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Merge pull request #4801 from martinbaker/parseLibDoc

Documentation for Parser Library

commit0fd2dab506724bca7429488697f4aabc09c36c5e authorNiklas Larsson <metaniklas@gmail.com> dateFri 10 Jan 2020, 03:18 (7 years ago) parent3b443e2d689c19
15 files changed+3922−1
docs/conf.py+1−1 docs/image/parserModules.png docs/image/parserModules.svg+1251 docs/image/parserTopLevel.png docs/image/parserTopLevel.svg+294 docs/image/recogniser.png docs/image/recogniser.svg+477 docs/image/tokenise.png docs/image/tokenise.svg+740 docs/index.rst+1 docs/parserLibrary/index.rst+24 docs/parserLibrary/introduction.rst+76 docs/parserLibrary/lexer.rst+282 docs/parserLibrary/parser.rst+622 docs/parserLibrary/whitespace.rst+154
docs/conf.py+1−1
@@ -51,7 +51,7 @@ master_doc = 'index'
5151
5252# General information about the project.
5353project = u'Idris'
54−copyright = u'2017-2019, The Idris Community'
54+copyright = u'2017-2020, The Idris Community'
5555author = u'The Idris Community'
5656
5757# The version info for the project you're documenting, acts as replacement for
docs/image/parserModules.pngnew file

Binary file not shown.

docs/image/parserModules.svgnew file+1251
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843+ sodipodi:role="line">module Idris.Syntax</tspan></text>
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870+ y="192.48962"
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873+ sodipodi:role="line">SExp</tspan></text>
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886+ sodipodi:role="line">module Idris.IDEMode.Parser</tspan></text>
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908+ sodipodi:role="line">module Idris.REPL</tspan></text>
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1002+ id="tspan968">Representation of expressions ready</tspan><tspan
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1007+ id="tspan974">for compiling: CExp</tspan><tspan
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1121+ y="230.92491"
1122+ 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;"
1123+ id="tspan1475">also in Idris 1</tspan><tspan
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1128+ id="tspan1477">library.</tspan></text>
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1148+ sodipodi:role="line">'IDEMode is for</tspan><tspan
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1152+ sodipodi:role="line"
1153+ id="tspan981">communicating</tspan><tspan
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349+ id="tspan1051">expect : Recognise c -&gt; Recognise False</tspan><tspan
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docs/index.rst+1
@@ -25,5 +25,6 @@ Documentation for the Idris Language
2525 effects/index
2626 proofs/index
2727 elaboratorReflection/index
28+ parserLibrary/index
2829 reference/index
2930 guides/index
docs/parserLibrary/index.rstnew file+24
@@ -0,0 +1,24 @@
1+.. _parserLibrary:
2+
3+########################
4+Lexer and Parser Library
5+########################
6+
7+A tutorial on the lexer and parser library in Idris.
8+
9+.. note::
10+
11+ The documentation for Idris has been published under the Creative
12+ Commons CC0 License. As such to the extent possible under law, *The
13+ Idris Community* has waived all copyright and related or neighboring
14+ rights to Documentation for Idris.
15+
16+ More information concerning the CC0 can be found online at: http://creativecommons.org/publicdomain/zero/1.0/
17+
18+.. toctree::
19+ :maxdepth: 1
20+
21+ introduction
22+ lexer
23+ parser
24+ whitespace
docs/parserLibrary/introduction.rstnew file+76
@@ -0,0 +1,76 @@
1+.. _parserLibraryIntro:
2+
3+***************************
4+Parser Library Introduction
5+***************************
6+
7+The parser library can be used to build Idris structures from text. It involves a
8+certain amount of complexity and so it would typically be used for big projects.
9+An example might be a compiler for another language, written in Idris.
10+
11+Of course the parser library can also be used to compile to Idris, this is what
12+is done in Idris 2 and that is what the this library appears to have been
13+written for.
14+
15+So a secondary use for this tutorial would be to help understanding the internal
16+workings of Idris 2.
17+
18+The parser library is used in a similar way to Parsec which is a library for
19+writing parsers in Haskell. It is based on higher-order parser combinators, so a
20+complicated parser can be made out of many smaller ones.
21+
22+.. list-table::
23+
24+ * - This is a two stage process:
25+ - Lexer - This takes the input string and turns it into a list of Tokens.
26+ - Parser - This takes the list of tokens and outputs the code.
27+
28+.. image:: ../image/parserTopLevel.png
29+ :width: 307px
30+ :height: 76px
31+ :alt: diagram illustrating these stages of lexer and parser
32+
33+The advantage of using two stages, like this, is that things like whitespace and
34+comments don't need to be considered in every parser rule.
35+
36+The Idris parser library differs from Parsec in that you need to say in the
37+Recogniser whether a rule is guaranteed to consume input. This means that the
38+Idris type system prevents the construction of recognisers/rules that can't
39+consume the input.
40+
41+The Lexer is similar but works at the level of characters rather than tokens, and
42+you need to provide a TokenMap which says how to build a token representation from
43+a string when a rule is matched.
44+
45+The following pages contain a tutorial for the :ref:`parserLibraryLexer` and a
46+tutorial for the :ref:`parserLibraryParser`. These tutorials have a running
47+example of a parser for integer expressions. This is a very simple example, there
48+may be easier ways to do something so simple, but it illustrates some of the
49+principles.
50+
51+Parser Library and Idris 2
52+--------------------------
53+
54+The parser library, in Idris 1, is almost the same as the code that the Idris 2
55+parser is built on. Even if you only want to use the Idris 1 parser library it
56+is useful to look at the code in the Idris 2 compilers to see how the library
57+can be used.
58+
59+Idris 2 has at least 3 compilers:
60+
61+- IDEMode - complies to SExp which is a Lisp-like structure used to communicate
62+ with external editors like Emacs and Vim.
63+- Idris.Parser - This is the main compiler which compiles from a file to
64+ PTerm (and eventually TT structure).
65+- REPL - compiles input from the command line.
66+
67+The following diagram is my first attempt to work out how some of the modules in
68+Idris 2 fit together (with a few of the dependencies between them shown). The
69+Idris 1 library is based on the modules at the bottom of the diagram (shown
70+in red).
71+
72+.. image:: ../image/parserModules.png
73+ :width: 460px
74+ :height: 496px
75+ :alt: diagram illustrating these stages of lexer and parser
76+
docs/parserLibrary/lexer.rstnew file+282
@@ -0,0 +1,282 @@
1+.. _parserLibraryLexer:
2+
3+Lexer
4+=====
5+
6+The lexer is run by calling the 'lex' function in the Text.Lexer.Core
7+module:
8+
9+.. code-block:: idris
10+
11+ lex : TokenMap a -> String -> (List (TokenData a), (Int, Int, String))
12+
13+This function takes a String and returns a list of tokens. With the tokens we
14+have indexes back to the original string which can be used in error messages:
15+
16+.. image:: ../image/tokenise.png
17+ :width: 330px
18+ :height: 73px
19+ :alt: diagram illustrating these stages of lexer
20+
21+TokenMap
22+--------
23+
24+In order to construct this list of tokens we need:
25+
26+- A way to recognise the tokens in the input string.
27+- A way to construct these individual tokens.
28+
29+This is given by the TokenMap which is a list of pairs containing
30+this information:
31+
32+.. code-block:: idris
33+
34+ (Lexer, String -> tokenType)
35+
36+So for each Lexer in the list, if a substring in the input matches, run
37+the associated function to produce a token of type `tokenType`
38+
39+from Text.Lexer.Core:
40+
41+.. code-block:: idris
42+
43+ TokenMap : (tokenType : Type) -> Type
44+ TokenMap tokenType = List (Lexer, String -> tokenType)
45+
46+We can create a tokenMap by using a function like this:
47+
48+.. code-block:: idris
49+
50+ myTokenMap : TokenMap Token
51+ myTokenMap = [(is 'a',CharLit)]
52+
53+Once we have a TokenMap we can use it to lex many strings.
54+
55+Recognisers
56+-----------
57+
58+The first part of each entry in the TokenMap is the recogniser.
59+
60+A simple recogniser is 'Pred' which uses a predicate (Char -> Bool) to
61+test whether to accept the character. It can be constructed using the
62+'is' function:
63+
64+.. code-block:: idris
65+
66+ *parserEx> is 'a'
67+ Pred (\ARG =>
68+ intToBool (prim__eqChar ARG 'a'))
69+ : Recognise True
70+
71+More complicated structures can be recognised as tokens, this is done using
72+the combinator structure of recognisers. This allows recognisers to be
73+combined, for example,
74+
75+.. list-table::
76+
77+ * - <+> means sequence two recognisers. If either consumes a character,
78+ the sequence is guaranteed to consume a character.
79+
80+ - .. code-block:: idris
81+
82+ *parserEx> is 'a' <+> is 'b'
83+ SeqEat (Pred (\ARG => intToBool (prim__eqChar ARG 'a')))
84+ (Delay (is 'b')) : Recognise True
85+
86+ * - <|> means if both consume, the combination is guaranteed
87+ to consumer a character:
88+
89+ - .. code-block:: idris
90+
91+ *parserEx> is 'a' <|> is 'b'
92+ Alt (Pred (\ARG => intToBool (prim__eqChar ARG 'a')))
93+ (Pred (\ARG => intToBool (prim__eqChar ARG 'b')))
94+ : Recognise True
95+
96+This diagram shows the recogniser combinator with some of its constructors:
97+
98+.. image:: ../image/recogniser.png
99+ :width: 487px
100+ :height: 249px
101+ :alt: recogniser data structure
102+
103+A recogniser consumes its input, that is it advances the index to its input
104+string, as it generates the token list. In some cases we don't want this to
105+happen, for instance, we may need to lookahead before consuming the input
106+string.
107+
108+If a recogniser does not consume input there is a danger of an infinite loop.
109+To prevent this the recogniser is dependent on a boolean called 'consumes' which
110+is true if the recogniser is guaranteed to consume at least one character.
111+
112+The constructors of Recognise allow us to ensure that, even though parts of
113+the recogniser may not consume, overall the recogniser will consume.
114+
115+Since 'Recognise True' is more common than 'Recognise False' it is convenient to
116+use 'Lexer' as a type synonym for 'Recognise True'.
117+
118+Whitespace and Comments
119+-----------------------
120+
121+An important reason to have a lexer is to simplify the parser when whitespace
122+or comments are required. Without this the parser would require a match for
123+every combination, with and without, whitespace and comments.
124+
125+In some languages the lexer needs to remove whitespace and comments so that
126+they don't appear in the token list. In some cases whitespace is significant
127+but a single whitespace token can stand for any number of spaces, tabs,
128+carriage returns and so on.
129+
130+In some cases, such as when parsing the Idris language itself, whitespace
131+is important to indicate blocks. In this case we might want to output a
132+start-of-block token when the indent increases and an end-of-block token
133+when the indent decreases.
134+
135+This topic will be discussed more fully on this page
136+:ref:`parserLibraryWhitespace`.
137+
138+Simple Expression Example for Lexer
139+-----------------------------------
140+
141+On this page we will implement a lexer to 'lex' a very simple expression as
142+a running example, on the next page, we will go on to implement a parser for it.
143+
144+First import the lexer and parser code:
145+
146+.. code-block:: idris
147+
148+ module ParserExample
149+
150+ import Text.Lexer
151+ import public Text.Parser.Core
152+ import public Text.Parser
153+
154+Then decide on the tokens that are needed. For this example the idea is to be
155+able to parse simple arithmetic expressions, like this:
156+
157+.. code-block:: idris
158+
159+ 1+(2*3)
160+
161+so we need:
162+
163+- Numbers (for now integer literals are good enough).
164+- Some operators (for now '+', '-' and '*' will do.
165+- Opening and closing Parentheses.
166+
167+We can define these, as tokens, like this:
168+
169+.. code-block:: idris
170+
171+ %default total
172+
173+ public export
174+ data ExpressionToken = Number Integer
175+ | Operator String
176+ | OParen
177+ | CParen
178+ | EndInput
179+
180+It may help with debugging and to implement error messages to
181+implement 'show' for these tokens:
182+
183+.. code-block:: idris
184+
185+ export
186+ Show ExpressionToken where
187+ show (Number x) = "number " ++ show x
188+ show (Operator x) = "operator " ++ x
189+ show OParen = "("
190+ show CParen = ")"
191+ show EndInput = "end of input"
192+
193+ export
194+ Show (TokenData ExpressionToken) where
195+ show (MkToken l c t) = "line=" ++ show l ++ " col=" ++ show c ++ "tok=" ++ show t
196+
197+The following defines the 'TokenMap' for this example:
198+
199+.. code-block:: idris
200+
201+ ||| integer arithmetic operators plus, minus and multiply.
202+ export
203+ opChars : String
204+ opChars = "+-*"
205+
206+ operator : Lexer
207+ operator = some (oneOf opChars)
208+
209+ toInt' : String -> Integer
210+ toInt' = cast
211+
212+ expressionTokens : TokenMap ExpressionToken
213+ expressionTokens =
214+ [(digits, \x => Number (toInt' x)),
215+ (operator, \x => Operator x),
216+ (is '(' ,\x => OParen),
217+ (is ')' ,\x => CParen)]
218+
219+This specifies the lexer. It gives, for each token, a function to recognise
220+the token type and a function to construct the token.
221+
222+The library module 'Text.Lexer' contains useful functions to help with this.
223+For example, the digits function used above, which reads one or more
224+numeric characters.
225+
226+We can now run the code with various strings to see what output the lexer
227+produces. This is done by calling the 'lex' function with the TokenMap and
228+input string as parameters:
229+
230+.. code-block:: idris
231+
232+ cd Idris-dev/libs/contrib
233+ idris -p contrib parserEx.idr
234+ ____ __ _
235+ / _/___/ /____(_)____
236+ / // __ / ___/ / ___/ Version 1.3.2
237+ _/ // /_/ / / / (__ ) http://www.idris-lang.org/
238+ /___/\__,_/_/ /_/____/ Type :? for help
239+
240+ Idris is free software with ABSOLUTELY NO WARRANTY.
241+ For details type :warranty.
242+ Type checking ./Text/Token.idr
243+ Type checking ./Text/Quantity.idr
244+ Type checking ./Control/Delayed.idr
245+ Type checking ./Data/Bool/Extra.idr
246+ Type checking ./Text/Lexer/Core.idr
247+ Type checking ./Text/Lexer.idr
248+ Type checking ./parserEx.idr
249+
250+ *parserEx> lex expressionTokens "1+2"
251+ ([MkToken 0 0 (Number 1),
252+ MkToken 0
253+ (case fspan (\ARG => not (intToBool (prim__eqChar ARG '\n'))) "1" of
254+ (incol, "") => c + cast (length incol)
255+ (incol, b) => cast (length incol))
256+ (Operator "+"),
257+ MkToken 0
258+ (case fspan (\ARG => not (intToBool (prim__eqChar ARG '\n'))) "+" of
259+ (incol, "") => c + cast (length incol)
260+ (incol, b) => cast (length incol))
261+ (Number 2)],
262+ 0,
263+ case fspan (\ARG => not (intToBool (prim__eqChar ARG '\n'))) "2" of
264+ (incol, "") => c + cast (length incol)
265+ (incol, b) => cast (length incol),
266+ getString (MkStrLen "" 0)) : (List (TokenData ExpressionToken),
267+ Int,
268+ Int,
269+ String)
270+
271+The lexer uses potentially infinite data structures. It has recursive
272+arguments (codata type) so code is lazy. In the output above the indexes
273+have not been computed but we can pick out the tokens:
274+
275+- (Number 1)
276+- (Operator "+")
277+- (Number 2)
278+
279+So the code is working.
280+
281+We can now go ahead and parse this token list. A parser for this example will
282+be constructed on the next page.
docs/parserLibrary/parser.rstnew file+622
@@ -0,0 +1,622 @@
1+.. _parserLibraryParser:
2+
3+Parser
4+======
5+
6+To run our parser we call 'parse'. This requires a Grammar and the output
7+from the lexer (a list of tokens).
8+
9+.. code-block:: idris
10+
11+ parse : (act : Grammar tok c ty) -> (xs : List tok) ->
12+ Either (ParseError tok) (ty, List tok)
13+
14+If successful this returns 'Right' with a pair of
15+
16+- the parse result.
17+- the unparsed tokens (the remaining input).
18+
19+otherwise it returns 'Left' with the error message.
20+
21+So we need to define the Grammar for our parser, this is done using the following
22+'Grammar' data structure. This is a combinator structure, similar in principle
23+to the recogniser combinator for the lexer, which was discussed on the
24+previous page.
25+
26+As with the Recogniser the Grammar type is dependent on a boolean 'consumes'
27+value which allows us to ensure that complicated Grammar structures will always
28+consume input.
29+
30+.. code-block:: idris
31+
32+ ||| Description of a language's grammar. The `tok` parameter is the type
33+ ||| of tokens, and the `consumes` flag is True if the language is guaranteed
34+ ||| to be non-empty - that is, successfully parsing the language is guaranteed
35+ ||| to consume some input.
36+ public export
37+ data Grammar : (tok : Type) -> (consumes : Bool) -> Type -> Type where
38+ Empty : (val : ty) -> Grammar tok False ty
39+ Terminal : String -> (tok -> Maybe a) -> Grammar tok True a
40+ NextIs : String -> (tok -> Bool) -> Grammar tok False tok
41+ EOF : Grammar tok False ()
42+
43+ Fail : Bool -> String -> Grammar tok c ty
44+ Commit : Grammar tok False ()
45+ MustWork : Grammar tok c a -> Grammar tok c a
46+
47+ SeqEat : Grammar tok True a -> Inf (a -> Grammar tok c2 b) ->
48+ Grammar tok True b
49+ SeqEmpty : {c1, c2 : Bool} ->
50+ Grammar tok c1 a -> (a -> Grammar tok c2 b) ->
51+ Grammar tok (c1 || c2) b
52+ Alt : {c1, c2 : Bool} ->
53+ Grammar tok c1 ty -> Grammar tok c2 ty ->
54+ Grammar tok (c1 && c2) ty
55+
56+So an example of a Grammer type may look something like this:
57+'Grammar (TokenData ExpressionToken) True Integer'.
58+
59+This is a complicated type name and a given parser will need to use it a lot.
60+So to reduce the amount of typing we can use the following type synonym (similar
61+to what is done in Idris 2
62+: https://github.com/edwinb/Idris2/blob/master/src/Parser/Support.idr
63+
64+.. code-block:: idris
65+
66+ public export
67+ Rule : Type -> Type
68+ Rule ty = Grammar (TokenData ExpressionToken) True ty
69+
70+Parser Example
71+--------------
72+
73+On the previous page we implemented a lexer to 'lex' a very simple expression, on
74+this page we will go on to implement a parser for this running example.
75+
76+.. list-table::
77+
78+ * - Expressed in Backus–Naur form (BNF) the syntax we are aiming at is something
79+ like this:
80+ - .. code-block:: idris
81+
82+ <expr> ::= <integer literal>
83+ | <expr>'+'<expr>
84+ | <expr>'-'<expr>
85+ | <expr>'*'<expr>
86+ | '('<expr>')'
87+
88+ <integer literal> ::= <digit>|<integer literal><digit>
89+
90+.. list-table::
91+
92+ * - To start, here is a Grammar to parse an integer literal (that is, a
93+ sequence of numbers).
94+
95+ - .. code-block:: idris
96+
97+ export
98+ intLiteral : Rule Integer
99+ intLiteral
100+ = terminal (\x => case tok x of
101+ Number i => Just i
102+ _ => Nothing)
103+
104+In order to try this out, here is a temporary function, this calls
105+parse which takes two parameters:
106+
107+- The grammar (in this case intLiteral)
108+- The token list from the lexer.
109+
110+.. code-block:: idris
111+
112+ test1 : String -> Either (ParseError (TokenData ExpressionToken))
113+ (Integer, List (TokenData ExpressionToken))
114+ test1 s = parse intLiteral (fst (lex expressionTokens s))
115+
116+As required, if we pass it a string which is a number literal then it will
117+return the number in the 'Right' option.
118+
119+.. code-block:: idris
120+
121+ *parserEx> test1 "123"
122+ Right (123, []) : Either (ParseError (TokenData ExpressionToken))
123+ (Integer, List (TokenData ExpressionToken))
124+
125+If we pass it a string which is not a number literal then it will return an
126+error message.
127+
128+.. code-block:: idris
129+
130+ *parserEx> test1 "a"
131+ Left (Error "End of input"
132+ []) : Either (ParseError (TokenData ExpressionToken))
133+ (Integer, List (TokenData ExpressionToken))
134+
135+If we pass it a number followed by something else, then it will still be
136+successful, this is because we are not specifically checking for end-of-file.
137+
138+.. code-block:: idris
139+
140+ *parserEx> test1 "123a"
141+ Right (123, []) : Either (ParseError (TokenData ExpressionToken))
142+ (Integer, List (TokenData ExpressionToken))
143+ *parserEx>
144+
145+.. list-table::
146+
147+ * - The 'intLiteral' function above uses the 'terminal' function to
148+ construct the grammar
149+ - .. code-block:: idris
150+
151+ ||| Succeeds if running the predicate on the
152+ ||| next token returns Just x, returning x.
153+ ||| Otherwise fails.
154+ export
155+ terminal : (tok -> Maybe a) -> Grammar tok True a
156+ terminal = Terminal
157+
158+This is defined here
159+: https://github.com/idris-lang/Idris-dev/blob/master/libs/contrib/Text/Parser/Core.idr
160+Idris 2 uses a slightly different version which stores an error message like
161+"Expected integer literal" which can be output if the rule fails
162+: https://github.com/edwinb/Idris2/blob/master/src/Text/Parser/Core.idr
163+
164+.. list-table::
165+
166+ * - The 'terminal' function is also used to construct the other
167+ elements of the grammar that we require, for instance,
168+ opening parenthesis:
169+
170+ - .. code-block:: idris
171+
172+ openParen : Rule Integer
173+ openParen = terminal (\x => case tok x of
174+ OParen => Just 0
175+ _ => Nothing)
176+
177+Integer value is not really relevant for parenthesis so '0' is used as
178+a default value.
179+
180+As before, we can test this out with a function like this:
181+
182+.. code-block:: idris
183+
184+ test2 : String -> Either (ParseError (TokenData ExpressionToken))
185+ (Integer, List (TokenData ExpressionToken))
186+ test2 s = parse openParen (fst (lex expressionTokens s))
187+
188+We can see below that it correctly parses an open parenthesis and gives an
189+error for anything else:
190+
191+.. code-block:: idris
192+
193+ *parserEx> test2 "("
194+ Right (0, []) : Either (ParseError (TokenData ExpressionToken))
195+ (Integer, List (TokenData ExpressionToken))
196+ *parserEx> test2 "123"
197+ Left (Error "Unrecognised token"
198+ [MkToken 0
199+ 0
200+ (Number 123)]) : Either (ParseError (TokenData ExpressionToken))
201+ (Integer,
202+ List (TokenData ExpressionToken))
203+
204+Now we have two Grammars we can try combining them. The following test looks
205+for 'openParen' followed by 'intLiteral', the two Grammars are combined using
206+'<*>'. The 'map const' part uses the integer value from the first.
207+
208+The following test is looking for '(' followed by a number:
209+
210+.. code-block:: idris
211+
212+ test3 : String -> Either (ParseError (TokenData ExpressionToken))
213+ (Integer, List (TokenData ExpressionToken))
214+ test3 s = parse (map const openParen <*> intLiteral) (fst (lex expressionTokens s))
215+
216+We can see below that '(' followed by a number is successfully parsed but other
217+token lists are not:
218+
219+.. code-block:: idris
220+
221+ *parserEx> test3 "(123"
222+ Right (0, []) : Either (ParseError (TokenData ExpressionToken))
223+ (Integer, List (TokenData ExpressionToken))
224+ *parserEx> test3 "(("
225+ Left (Error "Unrecognised token"
226+ [MkToken 0
227+ (case fspan (\ARG => not (intToBool (prim__eqChar ARG '\n')))
228+ "(" of
229+ (incol, "") => c + cast (length incol)
230+ (incol, b) => cast (length incol))
231+ OParen]) : Either (ParseError (TokenData ExpressionToken))
232+ (Integer, List (TokenData ExpressionToken))
233+
234+ *parserEx> test3 "123"
235+ Left (Error "Unrecognised token"
236+ [MkToken 0
237+ 0
238+ (Number 123)]) : Either (ParseError (TokenData ExpressionToken))
239+ (Integer,
240+ List (TokenData ExpressionToken))
241+ *parserEx> test3 "123("
242+ Left (Error "Unrecognised token"
243+ [MkToken 0 0 (Number 123),
244+ MkToken 0
245+ (case fspan (\ARG => not (intToBool (prim__eqChar ARG '\n')))
246+ "321" of
247+ (incol, "") => c + cast (length incol)
248+ (incol, b) => cast (length incol))
249+ OParen]) : Either (ParseError (TokenData ExpressionToken))
250+ (Integer, List (TokenData ExpressionToken))
251+
252+.. list-table::
253+
254+ * - The closing parenthesis is constructed in the same way.
255+
256+ - .. code-block:: idris
257+
258+ closeParen : Rule Integer
259+ closeParen = terminal (\x => case tok x of
260+ CParen => Just 0
261+ _ => Nothing)
262+
263+.. list-table::
264+
265+ * - Now we can generate a Grammar for an expression inside parenthesis
266+ like this.
267+
268+ - .. code-block:: idris
269+
270+ paren : Rule Integer -> Rule Integer
271+ paren exp = openParen *> exp <* closeParen
272+
273+The use of '*>' and '<*' instead of '<*>' is an easy way to use the integer
274+value from the inner expression.
275+
276+.. list-table::
277+
278+ * - Now for the operations, in this case: '+', '-' and '*'.
279+ The syntax we require is that operators like '+' are infix operators, which
280+ would require a definition like this:
281+
282+ - .. code-block:: idris
283+
284+ expr = (add expr (op "+") expr)
285+
286+This is a potentially infinite structure which is not total.
287+In order to work up to this gradually I will start with prefix operators
288+(sometimes known as Polish notation) then modify later for infix operators.
289+
290+.. list-table::
291+
292+ * - So prefix operators would have this sort of form:
293+
294+ - .. code-block:: idris
295+
296+ expr = (add (op "+") expr expr)
297+
298+where 'op' is defined like this:
299+
300+.. code-block:: idris
301+
302+ ||| Matches if this is an operator token and string matches, that is,
303+ ||| it is the required type of operator.
304+ op : String -> Rule Integer
305+ op s = terminal (\x => case tok x of
306+ (Operator s1) => if s==s1 then Just 0 else Nothing
307+ _ => Nothing)
308+
309+.. list-table::
310+
311+ * - and 'add' is defined like this:
312+
313+ - .. code-block:: idris
314+
315+ addInt : Integer -> Integer -> Integer
316+ addInt a b = a+b
317+
318+ export
319+ add : Grammar tok c1 Integer ->
320+ Grammar tok c2 Integer ->
321+ Grammar tok c3 Integer ->
322+ Grammar tok ((c1 || c2) || c3) Integer
323+ add x y z = map addInt (x *> y) <*> z
324+
325+Where:
326+
327+- x is the add operator.
328+- y is the first operand.
329+- z is the second operand.
330+
331+The resulting integer will be the sum of the two operands.
332+
333+The other operators are defined in a similar way:
334+
335+.. code-block:: idris
336+
337+ subInt : Integer -> Integer -> Integer
338+ subInt a b = a-b
339+
340+ export
341+ sub : Grammar tok c1 Integer ->
342+ Grammar tok c2 Integer ->
343+ Grammar tok c3 Integer ->
344+ Grammar tok ((c1 || c2) || c3) Integer
345+ sub x y z = map subInt (x *> y) <*> z
346+
347+
348+ multInt : Integer -> Integer -> Integer
349+ multInt a b = a*b
350+
351+ export
352+ mult : Grammar tok c1 Integer ->
353+ Grammar tok c2 Integer ->
354+ Grammar tok c3 Integer ->
355+ Grammar tok ((c1 || c2) || c3) Integer
356+ mult x y z = map multInt (x *> y) <*> z
357+
358+So the top level Grammar can now be defined as follows. Note that this is
359+partial as it is a potentially infinite structure and so not total.
360+
361+.. code-block:: idris
362+
363+ partial
364+ expr : Rule Integer
365+ expr = (add (op "+") expr expr)
366+ <|> (sub (op "-") expr expr)
367+ <|> (mult (op "*") expr expr)
368+ <|> intLiteral <|> (paren expr)
369+
370+.. list-table::
371+
372+ * - To make the testing easier we can use this function:
373+
374+ - .. code-block:: idris
375+
376+ partial
377+ test : String -> Either (ParseError (TokenData ExpressionToken))
378+ (Integer, List (TokenData ExpressionToken))
379+ test s = parse expr (fst (lex expressionTokens s))
380+
381+.. list-table::
382+
383+ * - First test a valid (prefix) expression:
384+
385+ - .. code-block:: idris
386+
387+ *parserEx> test "+1*6(4)"
388+ Right (25,
389+ []) : Either (ParseError (TokenData ExpressionToken))
390+ (Integer, List (TokenData ExpressionToken))
391+
392+Then an invalid syntax:
393+
394+.. code-block:: idris
395+
396+ *parserEx> test "))"
397+ Left (Error "Unrecognised token"
398+ [MkToken 0 0 CParen,
399+ MkToken 0
400+ (case fspan (\ARG =>
401+ not (intToBool (prim__eqChar ARG
402+ '\n')))
403+ ")" of
404+ (incol, "") => c + cast (length incol)
405+ (incol, b) => cast (length incol))
406+ CParen]) : Either (ParseError (TokenData ExpressionToken))
407+ (Integer,
408+ List (TokenData ExpressionToken))
409+
410+However if we try something that is invalid, but starts with a valid token,
411+then it will return 'Right' (to indicate success)
412+
413+.. code-block:: idris
414+
415+ *parserEx> test "1))"
416+ Right (1,
417+ [MkToken 0
418+ (case fspan (\ARG =>
419+ not (intToBool (prim__eqChar ARG '\n')))
420+ "1" of
421+ (incol, "") => c + cast (length incol)
422+ (incol, b) => cast (length incol))
423+ CParen,
424+ MkToken 0
425+ (case fspan (\ARG =>
426+ not (intToBool (prim__eqChar ARG '\n')))
427+ ")" of
428+ (incol, "") => c + cast (length incol)
429+ (incol, b) => cast (length incol))
430+ CParen]) : Either (ParseError (TokenData ExpressionToken))
431+ (Integer,
432+ List (TokenData ExpressionToken))
433+
434+Infix Notation
435+--------------
436+
437+So far we have implemented a prefix notation for operators (like this:
438+'+ expr expr') but the aim is to implemented an infix notation (like this:
439+'expr + expr'). To do this we must be able to deal with potentially
440+infinite data structures (see Codata Types here :ref:`sect-typefuns`).
441+
442+First alter the grammar to have infix operations:
443+
444+.. code-block:: idris
445+
446+ addInt : Integer -> Integer -> Integer
447+ addInt a b = a+b
448+
449+ export
450+ add : Grammar tok c1 Integer ->
451+ Grammar tok c2 Integer ->
452+ Grammar tok c3 Integer ->
453+ Grammar tok ((c1 || c2) || c3) Integer
454+ add x y z = map addInt (x <* y) <*> z
455+
456+ subInt : Integer -> Integer -> Integer
457+ subInt a b = a-b
458+
459+ export
460+ sub : Grammar tok c1 Integer ->
461+ Grammar tok c2 Integer ->
462+ Grammar tok c3 Integer ->
463+ Grammar tok ((c1 || c2) || c3) Integer
464+ sub x y z = map subInt (x <* y) <*> z
465+
466+
467+ multInt : Integer -> Integer -> Integer
468+ multInt a b = a*b
469+
470+ export
471+ mult : Grammar tok c1 Integer ->
472+ Grammar tok c2 Integer ->
473+ Grammar tok c3 Integer ->
474+ Grammar tok ((c1 || c2) || c3) Integer
475+ mult x y z = map multInt (x <* y) <*> z
476+
477+ partial
478+ expr : Rule Integer
479+ expr = (add expr (op "+") expr)
480+ <|> (sub expr (op "-") expr)
481+ <|> (mult expr (op "*") expr)
482+ <|> intLiteral <|> (paren expr)
483+
484+However, if this was run, the code would not terminate.
485+
486+Implement Left Recursion Elimination
487+------------------------------------
488+
489+Left factoring, like this, is a general problem.
490+
491+If we have a rule like this:
492+
493+.. code-block:: idris
494+
495+ A -> (x<*>y) <|> (x<*>z)
496+
497+If 'x<*>y' fails but 'x<*>z' would succeed a problem is that, 'x<*>y' has
498+already consumed 'x', so now 'x<*>z' will fail.
499+
500+so we could write code to backtrack. That is 'try' 'x<*>y' without consuming
501+so that, if the first token succeeds but the following tokens fail, then the
502+first tokens would not be consumed.
503+
504+Another approach is left factoring:
505+
506+Left Factoring
507+--------------
508+
509+Replace the rule with two rules (that is we add a non-terminal symbol) so
510+for example, instead of:
511+
512+.. code-block:: idris
513+
514+ A -> (x<*>y) <|> (x<*>z)
515+
516+we add an extra rule to give:
517+
518+.. code-block:: idris
519+
520+ A -> x<*>N
521+ N -> y <|> z
522+
523+That is we convert a general context-free grammar to a LL(1) grammar. Although
524+not every context-free grammar can be converted to a LL(1) grammar.
525+
526+This still does not solve the infinite recursion issue and there is another
527+problem: the precedence of the operators +, - and * is not explicit.
528+
529+To resolve this we can alter the example like this:
530+
531+.. code-block:: idris
532+
533+ paren : Rule Integer -> Rule Integer
534+ paren exp = openParen *> exp <* closeParen
535+
536+ addInt : Integer -> Integer -> Integer
537+ addInt a b = a+b
538+
539+ subInt : Integer -> Integer -> Integer
540+ subInt a b = a-b
541+
542+ multInt : Integer -> Integer -> Integer
543+ multInt a b = a*b
544+
545+ partial
546+ expr : Rule Integer
547+
548+ partial
549+ exprAtom : Rule Integer
550+ exprAtom = intLiteral <|> (paren expr)
551+
552+ partial
553+ expr1 : Rule Integer
554+ expr1 = map multInt exprAtom <*> ((op "*") *> exprAtom)
555+
556+ partial
557+ exprMult : Rule Integer
558+ exprMult = expr1 <|> exprAtom
559+
560+ partial
561+ expr2 : Rule Integer
562+ expr2 = map addInt exprMult <*> ((op "+") *> exprMult)
563+
564+ partial
565+ exprAdd : Rule Integer
566+ exprAdd = expr2 <|> exprMult
567+
568+ partial
569+ expr3 : Rule Integer
570+ expr3 = map subInt exprAdd <*> ((op "-") *> expr)
571+
572+ expr = expr3 <|> exprAdd
573+
574+As the following tests show, this now handles infix operators and precedence.
575+
576+.. list-table::
577+
578+ * - For example '*' is an infix operator:
579+
580+ - .. code-block:: idris
581+
582+ *parserExInfix> test "2*3"
583+ Right (6,
584+ []) : Either (ParseError (TokenData ExpressionToken))
585+ (Integer, List (TokenData ExpressionToken))
586+
587+ * - Check that atomic number literals work:
588+
589+ - .. code-block:: idris
590+
591+ *parserExInfix> test "2"
592+ Right (2,
593+ []) : Either (ParseError (TokenData ExpressionToken))
594+ (Integer, List (TokenData ExpressionToken))
595+
596+ * - Check that '*' has a higher precedence than '+'.
597+
598+ - .. code-block:: idris
599+
600+ *parserExInfix> test "2+3*4"
601+ Right (14,
602+ []) : Either (ParseError (TokenData ExpressionToken))
603+ (Integer, List (TokenData ExpressionToken))
604+
605+ * - Also '*' has a higher precedence than '+' when the order is reversed.
606+
607+ - .. code-block:: idris
608+
609+ *parserExInfix> test "3*4+2"
610+ Right (14,
611+ []) : Either (ParseError (TokenData ExpressionToken))
612+ (Integer, List (TokenData ExpressionToken))
613+
614+ * - Also precedence can be overridden by parenthesis.
615+
616+ - .. code-block:: idris
617+
618+ *parserExInfix> test "(2+3)*4"
619+ Right (20,
620+ []) : Either (ParseError (TokenData ExpressionToken))
621+ (Integer, List (TokenData ExpressionToken))
622+
docs/parserLibrary/whitespace.rstnew file+154
@@ -0,0 +1,154 @@
1+.. _parserLibraryWhitespace:
2+
3+Whitespace and Comments
4+=======================
5+
6+The previous two pages introduced the lexer and parser but have not yet
7+discussed how to handle whitespace and comments.
8+
9+In some grammars whitespace and comments would not be considered significant and
10+so we might be tempted not to generate any tokens for them. However, in the
11+running example, we may want to make spaces significant. For example, we might
12+want to implement function application expressed by juxtaposition as in
13+Haskell and Idris like this: ``f x``.
14+
15+Also, I'm not sure if it is an problem for error messages and so on if some
16+text does not have corresponding tokens.
17+
18+So, on this page, we will add a token for whitespace and comments.
19+
20+Whitespace and Comments in Lexer
21+--------------------------------
22+
23+To start with we can use the same token for both whitespace and comments. Here
24+it is called ``Comment`` and added to the ``ExpressionToken`` data structure
25+like this:
26+
27+.. code-block:: idris
28+
29+ public export
30+ data ExpressionToken = Number Integer
31+ | Operator String
32+ | OParen
33+ | CParen
34+ | Comment String
35+ | EndInput
36+
37+This is added to the ``TokenMap`` like this:
38+
39+.. code-block:: idris
40+
41+ ||| from https://github.com/edwinb/Idris2/blob/master/src/Parser/Lexer.idr
42+ comment : Lexer
43+ comment = is '-' <+> is '-' <+> many (isNot '\n')
44+
45+ expressionTokens : TokenMap ExpressionToken
46+ expressionTokens =
47+ [(digits, \x => Number (toInt' x)),
48+ (operator, \x => Operator x),
49+ (is '(' ,\x => OParen),
50+ (is ')' ,\x => CParen),
51+ (spaces, Comment),
52+ (comment, Comment)]
53+
54+As you can see, the comment is defined like a single line Idris comment,
55+it starts with ``--`` and continues for the remainder of the line.
56+
57+We don't need to define ``spaces`` because it is already defined in
58+: https://github.com/idris-lang/Idris-dev/blob/master/libs/contrib/Text/Lexer.idr
59+like this:
60+
61+.. code-block:: idris
62+
63+ ||| Recognise a single whitespace character
64+ ||| /\\s/
65+ space : Lexer
66+ space = pred isSpace
67+
68+ ||| Recognise one or more whitespace characters
69+ ||| /\\s+/
70+ spaces : Lexer
71+ spaces = some space
72+
73+Whitespace and Comments in Parser
74+---------------------------------
75+
76+Now that there are ``Comment`` tokens the parser needs to be able to handle them.
77+
78+.. code-block:: idris
79+
80+ commentSpace : Rule Integer
81+ commentSpace = terminal (\x => case tok x of
82+ Comment s => Just 0
83+ _ => Nothing)
84+
85+So far we don't have any syntax that requires spaces to be significant so we
86+need to define the grammar so that it will parse with, or without, spaces.
87+This needs to be done in a systematic way, here I have defined the grammar so
88+that there is an optional space to the right of every atom or operator:
89+
90+.. code-block:: idris
91+
92+ partial
93+ exprAtom : Rule Integer
94+ exprAtom = (intLiteral <* commentSpace)
95+ <|> intLiteral <|> (paren expr)
96+
97+ partial
98+ expr1 : Rule Integer
99+ expr1 = map multInt exprAtom <*> (
100+ (((op "*") <* commentSpace) <|> (op "*"))
101+ *> exprAtom)
102+
103+ partial
104+ exprMult : Rule Integer
105+ exprMult = expr1 <|> exprAtom
106+
107+ partial
108+ expr2 : Rule Integer
109+ expr2 = map addInt exprMult <*> (
110+ (((op "+") <* commentSpace) <|> (op "+"))
111+ *> exprMult)
112+
113+ partial
114+ exprAdd : Rule Integer
115+ exprAdd = expr2 <|> exprMult
116+
117+ partial
118+ expr3 : Rule Integer
119+ expr3 = map subInt exprAdd <*> (
120+ (((op "-") <* commentSpace) <|> (op "-"))
121+ *> expr)
122+
123+ expr = expr3 <|> exprAdd
124+
125+Defining Block Structure using Indents
126+--------------------------------------
127+
128+Many languages such as Python, Haskell and Idris use indents to delimit
129+the block structure of the language.
130+
131+We can see how Idris2 does it here
132+: https://github.com/edwinb/Idris2/blob/master/src/Parser/Support.idr
133+
134+.. code-block:: idris
135+
136+ export
137+ IndentInfo : Type
138+ IndentInfo = Int
139+
140+ export
141+ init : IndentInfo
142+ init = 0
143+
144+
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154+