n Haskell n Syntax n Lazy evaluation n Static typing and type inference n Algebraic data types n Pattern matching n Type classes

Transcription

1 Aoucemets Quiz 7 HW 9 is due o Friday Raibow grades HW 1-6 plus 8. Please, read our commets o 8! Exam 1-2 Quiz 1-6 Ay questios/cocers, let us kow ASAP Last Class Haskell Sytax Lazy evaluatio Static typig ad type iferece Algebraic data types Patter matchig Type classes Moads ad there is a lot more! Fall 18 CSCI 4430, A Milaova 1 Fall 18 CSCI 4430, A Milaova 2 Lecture Outlie Types Type systems Type checkig Type safety Type equivalece Types Read: Scott, Chapter 7 Types i C Fall 18 CSCI 4430, A Milaova 3 4 What Is a type? A set of values ad the valid operatios o those values Itegers: + - * / < <= = >= > Arrays: lookup(<array>,<idex>) assig(<array>,<idex>,<value>) iitialize(<array>), setbouds(<array>) User-defied types: Java iterfaces What Is the Role of Types? What is the role of types i programmig laguages? Sematic correctess Data abstractio Abstract Data Types (i Java) Documetatio (static types oly) 5 6 1

2 3 Views of Types Deotatioal (or set) poit of view: A type is simply a set of values. A value has a give type if it belogs to the set. E.g. it = { 1,2,... } char = { a, b,... } bool = { true, false } Abstractio-based poit of view: A type is a iterface cosistig of a set of operatios with well-defied meaig 7 3 Views of Types Costructive poit of view: Primitive/simple types: e.g., it, char, bool Composite/costructed types: Costructed by applyig type costructors poiter e.g., poiterto(it) array e.g., arrayof(char) or arrayof(char,20) or... record/struct e.g., record(age:it, ame:arrayof(char)) uio e.g. uio(it, poiterto(char)) CAN BE NESTED! poiterto(arrayof(poiterto(char))) For most of us, types are a mixture of these 3 views 8 What Is a Type System? A mechaism to defie types ad associate them with programmig laguage costructs Deduce types of costructs Deduce if a costruct is type correct or type icorrect What Is a Type System? Additioal rules for type equivalece, type compatibility Importat from pragmatic poit of view 9 10 What Is Type Checkig? The process of esurig that the program obeys the type rules of the laguage Type checkig ca be doe statically At compile-time, i.e., before executio Statically typed (or statically checked) laguage Type checkig ca be doe dyamically At rutime, i.e., durig executio Dyamically typed (or dyamically checked) laguage What Is Type Checkig? Statically typed (better term: statically checked) laguages Typically require type aotatios (e.g., A a, List<A> list) Typically have a complex type system, ad most of type checkig is performed statically (at compile-time) Ada, Pascal, Java, C++, Haskell, ML/OCaml A form of early bidig Dyamically typed (better term: dyamically checked) laguages. Also kow as Duck typed Typically require o type aotatios! All type checkig is performed dyamically (at rutime) Smalltalk, Lisp ad Scheme, Pytho, JavaScript 2

3 What Is Type Checkig? The process of esurig that the program obeys the type rules of the laguage Type safety Textbook defies term prohibited applicatio (also kow as forbidde error): ituitively, a prohibited applicatio is a applicatio of a operatio o values of the wrog type Type safety is the property that o operatio ever applies to values of the wrog type at rutime. I.e., o prohibited applicatio (forbidde error) ever occurs Laguage Desig Choices Desig choice: what is the set of forbidde errors? Obviously, we caot forbid all possible sematic errors Defie a set of forbidde errors Desig choice: Oce we ve chose the set of forbidde errors, how does the type system prevet them? Static checks oly? Dyamic checks oly? A combiatio of both? Furthermore, are we goig to absolutely disallow forbidde errors (be type safe), or are we goig to allow for programs to circumvet the system ad exhibit forbidde errors (i.e., be type usafe)? Forbidde Errors Example: idexig a array out of bouds a[i], a is of size Boud, i<0 or Boud i I C, C++, this is ot a forbidde error 0 i ad i<boud is ot checked (bouds are ot part of type) What are the tradeoffs here? I Pascal, this is a forbidde error. Preveted with static checks 0 i ad i<boud must be checked at compile time What are the tradeoffs here? I Java, this is a forbidde error. It is preveted with dyamic checks 0 i ad i<boud must be checked at rutime What are the tradeoffs here? 15 Type Safety Java vs C++: Java: Duck q; ; q.quack()class Duck has quack C++: Duck *q; ; q->quack()class Duck has quack Ca we write code that calls quack()o a object that is t a Duck? I Java? I C++? Java is said to be type safe while C++ is said to be type usafe 16 C++ Is Type Usafe What Is Type Checkig //#1 void* x = (void *) ew A; A virtual foo() B* q = (B*) x; //a safe dowcast? it case1 = q->foo()//what happes? B virtual foo() vritual foo(it) //#2 void* x = (void *) ew A; B* q = (B *) x; //a safe dowcast? it case2 = q->foo(66); //what happes? q->foo(66) is a prohibited applicatio (i.e., applicatio of a operatio o a value of the wrog type, i.e., forbidde error). Static type B* q promises the programmer that q will poit to a B object. However, laguage does ot hoor this promise type safe type usafe statically ot statically typed typed (i.e., dyamically typed) Assembly

4 What Is Type Checkig? Static typig vs. dyamic typig What are the advatages of static typig? Lecture Outlie Types Type systems Type checkig Type safety What are the advatages of dyamic typig? Type equivalece Types i C Type Equivalece ad Type Compatibility We ow move i the world of procedural vo Neuma laguages E.g., Fortra, Algol, Pascal ad C Value model Statically typed Type Equivalece ad Type Compatibility Questios e := expressio þ or ý Are e ad expressio of same type? a + b þ or ý Are a ad b of same type ad type supports +? foo(arg1, arg2,, argn) þ or ý Do the types of the argumets match the types of the formal parameters? Type 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 Loose ame equivalece 23 Structural 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 Fall 18 CSCI 4430, A Milaova 24 4

5 Structural Equivalece 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; 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? 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 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) 29 Exercise type cell = // record/struct 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. 30 5

6 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; Which variables are of equivalet type, accordig to the rules i C? 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

7 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 Lecture Outlie Types Type systems Type checkig Type safety Type equivalece Types i C 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 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) 41 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 42 7

8 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 43 Fall 18 CSCI 4430, A Milaova 44 Type Declaratios i C Type tree for type of field chukfu: poiterto () poiterto struct _chuk: struct ame: array id: it char Fall 18 CSCI 4430, A Milaova 45 8