Interpre'ng and Compiling Intex

Transcription

1 A New Mini-Language: Intex Interpre'ng and Compiling Intex CS5 Programming Languages Spring 08, Lyn Turbak Department of Computer Science Wellesley College Intex programs are simple arithme'c expressions on integers that can refer to integer arguments. Intex is the first in a sequence of mini-languages that can be extended to culminate in something that is similar to Racket. At each step along the way, we can add features that allow us to study different programming language dimensions. Intex: integer expressions, posi'onal program arguments B: Intex + named arguments & local naming Valex: B + condi'onals, mul'ple kinds of s (booleans, strings, lists), dynamic type checking, and syntac'c sugar HOFL (Racket-like language): Valex + first-class func'ons HOFLEC: HOFL + SML-like mutable cells Intex Intex Syntax Trees & Syntac'c Data Types numargs Intex Div Int Add body datatype pgm = Intex of int * exp and exp = Int of int of int of binop * exp * exp and binop = Add Sub Mul Div Rem (* Sample AST as SOP tree *) val avg = Intex(, (Add,, ), Int )) (* Sample AST as s-expression *) (intex (/ (+ ($ ) ($ )) ) ; can even write: (intex (/ (+ $ $) ) How do we write this Intex program as SML SOP tree? As s-expression? numargs Intex Div Int Mul body Sub Int 3 Int 5 9 Intex 3 Intex 4

2 Intex Implementa'on #: Intex Interpreter in SML Given an avg-in-intex program, how can we execute it? avg machine (I) q avg-in-intex program q Intex interpreter machine (I) ² Intex-in-SML-interpreter program ² SML interpreter machine in wx VM (ignore details) Intex Interpreter Without Error Checking: Skeleton (* Intex.pgm -> int list -> int *) fun run (Intex(numargs, exp)) args =??? (* Intex.exp -> int list -> int *) and eval (Int i) args =??? eval ( ) args =??? eval ((binop, exp, exp)) args =??? (* Intex.binop -> int * int -> int *) and binoptofun Add = op+ binoptofun Mul = op* binoptofun Sub = op- binoptofun Div = (fn(x,y) => x div y) binoptofun Rem = (fn(x,y) => x mod y) Intex 5 Intex 6 Intex Interpreter With Error Checking Try it out exception EvalError of string (* Intex.pgm -> int list -> int *) fun run (Intex(numargs, exp)) args = if numargs <> length args then raise EvalError "Mismatch between expected and actual number of args" else eval exp args - run (Intex(, (Mul,, ))) [5]; val it = 5 : int - run (Intex(,, ))) [5]; val it = : int (* Intex.exp -> int list -> int *) and eval (Int i) args = i eval ( ) args = if ( <= 0) orelse ( > length args) then raise EvalError " out of bounds" else List.nth(args, -) eval ((binop, exp, exp)) args = let val i = eval exp args val i = eval exp args in (case (binop, i) of (Div, 0) => raise EvalError "Division by 0" (Rem,0) => raise EvalError "Remainder by 0" _ => (binoptofun binop)(i, i)) end Intex 7 - run (Intex(,, ))) [0]; uncaught exception EvalError - run avg [5,5]; val it = : int - map (run fc) [[~40], [0], [3], [98], []]; val it = [~40,~8,0,36,0] : int list Intex 8

3 Handling Errors (* Intex.pgm -> int list -> string *) fun testrun pgm args = Int.toString (run pgm args) (* Convert to string so same type as error messages below *) handle EvalError msg => "EvalError: " ^ msg other => "Unknown exception: " ^ (exnmessage other) - testrun (Intex(,, ))) [5]; val it = "" : string - testrun (Intex(,, ))) [0]; val it = "EvalError: Division by 0" : string - map (testrun fc) [[~40], [0], [3], [98], []]; val it = ["~40","~8","0","36","0"] : string list Intex 9 Intex programs as S-expression strings Intex(, (Mul,, ) Intex(, (Add,, ), Int )) "(intex (* ($ ) ($ ))" "(intex (/ (+ ($ ) ($ )) ))" Intex(, (Mul, (Sub,, Int 3), Int 5), Int 9)) "(intex (/ (* (- ($ ) 3) 5) 9))" Intex Running Intex programs as S-expression strings (* string -> string -> string *) fun testrun' pgmsexpstring argssexpstring = testrun (stringtopgm pgmsexpstring) (sexpstringtointlist argssexpstring) handle SexpError (msg, sexp) => ("SexpError: " ^ msg ^ " " ^ (Sexp.sexpToString sexp)) Sexp.IllFormedSexp msg => ("SexpError: Ill-formed sexp " ^ msg) other => "Unknown exception: " ^ (exnmessage other) - testrun' "(intex (/ (+ ($ ) ($ )) ))" "(5 5)"; val it = "" : string - map (testrun' "(intex (/ (* (- ($ ) 3) 5) 9))") = ["(-40)", "(0)", "(3)", "(98)", "()"]; val it = ["~40","~8","0","36","0"] : string list - map (testrun' "(intex (/ ($ ) ($ )))")= = ["(-7)", "(0)", "(4)"]; val it = [","EvalError: Division by 0",""] : string list Intex A Read-Eval-Print Loop (REPL) in Intex - repl(); intex> (+ ) 3 intex> (#args 6 7) intex> (+ ($ ) ($ )) 3 intex> ( * $ $) 4 intex> (#run (intex (/ (+ ($ ) ($ )) )) 5 5) intex> (#run "avg.itx" 5 5) intex> (#run avg.itx 5 5) intex> (#quit) Moriturus te saluto! Intex

4 What do we know about this program? val test = Intex(, (Sub, (Mul,, 3), )) Dynamic vs. Sta'c Checking: Indices Dynamic check (at runjme) : eval ( ) args = if ( <= 0) orelse ( > length args) then raise EvalError " out of bounds" else List.nth(args, -) StaJc check (at compile Jme or checking Jme, before runjme) : Idea: We know numargs from program, so can use this to check all argument references without running the program. Such checks are done by examining thee program syntax tree. O[en there is a choice between a bo)om-up and top-down approach to processing the tree. Intex 3 You will do both approaches for checking in PS9. Intex 4 Sta'c Index Checking: Top Down (PS9). In top-down phase, pass numargs to every subexpression in program.. Check numargs against every. a. Return true for indices that pass test and subexps without arg indices b. Return false if any fails test. true true and and true Sta'c Index Checking: Bo_om Up (PS9). Calculate (min,max) for every subexpression in tree in bo_om-up fashion. Compare (min,max) at root of program body expression to (, numargs), returning true if a subrange and false otherwise. Check if in inclusive range (, numargs) (,) (,) (, - ) (,) (,) Intex 5 Intex 6

5 Intex Implementa'on #: Intex-to-Posaix-compiler in SML Given an avg-in-intex program, how can we execute it? Hand-Compiling Intex to PostFix Manually translate the following Intex programs to equivalent PostFix programs: (intex 0 (* (- 7 4) (/ 8 ))) (intex 4 (* (- $ $) (/ $3 $4))) avg machine (I) q avg-in-postfix program ² avg-in-intex program ² Intex-to-PostFix-compiler machine o Intex-to-PostFix-compiler-in-SML program o SML interpreter machine in wx VM (ignore details) q PostFix interpreter machine (I) ² PostFix-in-SML-interpreter program ² SML interpreter machine in wx VM (ignore details) Intex 7 ReflecJon: How did you figure out how to translate Intex indices into PostFix Nget indices? Intex 8 Can we automate this process? Yes! We can define an intextopostfix func'on with type Intex.pgm -> PostFix.pgm and then use it like this: intextopostfix Skeleton (* val intextopostfix: Intex.pgm -> PostFix.pgm *) fun intextopostfix (Intex.Intex(numargs, exp)) = PostFix.PostFix(numargs, exptocmds exp 0???) (*??? is the initial depth argument *) fun translatestring intexpgmstring = PostFix.pgmToString (intextopostfix (Intex.stringToPgm intexpgmstring)) - translatestring "(intex (* ($ ) ($ )))"; val it = "(postfix nget nget mul)" : string - translatestring "(intex (/ (+ ($ ) ($ )) ))"; val it = "(postfix nget 3 nget add div)" : string - translatestring "(intex 4 (* (- ($ ) ($ )) (/ ($ 3) ($ 4))))"; val it = "(postfix 4 nget 3 nget sub 4 nget 6 nget div mul)" : string Intex 9 (* val exptocmds: Intex.exp -> PostFix.cmd list *) (* depth arg statically tracks how many s are on stack above the program arguments *) and exptocmds (Intex.Int i) depth =??? exptocmds (Intex. ) depth =??? [PostFix.Int ( + depth), PostFix.Nget] (* specified argument is on stack at + depth *) exptocmds (Intex.(binop,exp,exp)) depth =??? (exptocmds exp depth) (* st rand is at same depth as whole binapp (exptocmds exp (depth + )) (* for nd rand, add to depth to account for st rand [PostFix.Arithop (binoptoarithop binop)] and binoptoarithop Intex.Add = PostFix.Add binoptoarithop Intex.Sub = PostFix.Sub binoptoarithop Intex.Mul = PostFix.Mul binoptoarithop Intex.Div = PostFix.Div binoptoarithop Intex.Rem = PostFix.Rem Intex 0