✨ parser for formula.

conftest.py

@@ -1,7 +1,18 @@
 import pytest
 from fol.lexer import Lexer
+from fol.parser import Parser
 
 
 @pytest.fixture
 def lexer():
     return Lexer()
+
+
+@pytest.fixture
+def parser():
+    def inner(text):
+        lexer = Lexer()
+        lexer.scan(text)
+        parser = Parser(lexer)
+        return parser
+    return inner

doc/grammar.bnf

@@ -4,10 +4,13 @@ FORALL ::= forall var IMP | IMP
 IMP ::= OR imp OR
 OR ::= AND (or AND)*
 AND ::= NOT (and NOT)*
-NOT ::= not? PRED
+NOT ::= not? GROUP
+GROUP ::= NOT | opar F cpar
 PRED ::= pred opar TERM (comma TERM)* cpar
 
 TERM ::=
 | var
 | const
-| var opar TERM (comma TERM)* cpar
+| FUN
+
+FUN ::= var opar TERM (comma TERM)* cpar

fol/__init__.py

@@ -0,0 +1,10 @@
+from fol import lexer
+from fol import parser
+
+
+def parse(text):
+    lex = lexer.Lexer()
+    lex.scan(text)
+    p = parser.Parser(lex)
+    root = p.parse()
+    return root

fol/lexer.py

@@ -3,6 +3,9 @@ class Token:
         self.name = name
         self.value = value
 
+    def is_a(self, name):
+        return self.name == name
+
     def __str__(self):
         if self.value is not None:
             return f'{self.name}[{self.value}]'
@@ -43,6 +46,17 @@ class Lexer:
 
         return None
 
+    def peek(self, lookahead=0):
+        tok = None
+        cursor = self.cursor
+
+        for i in range(lookahead + 1):
+            tok = self.next()
+
+        self.cursor = cursor
+
+        return tok
+
     def scan_spaces(self):
         while self.cursor < len(self.text) \
               and self.text[self.cursor].isspace():

fol/parser.py

@@ -0,0 +1,170 @@
+class Node:
+    def __init__(self, name, value=None):
+        self.name = name
+        self.value = value
+        self.children = []
+
+    def add_child(self, child):
+        self.children.append(child)
+
+    def __str__(self):
+        res = self.name
+        if self.value is not None:
+            res += f'[{self.value}]'
+
+        if len(self.children) > 0:
+            res += '('
+            sep = ''
+
+            for child in self.children:
+                res += sep + str(child)
+                sep = ','
+            res += ')'
+        return res
+
+
+class Parser:
+    def __init__(self, lexer):
+        self.lexer = lexer
+
+    def consume(self, name):
+        tok = self.lexer.peek()
+
+        if tok and tok.is_a(name):
+            self.lexer.next()
+            return tok
+
+        return None
+
+    def ensure(self, name):
+        tok = self.consume(name)
+
+        if tok is None:
+            raise Exception(f'invalid {name}')
+
+        if tok and not tok.is_a(name):
+            raise Exception(f'expected {name}, got {tok.name}')
+
+        return tok
+
+    def parse(self):
+        return self.parse_f()
+
+    def parse_f(self):
+        return self.parse_exists()
+
+    def parse_exists(self):
+        if self.consume('EXISTS'):
+            tok_var = self.ensure('VAR')
+            rhs = self.parse_forall()
+            node = Node('EXISTS')
+            node.add_child(Node('VAR', tok_var.value))
+            node.add_child(rhs)
+            return node
+
+        return self.parse_forall()
+
+    def parse_forall(self):
+        if self.consume('FORALL'):
+            tok_var = self.ensure('VAR')
+            rhs = self.parse_imp()
+            node = Node('FORALL')
+            node.add_child(Node('VAR', tok_var.value))
+            node.add_child(rhs)
+            return node
+
+        return self.parse_imp()
+
+    def parse_imp(self):
+        lhs = self.parse_or()
+
+        if self.consume('IMP'):
+            rhs = self.parse_or()
+            node = Node('IMP')
+            node.add_child(lhs)
+            node.add_child(rhs)
+            lhs = node
+
+        return lhs
+
+    def parse_or(self):
+        lhs = self.parse_and()
+
+        while self.consume('OR'):
+            rhs = self.parse_and()
+            node = Node('OR')
+            node.add_child(lhs)
+            node.add_child(rhs)
+            lhs = node
+
+        return lhs
+
+    def parse_and(self):
+        lhs = self.parse_not()
+
+        while self.consume('AND'):
+            rhs = self.parse_not()
+            node = Node('AND')
+            node.add_child(lhs)
+            node.add_child(rhs)
+            lhs = node
+
+        return lhs
+
+    def parse_not(self):
+        if self.consume('NOT'):
+            node = Node('NOT')
+            node.add_child(self.parse_pred())
+            return node
+
+        return self.parse_group()
+
+    def parse_group(self):
+        if self.consume('OPAR'):
+            node = self.parse_f()
+            self.ensure('CPAR')
+            return node
+        return self.parse_pred()
+
+    def parse_pred(self):
+        tok = self.ensure('PRED')
+        self.ensure('OPAR')
+
+        node = Node('PRED', tok.value)
+        node.add_child(self.parse_term())
+
+        while self.consume('COMMA'):
+            node.add_child(self.parse_term())
+
+        self.ensure('CPAR')
+        return node
+
+    def parse_term(self):
+        maybe_var = self.lexer.peek(0)
+        maybe_opar = self.lexer.peek(1)
+
+        if maybe_var and maybe_opar and maybe_var.is_a('VAR') \
+           and maybe_opar.is_a('OPAR'):
+            return self.parse_function()
+
+        tok = self.lexer.next()
+        if tok is None:
+            raise Exception('unexpected end')
+
+        if tok.name in ['VAR', 'CONST']:
+            return Node(tok.name, tok.value)
+
+        raise Exception(f'unknown term {tok.value}')
+
+    def parse_function(self):
+        tok = self.ensure('VAR')
+        self.ensure('OPAR')
+
+        node = Node('FUN', tok.value)
+        node.add_child(self.parse_term())
+
+        while self.consume('COMMA'):
+            node.add_child(self.parse_term())
+
+        self.ensure('CPAR')
+        return node

fol/tests/test_parser.py

@@ -0,0 +1,45 @@
+import pytest
+
+
+@pytest.mark.parametrize(['oracle', 'text'], [
+    ('PRED[Happy](VAR[x])', 'Happy(x)'),
+    ('PRED[Sad](VAR[y],VAR[z])', 'Sad(y, z)'),
+    # EXISTS
+    ('EXISTS(VAR[x],PRED[Happy](VAR[x]))', '\\exists x Happy(x)'),
+    # FORALL
+    ('FORALL(VAR[z],PRED[Sad](VAR[z]))', '\\forall z Sad(z)'),
+    # IMP
+    ('IMP(PRED[Rich](VAR[x]),PRED[Happy](VAR[x]))',
+     'Rich(x) -> Happy(x)'),
+    # OR
+    ('OR(OR(PRED[Rich](VAR[x]),PRED[Happy](VAR[x])),'
+     'PRED[Smart](VAR[x]))',
+     'Rich(x) | Happy(x) | Smart(x)'),
+    # AND
+    ('AND(AND(PRED[Rich](VAR[x]),PRED[Happy](VAR[x])),'
+     'PRED[Smart](VAR[x]))',
+     'Rich(x) & Happy(x) & Smart(x)'),
+
+    ('OR(AND(PRED[Rich](VAR[x]),'
+     'PRED[Happy](VAR[x])),PRED[Smart](VAR[x]))',
+     'Rich(x) & Happy(x) | Smart(x)'),
+
+    ('AND(PRED[Rich](VAR[x]),OR(PRED[Happy](VAR[x]),'
+     'PRED[Smart](VAR[x])))',
+     'Rich(x) & (Happy(x) | Smart(x))'),
+
+    # NOT
+    ('FORALL(VAR[x],NOT(PRED[Happy](VAR[x])))',
+     '\\forall x ~Happy(x)'),
+    # PRED
+    ('PRED[Rich](CONST[BOB])',
+     'Rich(BOB)'),
+    ('PRED[Rich](FUN[father](CONST[BOB]))',
+     'Rich(father(BOB))'),
+])
+def test_parser(parser, oracle, text):
+
+    p = parser(text)
+    root = p.parse()
+
+    assert oracle == str(root)