pde_state_machine.py 48 KB
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#!/usr/bin/env python3

# https://github.com/pytransitions/transitions
from transitions import Machine, State
from collections import OrderedDict
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import getpass
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from string_handling import *
from exaoutput import ExaOutput
from mmtinterface import *


class InterviewError(Exception):
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    """Errors that occur during the course of the interview and are not due to mmt server errors"""
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    def __init__(self, err):
        self.error = err
        super(InterviewError, self).__init__("Interview error: " + str(self.error))


class CriticalSubdict():
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    def __init__(self, subdict, output_function=print, outermost=True):
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        """The sub-part of a dictionary that needs to be restored if something goes wrong -
        To be used in with-statements.
        Catches errors only if it is the outermost one"""
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        self.subdict = subdict
        self.initial_subdict = self.subdict.copy()
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        self.output_function = output_function
        self.outermost = outermost
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    def __enter__(self):
        return self.subdict

    def __exit__(self, type, value, traceback):
        if type is not None:
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            # restore the initial state
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            self.subdict.clear()
            for key in self.initial_subdict:
                self.subdict[key] = self.initial_subdict[key]
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            # handling: give feedback, only if our own error, and the outermost subdict
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            if isinstance(value, MMTServerError) and self.outermost:
                self.please_repeat(value.args[0], value.longerr)
                return True
            elif isinstance(value, InterviewError) and self.outermost:
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                self.please_repeat(value.args[0])
                return True
            else:
                return False
        return True

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    def please_repeat(self, moreinfo=None, evenmoreinfo=None):
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        append = ""
        if moreinfo:
            append = "\nDetails: " + moreinfo
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        if evenmoreinfo:
            append += ". " + evenmoreinfo
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        self.output_function("I did not catch that. Could you please rephrase?" + append, 'stderr')
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class PDE_States:
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    """Just a state machine using pytranisitions that walks our theory graph and creates ephemeral theories and views"""

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    def __init__(self, output_function, after_state_change_function, prompt_function):
        # just act like we were getting the right replies from MMT
        self.cheating = True

        self.poutput = output_function
        self.please_prompt = prompt_function

        # Initialize a state machine
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        self.states = [
            State('greeting', on_exit=['greeting_exit']),
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            State('dimensions', on_enter=['dimensions_begin']),
            State('domain', on_enter=['domain_begin'], on_exit=['domain_exit']),
            State('unknowns', on_enter=['unknowns_begin'], on_exit=['unknowns_exit']),
            State('parameters', on_enter=['parameters_begin'], on_exit=['parameters_exit']),
            State('pdes', on_enter=['pdes_begin'], on_exit=['pdes_exit']),
            State('bcs', on_enter=['bcs_begin'], on_exit=['bcs_exit']),
            State('props', on_enter=['props_begin'], on_exit=['props_exit']),
            State('sim', on_enter=['sim_begin'], on_exit=['sim_exit']),
        ]
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        self.states.reverse()
        self.machine = Machine(model=self, states=self.states, initial=self.states[-1],
                               after_state_change=after_state_change_function, queued=True)
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        # this is why we were reverting the states => can always go back
        self.machine.add_ordered_transitions(
            trigger='last_state')  # TODO do something to avoid going back from the first state
        # self.to_dimensions()
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        self.machine.add_transition(trigger='greeting_over', source='greeting', dest='dimensions')
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        self.machine.add_transition(trigger='dimensions_parsed', source='dimensions', dest='domain',
                                    before='print_empty_line')
        self.machine.add_transition(trigger='domain_parsed', source='domain', dest='unknowns',
                                    before='print_empty_line')
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        self.machine.add_transition(trigger='unknowns_parsed', source='unknowns', dest='parameters')
        self.machine.add_transition(trigger='parameters_parsed', source='parameters', dest='pdes')
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        self.machine.add_transition(trigger='pdes_parsed', source='pdes', dest='bcs', before='print_empty_line')
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        self.machine.add_transition(trigger='bcs_parsed', source='bcs', dest='props', before='print_empty_line')
        self.machine.add_transition(trigger='props_parsed', source='props', dest='sim', before='print_empty_line')
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        self.machine.add_transition(trigger='sim_finished', source='sim', dest='sim', before='print_empty_line')

        # define what happens when input is received in a certain state
        self.stateDependentInputHandling = {
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            'greeting': self.greeting_handle_input,
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            'dimensions': self.dimensions_handle_input,
            'domain': self.domain_handle_input,
            'unknowns': self.unknowns_handle_input,
            'parameters': self.parameters_handle_input,
            'pdes': self.pdes_handle_input,
            'bcs': self.bcs_handle_input,
            'props': self.props_handle_input,
            'sim': self.sim_handle_input,
        }

        self.mmtinterface = MMTInterface()

        # for ladder-like views
        self.viewfrom = OrderedDict([
            ('domain', "mDomain"),
            ('unknowns', "mUnknown"),
            ('parameters', "mParameter"),
            ('pdes', "mPDE"),
            ('bcs', "mBCsRequired"),
            ('props', "mEllipticLinearDirichletBoundaryValueProblem"),
            ('sim', "mSolvability"),
        ])
        # to include all the necessary theories every time
        self.bgthys = OrderedDict([
            ('domain', ["mInterval", "http://mathhub.info/MitM/smglom/arithmetics?realarith"]),
            # new: RealArithmetics
            ('unknowns', ["http://mathhub.info/MitM/Foundation?Strings", "ephdomain",
                          "http://mathhub.info/MitM/smglom/calculus?higherderivative"]),
            ('parameters', ["http://mathhub.info/MitM/smglom/arithmetics?realarith", "ephdomain",
                            "http://mathhub.info/MitM/Foundation?Math"]),
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            ('pdes', ["mDifferentialOperators"]),  # +params, unknowns,
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            ('bcs',
             ["ephdomain", "mLinearity",
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              "http://mathhub.info/MitM/smglom/arithmetics?realarith"]),  # +params, unknowns, pdes, bctypes
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            ('props',
             ["mLinearity",
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              "http://mathhub.info/MitM/Foundation?Strings"]),  # +bcs, pde
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            ('sim',
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             ["http://mathhub.info/MitM/Foundation?Strings"]),  # +props
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        ])

        # the things we'd like to find out
        self.simdata = {
            "num_dimensions": None,
            "domain": {
                "name": None,
                "theoryname": None,
                # "viewname" : None,
                "axes": OrderedDict(),
                "from": None,
                "to": None,
            },
            "unknowns": OrderedDict(),
            "parameters": OrderedDict(),
            "pdes": {
                #               "theoryname": None,
                "pdes": [],
            },
            "bcs": {
                "theoryname": None,
                "bcs": None,
            },
            "props": {

            },
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            "sim": {
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                "type": None,
            },
        }

        axes = OrderedDict([
            ("x_1", "[0;1]"),
        ])
        self.examplesimdata = {
            "num_dimensions": 1,
            "domain": {
                "name": "Ω",
                "theoryname": "Omega",
                "axes": axes,  # names and intervals
                "from": 0.0,
                "to": 1.0,
            },
            "unknowns": {  # names and theorynames #TODO OrderedDict
                "u": {
                    "theoryname": "u",
                    "string": "u : Ω → ℝ",
                },
            },
            "parameters": {  # names and theorynames
                "μ": {
                    "theoryname": "mu",
                    "string": "μ : ℝ = 1",
                },
                "f": {
                    "theoryname": "f",
                    "string": "f : Ω → ℝ = [x] x ⋅ x",
                },
            },
            "pdes": {
                "pdes": [
                    {
                        "theoryname": "pde1",
                        "string": "μ ∆u = f(x)",  # TODO use function arithmetic
                        'lhsstring': 'μ Δu ',
                        'rhsstring': 'f(x)',
                        'op': 'Δ',
                        'lhsparsestring': ' [ anyu : Ω → ℝ ] Δ anyu ',
                        'rhsparsestring': ' [ x : Ω ]  f(x)',
                        # this is more of a wish list... cf https://github.com/UniFormal/MMT/issues/295
                        "expanded": "μ d²/dx_1² u = f(x_1)",
                        "order_in_unknown": {
                            "u": 2,
                        },
                    },
                ],
            },
            "bcs": {
                "theoryname": "ephbcs",
                "bcs": [
                    {
                        "name": "bc1",
                        "type": "Dirichlet",
                        "string": "u (0) = x_1**2",
                        "on": "0",
                    },
                    {
                        "name": "bc2",
                        "type": "Dirichlet",
                        "string": "u (1) = x_1**2",
                        "on": "1",
                    },
                ],
            },
            "props": {
                "theoryname": "ephboundaryvalueproblem",
                "ops": [
                    {
                        "name": "op1",
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                        "linear": True,  # or false or unknown
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                        "props": ["elliptic"]
                    }
                ]
            },
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            "sim": {
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                "type": "FD",
            },
        }

        self.testsimdata = {
            'num_dimensions': 1,
            'domain': {'name': 'Ω', 'theoryname': 'ephdomain', 'axes': OrderedDict([('x_1', '[0.0;1.0]')]),
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                       'from': 0.0, 'to': 1.0, 'boundary_name': 'Ω', 'viewname': 'ephdomainASmDomain'},
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            'unknowns': OrderedDict([('u', {'theoryname': 'u', 'string': 'u : Ω → ℝ', 'type': 'Ω → ℝ', 'codomain': 'ℝ',
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                                            'viewname': 'uASmUnknown'})]),
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            'parameters': {
                'f': {'theoryname': 'f', 'string': 'f = x', 'parsestring': 'f = [ x : Ω] x', 'type': '{ : Ω } Ω',
                      'viewname': 'fASmParameter'}},
            'pdes': {'pdes': [
                {'theoryname': 'ephpde1', 'string': 'Δu = 0.0', 'lhsstring': 'Δu', 'rhsstring': '0.0',
                 'viewname': 'ephpde1ASmPDE', 'op': 'Δ', 'lhsparsestring': ' [ anyu : Ω → ℝ ] Δ anyu ',
                 'rhsparsestring': ' [ x : Ω ]  0.0'}]},
            'bcs': {'theoryname': 'ephbcs', 'bcs': [
                {'name': 'bc0', 'string': 'u = f', 'lhsstring': 'u ', 'rhsstring': ' f', 'type': ('Dirichlet',),
                 'on': ('x',), 'measure': (2,)}], 'bctypes': {'theoryname': 'uBCTypes'},
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                    'viewname': 'ephbcsASmBCsRequired',
                    'measure_given': 2},
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            'props': {},
            'sim': {},
        }
        self.exaout = ExaOutput()

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        """Variables to signal callbacks depending on yes/no prompts"""
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        self.prompted = False
        self.if_yes = None
        self.if_no = None
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        self.pass_other = False

    def greeting_handle_input(self, userstring):
        self.greeting_over()
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    def greeting_exit(self):
        username = getpass.getuser()
        self.poutput("Hello, " + username + "! I am TheInterview, your partial differential equations and simulations expert. "
                     "Let's set up a simulation together.")
        self.poutput("")
        self.poutput("To get explanations, enter \"explain <optional keyword>\". ")
        self.poutput("To see a recap of what we know so far, enter \"recap <optional keyword>\". ")
        self.poutput("Otherwise, you can always try and use LaTeX-type input.")
        self.poutput("Have a look at the currently loaded MMT theories under " + self.mmtinterface.serverInstance)
        self.poutput("")
        self.poutput("")
        self.poutput("")

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    ##### for state dimensions
    def dimensions_begin(self):
        self.poutput("How many dimensions does your model have?")
        self.poutput("I am just assuming it's 1, since that is all we can currently handle.")  # TODO
        self.simdata["num_dimensions"] = 1
        self.dimensions_parsed()

    def dimensions_handle_input(self, userstring):
        # reply_diffops = self.mmtinterface.query_for("mDifferentialOperators")
        # self.poutput(reply_diffops.tostring())
        # self.poutput(element_to_string(reply_diffops.getConstant("derivative")))
        # self.poutput(element_to_string(reply_diffops.getConstant("laplace_operator")))
        try:
            numdim = int(userstring)
        except ValueError:
            self.poutput("Please enter a number.")
            return
        if numdim < 1:
            self.obviously_stupid_input()
            self.exaout.create_output(self.testsimdata)
            self.dimensions_begin()
        elif numdim == 1:  # or self.numdim == 2:
            self.simdata["num_dimensions"] = numdim
            self.dimensions_parsed()
        else:
            self.poutput(
                "Sorry, cannot handle " + str(numdim) + " dimensions as of now. Please try less than that.")

    ##### for state domain
    def domain_begin(self):
        self.poutput("What is the domain you would like to simulate for?     Ω : type ❘ = [?;?], e.g. Ω = [0.0;1.0]")
        self.poutput("By the way, you can always try and use LaTeX-type input.")
        self.simdata[self.state]["axes"] = OrderedDict()
        self.domain_mmt_preamble()

    def domain_handle_input(self, userstring):
        domain_name = get_first_word(userstring)
        # subdict = self.simdata[self.state]
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        with CriticalSubdict(self.simdata[self.state], self.poutput) as subdict:
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            parsestring = userstring
            mmtreply = self.mmtinterface.mmt_new_decl(domain_name, subdict["theoryname"], parsestring)
            mmttype = self.mmtinterface.mmt_infer_type(subdict["theoryname"], domain_name)
            if mmttype.inferred_type_to_string() != "type":
                raise InterviewError("This seems to not be a type. It should be!")
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            result = self.mmtinterface.query_for(subdict["theoryname"])
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            subdict["name"] = domain_name
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            (fro, to) = mmtreply.getIntervalBoundaries(result, domain_name)
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            subdict["axes"]["x_1"] = "[" + str(fro) + ";" + str(to) + "]"
            (subdict["from"], subdict["to"]) = (fro, to)

            self.poutput("we will just assume that the variable is called x for now.")
            # mmtreply = self.mmtinterface.mmt_new_decl(domain_name, subdict["theoryname"], "x : " + domain_name)
            self.trigger('domain_parsed')

    def domain_exit(self):
        self.domain_mmt_postamble()

    def domain_mmt_preamble(self):
        # set the current MMT theoryname for parsing the input TODO use right dimension
        self.simdata[self.state]["theoryname"] = "ephdomain"
        self.new_theory(self.simdata[self.state]["theoryname"])
        # (ok, root) = self.mmtinterface.query_for(self.simdata[self.state]["theoryname"])

    def domain_mmt_postamble(self):
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        with CriticalSubdict(self.simdata[self.state], self.poutput) as subdict:
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            subdict["boundary_name"] = subdict["name"]  # todo
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            if not self.cheating:
                self.mmtinterface.mmt_new_decl('mydomainpred', subdict["theoryname"],
                                               "myDomainPred = " + subdict["name"] + ".interval_pred")
                self.mmtinterface.mmt_new_decl('mydomain', subdict["theoryname"],
                                               "myDomain = intervalType " + subdict["name"])
                # and a view to understand our interval as a domain -- view ephDomainAsDomain : ?GeneralDomains → ?ephDomain =
                self.new_view(subdict)
                self.mmtinterface.mmt_new_decl('Vecspace', subdict["viewname"],
                                               "Vecspace = real_lit")  # TODO adjust for higher dimensions
                self.mmtinterface.mmt_new_decl('DomainPred', subdict["viewname"], "DomainPred = " + subdict[
                    "name"] + ".interval_pred")  # the . is unbound, apparently...
            else:
                self.new_view(subdict)
                self.mmtinterface.mmt_new_decl('dom', subdict["viewname"],
                                               "domain = " + subdict["name"])
                self.mmtinterface.mmt_new_decl('boun', subdict["viewname"],
                                               "boundary = " + subdict["boundary_name"])

    ##### for state unknowns
    def unknowns_begin(self):
        self.poutput("Which variable(s) are you looking for? / What are the unknowns in your model?  u : " +
                     self.simdata["domain"]["name"] + " → ??,  e.g., u : " + self.simdata["domain"]["name"] + " → ℝ ?")
        self.simdata["unknowns"] = OrderedDict()

    def unknowns_handle_input(self, userstring):
        unknown_name = get_first_word(userstring)
        # replace interval with domain
        parsestring = (
            userstring.replace(self.simdata["domain"]["name"],
                               "pred myDomainPred") if not self.cheating else userstring)

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        with CriticalSubdict(self.simdata[self.state], self.poutput) as usubdict:
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            # create mmt theory with includes
            once = self.new_theory(unknown_name)
            # self.include_in(unknown_name, self.simdata["domain"]["theoryname"])

            # and one to "throw away" to infer the type
            self.new_theory(unknown_name + "_to_go_to_trash")
            test = self.mmtinterface.mmt_new_decl(unknown_name, unknown_name + "_to_go_to_trash",
                                                  parsestring)

            type = self.get_inferred_type(unknown_name + "_to_go_to_trash", unknown_name)
            usubdict[unknown_name] = {
                "theoryname": unknown_name,
                "string": parsestring,
                "type": type,
                "codomain": type.replace(self.simdata["domain"]["name"] + " →", "", 1).strip(),
            }
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            with CriticalSubdict(self.simdata["unknowns"][unknown_name], self.poutput, False) as subdict:
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                if self.mmtinterface.query_for(unknown_name + "_to_go_to_trash").hasDefinition(unknown_name):
                    raise InterviewError("Unknowns cannot be defined!")
                if not type_is_function_from(subdict["type"], self.simdata["domain"]["name"]):
                    raise InterviewError("Unknown should be a function on " + self.simdata["domain"]["name"] + "!")

                # add unknown's type as constant
                twice = self.mmtinterface.mmt_new_decl(unknown_name, subdict["theoryname"],
                                                       "myUnkType = " + subdict["type"])
                twice = (self.mmtinterface.mmt_new_decl('diffable', subdict["theoryname"],
                                                        "anyuwillbediffable : {u : myUnkType} ⊦ twodiff u ") if not self.cheating else twice)
                self.new_view(subdict)
                self.mmtinterface.mmt_new_decl("codomain", subdict["viewname"], "ucodomain = " + subdict["codomain"])
                self.mmtinterface.mmt_new_decl("unktype", subdict["viewname"], "unknowntype = myUnkType")
                self.poutput("Ok, " + userstring)
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                # self.please_prompt("Are these all the unknowns?", lambda: self.trigger('unknowns_parsed'), pass_other=True) #TODO
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                self.trigger('unknowns_parsed')

    def unknowns_exit(self):
        for unknown in self.simdata["unknowns"]:
            self.poutput(self.simdata["unknowns"][unknown]["string"])
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        self.print_empty_line()
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    ##### for state parameters
    def parameters_begin(self):
        self.poutput(
            "Would you like to name additional parameters like constants or functions (that are independent of your unknowns)?  c : ℝ = ? or f : Ω → ℝ = ?")  # ℝ
        self.simdata["parameters"] = OrderedDict()

    def parameters_handle_input(self, userstring):
        # self.poutput ("parameterinput "+ userstring)
        if means_no(userstring):
            self.trigger('parameters_parsed')
            return

        parameter_name = get_first_word(userstring)
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        with CriticalSubdict(self.simdata["parameters"], self.poutput) as psubdict:
            psubdict[parameter_name] = {}
            with CriticalSubdict(self.simdata["parameters"][parameter_name], self.poutput, False) as subdict:
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                # create mmt theory
                self.new_theory(parameter_name)
                # we might need the other parameters created so far, so use them
                for otherparamentry in get_recursively(self.simdata["parameters"], "theoryname"):
                    self.include_in(parameter_name, otherparamentry)

                # sanitize userstring - check if this works for all cases
                parsestring = add_ods(userstring)
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                if parsestring.startswith(parameter_name + "(") or parsestring.startswith(
                        parameter_name + " ("):  # todo make smarter for more dimensions
                    parsestring = remove_apply_brackets(parsestring)
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                parsestring = functionize(parsestring, self.simdata["domain"]["name"])
                # self.poutput(parsestring)
                reply_pconstant = self.mmtinterface.mmt_new_decl("param", parameter_name, parsestring)
                reply_pconstant = self.mmtinterface.query_for(parameter_name)
                subdict["theoryname"] = parameter_name
                subdict["string"] = userstring
                subdict["parsestring"] = parsestring
                subdict["type"] = self.get_inferred_type(parameter_name, parameter_name)

                # if not reply_pconstant.hasDefinition(parameter_name) and not self.cheating:
                #    InterviewError("Please define this parameter.")

                # create view
                self.new_view(subdict)
                self.mmtinterface.mmt_new_decl("ptype", subdict["viewname"],
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                                               "ptype = " + subdict["type"])
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                self.mmtinterface.mmt_new_decl("param", subdict["viewname"],
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                                               "param = " + parameter_name)
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                self.poutput("Ok, " + parsestring)
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                self.please_prompt("Would you like to declare more parameters?", None,
                                   lambda: self.trigger('parameters_parsed'), True)
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    def parameters_exit(self):
        # print(str(self.simdata["parameters"]))
        for parameter in self.simdata["parameters"]:
            self.poutput(self.simdata["parameters"][parameter]["string"])
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        self.print_empty_line()
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    ##### for state pdes
    def pdes_begin(self):
        self.poutput(
            "Let's talk about your partial differential equation(s). What do they look like? Δu = 0.0, or laplace_operator Ω ℝ u = f ?")
        self.simdata["pdes"]["pdes"] = []

    def pdes_handle_input(self, userstring):
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        with CriticalSubdict(self.simdata["pdes"]["pdes"], self.poutput) as psubdict:
            psubdict.append({})
            with CriticalSubdict(self.simdata["pdes"]["pdes"][-1], self.poutput, False) as subdict:
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                subdict["theoryname"] = "ephpde" + str(len(self.simdata["pdes"]["pdes"]))
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                # create new theory including all unknowns and parameters
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                self.new_theory(subdict["theoryname"])
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                for unknownentry in get_recursively(self.simdata["unknowns"], "theoryname"):
                    self.include_in(subdict["theoryname"], unknownentry)
                for paramentry in get_recursively(self.simdata["parameters"], "theoryname"):
                    self.include_in(subdict["theoryname"], paramentry)
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                # TODO use symbolic computation to order into LHS and RHS
                parts = re.split("=", userstring)

                if len(parts) is not 2:
                    raise InterviewError("This does not look like an equation.")

                # store the info
                subdict["string"] = userstring
                subdict["lhsstring"] = parts[0].strip()
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                subdict["rhsstring"] = parts[1].strip()
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                subdict["rhsstring_expanded"] = self.try_expand(subdict["rhsstring"])  # TODO expand properly
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                # to make the left-hand side a function on x, place " [ variablename : domainname ] " in front
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                if "x" in parts[0]:
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                    parts[0] = " [ x : " + self.simdata["domain"]["name"] + " ] " + parts[0]
                # right-hand side: infer type, make function if not one yet
                if not type_is_function_from(self.get_inferred_type(subdict["theoryname"], parts[1]),
                                             self.simdata["domain"]["name"]):
                    parts[1] = " [ x : " + self.simdata["domain"]["name"] + " ] " + parts[1]

                # in lhs replace all unknown names used by more generic ones and add lambda clause in front
                for unkname in get_recursively(self.simdata["unknowns"], "theoryname"):
                    parts[0] = parts[0].replace(unkname, " any" + unkname)
                    parts[0] = " [ any" + unkname + " : " + self.simdata["unknowns"][unkname]["type"] + " ] " + parts[0]
                    # and include the original ones as theory
                    inc = self.include_in(subdict["theoryname"], unkname)
                for parname in get_recursively(self.simdata["parameters"], "theoryname"):
                    inc = self.include_in(subdict["theoryname"], parname)

                # send declarations to mmt
                self.mmtinterface.mmt_new_decl("lhs", subdict["theoryname"], " mylhs = " + parts[0])
                reply_lhsconstant = self.mmtinterface.query_for(subdict["theoryname"])

                self.mmtinterface.mmt_new_decl("rhs", subdict["theoryname"], " myrhs = " + parts[1])
                reply_rhsconstant = self.mmtinterface.query_for(subdict["theoryname"])

                # create view
                self.new_view(subdict)
                ltype = self.get_inferred_type(subdict["theoryname"], "mylhs")
                eqtype = get_last_type(ltype)
                rtype = self.get_inferred_type(subdict["theoryname"], "myrhs")
                self.mmtinterface.mmt_new_decl("eqtype", subdict["viewname"],
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                                               "eqtype = " + eqtype)
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                self.mmtinterface.mmt_new_decl("lhs", subdict["viewname"],
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                                               "lhs = " + "mylhs")
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                self.mmtinterface.mmt_new_decl("rhs", subdict["viewname"],
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                                               "rhs = " + "myrhs")
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                self.mmtinterface.mmt_new_decl("pde", subdict["viewname"],
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                                               "pde = " + "[u](mylhs u) funcEq myrhs")
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                reply = self.mmtinterface.query_for(subdict["theoryname"])

                for unkname in get_recursively(self.simdata["unknowns"], "theoryname"):
                    op = subdict["lhsstring"].replace(unkname, "")
                    op = op.strip()

                # store the info
                subdict["op"] = op
                subdict["lhsparsestring"] = parts[0]
                subdict["rhsparsestring"] = parts[1]

                # TODO query number of effective pdes and unknowns from mmt for higher dimensional PDEs
                # => can assume each to be ==1 for now
                numpdesgiven = len(self.simdata["pdes"]["pdes"])
                self.poutput("Ok, " + reply.tostring())
                if numpdesgiven == len(self.simdata["unknowns"]):
                    self.trigger('pdes_parsed')
                elif numpdesgiven > len(self.simdata["unknowns"]):
                    self.poutput("now that's too many PDEs. Please go back and add more unknowns.")
                else:
                    self.poutput("More PDEs, please!")
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    def pdes_exit(self):
        self.poutput("These are all the PDEs needed.")

    ##### for state bcs
    def bcs_begin(self):
        self.poutput("Let's discuss your boundary conditions. "
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                     "What do they look like? u(x) = f(x) or u(" + str(self.simdata["domain"]["to"]) + ") = \\alpha ?")
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        bctypetheoryname = self.redefine_bcs()
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        with CriticalSubdict(self.simdata["bcs"], self.poutput) as subdict:
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            subdict["theoryname"] = "ephbcs"
            subdict["bcs"] = []
            self.new_theory(subdict["theoryname"])
            # apparently, need to include everything explicitly so that view works
            for unknownentry in get_recursively(self.simdata["unknowns"], "theoryname"):
                self.include_in(subdict["theoryname"], unknownentry)
            for paramentry in get_recursively(self.simdata["parameters"], "theoryname"):
                self.include_in(subdict["theoryname"], paramentry)
            for pdeentry in get_recursively(self.simdata["pdes"], "theoryname"):
                self.include_in(subdict["theoryname"], pdeentry)
            self.include_in(subdict["theoryname"], bctypetheoryname)
            self.new_view(subdict)
            subdict["measure_given"] = 0

    def bcs_handle_input(self, userstring):
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        with CriticalSubdict(self.simdata["bcs"], self.poutput) as subdict:
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            currentname = "bc" + str(len(subdict["bcs"]))
            subdict["bcs"].append({"name": currentname})
            # TODO use symbolic computation to order into LHS and RHS
            parts = re.split("=", userstring)

            if len(parts) is not 2:
                raise InterviewError("This does not look like a boundary condition.")
            # store the info
            subdict["bcs"][-1]["string"] = userstring
            subdict["bcs"][-1]["lhsstring"] = parts[0].strip()
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            subdict["bcs"][-1]["rhsstring"] = parts[1].strip()  # TODO expand
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            subdict["bcs"][-1]["rhsstring_expanded"] = self.try_expand(subdict["bcs"][-1]["rhsstring"])

            # to make a function on x, place " [ variablename : boundaryname ] " in front
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            if "x" in parts[0]:
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                parts[0] = " [ x : " + self.simdata["domain"]['boundary_name'] + " ] " + parts[0]
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            if "x" in parts[1]:
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                parts[1] = " [ x : " + self.simdata["domain"]['boundary_name'] + " ] " + parts[1]

            # in lhs replace all unknown names used by more generic ones and add lambda clause in front
            for unkname in get_recursively(self.simdata["unknowns"], "theoryname"):
                parts[0] = parts[0].replace(unkname, " any" + unkname)
                parts[0] = " [ any" + unkname + " : " + self.simdata["unknowns"][unkname]["type"] + " ] " + parts[0]

                type = self.get_inferred_type(subdict["theoryname"], parts[0])
                if type_is_function_to(type, self.simdata["unknowns"][unkname]["type"]):
                    # right-hand side: infer type, make function if not one yet
                    rhstype = self.get_inferred_type(subdict["theoryname"], parts[1])
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                    if not type_is_function_from(rhstype, self.simdata["domain"]["name"]) \
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                            and not type_is_function_from(rhstype, self.simdata["domain"]["boundary_name"]):
                        parts[1] = " [ x : " + self.simdata["domain"]["boundary_name"] + " ] " + parts[1]
                    self.add_list_of_declarations(subdict["viewname"], [
                        "firstBC = myDirichletBCfun " + parts[1],
                        "secondBC = myDirichletBCfun " + parts[1],
                    ])
                    subdict["bcs"][-1]["type"] = "Dirichlet",
                    subdict["bcs"][-1]["on"] = "x",
                    subdict["bcs"][-1]["measure"] = 2,
                    subdict["measure_given"] = 2
                elif type_is_function_to(type, self.simdata["unknowns"][unkname]["codomain"]):
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                    # at_x = re.split('[\(\)]', subdict["bcs"][-1]["lhsstring"])[-1] #TODO
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                    at_x = subdict["bcs"][-1]["lhsstring"].split('(', 1)[1].split(')')[0].strip()
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                    if at_x != self.simdata["domain"]["from"] and at_x != self.simdata["domain"]["to"]:
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                        raise InterviewError(at_x + " is not on the boundary!")
                    if len(subdict["bcs"]) == 1:
                        self.mmtinterface.mmt_new_decl("bc1", subdict["viewname"],
                                                       "firstBC = solutionat " + at_x + " is " + parts[1])
                    elif len(subdict["bcs"]) == 2:
                        self.mmtinterface.mmt_new_decl("bc2", subdict["viewname"],
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                                                       "secondBC = solutionat " + at_x + " is " + parts[1])
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                    else:
                        raise InterviewError("too many boundary conditions saved")
                    subdict["measure_given"] += 1
                    subdict["bcs"][-1]["type"] = "Dirichlet",
                    subdict["bcs"][-1]["on"] = at_x,
                    subdict["bcs"][-1]["measure"] = 1,

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            # try:
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            #    type = self.get_inferred_type(subdict["theoryname"], "[u : Ω → ℝ] u(0.0)")
            #    type = self.get_inferred_type(subdict["theoryname"], "[u : Ω → ℝ] u")
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            # except MMTServerError as error:
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            #    self.poutput(error.args[0])

            self.poutput("Ok ")
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            if subdict["measure_given"] == len(self.simdata["unknowns"]) * 2:  # TODO times inferred order of PDE
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                self.trigger('bcs_parsed')
            elif subdict["measure_given"] > len(self.simdata["unknowns"]):
                raise InterviewError("now that's too many boundary conditions. ignoring last input.")
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            else:
                self.poutput("Please enter more boundary conditions")
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    def bcs_exit(self):
        self.poutput("These are all the boundary conditions needed.")
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        self.print_empty_line()
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    def redefine_bcs(self):
        for unknown in get_recursively(self.simdata["unknowns"], "theoryname"):
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            with CriticalSubdict(self.simdata["bcs"], self.poutput) as subdict:
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                subdict["bctypes"] = {}
                bctypetheoryname = unknown + "BCTypes"
                subdict["bctypes"]["theoryname"] = bctypetheoryname
                self.new_theory(bctypetheoryname)
                self.include_in(bctypetheoryname, unknown)
                self.include_in(bctypetheoryname, "mDifferentialOperators")
                self.add_list_of_declarations(bctypetheoryname,
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                                              [
                                                  "myDirichletBC: {where: " + self.simdata["domain"][
                                                      "boundary_name"] + ", rhs: " +
                                                  self.simdata["unknowns"][unknown]["codomain"] + "}(" +
                                                  self.simdata["domain"]["name"] + " → " +
                                                  self.simdata["unknowns"][unknown]["codomain"] + ") → prop "
                                                                                                  " ❘ = [where, rhs][u] u where ≐ rhs ❘  # solutionat 1 is 2 ",
                                                  "myDirichletBCfun : {rhs: " + self.simdata["domain"][
                                                      "boundary_name"] + " → " +
                                                  self.simdata["unknowns"][unknown]["codomain"] + " }(" +
                                                  self.simdata["domain"]["name"] + " → " +
                                                  self.simdata["unknowns"][unknown][
                                                      "codomain"] + ") → prop ❘ = [rhs] [u] ∀[x:" +
                                                  self.simdata["domain"]["boundary_name"] + " ] u x ≐ rhs x "
                                                                                            "❘ # solutionatboundaryis 1",
                                              ]
                                              )
                viewname = bctypetheoryname + "ASmBCTypes"
                subdict["bctypes"]["viewname"] = viewname
                self.mmtinterface.mmt_new_view(viewname, "mBCTypes", bctypetheoryname)
                self.include_former_views(viewname)
                self.add_list_of_declarations(viewname,
                                              ["DirichletBC = myDirichletBC ",
                                               # " = myDirichletBCfun"
                                               ])
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                return bctypetheoryname  # Todo adapt for more than 1

    ##### for state props
    def props_begin(self):
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        with CriticalSubdict(self.simdata["props"], self.poutput) as subdict:
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            # TODO try to find out things about the solvability ourselves
            subdict["theoryname"] = "ephBoundaryValueProblem"
            self.new_theory(subdict["theoryname"])
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            # apparently, need to include everything explicitly so that view works
            for unknownentry in get_recursively(self.simdata["unknowns"], "theoryname"):
                self.include_in(subdict["theoryname"], unknownentry)
            for paramentry in get_recursively(self.simdata["parameters"], "theoryname"):
                self.include_in(subdict["theoryname"], paramentry)
            for pdeentry in get_recursively(self.simdata["pdes"], "theoryname"):
                self.include_in(subdict["theoryname"], pdeentry)
            self.include_in(subdict["theoryname"], self.simdata["bcs"]["theoryname"])
            self.new_view(subdict)
            self.include_trivial_assignment(subdict["viewname"], "mDifferentialOperators")
            self.include_trivial_assignment(subdict["viewname"], "mLinearity")

            subdict["ops"] = []
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            for pde in self.simdata["pdes"]["pdes"]:
                self.poutput("Do you know something about the operator " + pde["op"] + "? "
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                                                                                       "Is it e.g. linear, or not elliptic ? ")
                subdict["ops"].append({})
                subdict["ops"][-1]["name"] = pde["op"]
                subdict["ops"][-1]["props"] = []
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    def props_handle_input(self, userstring):
        if means_no(userstring):
            self.trigger("props_parsed")
            return

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        with CriticalSubdict(self.simdata["props"], self.poutput) as subdict:
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            #            "linear": True, #or false or unknown
            #            "props": ["elliptic"]
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            parsestring = userstring.replace("not", "¬")
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            if "linear" in parsestring:
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                self.add_list_of_declarations(subdict["theoryname"], [
                    add_ods("user_linear : ⊦ " + parsestring + ' mylhs = sketch "user knowledge" ')
                ])
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                if "¬" in parsestring:
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                    subdict["ops"][-1]["linear"] = False
                else:
                    subdict["ops"][-1]["linear"] = True
                    self.add_list_of_declarations(subdict["viewname"], [
                        "isLinear = user_linear"
                    ])
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                self.poutput("OK!")
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            for property in ["elliptic"]:  # TODO more properties
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                if property in parsestring:
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                    self.add_list_of_declarations(subdict["theoryname"], [
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                        add_ods("user_" + property + " : ⊦ " + parsestring + ' mylhs = sketch "user knowledge" ')
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                    ])
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                    subdict["ops"][-1]["props"].append(parsestring)
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                    if "¬" not in parsestring:
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                        self.add_list_of_declarations(subdict["viewname"], [
                            "isElliptic = user_elliptic"
                        ])
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                    self.poutput("OK!")
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            self.poutput("do you know anything else?")

    def props_exit(self):
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        # TODO totality check on the view from uniquelysolvable to ephBoundaryValueProblem
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        return

    ##### for state sim
    def sim_begin(self):
        self.please_prompt("Would you like to try and solve the PDE using the Finite Difference Method in ExaStencils?",
                           self.sim_ok_fd)

    def sim_handle_input(self, userstring):
        self.please_prompt("Would you like to try and solve the PDE using the Finite Difference Method in ExaStencils?",
                           self.sim_ok_fd)

    def sim_exit(self):
        # generate output
        self.exaout.create_output(self.simdata)
        self.poutput("Generated ExaStencils input.")
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        # TODO generate and run simulation
Theresa Pollinger's avatar
Theresa Pollinger committed
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        # display solution using matplotlib
        # cf.https://github.com/ipython/ipython/blob/6a5220d032f5a60267b051783721aa0d5a0e3373/IPython/core/magics/pylab.py

        import matplotlib
        matplotlib.use('nbagg')
        import matplotlib.pyplot as plt
        #from ipykernel.core import InteractiveShell
        plt.ion()
        #try:
        #    gui, backend = self.shell.enable_matplotlib("nbagg")
        #except Exception as e:
        #    raise InterviewError("Unable to use matplotlib for display, sorry! \n" + e.args[0])
        plt.plot([1, 2, 3])

    def enable_matplotlib(self, gui=None):
        """Enable interactive matplotlib and inline figure support.
        stolen from
        https://github.com/ipython/ipython/blob/35a4f43a1bbcd371d6f917e6a2c258848df6e47d/IPython/core/interactiveshell.py .
        This takes the following steps:

        1. select the appropriate eventloop and matplotlib backend
        2. set up matplotlib for interactive use with that backend
        3. configure formatters for inline figure display
        4. enable the selected gui eventloop

        Parameters
        ----------
        gui : optional, string
          If given, dictates the choice of matplotlib GUI backend to use
          (should be one of IPython's supported backends, 'qt', 'osx', 'tk',
          'gtk', 'wx' or 'inline'), otherwise we use the default chosen by
          matplotlib (as dictated by the matplotlib build-time options plus the
          user's matplotlibrc configuration file).  Note that not all backends
          make sense in all contexts, for example a terminal ipython can't
          display figures inline.
        """
        from IPython.core import pylabtools as pt
        gui, backend = pt.find_gui_and_backend(gui, self.pylab_gui_select)

        if gui != 'inline':
            # If we have our first gui selection, store it
            if self.pylab_gui_select is None:
                self.pylab_gui_select = gui
            # Otherwise if they are different
            elif gui != self.pylab_gui_select:
                print('Warning: Cannot change to a different GUI toolkit: %s.'
                      ' Using %s instead.' % (gui, self.pylab_gui_select))
                gui, backend = pt.find_gui_and_backend(self.pylab_gui_select)

        pt.activate_matplotlib(backend)
        pt.configure_inline_support(self, backend)

        # Now we must activate the gui pylab wants to use, and fix %run to take
        # plot updates into account
        self.enable_gui(gui)
        self.magics_manager.registry['ExecutionMagics'].default_runner = \
            pt.mpl_runner(self.safe_execfile)

        return gui, backend
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    def sim_ok_fd(self):
        self.simdata["sim"]["type"] = "FiniteDifferences"
        self.sim_exit()

    #### functions for user interaction
    def obviously_stupid_input(self):
        self.poutput("Trying to be funny, huh?")

    # mmt input helper functions
    def include_in(self, in_which_theory, what):
        return self.mmtinterface.mmt_new_decl("inc", in_which_theory, "include " + assert_question_mark(what))

    def add_list_of_declarations(self, in_which_theory, declaration_list):
        for declaration in declaration_list:
            self.mmtinterface.mmt_new_decl("inc", in_which_theory, declaration)

    def include_bgthys(self, in_which_theory):
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        """Includes all the background theories specified in self.bgthys for the current state"""
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        ok = True
        for bgthy in self.bgthys[self.state]:
            ok = ok and self.include_in(in_which_theory, bgthy)
        return ok

    def new_theory(self, thyname):
        try:
            self.mmtinterface.mmt_new_theory(thyname)
            return self.include_bgthys(thyname)
        except MMTServerError as error:
            self.poutput(error.args[0])
            # self.poutput(error.with_traceback())
            raise
        # (ok, root) = self.mmtinterface.query_for(self.simdata[self.state]["theoryname"])

    def new_view(self, dictentry):
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        """Constructs a new entry 'viewname' into the given dictionary and creates the view,
        including all applicable former views"""
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        dictentry["viewname"] = self.construct_current_view_name(dictentry)
        # self.poutput("new view: "+dictentry["viewname"])
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        self.mmtinterface.mmt_new_view(dictentry["viewname"], self.viewfrom[self.state], dictentry["theoryname"])
        return self.include_former_views(dictentry["viewname"])

    def include_former_views(self, current_view_name):
        """recursively look for all views already done and try to include them into the current view."""
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        for viewstring in get_recursively(self.simdata, "viewname"):
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            if (current_view_name != viewstring):
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                try:
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                    self.include_in(current_view_name,
                                    "?" + re.split('AS', viewstring)[-1] + " = " + "?" + viewstring)
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                except MMTServerError as error:
                    # self.poutput("no backend available that is applicable to " + "http://mathhub.info/MitM/smglom/calculus" + "?" + re.split('AS', dictentry["viewname"])[-1] + "?")
                    # we are expecting errors if we try to include something that is not referenced in the source theory, so ignore them
Theresa Pollinger's avatar
Theresa Pollinger committed
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                    expected_str = "no backend available that is applicable to " + "http://mathhub.info/MitM/smglom/calculus" + "?" + re.split('AS', current_view_name)[-1] + "?"
                    if expected_str not in error.args[0]:
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                        raise

    def construct_current_view_name(self, dictentry):
        return self.construct_view_name(dictentry, self.state)

    def construct_view_name(self, dictentry, state):
        return dictentry["theoryname"] + "AS" + (self.viewfrom[state])

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    def include_trivial_assignment(self, in_view, theoryname):
        self.include_in(in_view, assert_question_mark(theoryname) + " = " + assert_question_mark(theoryname))

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    def get_inferred_type(self, in_theory, term):
        return self.mmtinterface.mmt_infer_type(in_theory, term).inferred_type_to_string()

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    def try_expand(self, term,
                   in_theory=None):  # TODO do using mmt definition expansion, issue UniFormal/MMT/issues/295
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        for param in reversed(self.simdata["parameters"]):
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            if param in term:
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                parts = self.simdata["parameters"][param]["string"].split("=")
                if (len(parts) != 2):
                    raise InterviewError("no definition for " + param + " given")
                paramdef = parts[-1]
                term = term.replace(param, paramdef.strip())
        return term

    def print_empty_line(self):
        self.poutput("\n")

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    def explain(self, userstring=None):
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        with CriticalSubdict({}, self.poutput):
            reply = self.mmtinterface.query_for(
                "http://mathhub.info/smglom/calculus/nderivative.omdoc?nderivative?nderivative")
            self.poutput(reply.tostring())
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    def recap(self, userstring=None):
        self.print_simdata()

    def print_simdata(self):
        for s in reversed(self.states):
            state_name = s.name
            if state_name in self.simdata:
                self.poutput(state_name + ": " + str(self.simdata[state_name]))
            if state_name == self.state:
                return