# ._cv_part guppy.heapy.AbstractAlgebra

import unittest
from guppy.heapy.test import support


class AA:
    def __mul__(self, other):
        return BOAPP('op', self, other)

    def __add__(self, other):
        return BOAPP('op2', self, other)

    def __eq__(self, other):
        return BOAPP('eq', self, other)


class ANAME(AA):
    def __init__(self, name):
        self.name = name

    def __str__(self):
        return self.name


class BOAPP(AA):
    def __init__(self, funcname, *args):
        self.funcname = funcname
        self.args = args

    def __str__(self):
        return '%s(%s)' % (self.funcname, ','.join([str(x) for x in self.args]))


class AlgebraicStructure:
    def __init__(self, mod, range, *ops, **kwds):
        self.mod = mod
        self.range = range
        self.ops = []
        for i, op in enumerate(ops):
            if hasattr(op, 'range') and op.range == range:
                pass
            elif callable(op) or op in mod.LE.binary_operation_name:
                opkwds = {}
                if 'identity' in kwds:
                    opkwds['identity'] = kwds['identity']
                op = mod.binary_operation.new(range, op, **opkwds)
            else:
                raise TypeError('%s is not a valid operation' % op)
            self.ops.append(op)
            setattr(self, 'op%d' % i, op)
        self.numops = len(self.ops)

        for k, v in list(kwds.items()):
            setattr(self, k, v)

    def eq(self, x, y, *more):
        if not x == y:
            return False
        for m in more:
            if not y == m:
                return False
        return True


class BinaryOperation:
    def __init__(self, range, op, identity=None, invert=None, zeros=None, zero=None, complement=None):
        self.range = range
        self.arity = 2
        if isinstance(op, str):
            opname = op
            func = eval('lambda x,y: x %s y' % opname)
        elif callable(op):
            func = op
            opname = str(func)
        self.opname = opname
        self.__call__ = func
        if identity is not None:
            self.identity = identity
        if invert is not None:
            self.invert = invert
        if zeros is not None:
            self.zeros = zeros

        if zero is not None:
            self.zero = zero

        if complement is not None:
            self.complement = complement

        # mimic alg. st.

        self.op0 = self

    def eq(self, x, y, *more):
        if not x == y:
            return False
        for m in more:
            if not y == m:
                return False
        return True


class BinaryAlgebraicStructureFamily:
    def __call__(self, names, cond):
        di = {}
        for name in names:
            di[name] = ANAME(name)
        c = eval(cond, di)
        assert isinstance(c, AA)

        def gentestfunc(binop):
            d = {'op': binop}
            expr = 'lambda %s:%s' % (','.join(names), c)

            d = {'op': binop,
                 'eq': lambda x, y: x == y}

            f = eval(expr, d)

            def testfunc(env, x, y):
                if not f(x, y):
                    return env.failed('not %s in %s' % ((x, y), expr))
                return True

            return testfunc
        return self.Set(self, (gentestfunc, cond))

    def c_test_contains(self, a, b, env):
        f, name = a.arg
        return env.forall_pairs(b.range,
                                f(b),
                                'not in %s' % name)


class TernaryAlgebraicStructureFamily:
    def __call__(self, names, cond):
        di = {}
        for name in names:
            di[name] = ANAME(name)
        c = eval(cond, di)
        assert isinstance(c, AA)

        def gentestfunc(binop):
            d = {'op': binop}
            expr = 'lambda %s:%s' % (','.join(names), c)

            d = {'op': binop,
                 'eq': lambda x, y: x == y}

            f = eval(expr, d)

            def testfunc(env, x, y, z):
                if not f(x, y, z):
                    return env.failed('not %s in %s' % ((x, y, z), expr))
                return True

            return testfunc
        return self.Set(self, (gentestfunc, cond))

    def c_test_contains(self, a, b, env):
        f, name = a.arg
        return env.forall_triples(b.range,
                                  f(b),
                                  'not in %s' % name)


class DistributiveAlgebraicStructureFamily:
    def __call__(self, names, cond):
        di = {}
        for name in names:
            di[name] = ANAME(name)
        c = eval(cond, di)
        assert isinstance(c, AA)

        def gentestfunc(binop1, binop2):
            d = {'op': binop1, 'op2': binop2}
            expr = 'lambda %s:%s' % (','.join(names), c)

            d = {'op': binop1,
                 'op2': binop2,
                 'eq': lambda x, y: x == y}

            f = eval(expr, d)

            def testfunc(env, x, y, z):
                if not f(x, y, z):
                    return env.failed('not %s in %s' % ((x, y, z), expr))
                return True

            return testfunc
        return self.Set(self, (gentestfunc, cond))

    def c_test_contains(self, a, b, env):
        f, name = a.arg
        op1, op2 = b
        if isinstance(op1, tuple):
            op1 = self.specmod.AA.binary_operation.new(*op1)
        if isinstance(op2, tuple):
            op2 = self.specmod.AA.binary_operation.new(*op2)
        if not op1.range == op2.range:
            return env.failed('Not the same range')
        return env.forall_triples(op1.range,
                                  f(op1, op2),
                                  'not in %s' % name)


class _GLUECLAMP_:
    def _get_abelian_group(self):
        return self.Spec.adaptuple(
            self.group.new,
            self.group & self.Spec.attr('op0', self.commutative))

    def _get_associative(self):
        return self.asuf('xyz', 'x * (y * z) == (x * y) * z')

    def algestruct(self, S, *args, **kwds):
        S = self.Spec.setcast(S)
        return AlgebraicStructure(self, S, *args, **kwds)

    def asuf(self, names, cond):
        if len(names) == 2:
            x = self.BinaryAlgebraicStructure(names, cond)
        elif len(names) == 3:
            x = self.TernaryAlgebraicStructure(names, cond)
        else:
            raise ValueError
        return self.Spec.adaptuple(self.binary_operation.new, x)

    def _get_binary_operation(self):
        def binop(S, func, **kwds):
            S = self.Spec.setcast(S)
            if isinstance(func, BinaryOperation) and func.range == S and not kwds:
                return func
            return BinaryOperation(S, func, **kwds)

        e = self.Spec
        return e.adaptuple(
            binop,
            e.expset("""(
                attr('range', set) &
                attr('arity', equals(2)) &
                expset('''mapping(range, range, '->', range)''', 'range')
        )"""))

    def _get_binary_relation(self):
        return self.relation

    def _get_BinaryAlgebraicStructure(self):
        return self.family(BinaryAlgebraicStructureFamily)

    def _get_boolean_algebra(self):
        def boolalg(set, op0, op1, complement, id0, id1):
            if complement in ('~', '-', 'not'):
                complement = eval('lambda x: %s x' % complement)
            return self.algestruct(
                set,
                self.binary_operation.new(
                    set, op0, identity=id0, zero=id1, complement=complement),
                self.binary_operation.new(
                    set, op1, identity=id1, zero=id0, complement=complement)
            )

        e = self.Spec
        return (e.adaptuple(
            boolalg,
            e.attr('op0', e.AA.commutative & e.AA.complemented & e.AA.monoid) &
            e.attr('op1', e.AA.commutative & e.AA.complemented & e.AA.monoid) &
            e.attr(('op0', 'op1'), e.AA.distributive) &
            e.attr(('op1', 'op0'), e.AA.distributive) &
            e.attr(('op0.zero', 'op1.identity'), e.LE.eq) &
            e.attr(('op1.zero', 'op0.identity'), e.LE.eq)
        ))

    def _get_complemented(self):
        # Not a standard term: expresses for an op op, that
        # x op x' = op.zero where x' = op.complement
        def p(env, x):
            op = x.op0
            zero = op.zero
            f = op
            complement = f.complement
            return env.forall(x.range, lambda env, y:
                              x.eq(f(y, complement(y)), zero), 'complemented')
        return self.Spec.predicate(p, 'complemented')

    def _get_commutative(self):
        return self.asuf('xy', 'x * y == y * x')

    def _get_DistributiveAlgebraicStructure(self):
        return self.family(DistributiveAlgebraicStructureFamily)

    def _get_distributive(self):
        return self.distributive_1 & self.distributive_2

    def _get_distributive_1(self):
        return self.DistributiveAlgebraicStructure(
            'xyz', 'x * (y + z) == (x * y) + (x * z)')

    def _get_distributive_2(self):
        return self.DistributiveAlgebraicStructure(
            'xyz', '(x + y) * z == (x * z) + (y * z)')

    def _get_field(self):
        e = self.Spec
        AA = self

        class Field:
            def __init__(self, S, add, mul, neg, invert, zero, one):
                if neg in ('-', '~', 'not'):
                    neg = eval('lambda x: %s x' % neg)

                self.range = S
                self.ring = AA.ring.new(S, add, mul, neg, zero)
                self.mulgroup = AA.group.new(
                    S - e.equals(zero), mul, invert, one)

        return e.adaptuple(
            Field,
            e.attr('ring', e.AA.ring) &
            e.attr('mulgroup', e.AA.abelian_group))

    def _get_group(self):
        def mkgroup(S, op, invert, identity):
            if invert in ('-', '~', 'not'):
                invert = eval('lambda x: %s x' % invert)
            return self.algestruct(S, op, identity=identity, invert=invert)

        def p(env, g):
            try:
                inv = g.invert
            except AttributeError:
                env.failed("no invert function")
            f = g.op0
            return env.forall(g.range, lambda env, x:
                              g.eq(f(inv(x), x), f(x, inv(x)), g.identity))

        e = self.Spec
        return e.adaptuple(
            mkgroup,
            self.monoid & self.Spec.predicate(p, 'group'))

    def _get_latticeform(self):
        # latticeform is a representation category

        class RelationSpec:

            def _get_spec_quadruple(self, e):
                binop = (e.boolean << (e.PyObject, e.PyObject) |
                         e.AA.LE.binary_operation_name)
                return e.cprod(
                    e.LE.setcastable,
                    e.relation.fuop,
                    binop,
                    binop)

            def _get_spec_struct(self, e):
                return (attr('range', e.set),
                        attr('LE'),
                        attr('GLB'),
                        attr('LUB')
                        )

            def map_quadruple_to_struct(self, e, xxx_todo_changeme):
                (S, LE, GLB, LUB) = xxx_todo_changeme
                S = e.setcast(S)
                LE = e.relation.paxa.fromuniversal(
                    (e.relation.defipair, (S, LE)))
                GLB = e.AA.binary_operation.new(S, GLB)
                LUB = e.AA.binary_operation.new(S, LUB)

                class C:
                    pass
                c = C()
                c.range = S
                c.LE = LE
                c.GLB = GLB
                c.LUB = LUB
                return c

        return self.Spec.repcat(RelationSpec)

    def _get_lattice(self):
        e = self.Spec

        def p(env, lat):
            def test(R, op, name):
                def testlb(env, x, y):
                    lb = op(x, y)
                    if not (R(lb, x) and R(lb, y)):
                        return env.failed('not an %s' % name)
                    if R(x, lb) or R(y, lb):
                        return True  # redundant fast way out

                    return env.forall(lat.range,
                                      lambda env, lb2:
                                      (not (R(lb2, x) and R(lb2, y)) or
                                       R(lb2, lb)))
                return env.forall_pairs(lat.range, testlb)

            return (test(lambda x, y: env.contains(lat.LE, (x, y)), lat.GLB, 'lower bound') and
                    test(lambda x, y: env.contains(lat.LE, (y, x)), lat.LUB, 'upper bound'))

        return (
            e.abstractset(
                self.latticeform.struct.fromuniversal,
                e.attr('range') &
                e.attr('LE', e.AA.partial_order.paxa) &
                e.attr('GLB', e.AA.binary_operation) &
                e.attr('LUB', e.AA.binary_operation) &
                e.predicate(p, 'lattice')
            )
        )

    def _get_LE(self):
        return self.Spec.LocalEnv(self.Spec, self._Specification_.LocalEnvExpr)

    def _get_monoid(self):
        def p(env, x):
            op = x.op0
            e = op.identity
            f = op
            return env.forall(x.range, lambda env, y:
                              x.eq(f(e, y), f(y, e), y))

        def mkmonoid(S, op, identity):
            return self.algestruct(S, op, identity=identity)

        e = self.Spec
        return e.adaptuple(
            mkmonoid,
            e.attr('op0', self.associative) &
            e.predicate(p, 'monoid'))

    def _get_ring(self):
        def mkring(S, add, mul, neg, zero):
            if neg in ('-', '~', 'not'):
                neg = eval('lambda x: %s x' % neg)
            return self.algestruct(
                S,
                self.binary_operation.new(S, add, identity=zero, invert=neg),
                self.binary_operation.new(S, mul))

        e = self.Spec
        return (e.adaptuple(
            mkring,
            (e.attr('op0', e.AA.abelian_group) &
             e.attr('op1', e.AA.semigroup) &
             e.attr(('op1', 'op0'), e.AA.distributive)
             )))

    def _get_semigroup(self):
        return self.Spec.adaptuple(self.binary_operation.new, self.Spec.attr('op0', self.associative))

    def _get_Spec(self):
        return self._parent.Spec

    def _get_TernaryAlgebraicStructure(self):
        return self.family(TernaryAlgebraicStructureFamily)

    def family(self, F):
        class C(F, self.Spec.SpecFamily):
            def __init__(innerself, *args, **kwds):
                self.Spec.SpecFamily.__init__(innerself, *args, **kwds)
                try:
                    ini = F.__init__
                except AttributeError:
                    pass
                else:
                    ini(innerself, *args, **kwds)
        C.__name__ = F.__name__
        return self.Spec.family(C)

    #
    # 2. Relations and their properties
    #

    def relpropred(self, s, name):
        return self.relprop(self.Spec.predicate(s, name))

    def _get_antisymmetric(self):
        # Assumes implicitly equality relation via '==' operation.
        # Could be generalized, see notes Jan 19 2005
        return self.relpropred(
            lambda env, R: env.forall_pairs(
                R.range,
                lambda env, x, y:
                (not (env.contains(R, (x, y)) and env.contains(R, (y, x))) or
                 x == y)),
            "antisymmetric wrt '==' op")

    def _get_equivalence_relation(self):
        return (
            self.reflexive &
            self.symmetric &
            self.transitive)

    def _get_irreflexive(self):
        return self.relpropred(
            lambda env, R: env.forall(R.range,
                                      lambda env, x: env.test_contains_not(R, (x, x), 'irrreflexive')),
            'reflexive')

    def _get_partial_order(self):
        return (
            self.reflexive &
            self.antisymmetric &
            self.transitive)

    def _get_total_order(self):
        return (
            self.partial_order &
            self.total_relation)

    def _get_total_relation(self):
        # Nonstandard name (?)
        return self.relpropred(
            lambda env, R: env.forall_pairs(
                R.range,
                lambda env, x, y:
                (env.contains(R, (x, y)) or env.contains(R, (y, x)))),
            "total_relation: xRy or yRx for all x,y in A")

    def _get_reflexive(self):
        return self.relpropred(
            lambda env, R: env.forall(
                R.range,
                lambda env, x: env.test_contains(R, (x, x), 'reflexive')),
            'reflexive')

    def _get_symmetric(self):
        return self.relpropred(
            lambda env, R: env.forall(
                R,
                lambda env, v:
                env.test_contains(R, (v[1], v[0]), 'symmetric')),
            'symmetric')

    def _get_transitive(self):
        return self.relpropred(
            lambda env, R: env.forall(
                R,
                lambda env, v:
                env.forall(R.range,
                           lambda env, z:
                           (not env.contains(R, (v[1], z)) or
                            env.test_contains(R, (v[0], z), 'transitive')))),
            'transitive')

    def relprop(self, s):
        e = self.Spec
        return e.abstractset(
            e.relation.paxa.fromuniversal,
            s)

        return e.adaptuple(
            self.relation.new,
            e.attr(('domain', 'range'), e.LE.eq) &
            s)


class _Specification_:
    """
        Specification of some general algebraic structures
    """

    def GetExamples(self, te, obj):
        AA = obj
        LE = AA.LE
        env = te.mod
        S3 = [
            [0, 1, 2, 3, 4, 5],
            [1, 0, 4, 5, 2, 3],
            [2, 5, 0, 4, 3, 1],
            [3, 4, 5, 0, 1, 2],
            [4, 3, 1, 2, 5, 0],
            [5, 2, 3, 1, 0, 4]]

        Type = env.Type
        asexs = [
            # Too slow now with many examples, cubic complexity for associative etc.
            # sets are tested more extensively elsewhere
            #(env.set, env.set, env.empty, ~env.empty, env.equals(0), env.equals(0, 1), env.equals(1)),
            (env.set,           env.set, env.empty),
            (env.Type.Int,      -1, 0, 1),
            #(env.Type.Float,   -2.5,-1.0, 0.0, 1.3, 2.0),
            #(env.Type.Float,   -2.0,-1.0, 0.0, 1.0, 2.0),
            (env.Type.Float,    -1.0, 0.0),
            (env.Type.String,   '', '1234%^', 'asdf*&('),
            (LE.algebraic_class, AA.binary_operation),
            (AA.binary_operation,
             (int, '*')),
            (~AA.binary_operation,
             (env.equals(1), '+')),
            (AA.commutative,    (int, '*')),
            (~AA.commutative,   (int, '-')),
            (AA.associative,    (int, '*')),
            (~AA.associative,   (int, '-')),
            (AA.distributive,   ((int, '*'), (int, '-'))),
            (AA.distributive_1, ((int, '*'), (int, '-'))),
            (AA.distributive_2, ((int, '*'), (int, '-'))),
            (~AA.distributive,  ((int, '*'), (int, '|'))),
            (~AA.distributive_1, ((int, '*'), (int, '|'))),
            (~AA.distributive_2, ((int, '*'), (int, '|'))),

            (AA.semigroup,      (int, '*')),
            (AA.semigroup,      (str, '+')),
            (~AA.semigroup,     (int, '-')),
            (AA.monoid,         (int, '*', 1)),
            (AA.monoid,         (str, '+', '')),
            (~AA.monoid,        (int, '*', 0)),
            (AA.group,          (int, '+', '-', 0)),
            (~AA.group,         (int, '*', '-', 1)),
            (AA.abelian_group,  (int, '+', '-', 0)),
            (AA.group & ~AA.abelian_group, (
                env.equals(0, 1, 2, 3, 4, 5),
                lambda x, y: S3[x][y],
                lambda x:[0, 1, 2, 3, 5, 4][x],
                0)),
            (AA.ring,           (int, '+', '*', '-', 0)),
            (~AA.ring,          (str, '+', '*', '-', 0),
             (int, '*', '*', '-', 0),
             (int, '+', '+', '-', 0),
             (int, '+', '*', '~', 0),
             (int, '+', '*', '-', 1)),
            (AA.field,          (float, '+', '*', '-', lambda x:1.0/x, 0.0, 1.0)),
            (~AA.field,         (float, '+', '*', '-', lambda x:2.0/x, 0.0, 1.0)),
            (AA.boolean_algebra, (env.equals(False, True), 'or', 'and', 'not', False, True),
             (int, '|', '&', '~', 0, ~0),
             (env.set, '|', '&', '~', env.empty, ~env.empty)
             ),
            (~AA.boolean_algebra,
             # Mutate each argument..
             (env.equals(True, True), 'or', 'or', 'not', False, True),
             (env.equals(False, True), 'and',
              'and', 'not', False, True),
             (env.equals(False, True), 'or',
              'or', 'not', False, True),
             (env.equals(False, True), 'or',
              'and', '~', False, True),
             (env.equals(False, True), 'or',
              'and', 'not', True, True),
             (env.equals(False, True), 'or',
              'and', 'not', False, False),
             )
        ]

        ex = []
        for a in asexs:
            name = a[0]
            exs = list(a[1:])
            if isinstance(name, str):
                x = env
                names = name.split('.')
                for name in names:
                    x = getattr(x, name)
            else:
                x = name
            ex.append((x, exs))

        return ex

    class LocalEnvExpr:
        exec("""\
if 1:
    binary_operation_name       <is> equals(
        '+', '-', '*', '/', '%', '|', '&', '**', '<<', '>>')
    algebraic_class     <is>    (setof(Type.Tuple) &
                                 attr('new', callable))


    relation_class      <is>    (setof( setof(any*any) |
                                        Type.Tuple))

    relational_operator_name <is>       equals(
    '<', '<=', '>', '>=', '==', '!=', 'in', 'not in', 'is', 'is not')
""".replace('<is>', ' = lambda IS: '))

    class GlueTypeExpr:
        exec("""
if 1:
    abelian_group       <in>     setof(AA.group)
    associative         <in>    setof(AA.binary_operation)
    binary_operation    <in>     doc('''
A \emp{binary operation} $*$ on a set $S$ is a function $*: S \cross S \mapsto S$.
The element in $S$ assigned to $(x, y)$ is denoted $x*y$.
\citemh(p.21)
''') & LE.algebraic_class
    boolean_algebra     <in>    LE.algebraic_class
    commutative         <in>    LE.algebraic_class
    distributive        <in>    setof(cprod(AA.binary_operation, AA.binary_operation))
    distributive_1      <in>    setof(cprod(AA.binary_operation, AA.binary_operation))
    distributive_2      <in>    setof(cprod(AA.binary_operation, AA.binary_operation))
    field               <in>    LE.algebraic_class
    group               <in>    (LE.algebraic_class & doc('''
'''     ))
    monoid              <in>    LE.algebraic_class
    ring                <in>    (LE.algebraic_class,
                                attr('new', argnames('S', 'add', 'mul', 'neg', 'zero')))
    semigroup           <in>    LE.algebraic_class

""".replace('<in>', '= lambda IN:'))

# Relations and functions

    def GetExamples(self, te, obj):
        AA = obj
        LE = AA.LE
        e = te.mod
        S = e.iso(0, 1, 2)

        def subsetof(x, y):
            # Subset relation treating ints as bitsets
            return x & y == x

        def D(S, op):
            return (e.relation.defipair, (S, op))

        def L(*args):
            return (AA.latticeform.quadruple, args)

        asexs = [
            (e.PyObject,                0),  # why not ()?
            #(AA.relation,              D(S, '==')),
            (AA.reflexive,              D(S, '==')),
            #(AA.reflexive,             AA.relation.new(S, '<=')),
            (~AA.reflexive,             D(S, '<')),
            (AA.symmetric,              D(S, '==')),
            (~AA.symmetric,             D(S, '<=')),
            (AA.transitive,             D(S, '<')),
            (~AA.transitive,            D(S, '!=')),
            (AA.irreflexive,            D(S, '<')),
            (~AA.irreflexive,           D(S, '<=')),
            (AA.antisymmetric,          D(S, '<=')),
            (~AA.antisymmetric,         D(S, '!=')),
            (AA.total_relation,         D(S, '<=')),
            (~AA.total_relation,        D(S, '!=')),
            (AA.equivalence_relation,   D(S, '==')),
            (~AA.equivalence_relation,  D(S, '<=')),
            (AA.partial_order,          D(S, subsetof)),
            (~AA.partial_order,         D(S, '<')),
            (AA.total_order,            D(S, '<=')),
            (~AA.total_order,           D(S, subsetof)),

            (e.Type.Int,                0, 1, 2, 3),
            (AA.lattice,                L(int, '<=', min, max)),
            (~AA.lattice,               L(int, '<=', '&', max)),
            (~AA.lattice,               L(int, '<=', min, '|')),
            (AA.lattice,                L(int, lambda x, y: x & y == x, '&', '|')),
            (~AA.lattice,               L(int, lambda x, y: x & y == x, min, '|')),
            (~AA.lattice,               L(int, lambda x, y: x & y == x, '&', max)),

            (AA.lattice.quadruple,      (int, '<=', min, max)),

        ]
        return asexs

    class GlueTypeExpr:
        exec("""\
if 1:
    reflexive           <in>    doc('x R x for every x in A',
                                AA.LE.relation_class)
    symmetric           <in>    doc('x R y implies y R x, for all x, y in A',
                                AA.LE.relation_class)
    transitive          <in>    doc('x R y, y R z implies x R z, for all x, y, z in A',
                                AA.LE.relation_class)
    irreflexive         <in>    doc('not (x R y), for all x in A',
                                AA.LE.relation_class)
    antisymmetric       <in>    doc('x R y, y R x implies x == y, for all x, y in A',
                                AA.LE.relation_class)
    total_relation      <in>    doc('x R y or y R x, for all x, y in A',
                                AA.LE.relation_class)
    equivalence_relation<in>    doc('Reflexive, symmetric and transitive',
                                AA.LE.relation_class)
    partial_order       <in>    doc('Reflexive, antisymmetric and transitive',
                                AA.LE.relation_class)
    total_order         <in>    doc('Partial order and x R y or y R x, for all x, y in A',
                                AA.LE.relation_class)

    lattice             <in>    attr('quadruple', doc('''\
Tuples (S, R, V, A), where:
        S:      set or convertible to set, i.e. 'setcastable'
        R:      relation operator on S
        V:      binary operator on S
        A:      binary operator on S

R, V and A are either operator symbols or functions.

(S, R) forms a partial order such that
every pair x, y of elements in S have a greatest
lower bound GLB and a least upper bound LUB.

The GLB is given by V(x, y) or x V y depending on if V is
a function or operator symbol. Likewise, ULB is given
by A(x, y) or x A y.

For example, these are lattice specifications:

(int, '<=', min, max)
(int, lambda x, y: x & y == x, '&', '|')

''',                            setof(tupleform(
                        ('S', 'R', 'V', 'A'),
                        attr('S', SPLE.setcastable) &
                        expset('''\
attr('R', AA.LE.relational_operator_name | boolean<<(S, S)) &
attr('V', AA.LE.binary_operation_name | setcast(S)<<(S, S)) &
attr('A', AA.LE.binary_operation_name | setcast(S)<<(S, S))
''',                     'S')
                        ))))
""".replace('<in>', '=lambda IN:'))


class TestCase(support.TestCase):
    pass


class FirstCase(TestCase):
    def test_1(self):
        Spec = self.heapy.Spec
        TestEnv = Spec.mkTestEnv(_Specification_)
        # print SpecSpec.getstr(1000)

        TestEnv.test(self.guppy.heapy.AbstractAlgebra)


if __name__ == '__main__':
    support.run_unittest(FirstCase, 1)
