Arithmetic evaluation/Ada: Difference between revisions
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Revision as of 12:26, 6 February 2010
The following implementation uses table-driven parsers provided by Simple components for Ada. A parser is controlled by the tables of prefix, infix and postfix operations. Between the operations it calls Get_Operand in order to recognize expression terms. The parser communicates with its back end using the primitive operations Call and Enclose. The former is used for operations, the latter is for brackets. For this example we generate the parsing tree from there. There are many other operations which are used for advanced parsing and optimization, here they are defined as trivially returning True or False.
A parsing tree node has one operation Evaluate in order to calculate the expression. The nodes are allocated in an arena implemented by a storage pool. The pools is organized as a stack, so that the whole tree is popped when no more needed. This is a standard technique in compiler construction.
The implementation provides an advanced error handling and skipping blanks and Ada comments (these are taken from the library). <lang ada> with Ada.Unchecked_Deallocation; with Parsers.String_Source; use Parsers.String_Source; with Parsers.Generic_Lexer.Ada_Blanks; with Parsers.Generic_Token.Segmented_Lexer; with Stack_Storage; with Tables.Names;
package Parsers.Simple is
type Operations is (Add, Sub, Mul, Div, Left_Bracket, Right_Bracket); type Priorities is mod 3; -- The levels of association
function "and" (Left, Right : Operations) return Boolean; function Is_Commutative (Left, Right : Operations) return Boolean; function Is_Inverse (Operation : Operations) return Boolean; function Group_Inverse (Operation : Operations) return Operations;
Tree_Pool : Stack_Storage.Pool (2048, 128); -- Arena for the tree -- Tree nodes type Node is abstract tagged limited null record; function Evaluate (Item : Node) return Integer is abstract; type Node_Ptr is access Node'Class; for Node_Ptr'Storage_Pool use Tree_Pool; procedure Free is new Standard.Ada.Unchecked_Deallocation (Node'Class, Node_Ptr); -- Stub of the arena type Mark is new Node with null record; overriding function Evaluate (Item : Mark) return Integer; -- Terminal nodes type Literal is new Node with record Location : Parsers.String_Source.Location; Value : Integer; end record; overriding function Evaluate (Item : Literal) return Integer; -- Non-terminal nodes type Argument_List is array (Positive range <>) of Node_Ptr; type Expression (Count : Positive) is new Node with record Operation : Operations; Location : Parsers.String_Source.Location; Operands : Argument_List (1..Count); end record; overriding function Evaluate (Item : Expression) return Integer;
package Tokens is -- The lexical tokens new Parsers.Generic_Token ( Operation_Type => Operations, Argument_Type => Node_Ptr, Priority_Type => Priorities, Sources => Code ); use Tokens;
procedure Check_Spelling (Name : String); function Check_Matched (Source : String; Pointer : Integer) return Boolean; package Token_Tables is new Tokens.Vocabulary.Names; -- The tables of prefix, infix and postfix operations Prefixes : aliased Token_Tables.Dictionary; Infixes : aliased Token_Tables.Dictionary; Postfixes : aliased Token_Tables.Dictionary;
package Lexers is new Tokens.Segmented_Lexer; -- Table driven lexers package Blank_Skipping_Lexers is -- Lexers that skip Ada blanks new Lexers.Token_Lexer.Implementation.Ada_Blanks (Lexers.Lexer);
type Simple_Expression is -- The lexer that uses our tables new Blank_Skipping_Lexers.Lexer ( Prefixes => Prefixes'Access, Infixes => Infixes'Access, Postfixes => Postfixes'Access ) with null record; overriding -- Evaluates an operator function Call ( Context : access Simple_Expression; Operation : Tokens.Operation_Token; List : Tokens.Arguments.Frame ) return Tokens.Argument_Token; overriding -- Evaluates an expression in brackets function Enclose ( Context : access Simple_Expression; Left : Tokens.Operation_Token; Right : Tokens.Operation_Token; List : Tokens.Arguments.Frame ) return Tokens.Argument_Token; overriding -- Recognizes an operand (float number) procedure Get_Operand ( Context : in out Simple_Expression; Code : in out Source; Argument : out Tokens.Argument_Token; Got_It : out Boolean );
end Parsers.Simple; </lang> Here is the implementation of the package. <lang ada> with Ada.Characters.Handling; use Ada.Characters.Handling; with Ada.Exceptions; use Ada.Exceptions; with Ada.IO_Exceptions; use Ada.IO_Exceptions; with Strings_Edit.Integers; use Strings_Edit.Integers;
package body Parsers.Simple is
function "and" (Left, Right : Operations) return Boolean is begin return True; end "and";
function Is_Commutative (Left, Right : Operations) return Boolean is begin return False; end Is_Commutative;
function Is_Inverse (Operation : Operations) return Boolean is begin return False; end Is_Inverse;
function Group_Inverse (Operation : Operations) return Operations is begin return Mul; end Group_Inverse;
procedure Check_Spelling (Name : String) is begin null; end Check_Spelling;
function Check_Matched (Source : String; Pointer : Integer) return Boolean is begin return ( not Is_Alphanumeric (Source (Pointer)) or else not Is_Alphanumeric (Source (Pointer - 1)) ); end Check_Matched;
function Call ( Context : access Simple_Expression; Operation : Tokens.Operation_Token; List : Tokens.Arguments.Frame ) return Tokens.Argument_Token is Result : Node_Ptr := new Expression (List'Length); begin declare This : Expression renames Expression (Result.all); begin This.Operation := Operation.Operation; This.Location := Operation.Location; for Argument in List'Range loop This.Operands (Integer (Argument)) := List (Argument).Value; end loop; end; return (Result, Operation.Location & Link (List)); end Call;
function Enclose ( Context : access Simple_Expression; Left : Tokens.Operation_Token; Right : Tokens.Operation_Token; List : Tokens.Arguments.Frame ) return Tokens.Argument_Token is Result : Node_Ptr := new Expression (List'Length); begin declare This : Expression renames Expression (Result.all); begin This.Operation := Left.Operation; This.Location := Left.Location & Right.Location; for Argument in List'Range loop This.Operands (Integer (Argument)) := List (Argument).Value; end loop; end; return (Result, Left.Location & Right.Location & Link (List)); end Enclose;
procedure Get_Operand ( Context : in out Simple_Expression; Code : in out Source; Argument : out Tokens.Argument_Token; Got_It : out Boolean ) is Line : String renames Get_Line (Code); Pointer : Integer := Get_Pointer (Code); Value : Integer; begin if Is_Decimal_Digit (Line (Pointer)) then Get (Line, Pointer, Value); Set_Pointer (Code, Pointer); Argument.Location := Link (Code); Argument.Value := new Literal; declare Result : Literal renames Literal (Argument.Value.all); begin Result.Value := Value; Result.Location := Argument.Location; end; Got_It := True; else Got_It := False; end if; exception when Constraint_Error => Raise_Exception ( Parsers.Syntax_Error'Identity, "Too large number at " & Image (Link (Code)) ); when Data_Error => Raise_Exception ( Parsers.Syntax_Error'Identity, "Malformed number at " & Image (Link (Code)) ); when End_Error => Got_It := False; end Get_Operand;
function Evaluate (Item : Mark) return Integer is begin return 0; end Evaluate;
function Evaluate (Item : Literal) return Integer is begin return Item.Value; end Evaluate;
function Evaluate (Item : Expression) return Integer is Argument : array (Item.Operands'Range) of Integer; begin for I in Argument'Range loop Argument (I) := Item.Operands (I).Evaluate; end loop; case Item.Operation is when Add => return Argument (1) + Argument (2); when Sub => return Argument (1) - Argument (2); when Mul => return Argument (1) * Argument (2); when Div => return Argument (1) / Argument (2); when others => return Argument (1); end case; exception when Constraint_Error => Raise_Exception ( Parsers.Syntax_Error'Identity, "Numeric error at " & Image (Item.Location) ); end Evaluate;
use type Tokens.Descriptors.Descriptor_Class; use Lexers.Lexical_Descriptors.Operation; use Lexers.Lexical_Arguments;
begin
Add_Operator (Infixes, "+", Add, 1, 1); Add_Operator (Infixes, "-", Sub, 1, 1); Add_Operator (Infixes, "*", Mul, 2, 2); Add_Operator (Infixes, "/", Div, 2, 2);
Add_Bracket (Prefixes, "(", Left_Bracket); Add_Bracket (Postfixes, ")", Right_Bracket);
end Parsers.Simple; </lang> The next is a little test. It reads a line from the keyboard and then evaluates it. The program stops when the input is empty: <lang ada> with Ada.Exceptions; use Ada.Exceptions; with Ada.Text_IO; use Ada.Text_IO; with Parsers.Simple; use Parsers.Simple; with Parsers.String_Source; use Parsers.String_Source; with Strings_Edit.Integers; use Strings_Edit.Integers; with Parsers.Generic_Source.Text_IO;
procedure Test_Simple_Parser is
use Lexers, Tokens;
package Text_IO is new Code.Text_IO; use Text_IO;
Parser : Simple_Expression; Result : Argument_Token; Stub : Node_Ptr;
begin
loop Put ("Expression:"); declare Line : aliased String := Get_Line; Code : Source (Line'Access); begin exit when Line'Length = 0; Stub := new Mark; -- Mark the tree stack begin Parse (Parser, Code, Result); Put_Line ( Image (Result.Location) & " = " & Image (Result.Value.Evaluate) ); exception when Error : Parsers.Syntax_Error => Put_Line ("Error : " & Exception_Message (Error)); end; Free (Stub); -- Release the stack end; end loop;
end Test_Simple_Parser; </lang> Sample exchange. When the expression is evaluated its range in the source string is indicated. Upon errors, the location of is shown as well:
Expression:(3 * 50) - (100 / 10) 1..21 = 140 Expression:1+ Error : Operand expected at 3 Expression:39999999999*9999999999+23 Error : Too large number at 1 Expression:5/0 Error : Numeric error at 2..2 Expression: