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tidy up parser library documentation
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martinbaker
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y="81.947746"
|
||||
x="84.339279"
|
||||
y="95.970665"
|
||||
x="79.841362"
|
||||
sodipodi:role="line"
|
||||
id="tspan968">Representation of expressions ready</tspan><tspan
|
||||
style="font-style:normal;font-variant:normal;font-weight:bold;font-stretch:normal;font-size:3.52777767px;font-family:sans-serif;-inkscape-font-specification:'sans-serif Bold';fill:#000000;stroke-width:0.26458332"
|
||||
y="86.357468"
|
||||
x="84.339279"
|
||||
y="100.38039"
|
||||
x="79.841362"
|
||||
sodipodi:role="line"
|
||||
id="tspan974">for compiling: CExp</tspan><tspan
|
||||
style="font-style:normal;font-variant:normal;font-weight:bold;font-stretch:normal;font-size:3.52777767px;font-family:sans-serif;-inkscape-font-specification:'sans-serif Bold';fill:#000000;stroke-width:0.26458332"
|
||||
y="90.767189"
|
||||
x="84.339279"
|
||||
y="104.79011"
|
||||
x="79.841362"
|
||||
sodipodi:role="line"
|
||||
id="tspan972">Type erased, explicit case trees</tspan></text>
|
||||
<text
|
||||
@ -1047,22 +1047,22 @@
|
||||
sodipodi:role="line">command line options</tspan></text>
|
||||
<text
|
||||
id="text988"
|
||||
y="106.82006"
|
||||
x="22.69136"
|
||||
y="89.886726"
|
||||
x="22.162193"
|
||||
style="font-style:normal;font-weight:normal;font-size:10.58333302px;line-height:1.25;font-family:sans-serif;letter-spacing:0px;word-spacing:0px;fill:#0000ff;fill-opacity:1;stroke:none;stroke-width:0.26458332"
|
||||
xml:space="preserve"
|
||||
inkscape:export-xdpi="61.120499"
|
||||
inkscape:export-ydpi="61.120499"><tspan
|
||||
style="font-style:normal;font-variant:normal;font-weight:bold;font-stretch:normal;font-size:4.23333311px;font-family:sans-serif;-inkscape-font-specification:'sans-serif Bold';fill:#0000ff;stroke-width:0.26458332"
|
||||
y="106.82006"
|
||||
x="22.69136"
|
||||
y="89.886726"
|
||||
x="22.162193"
|
||||
id="tspan986"
|
||||
sodipodi:role="line">module Idris.Error</tspan></text>
|
||||
<rect
|
||||
inkscape:export-ydpi="61.120499"
|
||||
inkscape:export-xdpi="61.120499"
|
||||
y="102.32182"
|
||||
x="21.103861"
|
||||
y="85.388489"
|
||||
x="20.574694"
|
||||
height="9.5250101"
|
||||
width="37.835419"
|
||||
id="rect990"
|
||||
@ -1072,17 +1072,17 @@
|
||||
inkscape:export-xdpi="61.120499"
|
||||
xml:space="preserve"
|
||||
style="font-style:normal;font-weight:normal;font-size:10.58333302px;line-height:1.25;font-family:sans-serif;letter-spacing:0px;word-spacing:0px;fill:#0000ff;fill-opacity:1;stroke:none;stroke-width:0.26458332"
|
||||
x="23.220528"
|
||||
y="110.52423"
|
||||
x="22.69136"
|
||||
y="93.590897"
|
||||
id="text994"><tspan
|
||||
sodipodi:role="line"
|
||||
id="tspan992"
|
||||
x="23.220528"
|
||||
y="110.52423"
|
||||
x="22.69136"
|
||||
y="93.590897"
|
||||
style="font-style:normal;font-variant:normal;font-weight:bold;font-stretch:normal;font-size:3.52777767px;font-family:sans-serif;-inkscape-font-specification:'sans-serif Bold';fill:#000000;stroke-width:0.26458332">perror</tspan></text>
|
||||
<path
|
||||
style="fill:none;stroke:#0000ff;stroke-width:0.70555556;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:4;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#marker1000)"
|
||||
d="m 142.54761,98.087086 c -7.32197,0.078 -68.613479,2.584834 -83.608332,4.234734"
|
||||
d="m 66.876776,99.410007 c -0.17822,-10.50534 -0.880145,-7.9985 -7.143748,-8.99444"
|
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id="path996"
|
||||
inkscape:connector-curvature="0"
|
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inkscape:export-xdpi="61.120499"
|
||||
@ -1105,7 +1105,7 @@
|
||||
inkscape:export-ydpi="61.120499" />
|
||||
<text
|
||||
xml:space="preserve"
|
||||
style="font-style:normal;font-weight:normal;font-size:10.58333302px;line-height:0.40000001;font-family:sans-serif;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.26458332"
|
||||
style="font-style:normal;font-weight:normal;font-size:10.58333302px;line-height:0.40000001;font-family:sans-serif;letter-spacing:0px;word-spacing:0px;fill:#ff0000;fill-opacity:1;stroke:none;stroke-width:0.26458332;"
|
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x="158.75"
|
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y="226.09137"
|
||||
id="text1473"
|
||||
@ -1115,16 +1115,16 @@
|
||||
id="tspan1471"
|
||||
x="158.75"
|
||||
y="226.09137"
|
||||
style="font-style:normal;font-variant:normal;font-weight:bold;font-stretch:normal;font-size:4.23333311px;line-height:0.40000001;font-family:sans-serif;-inkscape-font-specification:'sans-serif Bold';fill:#000000;stroke-width:0.26458332">'text' modules are</tspan><tspan
|
||||
style="font-style:normal;font-variant:normal;font-weight:bold;font-stretch:normal;font-size:4.23333311px;line-height:0.40000001;font-family:sans-serif;-inkscape-font-specification:'sans-serif Bold';fill:#ff0000;stroke-width:0.26458332;">'text' modules are</tspan><tspan
|
||||
sodipodi:role="line"
|
||||
x="158.75"
|
||||
y="230.92491"
|
||||
style="font-style:normal;font-variant:normal;font-weight:bold;font-stretch:normal;font-size:4.23333311px;line-height:0.40000001;font-family:sans-serif;-inkscape-font-specification:'sans-serif Bold';fill:#000000;stroke-width:0.26458332"
|
||||
style="font-style:normal;font-variant:normal;font-weight:bold;font-stretch:normal;font-size:4.23333311px;line-height:0.40000001;font-family:sans-serif;-inkscape-font-specification:'sans-serif Bold';fill:#ff0000;stroke-width:0.26458332;"
|
||||
id="tspan1475">also in Idris 1</tspan><tspan
|
||||
sodipodi:role="line"
|
||||
x="158.75"
|
||||
y="235.75845"
|
||||
style="font-style:normal;font-variant:normal;font-weight:bold;font-stretch:normal;font-size:4.23333311px;line-height:0.40000001;font-family:sans-serif;-inkscape-font-specification:'sans-serif Bold';fill:#000000;stroke-width:0.26458332"
|
||||
style="font-style:normal;font-variant:normal;font-weight:bold;font-stretch:normal;font-size:4.23333311px;line-height:0.40000001;font-family:sans-serif;-inkscape-font-specification:'sans-serif Bold';fill:#ff0000;stroke-width:0.26458332;"
|
||||
id="tspan1477">library.</tspan></text>
|
||||
<path
|
||||
inkscape:connector-curvature="0"
|
||||
|
||||
|
Before Width: | Height: | Size: 60 KiB After Width: | Height: | Size: 60 KiB |
@ -52,13 +52,13 @@ Idris 2 has at least 3 compilers:
|
||||
PTerm (and eventually TT structure).
|
||||
- REPL - compiles input from the command line.
|
||||
|
||||
The following diagram is my attempt to work out how the modules in Idris 2 fit together.
|
||||
The following diagram is my first attempt to work out how some of the modules in
|
||||
Idris 2 fit together (with a few of the dependencies between them shown). The
|
||||
Idris 1 library is based on the modules at the bottom of the diagram (shown
|
||||
in red).
|
||||
|
||||
.. image:: ../image/parserModules.png
|
||||
:width: 460px
|
||||
:height: 496px
|
||||
:alt: diagram illustrating these stages of lexer and parser
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
@ -26,8 +26,7 @@ In order to construct this list of tokens we need:
|
||||
- A way to recognise the tokens in the input string.
|
||||
- A way to construct these individual tokens.
|
||||
|
||||
This is given by the TokenMap. This is a mapping from lexers to the tokens
|
||||
they produce. This is a list of pairs:
|
||||
This is given by the TokenMap which is a list of pairs containing this information:
|
||||
|
||||
.. code-block:: idris
|
||||
|
||||
@ -108,7 +107,7 @@ If a recogniser does not consume input there is a danger of an infinite loop.
|
||||
To prevent this the recogniser is dependent on a boolean called 'consumes' which
|
||||
is true if the recogniser is guaranteed to consume at least one character.
|
||||
|
||||
The constructors of Recognise allow us to ensure that, event though parts of
|
||||
The constructors of Recognise allow us to ensure that, even though parts of
|
||||
the recogniser may not consume, overall the recogniser will consume.
|
||||
|
||||
Since 'Recognise True' is more common than 'Recognise False' it is convenient to
|
||||
@ -133,12 +132,12 @@ when the indent decreases.
|
||||
|
||||
This topic needs to be more fully expanded here. Until someone does that, a
|
||||
possible way to get more information is to see how it is done in Idris 2
|
||||
_`here`: https://github.com/edwinb/Idris2/blob/master/src/Parser/Lexer.idr
|
||||
: https://github.com/edwinb/Idris2/blob/master/src/Parser/Lexer.idr
|
||||
|
||||
Simple Expression Example for Lexer
|
||||
-----------------------------------
|
||||
|
||||
On this page we will implement a lexer to lex a very simple expression as
|
||||
On this page we will implement a lexer to 'lex' a very simple expression as
|
||||
a running example, on the next page, we will go on to implement a parser for it.
|
||||
|
||||
First import the lexer and parser code:
|
||||
@ -268,7 +267,7 @@ input string as parameters:
|
||||
Int,
|
||||
String)
|
||||
|
||||
The lexer uses potentially infinite data structures. It has recursive arguments (codata type) so code is lazy. In the example the indexes have not been computed but we can
|
||||
The lexer uses potentially infinite data structures. It has recursive arguments (codata type) so code is lazy. In the output above the indexes have not been computed but we can
|
||||
pick out the tokens:
|
||||
|
||||
- (Number 1)
|
||||
|
||||
@ -12,14 +12,14 @@ To run our parser we call 'parse'. This requires a Grammar and the output from t
|
||||
|
||||
If successful this returns 'Right' with a pair of
|
||||
|
||||
- the parse result
|
||||
- the unparsed tokens (the remaining input)
|
||||
- the parse result.
|
||||
- the unparsed tokens (the remaining input).
|
||||
|
||||
otherwise it returns 'Left' with the error message.
|
||||
|
||||
So we need to define the Grammar for our parser, this is done using the following
|
||||
'Grammar' data structure, this is a combinator structure similar in principle to the
|
||||
recogniser combinator for the lexer which was discussed on the previous page.
|
||||
'Grammar' data structure. This is a combinator structure, similar in principle to the
|
||||
recogniser combinator for the lexer, which was discussed on the previous page.
|
||||
|
||||
As with the Recogniser the Grammar type is dependent on a boolean 'consumes'
|
||||
value which allows us to ensure that complicated Grammar structures will always
|
||||
@ -71,28 +71,31 @@ Parser Example
|
||||
On the previous page we implemented a lexer to 'lex' a very simple expression, on
|
||||
this page we will go on to implement a parser for this running example.
|
||||
|
||||
Expressed in Backus–Naur form (BNF) the syntax we are aiming at is something
|
||||
like this:
|
||||
.. list-table::
|
||||
|
||||
.. code-block:: idris
|
||||
* - Expressed in Backus–Naur form (BNF) the syntax we are aiming at is something
|
||||
like this:
|
||||
- .. code-block:: idris
|
||||
|
||||
<expr> ::= <integer literal>
|
||||
<expr> ::= <integer literal>
|
||||
| <expr>'+'<expr>
|
||||
| <expr>'-'<expr>
|
||||
| <expr>'*'<expr>
|
||||
| '('<expr>')'
|
||||
|
||||
<integer literal> ::= <digit>|<integer literal><digit>
|
||||
<integer literal> ::= <digit>|<integer literal><digit>
|
||||
|
||||
To start, here is a Grammar to parse an integer literal (that is, a sequence of
|
||||
numbers).
|
||||
.. list-table::
|
||||
|
||||
.. code-block:: idris
|
||||
* - To start, here is a Grammar to parse an integer literal (that is, a
|
||||
sequence of numbers).
|
||||
|
||||
export
|
||||
intLiteral : Rule Integer
|
||||
intLiteral
|
||||
= terminal (\x => case tok x of
|
||||
- .. code-block:: idris
|
||||
|
||||
export
|
||||
intLiteral : Rule Integer
|
||||
intLiteral
|
||||
= terminal (\x => case tok x of
|
||||
Number i => Just i
|
||||
_ => Nothing)
|
||||
|
||||
@ -137,33 +140,41 @@ successful, this is because we are not specifically checking for end-of-file.
|
||||
(Integer, List (TokenData ExpressionToken))
|
||||
*parserEx>
|
||||
|
||||
The 'intLiteral' function above uses the 'terminal' function to construct
|
||||
the grammar, this is defined here
|
||||
.. list-table::
|
||||
|
||||
* - The 'intLiteral' function above uses the 'terminal' function to
|
||||
construct the grammar
|
||||
- .. code-block:: idris
|
||||
|
||||
||| Succeeds if running the predicate on the
|
||||
||| next token returns Just x, returning x.
|
||||
||| Otherwise fails.
|
||||
export
|
||||
terminal : (tok -> Maybe a) -> Grammar tok True a
|
||||
terminal = Terminal
|
||||
|
||||
This is defined here
|
||||
: https://github.com/idris-lang/Idris-dev/blob/master/libs/contrib/Text/Parser/Core.idr
|
||||
Idris 2 uses a slightly different version which stores an error message like
|
||||
"Expected integer literal" which can be output if the rule fails
|
||||
: https://github.com/edwinb/Idris2/blob/master/src/Text/Parser/Core.idr
|
||||
|
||||
.. code-block:: idris
|
||||
.. list-table::
|
||||
|
||||
||| Succeeds if running the predicate on the next token returns Just x,
|
||||
||| returning x. Otherwise fails.
|
||||
export
|
||||
terminal : (tok -> Maybe a) -> Grammar tok True a
|
||||
terminal = Terminal
|
||||
* - The 'terminal' function is also used to construct the other
|
||||
elements of the grammar that we require, for instance,
|
||||
opening parenthesis:
|
||||
|
||||
The 'terminal' function is also used to construct the other elements of the
|
||||
grammar that we require, for instance, opening parenthesis:
|
||||
- .. code-block:: idris
|
||||
|
||||
.. code-block:: idris
|
||||
|
||||
openParen : Rule Integer
|
||||
openParen = terminal (\x => case tok x of
|
||||
openParen : Rule Integer
|
||||
openParen = terminal (\x => case tok x of
|
||||
OParen => Just 0
|
||||
_ => Nothing)
|
||||
|
||||
Integer value is not really relevant for parenthesis so '0' is used as
|
||||
a default value.
|
||||
|
||||
As before, we can test this out with a function like this:
|
||||
|
||||
.. code-block:: idris
|
||||
@ -236,42 +247,49 @@ token lists are not:
|
||||
OParen]) : Either (ParseError (TokenData ExpressionToken))
|
||||
(Integer, List (TokenData ExpressionToken))
|
||||
|
||||
The closing parenthesis is constructed in the same way.
|
||||
.. list-table::
|
||||
|
||||
.. code-block:: idris
|
||||
* - The closing parenthesis is constructed in the same way.
|
||||
|
||||
closeParen : Rule Integer
|
||||
closeParen = terminal (\x => case tok x of
|
||||
- .. code-block:: idris
|
||||
|
||||
closeParen : Rule Integer
|
||||
closeParen = terminal (\x => case tok x of
|
||||
CParen => Just 0
|
||||
_ => Nothing)
|
||||
|
||||
Now we can generate a Grammar for an expression inside parenthesis like this.
|
||||
.. list-table::
|
||||
|
||||
.. code-block:: idris
|
||||
* - Now we can generate a Grammar for an expression inside parenthesis like this.
|
||||
|
||||
paren : Rule Integer -> Rule Integer
|
||||
paren exp = openParen *> exp <* closeParen
|
||||
- .. code-block:: idris
|
||||
|
||||
paren : Rule Integer -> Rule Integer
|
||||
paren exp = openParen *> exp <* closeParen
|
||||
|
||||
The use of '*>' and '<*' instead of '<*>' is an easy way to use the integer
|
||||
value from the inner expression.
|
||||
|
||||
Now for the operations, in this case: '+', '-' and '*'.
|
||||
The syntax we require is that operators like '+' are infix operators, which
|
||||
would require a definition like this:
|
||||
.. list-table::
|
||||
|
||||
.. code-block:: idris
|
||||
* - Now for the operations, in this case: '+', '-' and '*'.
|
||||
The syntax we require is that operators like '+' are infix operators, which
|
||||
would require a definition like this:
|
||||
|
||||
expr = (add expr (op "+") expr)
|
||||
- .. code-block:: idris
|
||||
|
||||
expr = (add expr (op "+") expr)
|
||||
|
||||
This is a potentially infinite structure which is not total.
|
||||
In order to work up to this gradually I will start with prefix operators (sometimes known as Polish notation)
|
||||
then modify later for infix operators.
|
||||
In order to work up to this gradually I will start with prefix operators (sometimes known as Polish notation) then modify later for infix operators.
|
||||
|
||||
So prefix operators would have this sort of form:
|
||||
.. list-table::
|
||||
|
||||
.. code-block:: idris
|
||||
* - So prefix operators would have this sort of form:
|
||||
|
||||
expr = (add (op "+") expr expr)
|
||||
- .. code-block:: idris
|
||||
|
||||
expr = (add (op "+") expr expr)
|
||||
|
||||
where 'op' is defined like this:
|
||||
|
||||
@ -284,19 +302,21 @@ where 'op' is defined like this:
|
||||
(Operator s1) => if s==s1 then Just 0 else Nothing
|
||||
_ => Nothing)
|
||||
|
||||
and 'add' is defined like this:
|
||||
.. list-table::
|
||||
|
||||
.. code-block:: idris
|
||||
* - and 'add' is defined like this:
|
||||
|
||||
addInt : Integer -> Integer -> Integer
|
||||
addInt a b = a+b
|
||||
- .. code-block:: idris
|
||||
|
||||
export
|
||||
add : Grammar tok c1 Integer ->
|
||||
Grammar tok c2 Integer ->
|
||||
Grammar tok c3 Integer ->
|
||||
Grammar tok ((c1 || c2) || c3) Integer
|
||||
add x y z = map addInt (x *> y) <*> z
|
||||
addInt : Integer -> Integer -> Integer
|
||||
addInt a b = a+b
|
||||
|
||||
export
|
||||
add : Grammar tok c1 Integer ->
|
||||
Grammar tok c2 Integer ->
|
||||
Grammar tok c3 Integer ->
|
||||
Grammar tok ((c1 || c2) || c3) Integer
|
||||
add x y z = map addInt (x *> y) <*> z
|
||||
|
||||
Where:
|
||||
|
||||
@ -343,22 +363,26 @@ partial as it is a potentially infinite structure and so not total.
|
||||
<|> (mult (op "*") expr expr)
|
||||
<|> intLiteral <|> (paren expr)
|
||||
|
||||
To make the testing easier we can use this function:
|
||||
.. list-table::
|
||||
|
||||
.. code-block:: idris
|
||||
* - To make the testing easier we can use this function:
|
||||
|
||||
partial
|
||||
test : String -> Either (ParseError (TokenData ExpressionToken))
|
||||
- .. code-block:: idris
|
||||
|
||||
partial
|
||||
test : String -> Either (ParseError (TokenData ExpressionToken))
|
||||
(Integer, List (TokenData ExpressionToken))
|
||||
test s = parse expr (fst (lex expressionTokens s))
|
||||
test s = parse expr (fst (lex expressionTokens s))
|
||||
|
||||
First test a valid (prefix) expression:
|
||||
.. list-table::
|
||||
|
||||
.. code-block:: idris
|
||||
* - First test a valid (prefix) expression:
|
||||
|
||||
*parserEx> test "+1*6(4)"
|
||||
Right (25,
|
||||
[]) : Either (ParseError (TokenData ExpressionToken))
|
||||
- .. code-block:: idris
|
||||
|
||||
*parserEx> test "+1*6(4)"
|
||||
Right (25,
|
||||
[]) : Either (ParseError (TokenData ExpressionToken))
|
||||
(Integer, List (TokenData ExpressionToken))
|
||||
|
||||
Then an invalid syntax:
|
||||
|
||||
Loading…
Reference in New Issue
Block a user