rédaction calepin : reste pouvoir expression + partie avec lamba-expression Python

lambda_calcul.py

@@ -53,17 +53,6 @@ class Lambda_parser(Parser):
     '''
     tokens = Lambda_lexer.tokens
     
-    # @_('VAR')
-    # def term(self, p):
-    #     return Lambda_terme(0, p[0])
-    
-    # @_('LAMBDA VAR POINT term')
-    # def term(self, p):
-    #     return Lambda_terme(1, p[1], p.term)
-    
-    # @_('LPAR term term RPAR')
-    # def term(self, p):
-    #     return Lambda_terme(2, p.term0, p.term1)
 
     @_('VAR')
     def term(self, p):
@@ -77,7 +66,12 @@ class Lambda_parser(Parser):
     def term(self, p):
         return (2, p.term0, p.term1)
 
-
+    def error(self, p):
+        if p:
+            raise LambdaSyntaxError('{} inattendu en position {}'.format(p.type, p.index))
+        else:
+            raise LambdaSyntaxError('description inachevée')
+        
 parser = Lambda_parser()
 
 ##################################################
@@ -126,6 +120,19 @@ class Lambda_terme():
     >>> print(T5)
     (λz.(λx.(y x) z) t)
 
+    Sous-termes d'un terme
+    >>> for t in T5.sous_termes():
+    ...     print(t)
+    (λz.(λx.(y x) z) t)
+    λz.(λx.(y x) z)
+    (λx.(y x) z)
+    λx.(y x)
+    (y x)
+    y
+    x
+    z
+    t
+    
     Autres prédicats
     >>> [(t.est_redex(), t.est_forme_normale()) for t in (T1, T2, T3, T4, T5)]
     [(False, True), (False, True), (True, False), (False, False), (True, False)]
@@ -215,7 +222,20 @@ class Lambda_terme():
         else:
             return '({:s} {:s})'.format(str(self._content[1]), str(self._content[2]))
     
-    
+    def __eq__(self, terme):
+        if not isinstance(terme, Lambda_terme):
+            raise Lambda_termeError('Comparaison inpossible impossible')
+        if self.est_variable():
+            return terme.est_variable() and self._content[1] == terme._content[1]
+        elif self.est_application():
+            return (terme.est_application() and 
+                    self._content[1] == terme._content[1] and
+                    self._content[2] == terme._content[2])
+        else:
+            return (terme.est_abstraction() and
+                    self._content[2] == terme._content[2].subs(terme._content[1],
+                                                               Lambda_terme(self._content[1])))
+                    
     def applique(self, terme):
         if not isinstance(terme, Lambda_terme):
             raise Lambda_termeError('Application impossible')
@@ -226,6 +246,31 @@ class Lambda_terme():
             raise Lambda_termeError("Variable d'Abstraction invalide")
         return Lambda_terme(1, var, self)
     
+    def variables(self):
+        if self.est_variable():
+            return ({self._content[1]}, set())
+        elif self.est_application():
+            var_libres1, var_liees1 = self._content[1].variables()
+            var_libres2, var_liees2 = self._content[2].variables()
+            return (var_libres1.union(var_libres2),
+                    var_liees1.union(var_liees2))
+        else:
+            var_libres, var_liees = self._content[2].variables()
+            if self._content[1] in var_libres:
+                var_libres.discard(self._content[1])
+                var_liees.add(self._content[1])
+            return (var_libres, var_liees)
+        
+    def sous_termes(self):
+        if self.est_variable():
+            ss_termes = []
+        elif self.est_abstraction():
+            ss_termes = self._content[2].sous_termes()
+        else:
+            ss_termes = self._content[1].sous_termes()
+            ss_termes.extend(self._content[2].sous_termes())
+        return [self] + ss_termes
+    
     def est_redex(self):
         return self.est_application() and self._content[1].est_abstraction()
     
@@ -236,18 +281,7 @@ class Lambda_terme():
             return self._content[2].est_forme_normale()
         else:
             return (not self._content[1].est_abstraction() and
-                    all(self._content[k].est_forme_normale() for k in (1, 2)))
-        
-    def variables_libres(self):
-        if self.est_variable():
-            return {self._content[1]}
-        elif self.est_application():
-            var_libres = self._content[2].variables_libres()
-            return var_libres.union(self._content[1].variables_libres())
-        else:
-            var_libres = self._content[2].variables_libres()
-            var_libres.discard(self._content[1])
-            return var_libres
+                    all(self._content[k].est_forme_normale() for k in (1, 2)))    
     
     def subs(self, var, terme):
         if not isinstance(var, str):
@@ -266,13 +300,13 @@ class Lambda_terme():
         else:
             var_abstr = self._content[1]
             corps_abstr = self._content[2]
-            var_libres_corps = corps_abstr.variables_libres()
+            var_libres_corps, _ = corps_abstr.variables()
             if var == var_abstr or var not in var_libres_corps:
                 return self
-            elif var_abstr not in terme.variables_libres():
+            elif var_abstr not in terme.variables()[0]:
                 return Lambda_terme(1, var_abstr, corps_abstr.subs(var, terme))
             else:
-                nouvelle_var = _autre_variable(var_abstr, corps_abstr.variables_libres())
+                nouvelle_var = _autre_variable(var_abstr, var_libres_corps)
                 return Lambda_terme(1, 
                                     nouvelle_var, 
                                     corps_abstr.subs(var_abstr,

tikz_diamant.tex

@@ -0,0 +1,21 @@
+\documentclass{standalone}
+
+\usepackage{tikz}
+\usetikzlibrary{automata,positioning}
+
+\begin{document}
+\begin{tikzpicture}[shorten >=1pt,node distance=3cm,on grid,>=stealth,
+  every state/.style={draw=none}]
+
+  \node[state] (T)  {$T$};
+  \node[state] (R1) [below left=of T] {$R_1$};
+  \node[state] (R2) [below right=of T] {$R_2$};
+  \node[state] (R) [below right=of R1] {$R$};
+
+  \path [every node/.style={font=\footnotesize, below}]
+  (T) edge[->>] node[near end] {$\beta$}  (R1)
+      edge[->>] node[near end] {$\beta$}  (R2)
+  (R1) edge[->>] node[near end] {$\beta$} (R)
+  (R2) edge[->>] node[near end] {$\beta$} (R);    
+\end{tikzpicture}
+\end{document}