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How to use short_circuit method in hypothesis

Best Python code snippet using hypothesis
lambek.py
Source:lambek.py
1#2# lambek.py3#4# Edward Loper5# Created [12/10/00 03:41 AM]6# $Id$7#8"""Lambek Calculus Theorem Prover9"""10# For while I'm coding..11#import term;reload(term)12#import typedterm; reload(typedterm)13_VERBOSE = 014_VAR_NAMES = 115_SHOW_VARMAP = not _VAR_NAMES16from term import *17from typedterm import *18from lexicon import *19import sys, re20class Sequent:21    """A sequent maps an ordered sequence of TypedTerm's to an ordered 22    sequence of TypedTerm's."""23    # left and right are lists of TypedTerms.24    def __init__(self, left, right):25        # Check types, because we're paranoid.26        if type(left) not in [types.ListType, types.TupleType] or \27           type(right) not in [types.ListType, types.TupleType]:28            raise TypeError('Expected lists of TypedTerms')29        for elt in left+right:30            if not isinstance(elt, TypedTerm):31                raise TypeError('Expected lists of TypedTerms')32        33        self.left = left34        self.right = right35    def __repr__(self):36        left_str = `self.left`[1:-1]37        right_str = `self.right`[1:-1]38        return left_str + ' => ' + right_str39    def to_latex(self, pp_varmap=None):40        if pp_varmap == None: pp_varmap = {}41        for te in self.left+self.right:42            extend_pp_varmap(pp_varmap, te.term)43        str = ''44        for i in range(len(self.left)):45            str += self.left[i].to_latex(pp_varmap) + ', '46        str = str[:-2] + ' \Rightarrow '47        for i in range(len(self.right)):48            str += self.right[i].to_latex(pp_varmap) + ', '49        return str[:-2]50        51    def pp(self, pp_varmap=None):52        if pp_varmap == None: pp_varmap = {}53        for te in self.left+self.right:54            extend_pp_varmap(pp_varmap, te.term)55        str = ''56        for i in range(len(self.left)):57            str += self.left[i].pp(pp_varmap) + ', '58        str = str[:-2] + ' => '59        for i in range(len(self.right)):60            str += self.right[i].pp(pp_varmap) + ', '61        return str[:-2]62    def simplify(self, varmap):63        left = [te.simplify(varmap) for te in self.left]64        right = [te.simplify(varmap) for te in self.right]65        return Sequent(left, right)66    67class Proof:68    "Represents 1 step of a proof tree.."69    # rule: which rule was used (str)70    # assumptions: what is assumed (list of Proofs)71    # conclusion: what is concluded (Sequent)72    def __init__(self, rule, assumptions, conclusion, varmap):73        self.rule = rule74        self.assumptions = assumptions75        self.conclusion = conclusion76        self.varmap = varmap77    def __repr__(self):78        return self.rule+' '+`self.assumptions`+' -> '\79               +`self.conclusion`80    def simplify(self, varmap=None):81        if varmap == None:82            varmap = self.varmap83        assum = [a.simplify(varmap) for a in self.assumptions] 84        concl = self.conclusion.simplify(varmap)85        return Proof(self.rule, assum, concl, varmap)86    def to_latex_array(self, depth = 1, pp_varmap=None):87        if pp_varmap == None: pp_varmap={}88        # Draw asumptions89        str = '\\begin{array}{c}\n'90        for assumption in self.assumptions:91            str += '      '*depth + \92                   assumption.to_latex(depth+1, pp_varmap) + \93                   ' \\quad \n'94        str = str[:-1] + '\\\\'+'\\hline'+'\n'95        # Add conclusion96        str += '      '*depth + '{' + \97               self.conclusion.to_latex(pp_varmap) + '}'98        # Close array99        str += '\\\\\n'+'      '*depth+'\\end{array}'100        101        # The rule type102        str += ' \\textrm{' + \103               re.sub(r'\\', r'$\\backslash$', self.rule) + '}' 104        if depth == 1:105            return '$$\n'+str+'\n$$'106        else:107            return '{'+str+'}'108    109    def to_latex(self, depth = 1, pp_varmap=None):110        if pp_varmap == None: pp_varmap={}111        # Draw asumptions112        str = '\\frac{\\textrm{$ \n'113        for assumption in self.assumptions:114            str += '      '*depth + \115                   assumption.to_latex(depth+1, pp_varmap) + \116                   ' \\quad \n'117        str = str[:-1] + '$}}\n'118        # Add conclusion119        str += '      '*depth + '{' + \120               self.conclusion.to_latex(pp_varmap) + '}'121        # The rule type122        rule = re.sub(r'\\', r'$\\backslash$', self.rule)123        rule = re.sub(r'\*', r'$\\cdot$', rule)124        str += ' \\textrm{' + rule + '}'125        if depth == 1:126            return '$$\n'+str+'\n$$'127        else:128            return '{'+str+'}'129    130    # Returns (str, right)131    def pp(self, left=0, toplevel=1, pp_varmap=None):132        if pp_varmap == None: pp_varmap={}133        right = left134        str = ''135        136        if _VAR_NAMES:137            concl = self.conclusion.pp(pp_varmap)138        else:139            concl = `self.conclusion`140        # Draw assumptions141        for assumption in self.assumptions:142            (s, right) = assumption.pp(right, 0, pp_varmap)143            str = _align_str(str, s)144            right += 5145        # Draw line.146        right = max(right-5, left+len(concl))147        str += ' '*left + '-'*(right-left) + ' ' + self.rule + '\n' 148        # Draw conclusion149        start = left+(right-left-len(concl))/2150        str += ' '*start + concl + '\n'151        if toplevel:152            if _SHOW_VARMAP:153                return str+'\nVarmap: '+ `self.varmap`+'\n'154            else:155                return str156        else:157            return (str, right)158def _align_str(s1, s2):159    lines1 = s1.split('\n')160    lines2 = s2.split('\n')161    if lines1[-1] == '': lines1 = lines1[:-1]162    if lines2[-1] == '': lines2 = lines2[:-1]163    str = ''164    while len(lines1) > len(lines2):165        str += lines1[0] + '\n'166        lines1 = lines1[1:]167        168    while len(lines2) > len(lines1):169        str += lines2[0] + '\n'170        lines2 = lines2[1:]171    for n in range(len(lines1)):172        x = 0173        for x in range(min(len(lines1[n]), len(lines2[n]))):174            if lines1[n][x] == ' ':175                str += lines2[n][x]176            elif lines2[n][x] == ' ':177                str += lines1[n][x]178            else:179                raise ValueError('Overlapping strings')180        str += lines1[n][x+1:]181        str += lines2[n][x+1:]182        str += '\n'183    return str184        185######################################186# PROOF LOGIC187######################################188# Prove a sequent.  Variables can have their values filled in.189# If short_circuit is 1, return once we find any proof.  If190# short_circuit is 0, return all proofs.191def prove(sequent, short_circuit=0):192    proofs = _prove(sequent, VarMap(), short_circuit, 0)193    return [proof.simplify() for proof in proofs]194def _prove(sequent, varmap, short_circuit, depth):195    if _VERBOSE:196        print ('  '*depth)+'Trying to prove', sequent197    proofs = []198    if proofs == [] or not short_circuit:199        proofs = proofs + introduce(sequent, varmap, short_circuit, depth+1)200    if proofs == [] or not short_circuit:201        proofs = proofs + rslash_l(sequent, varmap, short_circuit, depth+1)202    if proofs == [] or not short_circuit:203        proofs = proofs + lslash_l(sequent, varmap, short_circuit, depth+1)204    if proofs == [] or not short_circuit:205        proofs = proofs + rslash_r(sequent, varmap, short_circuit, depth+1)206    if proofs == [] or not short_circuit:207        proofs = proofs + lslash_r(sequent, varmap, short_circuit, depth+1)208    if proofs == [] or not short_circuit:209        proofs = proofs + dot_l(sequent, varmap, short_circuit, depth+1)210    if proofs == [] or not short_circuit:211        proofs = proofs + dot_r(sequent, varmap, short_circuit, depth+1)212    if _VERBOSE:213        print '  '*depth+'Found '+`len(proofs)`+' proof(s)'214    return proofs215def introduce(sequent, varmap, short_circuit, depth):216    if len(sequent.left) != 1 or \217       len(sequent.right) != 1 or \218       sequent.left[0].type != sequent.right[0].type:219        return []220    newseq = Sequent(sequent.left, sequent.right)221    r_term = sequent.right[0].term222    l_term = sequent.left[0].term223    # Try to unify224    te = sequent.left[0].unify(sequent.right[0], varmap)225    if te == None: newseq = sequent226    else: newseq = Sequent([te], [te])227    return [Proof('I', (), newseq, varmap)]228def rslash_l(sequent, varmap_in, short_circuit, depth):229    proofs = []230    for i in range(len(sequent.left)-1):231        if isinstance(sequent.left[i].type, RSlash) and \232           len(sequent.right) == 1:233            # Set up some variables...234            beta = Var()235            alpha = sequent.left[i].term236            A = sequent.left[i].type.result237            B = sequent.left[i].type.arg238            Gamma1 = sequent.left[:i]239            gamma = sequent.right[0].term240            C = sequent.right[0].type241            # Try all combinations of Delta, Gamma2..242            for j in range(i+1, len(sequent.left)):243                Delta = sequent.left[i+1:j+1]244                Gamma2 = sequent.left[j+1:]245                # Try proving the left assumption.246                l_seq = Sequent(Delta, [TypedTerm(beta, B)])247                l_proofs = _prove(l_seq, varmap_in, short_circuit, depth)248                # For each proof, try proving the right half.  Make249                # sure to keep beta bound to the same thing..250                for l_proof in l_proofs:251                    beta = l_proof.conclusion.right[0].term252                    r_seq = Sequent(Gamma1+\253                                    [TypedTerm(Appl(alpha, beta), A)]+\254                                    Gamma2, [TypedTerm(gamma, C)])255                    r_proofs = _prove(r_seq, varmap_in, short_circuit, depth)256                    for r_proof in r_proofs:257                        varmap = r_proof.varmap + l_proof.varmap258                        right = r_proof.conclusion.right[0]259                        right = right.unify(TypedTerm(gamma, C), varmap)260                        proofs.append(Proof('/L', [l_proof, r_proof],\261                                            Sequent(sequent.left,[right]),\262                                            varmap))263                        if short_circuit: return proofs264    return proofs265def lslash_l(sequent, varmap_in, short_circuit, depth):266    proofs = []267    for i in range(1, len(sequent.left)):268        if isinstance(sequent.left[i].type, LSlash) and \269           len(sequent.right) == 1:270            # Set up some variables...271            beta = Var()272            alpha = sequent.left[i].term273            A = sequent.left[i].type.result274            B = sequent.left[i].type.arg275            gamma = sequent.right[0].term276            C = sequent.right[0].type277            Gamma2 = sequent.left[i+1:]278            # Try all combinations of Delta, Gamma2..279            for j in range(i):280                Delta = sequent.left[j:i]281                Gamma1 = sequent.left[:j]282                # Try proving the left assumption.283                l_seq = Sequent(Delta, [TypedTerm(beta, B)])284                l_proofs = _prove(l_seq, varmap_in, short_circuit, depth)285                # For each proof, try proving the right half.  Make286                # sure to keep beta bound to the same thing..287                for l_proof in l_proofs:288                    beta = l_proof.conclusion.right[0].term289                    r_seq = Sequent(Gamma1+\290                                    [TypedTerm(Appl(alpha, beta), A)]+\291                                    Gamma2, [TypedTerm(gamma, C)])292                    r_proofs = _prove(r_seq, varmap_in, short_circuit, depth)293                    for r_proof in r_proofs:294                        varmap = r_proof.varmap + l_proof.varmap295                        right = r_proof.conclusion.right[0]296                        right = right.unify(TypedTerm(gamma, C), varmap)297                        298                        proofs.append(Proof('\\L', [l_proof, r_proof],\299                                            Sequent(sequent.left,[right]),300                                            varmap))301                        if short_circuit: return proofs302    return proofs303def rslash_r(sequent, varmap, short_circuit, depth):304    proofs = []305    # Make sure the right side is properly formatted..306    if len(sequent.right) != 1 or \307       not isinstance(sequent.right[0].type, RSlash):308        return proofs309    # Set up variables..310    x = Var()311    varmap.add(x, None)312    alpha = Appl(sequent.right[0].term, x)313    B = sequent.right[0].type.result314    A = sequent.right[0].type.arg315    Gamma = sequent.left316    seq = Sequent(Gamma + [TypedTerm(x, A)], \317                  [TypedTerm(alpha, B)])318    s_proofs = _prove(seq, varmap, short_circuit, depth)319    for proof in s_proofs:320        varmap = proof.varmap.copy()321        right1 = TypedTerm(Abstr(x, proof.conclusion.right[0].term),\322                           RSlash(B, A))323        right2 = TypedTerm(Abstr(x, alpha), sequent.right[0].type)324        right = right1.unify(right2, varmap)325        if right == None: continue326        varmap.add(x, None)327        concl = Sequent(Gamma, [right])328        proofs.append(Proof('/R', [proof], concl, varmap))329    return proofs330def lslash_r(sequent, varmap, short_circuit, depth):331    proofs = []332    # Make sure the right side is properly formatted..333    if len(sequent.right) != 1 or \334       not isinstance(sequent.right[0].type, LSlash):335        return proofs336    # Set up variables..337    x = Var()338    varmap.add(x, None)339    alpha = Appl(sequent.right[0].term, x)340    B = sequent.right[0].type.result341    A = sequent.right[0].type.arg342    Gamma = sequent.left343    seq = Sequent([TypedTerm(x, A)] + Gamma, \344                  [TypedTerm(alpha, B)])345    s_proofs = _prove(seq, varmap, short_circuit, depth)346    for proof in s_proofs:347        right1 = TypedTerm(Abstr(x, proof.conclusion.right[0].term),\348                           LSlash(A, B))349        right2 = TypedTerm(Abstr(x, alpha), sequent.right[0].type)350        right = right1.unify(right2, varmap)351        if right == None: continue352        varmap = varmap + proof.varmap353        varmap.add(x, None)354        concl = Sequent(Gamma, [right])355        proofs.append(Proof('\\R', [proof], concl, varmap))356    return proofs357def dot_l(sequent, varmap, short_circuit, depth):358    proofs = []359    for i in range(0, len(sequent.left)):360        if isinstance(sequent.left[i].type, Dot) and \361           len(sequent.right) == 1:362            Gamma1 = sequent.left[:i]363            Gamma2 = sequent.left[i+1:]364            A = sequent.left[i].type.left365            B = sequent.left[i].type.right366            alpha = sequent.left[i].term367            # Deal with alpha if we can368            if isinstance(alpha, Tuple):369                alpha1 = alpha.left370                alpha2 = alpha.right371            elif isinstance(alpha, Var):372                alpha_var = alpha373                alpha1 = Var()374                alpha2 = Var()375                alpha = Tuple(alpha1, alpha2)376                varmap.add(alpha_var, alpha)377            else:378                # We can't deal.. :(  Move on...379                continue380            left = Gamma1 + [TypedTerm(alpha1, A)] + \381                   [TypedTerm(alpha2, B)] + Gamma2382            right = sequent.right383            s_proofs = _prove(Sequent(left, right), varmap, \384                              short_circuit, depth)385            for proof in s_proofs:386                varmap = proof.varmap.copy()387                sequent.right[0].unify(proof.conclusion.right[0], varmap) 388                proofs.append(Proof('*L', [proof], sequent, varmap))389                if short_circuit: return proofs390                391    return proofs392def dot_r(sequent, varmap_in, short_circuit, depth):393    proofs = []394    for i in range(1, len(sequent.left)):395        if isinstance(sequent.right[0].type, Dot) and \396           len(sequent.right) == 1:397            Gamma1 = sequent.left[:i]398            Gamma2 = sequent.left[i:]399            A = sequent.right[0].type.left400            B = sequent.right[0].type.right401            alphabeta = sequent.right[0].term402            # Deal with alpha if we can403            if isinstance(alphabeta, Tuple):404                alpha = alphabeta.left405                beta = alphabeta.right406            elif isinstance(alphabeta, Var):407                alphabeta_var = alphabeta408                alpha = Var()409                beta = Var()410                alphabeta = Tuple(alpha, beta)411                varmap_in.add(alphabeta_var, alphabeta)412            else:413                # We can't deal.. :(  Move on...414                continue415            left = Sequent(Gamma1, [TypedTerm(alpha, A)])416            right = Sequent(Gamma2, [TypedTerm(beta, B)])417            for r_proof in _prove(right, varmap_in, short_circuit, depth):418                for l_proof in _prove(left, varmap_in, short_circuit, depth):419                    varmap = r_proof.varmap + l_proof.varmap420                    right = TypedTerm(Tuple(l_proof.conclusion.right[0].term,\421                                            r_proof.conclusion.right[0].term),422                                      sequent.right[0].type)423                    right = right.unify(sequent.right[0], varmap)424                    concl = Sequent(Gamma1+Gamma2, [right])425                    proofs.append(Proof('*R', [l_proof, r_proof],\426                                        concl, varmap))427                    if short_circuit: return proofs428    return proofs429######################################430# TESTING431######################################432def find_proof(left, right, short_circuit=1):433    sq = Sequent(left, right)434    proofs = prove(sq, short_circuit)435    if proofs:436        print '#'*60437        print "## Proof(s) for", sq.pp()438        for proof in proofs:439            print440            print proof.to_latex()441    else:442        print '#'*60443        print "## Can't prove", sq.pp()444def test_lambek():445    lex = Lexicon()446    lex.load(open('lexicon.txt', 'r'))447    find_proof(lex.parse('[np/n] [n]'), lex.parse('[np]'))448    find_proof(lex.parse('[np] [np\s]'), lex.parse('[s]'))449    find_proof(lex.parse('[n] [np\s]'), lex.parse('[(np/n)\s]'))450    find_proof(lex.parse('dog sleeps'), lex.parse('[(np/n)\s]'))451    find_proof(lex.parse('the kid runs'), lex.parse('[s]'))452    find_proof(lex.parse('john believes tom likes'), lex.parse('[s/np]'))453    find_proof(lex.parse('john likes mary'), lex.parse('[s]'))454    find_proof(lex.parse('likes'), lex.parse('[np\s/np]'), 0)455    find_proof(lex.parse('[a/b] [b]'), lex.parse('foo'))456    find_proof(lex.parse('[(np/n)*n]'), lex.parse('[np]'))457    find_proof(lex.parse('[(np\\s)/np]'), lex.parse('[np\\(s/np)]'))458    find_proof(lex.parse('gives2 tom mary'), lex.parse('[np\\s]'))459    find_proof(lex.parse('gives'), lex.parse('[np\\s/(np*np)]'))460    find_proof(lex.parse('the city tom likes'), lex.parse('[np*(s/np)]'))461HELP="""% Lambek Calculus Theorem Proover462%463% Type a sequent you would like prooved.  Examples are:464%   [np/n] [n] => [np]465%   [np] [np\s] => [s]466%   [n] [np\s] => [(np/n)\s]467%   dog sleeps => [(np/n)\s]468%   the kid runs => [s]469%   john believes tom likes => [s/np]470%   john likes mary => [s]471%   likes => [np\s/np]472%   [a/b] [b] => foo473%   [(np/n)*n] => [np]474%   [(np\\s)/np] => [np\\(s/np)]475%   gives2 tom mary => [np\\s]476%   gives => [np\\s/(np*np)]477%   the city tom likes => [np*(s/np)]478%479% Other commands:480%   help         -- show this information481%   latexmode    -- toggle latexmode (outputs in LaTeX)482%   shortcircuit -- toggle shortcircuit mode (return just one proof)483%   lexicon      -- display the lexicon contents484%   quit         -- quit485"""486    487def mainloop(input, out, lex, latexmode, shortcircuit):488    while 1:489        out.write('%>> ')490        str = input.readline()491        if str == '': return492        str = str.strip()493        if (str=='') or (str[0]=='#') or (str[0]=='%'): continue494        if str.find('=>') == -1:495            if str.lower().startswith('latex'):496                if str.lower().endswith('off'): latexmode = 0497                elif str.lower().endswith('on'): latexmode = 1498                else: latexmode = not latexmode499                if latexmode: print >>out, '% latexmode on'500                else: print >>out, 'latexmode off'501            elif str.lower().startswith('short'):502                if str.lower().endswith('off'): shortcircuit = 0503                elif str.lower().endswith('on'): shortcircuit = 1504                else: shortcircuit = not shortcircuit505                if shortcircuit: print >>out, '%shortcircuit on'506                else: print >>out, '% shortcircuit off'507            elif str.lower().startswith('lex'):508                words = lex.words()509                print >>out, '% Lexicon: '510                for word in words:511                    print >>out, '%  ' + word + ':', \512                          ' '*(14-len(word)) + lex[word].pp() 513            elif str.lower().startswith('q'): return514            elif str.lower().startswith('x'): return515            else:516                print >>out, HELP517        else:518            try:519                (left, right) = str.split('=>')520                seq = Sequent(lex.parse(left), lex.parse(right))521                proofs = prove(seq, shortcircuit)522                print >>out523                print >>out, '%'*60524                if proofs:525                    print >>out, "%% Proof(s) for", seq.pp()526                    for proof in proofs:527                        print >>out528                        if latexmode: print >>out, proof.to_latex()529                        else: print >>out, proof.pp()530                else:531                    print >>out, "%% Can't prove", seq.pp()532            except KeyError, e:533                print 'Mal-formatted sequent'534                print 'Key error (unknown lexicon entry?)'535                print e536            except ValueError, e:537                print 'Mal-formatted sequent'538                print e539# Usage: argv[0] lexiconfile540def main(argv):541    if (len(argv) != 2) and (len(argv) != 4):542        print 'Usage:', argv[0], '<lexicon_file>'543        print 'Usage:', argv[0], '<lexicon_file> <input_file> <output file>'544        return545    lex = Lexicon()546    try: lex.load(open(argv[1], 'r'))547    except:548        print "Error loading lexicon file"549        return550    if len(argv) == 2:551        mainloop(sys.stdin, sys.stdout, lex, 0, 1)552    else:553        out = open(argv[3], 'w')554        print >>out, '\documentclass{article}'555        print >>out, '\usepackage{fullpage}'556        print >>out, '\\begin{document}'557        print >>out558        mainloop(open(argv[2], 'r'), out, lex, 1, 1)559        print >>out560        print >>out, '\\end{document}'561if __name__ == '__main__':562    main(sys.argv)...
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