomb as there are o rateperhour, etc. because payclass=salaried} writel(employee.rateperhour, employee.reghours employee.overtime); writel(employee.mothlyrate); ed. Output: E E+02 Algol68 Discrimiated Uios uio(it, real, bool) kitchesik; kitchesik := 3; kitchesik := 3.14; kitchesik := true; if radom <.5 the kitchesik := 1 else kitchesik := 2.78 fi; case kitchesik i (it j): prit (( iteger,j)); (real r): prit (( real,r)); (bool b): prit (( bool,b)); esac; Fall 18 CSCI 4430, A Milaova/BG Ryder 35 Fall 18 CSCI 4430, A Milaova/BG Ryder 36 6

7 Composite Types: Array Array Homogeeous, idexed collectio of values Access to idividual elemets through subscript There are may desig choices Subscript sytax Subscript type, elemet type Whe to set bouds, compile time or ru time? How to iitialize? What built-i operatios are allowed? Defiitio of type. What is part of the type? bouds/dimesio/elemet type Pascal dimesio/elemet type C, FORTRAN, Algol68 What is the lifetime of the array? Global lifetime, static shape (i static memory) Local lifetime (i stack memory) Static shape (stored i fixed-legth portio of stack frame) Shape boud whe cotrol eters a scope (e.g., Ada, Fortra allow defiitio of array bouds whe fuctio is etered; stored i variable-legth portio of stack frame) Global lifetime, dyamic shape (i heap memory) Fall 18 CSCI 4430, A Milaova/BG Ryder 37 Fall 18 CSCI 4430, A Milaova/BG Ryder 38 Example: Algol68 Arrays Array type icludes dimesio ad elemet type; it does ot iclude bouds [1:12] it moth; [1:7] it day; row it [0:10,0:10] real matrix; [-4:10,6:9] real table; row row real Note table ad matrix are equivalet! Example - [1:10] [1:5,1:5] it kiglear; What is the type of kiglear? What is the type of kiglear[j]? What is the type of kiglear[j][1,2]? kiglear[1,2,3]? Example: Algol68 Arrays Trimmig: yields some cross sectio of a origial Algol68 array (slicig a array ito subarrays) Subscriptig: limitig 1 dimesio to a sigle idex value [1:10]it a,b;[1:20]real x; [1:20,1:20]real xx; b[1:4] := a[1:4] assigs first 4 elemets of a ito first 4 elemets of b b := a? b[1:10]:= a[1:10] -? xx[4,1:20]:= x? xx[8:9,7] := x[1:2] assigs x[1] ito xx[8,7] ad x[2] ito xx[9,7] Fall 18 CSCI 4430, A Milaova/BG Ryder 39 Fall 18 CSCI 4430, A Milaova/BG Ryder 40 Array Addressig Oe dimesioal array X[low:high] each elemet is E bytes Assumig that elemets are stored ito cosecutive memory locatios, startig at address addr(x[low]), what is the address of X[j]? addr(x[low]) + (j-low)*e E.g, let X[0:10] be a array of reals (4 bytes) X[3]? is addr(x[0]) + (3-0)*4 = addr(x) + 12 X[1] is at address addr(x[0]) + 4 X[2] is at address addr(x[0]) + 8, etc Fall 18 CSCI 4430, A Milaova/BG Ryder 41 Array Addressig Memory is a sequece of cotiguous locatios Two memory layouts for two-dimesioal arrays: Row-major order ad colum-major order Row-major order: y[0,0], y[0,1], y[0,2],, y[0,], y[1,*], y[2,*], y[low1:hi1,low2:hi2] i Algol68, locatio y[j,k] is addr(y[low1,low2]) + (hi2-low2+1)*e*(j-low1) + (k-low2)*e #locs per row #rows i frot # elemets i row j i of row j frot of elemet [j,k] Fall 18 CSCI 4430, A Milaova/BG Ryder 42 7

8 Array Addressig Composite Types: Poiters Cosider y[0:2, 0:5] it matrix. Assume row-major order ad fid the address of y[1,3]. address of y[1,3] = addr(y[0,0])+(5-0+1)*4*(1-0)+(3-0)*4 6 elemets per row 1 row before row 1 3 elemets i row 1 before 3 = addr(y[0,0]) = addr(y[0,0])+36 Aalogous formula holds for colum-major order Row-major ad colum-major layouts geeralize to A variable or field whose value is a referece to some memory locatio I C: it *p; Operatios Allocatio ad deallocatio of objects o heap p = malloc(sizeof(it)); free(p); Assigmet of oe poiter ito aother it *q = p; it *p = &a; Dereferecig of poiter *q = 1; Poiter arithmetic p + 2 -dimesioal arrays Poiters: Recursive Types A recursive type is a type whose objects may cotai objects of the same type Necessary to build liked structures such as liked lists Poiters are ecessary to defie recursive types i laguages that use the value model for variables: struct cell { it um; struct cell *ext; } Poiters: Recursive Types Recursive types are defied aturally i laguages that use the referece model for variables: class Cell { it um; Cell ext; } Cell() { } Fall 18 CSCI 4430, A Milaova/BG Ryder 45 Fall 18 CSCI 4430, A Milaova/BG Ryder 46 8