def preproof():
while True:
yield (proof_kwd() << shift_eq >> (
lambda pk: choice([
use(suppress()) << shift_eq >> (lambda supp: choice([
intf.locate(kwd('BY')) << times2 >> only() << times2 >>
use(usebody()) << times >> read_method() << apply >>
(lambda args: tla_ast.PreBy(supp, args[0][0][1], args[0][
1], args[1])),
intf.locate(
kwd('OBVIOUS') << second >> read_method() << apply >>
(lambda meth: tla_ast.PreObvious(supp, meth)))
])),
# locate (kwd "OMITTED" <!> (PreOmitted Explicit)) ;
intf.locate(
kwd('OMITTED') << bang >> tla_ast.PreOmitted(tla_ast.
Explicit())),
# locate begin
# preno <**> use prestep
# <$> (fun (pn, stp) ->
# PreStep (pk, pn, stp))
# end ;
intf.locate(preno() << times2 >> use(prestep()) << apply >>
(lambda pn_stp: tla_ast.PreStep(
pk, pn_stp[0], pn_stp[1])))
])))
def apply_def(local):
# let ex = if Option.is_some l then Local else Export in
if local is None:
ex = nodes.Export()
else:
ex = nodes.Local()
def choices():
# NOTE: The order of choices was INSTANCE, def
# changed for efficiency reasons
#
# use (defn false)
yield use(
ep.defn(False)
# <$> (fun df -> [ Definition (df, User, Hidden, ex) ]) ;
) << apply >> (
lambda df:
[nodes.Definition(df, nodes.User(), nodes.Hidden(), ex)])
# use (instance false)
yield use(
ep.instance(False)
# <$> (fun inst -> [ Anoninst (inst, ex) ]) ;
) << apply >> (lambda inst: [nodes.AnonymousInstance(inst, ex)])
return choice_iter(choices)
def suppress():
while True:
yield choice([
intf.pragma(punct('_') << or_ >> intf.ident('suppress')) << bang >>
tla_ast.Suppress(),
succeed(tla_ast.Emit())
])
def proof():
while True:
yield choice([
star1(use(preproof())),
intf.locate(succeed(tla_ast.PreOmitted(tla_ast.Implicit()))) <<
apply >> (lambda pp: [pp])
]) << apply >> toplevel
def apply_theorem_proof(args):
(((name, body), meth), prf) = args
ctx = body.context
goal = body.goal
goal_ = with_meth(goal, meth)
body_ = nodes.Sequent(ctx, goal_)
return [nodes.Theorem(name, body_, prf)]
def f(form):
if isinstance(form, tokens.ST):
step_name = form.kind
step_label = form.string
ndots = form.i
if isinstance(step_name, tokens.StepStar):
return tla_ast.StepStar(step_label)
elif isinstance(step_name, tokens.StepPlus):
return tla_ast.StepPlus(step_label)
elif isinstance(step_name, tokens.StepNum):
return tla_ast.StepNum(step_name.value, step_label)
else:
raise TypeError(step_name)
else:
return None
def apply_module(nm_exs_mus):
(name, extends), modunits = nm_exs_mus
extends = list() if extends is None else extends
return nodes.Module(name=name,
extendees=extends,
instancees=list(),
body=[i for j in modunits for i in j])
def choices():
# NOTE: The order of choices was INSTANCE, def
# changed for efficiency reasons
#
# use (defn false)
yield use(
ep.defn(False)
# <$> (fun df -> [ Definition (df, User, Hidden, ex) ]) ;
) << apply >> (
lambda df:
[nodes.Definition(df, nodes.User(), nodes.Hidden(), ex)])
# use (instance false)
yield use(
ep.instance(False)
# <$> (fun inst -> [ Anoninst (inst, ex) ]) ;
) << apply >> (lambda inst: [nodes.AnonymousInstance(inst, ex)])
def sequent():
while True:
yield choice([
use(ep.sequent(False)),
use(ep.expr(False)) << apply >>
(lambda e: tla_ast.Sequent(list(), e))
])
def f():
return choice([
# ['CONSTANT' | 'CONSTANTS'] opdecl (',' opdecl)*
kwd('CONSTANT') << or_ >> kwd('CONSTANTS') << second_commit >>
sep1(punct(','), use(ep.opdecl())) << apply >>
(lambda cs: [nodes.Constants(cs)]),
# 'RECURSIVE' opdecl (',' opdecl)*
kwd('RECURSIVE') << second_commit >> sep1(
punct(','), use(ep.opdecl())) << apply >>
(lambda cs: [nodes.Recursives(cs)]),
# ['VARIABLE' | 'VARIABLES'] anyident (',' anyident)*
kwd('VARIABLE') << or_ >> kwd('VARIABLES') << second_commit >>
sep1(punct(','), locate(intf.anyident())) << apply >>
(lambda vs: [nodes.Variables(vs)])
])
def f():
return (
(kwd('THEOREM') << or_ >> kwd('PROPOSITION') << or_ >>
kwd('COROLLARY') << or_ >> kwd('LEMMA')) << second_commit >>
optional(intf.locate(intf.anyident() << first >> punct('==')))
<< times >> choice([
use(ep.sequent(False)),
use(ep.expr(False)) << apply >>
(lambda e: nodes.Sequent(list(), e))
]) << times >> optional(use(pfp.method_prs_read_method())) <<
times >> use(pfp.proof()) << apply >> apply_theorem_proof)
def choices():
# choice [
# choice [
# (kwd "CONSTANT" <|> kwd "CONSTANTS") >*>
# sep1 (punct ",") (use opdecl)
# <$> (fun cs -> [ Constants cs ]) ;
#
# (kwd "RECURSIVE") >*>
# sep1 (punct ",") (use opdecl)
# <$> (fun cs -> [ Recursives cs ]) ;
#
# (kwd "VARIABLE" <|> kwd "VARIABLES") >*>
# sep1 (punct ",") (locate anyident)
# <$> (fun vs -> [ Variables vs ]) ;
# ] ;
# variable and constant declarations, and recursive operators
def f():
return choice([
# ['CONSTANT' | 'CONSTANTS'] opdecl (',' opdecl)*
kwd('CONSTANT') << or_ >> kwd('CONSTANTS') << second_commit >>
sep1(punct(','), use(ep.opdecl())) << apply >>
(lambda cs: [nodes.Constants(cs)]),
# 'RECURSIVE' opdecl (',' opdecl)*
kwd('RECURSIVE') << second_commit >> sep1(
punct(','), use(ep.opdecl())) << apply >>
(lambda cs: [nodes.Recursives(cs)]),
# ['VARIABLE' | 'VARIABLES'] anyident (',' anyident)*
kwd('VARIABLE') << or_ >> kwd('VARIABLES') << second_commit >>
sep1(punct(','), locate(intf.anyident())) << apply >>
(lambda vs: [nodes.Variables(vs)])
])
yield ((tokens.KWD, ), f)
# optional (kwd "LOCAL") >>= begin fun l ->
# let ex = if Option.is_some l then Local else Export in
# choice [
# use (instance false)
# <$> (fun inst -> [ Anoninst (inst, ex) ]) ;
#
# use (defn false)
# <$> (fun df -> [ Definition (df, User, Hidden, ex) ]) ;
# ]
# end ;
yield optional(kwd('LOCAL')) << shift_eq >> apply_def
# use Proof.Parser.suppress
# <*> (kwd "USE" <|> kwd "HIDE")
# <**> use Proof.Parser.usebody
# <$> (fun ((supp, uh), use) -> match uh with
# | "USE" -> [ Mutate (`Use (supp = Proof.Parser.Suppress), use) ]
# | _ -> [ Mutate (`Hide, use) ]) ;
def f():
return (use(pfp.suppress()) << times >>
(kwd('USE') << or_ >> kwd('HIDE')) << times2 >>
pfp.usebody() << apply >> apply_use_hide)
yield ((
tokens.KWD('USE'),
tokens.KWD('HIDE'),
tokens.PUNCT('_'),
tokens.ID('suppress'),
), f)
# (kwd "AXIOM" <|> kwd "ASSUME" <|> kwd "ASSUMPTION") >*>
# optional (locate anyident <<< punct "==") <**> use (expr false)
# <*> optional (use Method_prs.read_method)
# <$> (fun ((nm, e), meth) -> [ Axiom (nm, with_meth e meth) ]) ;
def f():
# RULE: ('AXIOM' | 'ASSUME' | 'ASSUMPTION')
# [anyident '=='] expr [read_method]
return (
(kwd('AXIOM') << or_ >> kwd('ASSUME') << or_ >>
kwd('ASSUMPTION')) << second_commit >> optional(
intf.locate(intf.anyident() << first >> punct('==') <<
times2 >> use(ep.expr(False)))) << times >>
optional(use(pfp.read_method())) << apply >> apply_axiom)
yield ((
tokens.KWD('AXIOM'),
tokens.KWD('ASSUME'),
tokens.KWD('ASSUMPTION'),
), f)
# (kwd "THEOREM" <|> kwd "PROPOSITION" <|>
# kwd "COROLLARY" <|> kwd "LEMMA") >*>
# optional (locate anyident <<< punct "==")
# <*> choice [ use (sequent false) ;
# use (expr false)
# <$> (fun e -> { context = Deque.empty ; active = e }) ]
# <*> optional (use Method_prs.read_method)
# <*> use Proof.Parser.proof
# <$> (fun (((nm, bod), meth), prf) ->
# [ Theorem (nm, {
# bod with active = with_meth bod.active meth },
# 0, prf, prf, empty_summary) ]) ;
def f():
return (
(kwd('THEOREM') << or_ >> kwd('PROPOSITION') << or_ >>
kwd('COROLLARY') << or_ >> kwd('LEMMA')) << second_commit >>
optional(intf.locate(intf.anyident() << first >> punct('==')))
<< times >> choice([
use(ep.sequent(False)),
use(ep.expr(False)) << apply >>
(lambda e: nodes.Sequent(list(), e))
]) << times >> optional(use(pfp.method_prs_read_method())) <<
times >> use(pfp.proof()) << apply >> apply_theorem_proof)
yield ((
tokens.KWD('THEOREM'),
tokens.KWD('PROPOSITION'),
tokens.KWD('COROLLARY'),
tokens.KWD('LEMMA'),
), f)
#
# enabled (punct "----" <*> kwd "MODULE")
# >*> use parse <$> (fun m -> [ Submod m ]) ;
yield (enabled(punct('----') << times >> kwd('MODULE')) <<
second_commit >> use(parse()) << apply >>
(lambda mod: [nodes.Submodule(mod)]))
#
# punct "----" <!> [] ;
yield intf.punct('----') << bang >> list()
def to_proof(currlv, arg):
# | [] ->
if not arg:
# (Omitted Implicit @@ currlv, [])
omitted = tla_ast.Omitted(tla_ast.Implicit())
return (omitted, list())
# | {core = PreBy (supp, onl, use, meth)} as p :: ps ->
elif isinstance(arg[0], tla_ast.PreBy):
p = arg[0]
ps = arg[1:]
supp = p.supp
only = p.only
usable = p.usable
meth = p.method
# let p = By (use, onl = Only) @@ p in
p = tla_ast.By(usable, isinstance(only, tla_ast.Only))
# let p = Property.assign p Props.step
# (Unnamed (currlv.core, 0)) in
p.step_number = tla_ast.Unnamed(currlv, 0)
# (annotate supp meth p, ps)
annotate(supp, meth, p)
return (p, ps)
# | {core = PreObvious (supp, meth)} as p :: ps ->
elif isinstance(arg[0], tla_ast.PreObvious):
p = arg[0]
ps = arg[1:]
supp = p.supp
meth = p.method
# let p = Obvious @@ p in
obvious = tla_ast.Obvious()
# (annotate supp meth p, ps)
annotate(supp, meth, obvious)
return (obvious, ps)
# | {core = PreOmitted om} as p :: ps ->
elif isinstance(arg[0], tla_ast.PreOmitted):
p = arg[0]
ps = arg[1:]
om = p.omission
# (Omitted om @@ p, ps)
omitted = tla_ast.Omitted(om)
return (omitted, ps)
else:
# | ps -> begin
ps = arg
# try
try:
# let (ss, qp, ps) = to_steps ~first:true currlv ps in
(ss, qp, ps) = to_steps(first=True, currlv=currlv, ps=ps)
# let sloc = List.fold_left begin
# fun l s -> Loc.merge l (Util.get_locus s)
# end (try
# Util.get_locus qp.core
# with _ -> Util.get_locus
# (get_qed_proof qp.core)) ss in
# TODO: locus
# let prf = Util.locate (Steps (ss, qp.core)) sloc in
prf = tla_ast.Steps(ss, qp)
# let prf = Property.assign prf Props.step
# (Property.get qp Props.step) in
prf.step_number = qp.step_number
# (prf, ps)
return (prf, ps)
# with Backtrack ->
except Backtrack:
# (Omitted Implicit @@ currlv, ps)
omitted = tla_ast.Omitted(tla_ast.Implicit())
return (omitted, ps)
def to_step(currlv, st, ps):
# | PreQed ->
if isinstance(st, tla_ast.PreQed):
# let (p, ps) = to_proof (currlv + 1 @@ st) ps in
p, ps = to_proof(currlv + 1, ps)
# (QED p, ps)
return (QED(p), ps)
# | PreHide use ->
elif isinstance(st, tla_ast.PreHide):
use = st.usable
# (STEP (Hide use @@ st), ps)
hide = tla_ast.Hide(use)
return (STEP(hide), ps)
# | PreUse (supp, onl, use, meth) ->
elif isinstance(st, tla_ast.PreUse):
supp = st.supp
only = st.only
usable = st.usable
meth = st.method
# let u = Use (use, onl = Only) @@ st in
use = tla_ast.Use(usable, isinstance(only, tla_ast.Only))
# (STEP (annotate supp meth u), ps)
annotate(supp, meth, use)
return (STEP(use), ps)
# | PreDefine dfs ->
elif isinstance(st, tla_ast.PreDefine):
dfs = st.definitions
# (STEP (Define dfs @@ st), ps)
define = tla_ast.Define(dfs)
return (STEP(define), ps)
# | PreHave (supp, e, meth) ->
elif isinstance(st, tla_ast.PreHave):
supp = st.supp
e = st.expr
meth = st.method
# let h = Have e @@ st in
have = tla_ast.Have(e)
# (STEP (annotate supp meth h), ps)
annotate(supp, meth, have)
return (STEP(have), ps)
# | PreTake (supp, bs, meth) ->
elif isinstance(st, tla_ast.PreTake):
supp = st.supp
bs = st.bounds
meth = st.method
# let t = Take bs @@ st in
take = tla_ast.Take(bs)
# (STEP (annotate supp meth t), ps)
annotate(supp, meth, take)
return (STEP(take), ps)
# | PreWitness (supp, es, meth) ->
elif isinstance(st, tla_ast.PreWitness):
supp = st.supp
es = st.exprs
meth = st.method
# let w = Witness es @@ st in
witness = tla_ast.Witness(es)
# (STEP (annotate supp meth w), ps)
annotate(supp, meth, witness)
return (STEP(witness), ps)
# | PreAssert sq ->
elif isinstance(st, tla_ast.PreAssert):
sq = st.sequent
# let (p, ps) = to_proof (currlv + 1 @@ st) ps in
p, ps = to_proof(currlv + 1, ps)
# let st = enlarge_loc st p in
enlarge_loc(st, p)
# (STEP (Assert (sq, p) @@ st), ps)
assert_ = tla_ast.Assert(sq, p)
return (STEP(assert_), ps)
# | PreSuffices sq ->
elif isinstance(st, tla_ast.PreSuffices):
sq = st.sequent
# let (p, ps) = to_proof (currlv + 1 @@ st) ps in
p, ps = to_proof(currlv + 1, ps)
# let st = enlarge_loc st p in
enlarge_loc(st, p)
# (STEP (Suffices (sq, p) @@ st), ps)
suffices = tla_ast.Suffices(sq, p)
return (STEP(suffices), ps)
# | PreCase e ->
elif isinstance(st, tla_ast.PreCase):
e = st.expr
# let (p, ps) = to_proof (currlv + 1 @@ st) ps in
p, ps = to_proof(currlv + 1, ps)
# let st = enlarge_loc st p in
enlarge_loc(st, p)
# (STEP (Pcase (e, p) @@ st), ps)
pcase = tla_ast.Pcase(e, p)
return (STEP(pcase), ps)
# | PrePick (bs, e) ->
elif isinstance(st, tla_ast.PrePick):
bs = st.bounds
e = st.expr
# let (p, ps) = to_proof (currlv + 1 @@ st) ps in
p, ps = to_proof(currlv + 1, ps)
# let st = enlarge_loc st p in
enlarge_loc(st, p)
# (STEP (Pick (bs, e, p) @@ st), ps)
pick = tla_ast.Pick(bs, e, p)
return (STEP(pick), ps)
else:
raise TypeError(st)
def only():
while True:
yield choice([
kwd('ONLY') << bang >> tla_ast.Only(),
succeed(tla_ast.Default())
])
def set_level(n, preno):
label = preno.label
if label == '':
return tla_ast.Unnamed(n, uuid.uuid4())
else:
return tla_ast.Named(n, label, False)
def with_meth(e, meth):
if meth is None:
return e
else:
return nodes.With(e, meth)
def apply_axiom(args):
((nm, e), meth) = args
return [nodes.Axiom(nm, with_meth(e, meth))]
def to_steps(first, currlv, ps):
# | {core = PreStep (kwd, sn, st)} as p :: ps ->
p = ps[0]
ps = ps[1:]
kwd = p.boolean # PROOF keyword
sn = p.preno # step number
st = p.prestep
# if not first && kwd then begin
# Errors.set p
# ("PROOF keyword found in step that "
# "does not begin subproof");
# Util.eprintf ~at:p
# ("PROOF keyword found in step that " ^
# "does not begin subproof\n%!");
# failwith "Proof.Parser"
# end ;
assert (first or not kwd)
# let thislv = match sn, kwd, first with
# | Num (n, _), _, _ -> n
if isinstance(sn, tla_ast.StepNum):
n = sn.level
thislv = int(n)
# | Star _, true, true ->
elif (isinstance(sn, tla_ast.StepStar) and kwd and first):
# (*
# * Util.eprintf ~at:p
# * "%d: <*> -> %d (because first and PROOF)\n%!"
# * currlv.core currlv.core ;
# *)
# currlv.core
thislv = currlv
# | Star _, false, true ->
elif (isinstance(sn, tla_ast.StepStar) and not kwd and first):
# (*
# * Util.eprintf ~at:p
# * "%d: <*> -> %d (because first and no PROOF)\n%!"
# * currlv.core (currlv.core - 1) ;
# *)
# currlv.core - 1
thislv = currlv - 1
# | Star _, _, false ->
elif (isinstance(sn, tla_ast.StepStar) and not first):
# assert (not kwd) ;
assert not kwd
# (*
# * Util.eprintf ~at:p
# * "%d: <*> -> %d (because not first)\n%!"
# * currlv.core currlv.core ;
# *)
# currlv.core
thislv = currlv
# | Plus _, _, false ->
elif (isinstance(sn, tla_ast.StepPlus) and not first):
# Errors.set p "<+> used but no subproof expected" ;
# Util.eprintf ~at:p
# "<+> used but no subproof expected\n%!" ;
# failwith "Proof.Parser"
raise Exception('<+> usedd but no subproof expected')
# | Plus _, _, _ ->
elif isinstance(sn, tla_ast.StepPlus):
# (*
# * Util.eprintf ~at:p
# * "%d: <+> -> %d\n%!"
# * currlv.core currlv.core ;
# *)
# currlv.core
thislv = currlv
else:
raise ValueError(sn, kwd, first)
# in
# if thislv < currlv.core then
if thislv < currlv:
# raise Backtrack ;
raise Backtrack()
# if not first && thislv > currlv.core then
if not first and thislv > currlv:
# raise Backtrack ;
raise Backtrack()
# let sn = set_level thislv sn in begin
sn = set_level(thislv, sn)
# match to_step thislv (st @@ p) ps with
to_stp = to_step(thislv, st, ps)
# | (STEP s, nps) ->
if isinstance(to_stp[0], STEP):
s = to_stp[0].step
nps = to_stp[1]
# let s = Property.assign s Props.step sn in
s.step_number = sn
# let thislv = Util.locate thislv
# (Loc.right_of (Util.get_locus s)) in
# TODO: locate
# let (ss, qp, ps) = to_steps thislv nps in
ss, qp, ps = to_steps(first=False, currlv=thislv, ps=nps)
# (s :: ss, qp, ps)
return ([s] + ss, qp, ps)
# | (QED qp, ps) ->
elif isinstance(to_stp[0], QED):
qp = to_stp[0].proof
ps = to_stp[1]
# let qp = { core =
# {core = Qed qp;
# props = [Props.step.Property.set sn]} ;
# props = [Props.step.Property.set sn] } in
# ([], qp, ps)
qed = tla_ast.Qed(qp)
qed.step_number = sn
return (list(), qed, ps)
def apply_use_hide(args):
((supp, uh), use) = args
if uh == 'USE':
return [nodes.Mutate(nodes.ModuleUse(nodes.Suppress()), use)]
else:
return [nodes.Mutate(nodes.ModuleHide(), use)]
def prestep():
while True:
yield choice([
# choice [
# kwd "QED" <!> PreQed ;
kwd('QED') << bang >> tla_ast.PreQed(),
#
# kwd "HIDE"
# >*> use usebody
# <$> (fun use -> PreHide use) ;
kwd('HIDE') << second_commit >> use(usebody()) << apply >>
(lambda use: tla_ast.PreHide(use)),
#
# kwd "SUFFICES"
# >*> use sequent
# <$> (fun sq -> PreSuffices sq) ;
kwd('SUFFICES') << second_commit >> use(sequent()) << apply >>
(lambda sq: tla_ast.PreSuffices(sq)),
#
# kwd "CASE"
# >*> use (expr false)
# <$> (fun e -> PreCase e) ;
kwd('CASE') << second_commit >> use(ep.expr(False)) << apply >>
(lambda e: tla_ast.PreCase(e)),
#
# kwd "PICK"
# >*> use (bounds false)
# <**> (punct ":"
# >>> use (expr false))
# <$> (fun (bs, e) -> PrePick (bs, e)) ;
kwd('PICK') << second_commit >> use(ep.bounds(False)) << times2 >>
(punct(':') << second >> use(ep.expr(False))) << apply >>
(lambda bs_e: tla_ast.PrePick(bs_e[0], bs_e[1])),
#
# use suppress >>= begin fun supp ->
use(suppress()) << shift_eq >> (
lambda supp: choice([
# choice [
# kwd "USE"
# >*> only
# <*> use usebody
# <*> read_method
# <$> (fun ((onl, use), meth) ->
# PreUse (supp, onl, use, meth)) ;
kwd('USE') << second_commit >> only() << times >> use(
usebody()) << times >> read_method() << apply >>
(lambda args: tla_ast.PreUse(supp, args[0][0], args[0][1],
args[1])),
#
# kwd "HAVE"
# >*> use (expr false)
# <*> read_method
# <$> (fun (e, meth) -> PreHave (supp, e, meth)) ;
kwd('HAVE') << second_commit >> use(ep.expr(
False)) << times >> read_method() << apply >>
(lambda e_meth: tla_ast.PreHave(supp, e_meth[0], e_meth[1])
),
#
# kwd "TAKE"
# >*> use (bounds false)
# <*> read_method
# <$> (fun (bs, meth) -> PreTake (supp, bs, meth)) ;
kwd('TAKE') << second_commit >> use(ep.bounds(
False)) << times >> read_method() << apply >>
(lambda bs_meth: tla_ast.PreTake(supp, bs_meth[0], bs_meth[
1])),
#
# kwd "WITNESS"
# >*> sep1 (punct ",") (use (expr false))
# <*> read_method
# <$> (fun (es, meth) -> PreWitness (supp, es, meth)) ;
kwd('WITNESS') << second_commit >> sep1(
punct(','), use(ep.expr(False))
) << times >> read_method() << apply >>
(lambda es_meth: tla_ast.PreWitness(
supp, es_meth[0], es_meth[1]))
# ]
# end ;
])),
#
# attempt (optional (kwd "DEFINE") >>> star1 (use (defn false)))
# <$> (fun dfs -> PreDefine dfs) ;
attempt(
optional(kwd('DEFINE')) << second >> star1(use(ep.defn(False)))
) << apply >> (lambda defns: tla_ast.PreDefine(defns)),
#
# use sequent <$> (fun sq -> PreAssert sq) ;
use(sequent()) << apply >> (lambda sq: tla_ast.PreAssert(sq))
# ]
])
def definable():
while True:
yield intf.locate(
sep1(intf.punct('!'), choice([intf.anyop(),
intf.anyident()])) << apply >>
(lambda ids: tla_ast.Dvar('!'.join(ids))))
def _generate_tlaops():
tlaops = [
('Logic', [
('=>', (1, 1), Infix(Non()), list(), nodes.Implies()),
('<=>', (2, 2), Infix(Non()), ['\\equiv'], nodes.Equiv()),
('/\\', (3, 3), Infix(Left()), ['\\land'], nodes.Conj()),
('\\/', (3, 3), Infix(Left()), ['\\lor'], nodes.Disj()),
('~', (4, 4), Prefix(), ['\\neg', '\\lnot'], nodes.Neg()),
('=', (5, 5), Infix(Non()), list(), nodes.Eq()),
('#', (5, 5), Infix(Non()), ['/='], nodes.Neq()),
]),
('Sets', [
('SUBSET', (8, 8), Prefix(), list(), nodes.SUBSET()),
('UNION', (8, 8), Prefix(), list(), nodes.UNION()),
('DOMAIN', (9, 9), Prefix(), list(), nodes.DOMAIN()),
('\\subseteq', (5, 5), Infix(Non()), list(), nodes.Subseteq()),
('\\in', (5, 5), Infix(Non()), list(), nodes.Mem()),
('\\notin', (5, 5), Infix(Non()), [], nodes.Notmem()),
('\\', (8, 8), Infix(Non()), ['\\setminus'], nodes.Setminus()),
('\\cap', (8, 8), Infix(Left()), ['\\intersect'], nodes.Cap()),
('\\cup', (8, 8), Infix(Left()), ['\\union'], nodes.Cup()),
('\\X', (10, 13), Infix(Non()), ['\\times'], None),
]),
('Modal', [
("'", (15, 15), Postfix(), list(), nodes.Prime()),
('~>', (2, 2), Infix(Non()), ['\\leadsto'], nodes.LeadsTo()),
('ENABLED', (4, 15), Prefix(), list(), nodes.ENABLED()),
('UNCHANGED', (4, 15), Prefix(), list(), nodes.UNCHANGED()),
('\\cdot', (5, 14), Infix(Left()), list(), nodes.Cdot()),
('-+->', (2, 2), Infix(Non()), list(), nodes.WhilePlus()),
('[]', (4, 15), Prefix(), list(), nodes.Box(True)),
('<>', (4, 15), Prefix(), list(), nodes.Diamond()),
]),
('User', [(name, prec, fix, als, None) for name, prec, fix, als in [
('^', (14, 14), Infix(Non()), list()),
('/', (13, 13), Infix(Non()), list()),
('*', (13, 13), Infix(Left()), list()),
('-.', (12, 12), Prefix(), ['-']),
('-', (11, 11), Infix(Left()), list()),
('+', (10, 10), Infix(Left()), list()),
('^+', (15, 15), Postfix(), list()),
('^*', (15, 15), Postfix(), list()),
('^#', (15, 15), Postfix(), list()),
('<', (5, 5), Infix(Non()), list()),
('=<', (5, 5), Infix(Non()), ['<=', '\\leq']),
('>', (5, 5), Infix(Non()), list()),
('>=', (5, 5), Infix(Non()), ['\\geq']),
('...', (9, 9), Infix(Non()), list()),
('..', (9, 9), Infix(Non()), list()),
('|', (10, 11), Infix(Left()), list()),
('||', (10, 11), Infix(Left()), list()),
('&&', (13, 13), Infix(Left()), list()),
('&', (13, 13), Infix(Left()), list()),
('$$', (9, 13), Infix(Left()), list()),
('$', (9, 13), Infix(Left()), list()),
('??', (9, 13), Infix(Left()), list()),
('%%', (10, 11), Infix(Left()), list()),
('%', (10, 11), Infix(Left()), ['\\mod']),
('##', (9, 13), Infix(Left()), list()),
('++', (10, 10), Infix(Left()), list()),
('--', (11, 11), Infix(Left()), list()),
('**', (13, 13), Infix(Left()), list()),
('//', (13, 13), Infix(Non()), list()),
('^^', (14, 14), Infix(Non()), list()),
('@@', (6, 6), Infix(Left()), list()),
('!!', (9, 13), Infix(Non()), list()),
('|-', (5, 5), Infix(Non()), list()),
('|=', (5, 5), Infix(Non()), list()),
('-|', (5, 5), Infix(Non()), list()),
('=|', (5, 5), Infix(Non()), list()),
('<:', (7, 7), Infix(Non()), list()),
(':>', (7, 7), Infix(Non()), list()),
(':=', (5, 5), Infix(Non()), list()),
('::=', (5, 5), Infix(Non()), list()),
('(+)', (10, 10), Infix(Left()), ['\\oplus']),
('(-)', (11, 11), Infix(Left()), ['\\ominus']),
('(.)', (13, 13), Infix(Left()), ['\\odot']),
('(/)', (13, 13), Infix(Non()), ['\\oslash']),
('(\\X)', (13, 13), Infix(Left()), ['\\otimes']),
('\\uplus', (9, 13), Infix(Left()), list()),
('\\sqcap', (9, 13), Infix(Left()), list()),
('\\sqcup', (9, 13), Infix(Left()), list()),
('\\div', (13, 13), Infix(Non()), list()),
('\\wr', (9, 14), Infix(Non()), list()),
('\\star', (13, 13), Infix(Left()), list()),
('\\o', (13, 13), Infix(Left()), ['\\circ']),
('\\bigcirc', (13, 13), Infix(Left()), list()),
('\\bullet', (13, 13), Infix(Left()), list()),
('\\prec', (5, 5), Infix(Non()), list()),
('\\succ', (5, 5), Infix(Non()), list()),
('\\preceq', (5, 5), Infix(Non()), list()),
('\\succeq', (5, 5), Infix(Non()), list()),
('\\sim', (5, 5), Infix(Non()), list()),
('\\simeq', (5, 5), Infix(Non()), list()),
('\\ll', (5, 5), Infix(Non()), list()),
('\\gg', (5, 5), Infix(Non()), list()),
('\\asymp', (5, 5), Infix(Non()), list()),
('\\subset', (5, 5), Infix(Non()), list()),
('\\supset', (5, 5), Infix(Non()), list()),
('\\supseteq', (5, 5), Infix(Non()), list()),
('\\approx', (5, 5), Infix(Non()), list()),
('\\cong', (5, 5), Infix(Non()), list()),
('\\sqsubset', (5, 5), Infix(Non()), list()),
('\\sqsubseteq', (5, 5), Infix(Non()), list()),
('\\sqsupset', (5, 5), Infix(Non()), list()),
('\\sqsupseteq', (5, 5), Infix(Non()), list()),
('\\doteq', (5, 5), Infix(Non()), list()),
('\\propto', (5, 5), Infix(Non()), list()),
]])
]
return tlaops
