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

This commit is contained in:
Éric Wegrzynowski 2021-02-11 13:30:06 +01:00
parent 7c957049db
commit 30267226b3
5 changed files with 3568 additions and 1507 deletions

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@ -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):
@ -77,6 +66,11 @@ 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)]
@ -215,6 +222,19 @@ 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):
@ -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()
@ -238,17 +283,6 @@ class Lambda_terme():
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
def subs(self, var, terme):
if not isinstance(var, str):
raise Lambda_termeError('subst possible uniquement pour les variables')
@ -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,

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tikz_diamant.tex Normal file
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@ -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}