Author: Tomohiro Oda
This example is created by Tomohiro Oda and it illustrates how it is possible to use higher-order functions in VDM-SL to create parser elements that can be put together in a compositional fashion. This model can be used as a kind of library that one can play with manipulating strings into a VDM AST representation.
Properties | Values |
---|---|
Language Version: | classic |
Entry point : | MMParser`eval(“1+1+4+0”) |
module MMParser
/***
MMParser
Author: Tomohiro Oda
Version: 0.01
License: the MIT License
Copyright (c) 2013 Tomohiro Oda and Software Research Associates, Inc.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in
all copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
THE SOFTWARE.
***/
imports from VCParser all
exports functions eval: seq of char -> [int]
definitions
types
TREE = VCParser`TREE;
PARSED = VCParser`PARSED;
values
concat = VCParser`concat;
series = VCParser`series;
either = VCParser`either;
star = VCParser`star;
trimBlanks = VCParser`trimBlanks;
integer = VCParser`integer;
takeChar = VCParser`takeChar;
label = VCParser`label;
transtree = VCParser`transtree;
parseInt = trimBlanks(integer);
parseMul = series([takeChar('*'), parseInt]);
parseDiv = series([takeChar('/'), parseInt]);
parseTerm = transtree(liftOperator, series([
parseInt,
star(either([parseMul, parseDiv]))]));
parseAdd = series([takeChar('+'), parseTerm]);
parseSub = series([takeChar('-'), parseTerm]);
parseExpression = transtree(liftOperator, series([
parseTerm,
star(either([parseAdd, parseSub]))]));
liftOperator = lambda tree:VCParser`TREE &
let mk_VCParser`TREE(-, [left, right]) = tree in
let mk_VCParser`TREE(-, rights) = right in cases rights:
[] -> left,
[mk_VCParser`TREE(-, [mk_VCParser`TREE(-, operator), operand])]^rest ->
liftOperator(mk_VCParser`TREE(nil, [
mk_VCParser`TREE(operator, [left, operand]),
mk_VCParser`TREE(nil, rest)]))
end;
functions
evalInt : seq of char -> int
evalInt(string) == cases string:
"-"^rest -> evalInt(rest) * -1,
[] -> 0,
others -> evalInt([string(i) | i in set {1,...,len string -1}]) * 10 +
{'0' |-> 0, '1' |-> 1, '2' |-> 2, '3' |-> 3, '4' |-> 4, '5' |-> 5,
'6' |-> 6, '7' |-> 7, '8' |-> 8, '9'|-> 9}(string(len string))
end;
evalTree : TREE -> int
evalTree(tree) == cases tree:
mk_VCParser`TREE("int", contents) -> evalInt(contents),
mk_VCParser`TREE("*", [e1, e2]) -> evalTree(e1) * evalTree(e2),
mk_VCParser`TREE("/", [e1, e2]) -> evalTree(e1) / evalTree(e2),
mk_VCParser`TREE("+", [e1, e2]) -> evalTree(e1) + evalTree(e2),
mk_VCParser`TREE("-", [e1, e2]) -> evalTree(e1) - evalTree(e2)
end;
eval : seq of char -> [int]
eval(string) == cases parseExpression(string):
mk_VCParser`PARSED(tree, []) -> evalTree(tree),
others -> nil
end;
end MMParser
module VCParser
/***
VCParser
Author: Tomohiro Oda
Version: 0.01
License: the MIT License
Copyright (c) 2013 Tomohiro Oda and Software Research Associates, Inc.
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in
all copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
THE SOFTWARE.
***/
exports all
definitions
types
SOURCE = seq of char;
ERROR :: message:seq of char;
LABEL = [seq of char];
TREE :: label : LABEL contents : seq of TREE | seq of char;
PARSED :: parsed : (TREE | ERROR) remaining : SOURCE;
PARSER = SOURCE -> PARSED;
values
/***
messages
***/
UNEXPECTED_EOF = "Unexpected EOF";
UNEXPECTED = "Unexpected ";
EXPECTED = "Expected ";
/***
parsers
***/
any = lambda source:SOURCE &
cases source:
[] -> mk_PARSED(mk_ERROR(UNEXPECTED_EOF), source),
others -> mk_PARSED(mk_TREE(nil, [hd source]), tl source)
end;
digit = label("digit", either([takeChar("0123456789"(index)) | index in set {1,...,10}]));
lowerAlphabet = label("lowerAlphabet", either([takeChar("abcdefghijklmnopqrstuvwxyz"(index)) | index in set {1,...,26}]));
upperAlphabet = label("upperAlphabet", either([takeChar("ABCDEFGHIJKLMNOPQRSTUVWXYZ"(index)) | index in set {1,...,26}]));
alphabet = label("alphabet", either([lowerAlphabet, upperAlphabet]));
natnum = label("nat",
concat(series([
concat(series([pass(fail(takeChar('0'))),digit])),
concat(star(digit))])));
integer = label("int",
concat(series([option(takeChar('-')), natnum])))
functions
/***
parser generators
***/
takeChar : char -> PARSER
takeChar(c) == lambda source : SOURCE &
cases source:
[] -> mk_PARSED(mk_ERROR(UNEXPECTED_EOF), source),
others -> if hd source = c then mk_PARSED(mk_TREE(nil, [c]), tl source) else mk_PARSED(mk_ERROR(EXPECTED^"'"^[c]^"'"), source)
end;
takeString : seq1 of char -> PARSER
takeString(string) ==
concat(series([takeChar(string(index)) | index in set inds string]));
/***
parser combinators
***/
series : seq1 of PARSER -> PARSER
series(parsers) == lambda source: SOURCE &
let mk_PARSED(tree1, source1) = (hd parsers)(source) in
cases mk_(tree1, tl parsers):
mk_(mk_ERROR(msg), -) -> mk_PARSED(tree1, source1),
mk_(-, []) -> mk_PARSED(mk_TREE(nil, [tree1]), source1),
mk_(-, rest) ->
let mk_PARSED(tree2, source2) = series(rest)(source1) in
cases tree2:
mk_TREE(-, trees2) -> mk_PARSED(mk_TREE(nil, [tree1]^trees2), source2),
mk_ERROR(message) -> mk_PARSED(tree2, source2)
end
end;
either : seq1 of PARSER -> PARSER
either(parsers) == lambda source: SOURCE &
let mk_PARSED(tree1, source1) = (hd parsers)(source) in
cases mk_(tree1, tl parsers):
mk_(mk_ERROR(msg), []) -> mk_PARSED(tree1, source1),
mk_(mk_ERROR(msg), -) -> either(tl parsers)(source),
mk_(tree, rest) -> mk_PARSED(tree1, source1)
end;
star : PARSER -> PARSER
star(parser) == lambda source: SOURCE &
cases parser(source):
mk_PARSED(mk_ERROR(-), -) -> mk_PARSED(mk_TREE(nil, []), source),
mk_PARSED(tree, rest) ->
let mk_PARSED(mk_TREE(-, trees), source2) = star(parser)(rest) in
mk_PARSED(mk_TREE(nil, [tree]^trees), source2)
end;
option : PARSER -> PARSER
option(parser) == lambda source:SOURCE &
cases parser(source):
mk_PARSED(mk_ERROR(-), -) -> mk_PARSED(mk_TREE(nil, []), source),
success -> success
end;
trimBlanks : PARSER -> PARSER
trimBlanks(parser) ==
(lambda parsed:PARSED &
cases parsed:
mk_PARSED(mk_ERROR(-),-) -> parsed,
mk_PARSED(mk_TREE(-, contents), rest) ->
mk_PARSED(contents(2), rest)
end)
comp
(series([
star(either([takeChar(' '), takeChar('\t')])),
parser,
star(either([takeChar(' '), takeChar('\t')]))]));
fail : PARSER -> PARSER
fail(parser) == lambda source: SOURCE &
let mk_PARSED(tree1, source1) = parser(source) in
cases tree1:
mk_ERROR(-) -> mk_PARSED(mk_TREE(nil, []), source),
mk_TREE(-, -) -> mk_PARSED(
mk_ERROR(UNEXPECTED^[source(index) | index in set {1,...,len source - len source1}]), source)
end;
concat : PARSER -> PARSER
concat(parser) == (lambda p:PARSED & cases p:
mk_PARSED(mk_ERROR(message), rest) -> p,
mk_PARSED(mk_TREE(label, contents), rest) ->
if contents = [] then
mk_PARSED(mk_TREE(nil, contents), rest)
elseif is_(contents, seq of char) then
mk_PARSED(mk_TREE(nil, contents), rest)
else
mk_PARSED(mk_TREE(nil, conc([let mk_TREE(-, subcontent) = contents(index) in subcontent | index in set inds contents])), rest)
end) comp parser;
pass : PARSER -> PARSER
pass(parser) == lambda source:SOURCE &
cases parser(source):
mk_PARSED(mk_TREE(label, contents), rest) ->mk_PARSED(mk_TREE(label, []), rest),
err -> err
end;
label : LABEL * PARSER -> PARSER
label(newLabel, parser) == (lambda parsed : PARSED &
cases parsed:
mk_PARSED(mk_TREE(-, contents), source) -> mk_PARSED(mk_TREE(newLabel, contents), source),
others -> parsed
end) comp parser;
trans : (PARSED->PARSED) * PARSER->PARSER
trans(modifier, parser) == modifier comp parser;
transtree : (TREE -> TREE) * PARSER -> PARSER
transtree(modifier, parser) == trans(
lambda parsed: PARSED & cases parsed:
mk_PARSED(mk_ERROR(message), rest) -> parsed,
mk_PARSED(tree, rest) -> mk_PARSED(modifier(tree), rest)
end, parser);
iferror : seq of char * PARSER -> PARSER
iferror(message, parser) == trans(
(lambda parsed: PARSED &
cases parsed:
mk_PARSED(mk_ERROR(-), rest) ->
mk_PARSED(mk_ERROR(message), rest),
mk_PARSED(mk_TREE(-, -), -) -> parsed
end), parser)
end VCParser