A fe w n o te s o n g ra m m a rs , la n g u a g e s p e c ific a tio n s , a n d in te rp re te rs K e u n w o o L e e C S E 3 4 1 : P ro g ra m m in g L a n g u a g e s U n iv e rs ity o f W a s h in g to n W in te r 2 0 0 4 Outline Language syntax B ! grammars " egular expressions Operational semantics revisited C a se study: MicroC S y n tax S e mantics In terpreter S o you want to design a language... What do you do? Specify syntax Specify semantics r ite a prototype interpreter Goal of this lecture-and-a-half: whirlwind overview of eac! step, and conceptual tools Syntax: terminology a la n g uage is a subset of the finite-length strings over some alphabet of symbols a g r a mmar s%ecifies which strings belong in teh alphabet a p a r ser turns a string in a language into a more stru)tured representation (usually a syntax tree, relevant to that language & ackus$Naur form n amed for John &ackus * Peter (aur U sed to specify context-free grammars (correspond to context-free languages, C !-s have four %arts: 1. terminals: "atomic. textual entities, e.g. identifiers/ keywords/ #iterals 2. nonterminals: .structured. textual entities, e.g. if/then/else or val *eclarations 3. productions: rules for &uilding nonterminals 4. a unique 1start1 production Productions o nterminal on left/ sequence of terminals and nonterminals on right/ separated by ::= ifExpr ::4 if expr then expr else expr May have cases separated by bars: expr ::= binOpExpr 6 unaryOpExpr 6 ifExpr 6 000 Example constLiteral ::= &OOL_LITERAL 6 INT_LITERAL expr ::= constLiteral 6 IDENTIFIE5 6 expr 8 expr 6 not expr 6 expr 9 expr 6 let decl in expr end 6 if expr then expr else expr 6 : expr ; decl ::= val ID2(TIFIE5 9 expr & (7 1alpha%et"" & ( 7 g r a mmar alphabet = terminals 9 tokens, not individual characters C a n s p ecify format of tokens using &(7 too, but cumbersome < s u ally use regular expressions instead 5 egular expressions r e g exp 9 an expression that may "match" a string; recursively defined as: base case: a character7 a matches "a" indu)tive cases: concatenation: aa matches "aa" r epetition :>leene star;: a* matches "a", .aaaa", .aaaaaaaa", .. u n ion (alternation;: a|b matches "a" or .& Inductive cases may use parens to enforce order of operators 5 egexp examples (a*b)|c matches: 1%1, 1c", 1aaaab" a((b*c*)|d*) matches: "a", 1abb%bc", 1ac", "ab%%cccccc", "ad1 a|b|c|d matches: "a", 1%1, 1c1, 1d1 5 2 syntactic sugars [A&C627#@ = (AA&ACA6A2A7A#; [A$B@ 9 [A&C....XYB@ A " 9 1 optional A1 e.g., AB:C 4 (AC|ABC, A 8 = "one or more A1 e.g., 9;B = 99<B . 9 1 a n y character1 e.g., 0< 4(.any string/ including empty string. [^A@ = "Any character %ut A.1 5 egexps for tokens Integer literals: IN42#25 9 [0-9]+ Identifiers: ID2(TI725 9 [A-Za-z][A-Za-z0-9]+ > e ywords (easy): IF 9 if 4F2( 9 then Extended B(7 Sequences: tupleExpr ::= : expr* ; 6 e lim ited sequences: tupleExpr ::4 : expr* = , ; A t-least-one sequences: tupleExpr ::= : expr , expr;= , ; Optional sequences: valDecl ::= val I62(TI7IER 4 expr > = ? Parsing, lexing Lexer: string $> token stream Parser: token stream $G syntax tree U sually build using lexer generator and parser generator: lexer gen and parser gen can take syntax spe)ification and automatically generate code for each bison, yacc/ @ava))/ sablecc, ml-yacc Semantics revisited 5 eview: 1Language Construct X in a Nutshell" Syntax: if expr1 then expr2 else expr3 6 ynamic semantics eva# expr1 to v if v is true, eval expr2 to v2 and return else eval expr3 to v3 and return Static semantics constraints: expr1 boolean/ expr2 and expr3 agree result type: type of expr2 and expr3 7 ormal notation +*ynamic semanti)s only) F omework 3 eval... | evalExp env (8f (e/ e1/ e2,,(4 case evalExp env e of Integer i 4A raise Fai# .Bype error: non-boolean used for test." | Boolean b => if b then evalExp env e1 else evalExp env e2 Summary One way to do language design: S pecify syntax U s e BN!/ regexps S pecify semantics U s e operational semantics (in English, or in , Implement prototype interpreter You basically 1now how000 O perational semantics of language closely related to actual code for interpreterH Break: ML project overview C ase study: MicroC program ::9 d eclJ stmtJ decl ::= typeName I62(TI7I25 ?9 expr@ = typeName ::= int A flo at stmt ::= expr = A if : expr ; stmt else stmt A while : expr ; stmt A K stmt*L= M expr ::= I(43LI42RAL A 7LOAT3LI425AL A I62(4I7I25 A I62(4I7I25 9 expr A expr + expr A expr == expr A MicroC program int x 9 $,N= int y 9 N= while (x = x + 1) { y 9 y 8 x= M M icroC semantics We'll just do dynamic semantics of assignment exprs: IDEN4IFIER = expr If an expression e evaluates to a value v in an environment Env/ then the expression varName 4 e evaluates to v and %roduces the updated environment Env', where Env' is Env with +varName, v) substituted for the old binding of varName U seful insight: expressions produce both value and new environment (due to side effectsD, Interpreter HOWTO 1. Eata type for each syntactic form 2. Lexer & parser 3. Eata type for values and environments 4. 8mplement dynamic semantics for ea)h syntacti) form G0 +For statically type* #anguages) implement static semanti)s of each syntactic form Syntax datatypes datatype ex%r 4 8ntEx%r of int ex%r ::4(8 B_LITE"9L | FloatE$%r of rea# 6 FLI9BHL8BE"9L | AssignE$%r of string < e$%r 6 8DE B8!8E" | VarE$%r of string 6 8DE B8!8E" 4 e$%r 6(9**E$%r of e$%r < e$%r 6 e$%r ; e$%r | EqE$%r of e$%r < e$%r 6 e$%r 44 e$%r datatype stm t 4 EvalStmt of ex%r stm t ::= e$%r 7 6(8fS tm t of e$%r < stm t < stmt 6 if + e $%r , stmt else stmt | WhileStm t of e$%r < stm t 6 while + e$%r , stmt | Blo)kStmt of stmt lis t 6 J stm t<=7 K datatype typeName 4 TInt | TFloat datatype de)# 4 De)# of typeName * strin g < e $%r datatype program 4 Program of *e)# lis t < stmt list Values and envs. datatype value 9 IntVal of int | FloatPal of real type environment 9 :string * value) list :J returns the value bound to name in e *) fun loo'upEnv(e:environment, name:string) = ... :J returns the environment e with nam e's binding updated to newPalue J; fun update2nv(e:environment, name:string, newValue:value) = ... Evaluator (exprs) e valExpr has type: environment * expr $G value * environment fun evalExpr(env, IntExpr i) 4 +IntVal i, env) | evalExpr(env, VarExpr s,(4 #ookupEnv(env, s, | evalExpr(env, AssignExpr(id, ex%,, 4 #et val (v/ newEnv,(4 evalExpr(env, ex%, in +v, updateEnv(newEnv/ id, v,, end 6(000 Evaluator (stmts) evalStmt has type: environment * stmt $G environment fun evalStmt(env/ E va#S tm t e, 4 #et va# +H/ newEnv, 4 evalE$%r(env, e, in newEnv en* | evalStmt(env, 8fStm t(e/ s1/ s2)) 4 #et va# (v, newEnv) 4 evalEx%r(env/ e, va# v8sZero 4 case v of 8ntVa# i => i 4 0 6 FloatLa# f 4A f N4 0.0 an*a#so f A4 000 in if vIsZero then evalStmt(newEnv/ s1, else evalStmt(new Env/ s2, en* 6(000 Evaluator (decls) e v alEecl has type: environment J decl $G environment fun evalDe)#+env, Ee)#(t/ name/ ex%,, 4 let va# (v, newEnv) = evalExpr(env, exp) in updateEnv(newEnv/ name, v) en* Evaluator (program) fun eval(Program(decls, stmts)) = #et fun evalDeclList(env, nil) = env 6 evalDeclList(env, *::*s) = evalEeclList(evalDecl(env, *,/ ds) fun evalStmtList+env, nil, = env 6 evalStmtList(env, s::ss) = evalStmtList(evalStmt(env, s)/ ss) val *eclsEnv = evalDeclList+nil/ decls) in evalStmtList+*eclsEnv, stmts) end.