留学生考试辅导 (* This file defines a very simple interpreter for a little expression l

(* This file defines a very simple interpreter for a little expression language
* similar to Ocaml.

(*************************************************************)

Copyright By PowCoder代写 加微信 powcoder

(* The first module holds a couple of utilities for strings. *)
(*************************************************************)
module Util =
(* explode a string into a list of characters *)
let explode(s:string) : char list =
let rec loop i cs =
if i < 0 then cs else loop (i - 1) ((String.get s i)::cs) loop (String.length s - 1) [] (* collapse a list of characters into a string *) let implode(cs:char list) : string = let buf = Bytes.create (List.length cs) in let rec loop i cs = match cs with | [] -> buf
| c::cs -> Bytes.set buf i c ; loop (i+1) cs
Bytes.to_string (loop 0 cs)

(*************************************************************************)
(* The second module defines the abstract syntax or AST for the language *)
(*************************************************************************)
module Ast =
(* This is a type abbreviation *)
type var = string

(* we only have one type for this little language *)
type tipe = IntType

(* Define the abstract syntax for a little expression language *)
type binop = Plus | Minus | Times | Div

type exp =
| Int of int
| Binop of exp * binop * exp
| Var of var
| Let of var * exp * exp

(* Some example expressions as abstract syntax trees *)

(* let x = 42 in x * x *)
let e1 = Let(“x”,Int 42,Binop(Var “x”,Times,Var “x”))

(* (let x = 42 in x * x) / 3 *)
let e2 = Binop(e1,Div,Int 3)

(* let y = ((let x = 42 in x * x) / 3) in y – 14 *)
let e3 = Let(“y”,e2,Binop(Var “y”,Minus,Int 14))

(* Convert the abstract syntax tree to a string *)
let rec exp2string(e:exp):string =
let binop2string(b:binop):string =
(match b with
Plus -> “+”
| Times -> “*”
| Minus -> “-”
| Div -> “/”)
match e with
Int i -> string_of_int i
| Binop (e1,b,e2) ->
“(” ^ (exp2string e1) ^ ” ” ^ (binop2string b) ^ ” ” ^ (exp2string e2) ^ “)”
| Var x -> x
| Let(x,e1,e2) ->
“(let ” ^ x ^ ” = ” ^ (exp2string e1) ^ ” in ” ^ (exp2string e2) ^ “)”
end (* module Ast *);;

(************************************************************************)
(* An abstract signature for environments *)
(************************************************************************)
module type ENV =
type ‘a env
exception UnboundVariable of Ast.var
val empty : unit -> ‘a env
val lookup : Ast.var -> ‘a env -> ‘a
val extend : Ast.var -> ‘a -> ‘a env -> ‘a env

(*************************************************************************)
(* One (inefficient) implementation of environments as association lists *)
(*************************************************************************)
module Env : ENV =
type ‘a env = (var * ‘a) list

(* Declares a new exception *)
exception UnboundVariable of var

(* The empty environment — an empty association list *)
let empty():’a env = []

(* Lookup variable x in the environment, returning the associated value,
* and raising the exception UnboundVariable if the variable is not found. *)
let rec lookup(x:var) (env:’a env) =
match env with
[] -> raise (UnboundVariable x)
| (y,i)::rest -> if (x = y) then i else lookup x rest

(* Extend env so that it maps x to i *)
let extend (x:var) (i:’a) (env:’a env) = (x,i)::env

(**************************************************************************)
(* Evaluate an expression in an environment mapping variables to integers *)
(**************************************************************************)
module Eval : sig val evaluate : Ast.exp -> int end =
let rec eval (e: exp) (env: int Env.env) : int =
let binop2fn b =
match b with
| Plus -> (+) (* op is needed for infix functions like + *)
| Minus -> (-)
| Times -> (fun x y -> x*y) (* conflicts with comments… *)
| Div -> (/)
match e with
| Int i -> i
| Binop (e1,b,e2) -> (binop2fn b) (eval e1 env) (eval e2 env)
| Var x -> Env.lookup x env
| Let (x,e1,e2) ->
let i = eval e1 env in
eval e2 (Env.extend x i env)

(* Evaluate an expression — start off with the empty environment *)
let evaluate (e:exp) : int = eval e (Env.empty())

(* A little error support code *)
module Error =
exception Error of string
let error s = raise (Error s)

(************************************************************************)
(* A simple type-checker for expressions *)
(************************************************************************)
module TypeCheck : sig val typecheck : Ast.exp -> Ast.tipe end =
(* Similar module to the evaluator…the only error we catch is unbound
* variables. *)
let rec tc (e : exp) (env : Ast.tipe Env.env) : tipe =
match e with
| Int _ -> IntType
| Binop (e1,_,e2) ->
(match (tc e1 env, tc e2 env) with
(IntType,IntType) -> IntType)
| Var x ->
(try Env.lookup x env with Env.UnboundVariable x ->
Error.error(“unbound variable “^x))
| Let (x,e1,e2) ->
let t = tc e1 env in
tc e2 (Env.extend x t env)

let typecheck (e : exp) : tipe = tc e (Env.empty())

(************************************************************************)
(* lexing — break input into tokens *)
(************************************************************************)
module type LEX =
type token =
INT of int | VAR of Ast.var | PLUS | TIMES | MINUS | DIV | LET | IN |
LPAREN | RPAREN | EQUALS | EOF
val token2string : token -> string
val lex : char list -> token * (char list)

module Lex : LEX =
type token =
INT of int | VAR of Ast.var | PLUS | TIMES | MINUS | DIV | LET | IN |
LPAREN | RPAREN | EQUALS | EOF

let token2string t =
match t with
INT i -> string_of_int i
| VAR x -> x
| PLUS -> “+”
| MINUS -> “-”
| DIV -> “/”
| TIMES -> “*”
| LET -> “let”
| IN -> “in”
| LPAREN -> “(”
| RPAREN -> “)”
| EQUALS -> “=”
| EOF -> “

let rec lex (cs: char list) : token * (char list) =
(match cs with
| [] -> (EOF,[])
| ‘ ‘ :: rest -> lex rest (* skip whitespace *)
| ‘\n’ :: rest -> lex rest (* skip whitespace *)
| ‘(‘ :: ‘*’ :: rest -> lex_comment 1 rest (* comment start *)
| ‘+’ :: rest -> (PLUS,rest)
| ‘-‘ :: rest -> (MINUS,rest)
| ‘*’ :: rest -> (TIMES,rest)
| ‘/’ :: rest -> (DIV,rest)
| ‘(‘ :: rest -> (LPAREN,rest)
| ‘)’ :: rest -> (RPAREN,rest)
| ‘=’ :: rest -> (EQUALS,rest)
| c :: rest ->
if (c >= ‘a’ && c <= 'z') || (c >= ‘A’ && c <= 'Z') then let (x,rest) = lex_var [c] rest in if x = "let" then (LET,rest) (* check keywords *) else if x = "in" then (IN, rest) else (VAR x, rest) else if (c >= ‘0’ && c <= '9') then lex_num ((int_of_char c) - (int_of_char '0')) rest Error.error (Printf.sprintf "bad character %c" c)) (* process comments -- depth records the nesting depth of comments -- we go back * to the lexer only when it drops down to zero *) and lex_comment (depth:int) (cs:char list) : token * (char list) = (match cs with | '*' :: ')' :: rest -> (* close comment*)
let new_depth = depth – 1 in (* see if nesting depth drops to zero *)
if new_depth = 0 then lex rest (* if so, continue with lexer *)
else lex_comment new_depth rest (* otherwise, continue with comment *)
| ‘(‘ :: ‘*’ :: rest -> lex_comment (depth + 1) rest (* increase comment depth *)
| c :: rest -> lex_comment depth rest (* skip any other characters *)
| [] -> Error.error “missing comment end”) (* oops — missing end comment *)

(* accum represents the value of the number so far *)
and lex_num (accum:int) (cs:char list) : token * (char list) =
(match cs with
| c :: rest ->
(* see if c is a digit *)
if c >= ‘0’ && c <= '9' then (* convert the digit to an integer and fold into accumulator *) lex_num (accum*10 + (int_of_char c) - (int_of_char '0')) rest else (INT accum, cs) | [] -> (INT accum, cs))

(* accum represents the identifier so far, but as a reversed list of characters *)
and lex_var (accum:char list) (cs:char list) : string * (char list) =
(match cs with
| c :: rest ->
(* make sure c is a letter, digit, or underscore — if so, push it on accum *)
if c = ‘_’ || (c >= ‘a’ && c <= 'z') || (c >= ‘A’ && c >= ‘Z’) then
lex_var (c::accum) rest
(* be sure to reverse the list and then collapse it with implode *)
else (Util.implode(List.rev accum), cs)
| [] -> (Util.implode(List.rev accum), cs))
end (* Lex *)

(************************************************************************)
(* parsing — take in a string, use the lexer to tokenize it, and *)
(* build an expression. *)
(************************************************************************)
module Parse : sig val parse : string -> Ast.exp end =

let token_error (s:string) (t:token) =
Error.error(“expecting “^s^” but found ‘”^(token2string t)^”‘”)

(* aexp ::= INT | VAR | ‘(‘ exp ‘)’ | ‘let’ VAR ‘=’ exp ‘in’ exp *)
let rec parse_aexp (cs : char list) : exp * (char list) =
(match lex cs with
| (INT i, cs) -> (Int i, cs)
| (VAR x, cs) -> (Var x, cs)
| (LPAREN, cs) ->
(let (e,cs) = parse_exp cs in
match lex cs with
| (RPAREN, cs) -> (e, cs)
| (t,_) -> token_error “‘)'” t)
| (LET, cs) ->
(match lex cs with
| (VAR x, cs) ->
(match lex cs with
| (EQUALS,cs) ->
(match parse_exp cs with
| (e1,cs) ->
(match lex cs with
| (IN,cs) ->
(match parse_exp cs with
| (e2,cs) -> (Let(x,e1,e2),cs))
| (t,_) -> token_error “‘in'” t))
| (t,_) -> token_error “‘='” t)
| (t,_) -> token_error “” t)
| (t,_) -> token_error “ or or ‘(‘ or ‘let'” t)

(* term ::= aexp | term ‘*’ aexp | term ‘/’ aexp *)
and parse_term (cs:char list) : exp * (char list) =
(let rec loop(e,cs) =
match lex cs with
(TIMES,cs) ->
let (e2,cs) = parse_aexp cs in loop(Binop(e,Times,e2),cs)
| (DIV,cs) ->
let (e2,cs) = parse_aexp cs in loop(Binop(e,Div,e2),cs)
| _ -> (e,cs)
loop (parse_aexp cs))

(* exp ::= term | exp ‘+’ term | exp ‘-‘ term *)
and parse_exp (cs:char list) : exp * (char list) =
(let rec loop(e,cs) =
match lex cs with
(PLUS,cs) ->
let (e2,cs) = parse_term cs in loop(Binop(e,Plus,e2),cs)
| (MINUS,cs) ->
let (e2,cs) = parse_term cs in loop(Binop(e,Minus,e2),cs)
| _ -> (e,cs)
loop (parse_term cs))

(* prog ::= exp EOF *)
let parse (s:string) : exp =
let (e,cs) = parse_exp (Util.explode s) in
match lex cs with
(EOF,_) -> e
| (t,_) -> token_error “” t
end (* parse *)

(************************************************************************)
(* Put it all together *)
(************************************************************************)
module MyLanguage : sig val calc : string -> unit end =
let calc(x:string) =
let e = Parse.parse x in
let _ = TypeCheck.typecheck e in
let i = Eval.evaluate e in
Printf.printf “The result is %d\n” i
| Error.Error s -> Printf.printf “error: %s\n” s

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