Closes: #4546

The algorithm uses an array to store the headers and validators and populates it at every bisection (which is an unsuccessful verification). When a successful verification finally occurs it updates the new trusted header, trims that header from the cache (the array) and sets the depth pointer back to 0. Instead of retrieving new headers it will use the cached headers, incrementing in depth until it reaches the end of the cache which by then it will start to retrieve new headers from the provider. 

Mathematically, this method doesn't properly bisect after the first round but it will always choose a pivot header that is within 1/8th of the upper header's height. I.e. if we are trying to jump 128 headers, the maximum offset from bisection height (64) is 64 + 16(128/8) = 80, therefore a better heuristic would be to obtain the new pivot header height as the middle of these two numbers which would therefore mean to multiply it by 9/16ths instead of 1/2  (sorry this might be a bit more complicated in writing but I can try better explain if someone is interested). Therefore I would also, upon consensus, propose that we change the pivot height to 9/16th's of the previous height

We first introduced auto-update as a separate struct AutoClient, which
was wrapping Client and calling Update periodically.

// AutoClient can auto update itself by fetching headers every N seconds.
type AutoClient struct {
    base         *Client
    updatePeriod time.Duration
    quit         chan struct{}

    trustedHeaders chan *types.SignedHeader
    errs           chan error
}

// NewAutoClient creates a new client and starts a polling goroutine.
func NewAutoClient(base *Client, updatePeriod time.Duration) *AutoClient {
    c := &AutoClient{
        base:           base,
        updatePeriod:   updatePeriod,
        quit:           make(chan struct{}),
        trustedHeaders: make(chan *types.SignedHeader),
        errs:           make(chan error),
    }
    go c.autoUpdate()
    return c
}

// TrustedHeaders returns a channel onto which new trusted headers are posted.
func (c *AutoClient) TrustedHeaders() <-chan *types.SignedHeader {
    return c.trustedHeaders
}

// Err returns a channel onto which errors are posted.
func (c *AutoClient) Errs() <-chan error {
    return c.errs
}

// Stop stops the client.
func (c *AutoClient) Stop() {
    close(c.quit)
}

func (c *AutoClient) autoUpdate() {
    ticker := time.NewTicker(c.updatePeriod)
    defer ticker.Stop()

    for {
        select {
        case <-ticker.C:
            lastTrustedHeight, err := c.base.LastTrustedHeight()
            if err != nil {
                c.errs <- err
                continue
            }

            if lastTrustedHeight == -1 {
                // no headers yet => wait
                continue
            }

            newTrustedHeader, err := c.base.Update(time.Now())
            if err != nil {
                c.errs <- err
                continue
            }

            if newTrustedHeader != nil {
                 c.trustedHeaders <- newTrustedHeader
            }
        case <-c.quit:
            return
        }
    }
}

Later we merged it into the Client itself with the assumption that most clients will want it.

But now I am not sure. Neither IBC nor cosmos/relayer are using it. It increases complexity (Start/Stop methods).

That said, I think it makes sense to remove it until we see a need for it (until we better understand usage behavior). We can always introduce it later 😅. Maybe in the form of AutoClient.

* docs: update Light Client Protocol page

Closes #4331

* one way to get hash & height

* rename adjusted to adjacent

Refs https://github.com/tendermint/tendermint/pull/3989#discussion_r352140829

* rename ErrTooMuchChange to ErrNotEnoughVotingPowerSigned

Refs https://github.com/tendermint/tendermint/pull/3989#discussion_r352142785

* verify commit is properly signed

* remove no longer trusted headers

* restore trustedHeader and trustedNextVals

* check trustedHeader using options

Refs https://github.com/tendermint/tendermint/pull/4209#issuecomment-562462165

* use correct var when checking if headers are adjacent

in bisection func
+ replace TODO with a comment

https://github.com/tendermint/tendermint/pull/3989#discussion_r352125455

* return header in VerifyHeaderAtHeight

because that way we avoid DB call

+ add godoc comments
+ check if there are no headers yet in AutoClient

https://github.com/tendermint/tendermint/pull/3989#pullrequestreview-315454506

* TestVerifyAdjacentHeaders: add 2 more test-cases

+ add TestVerifyReturnsErrorIfTrustLevelIsInvalid

* lite: avoid overflow when parsing key in db store!

* lite: rename AutoClient#Err to Errs

* lite: add a test for AutoClient

* lite: fix keyPattern and call itr.Next in db store

* lite: add two tests for db store

* lite: add TestClientRemovesNoLongerTrustedHeaders

* lite: test Client#Cleanup

* lite: test restoring trustedHeader

https://github.com/tendermint/tendermint/pull/4209#issuecomment-562462165

* lite: comment out unused code in test_helpers

* fix TestVerifyReturnsErrorIfTrustLevelIsInvalid after merge

* change defaultRemoveNoLongerTrustedHeadersPeriod

and add docs

* write more doc

* lite: uncomment testable examples

* use stdlog.Fatal to stop AutoClient tests

* make lll linter happy

* separate errors for 2 cases

- the validator set of a skipped header cannot be trusted, i.e. <1/3rd
  of h1 validator set has signed (new error, something like
  ErrNewValSetCantBeTrusted)
- the validator set is trusted but < 2/3rds has signed
  (ErrNewHeaderCantBeTrusted)

https://github.com/tendermint/tendermint/pull/4209#discussion_r360331253

* remove all headers (even the last one) that are outside

of the trusting period. By doing this, we avoid checking the
trustedHeader's hash in checkTrustedHeaderUsingOptions (case #1).

https://github.com/tendermint/tendermint/pull/4209#discussion_r360332460

* explain restoreTrustedHeaderAndNextVals better

https://github.com/tendermint/tendermint/pull/4209#discussion_r360602328

* add ConfirmationFunction option

for optionally prompting for user input Y/n before removing headers

Refs https://github.com/tendermint/tendermint/pull/4209#discussion_r360602945

* make cleaning optional

https://github.com/tendermint/tendermint/pull/4209#discussion_r364838189

* return error when user refused to remove headers

* check for double votes in VerifyCommitTrusting

* leave only ErrNewValSetCantBeTrusted error

to differenciate between h2Vals.VerifyCommit and
h1NextVals.VerifyCommitTrusting

* fix example tests

* remove unnecessary if condition

https://github.com/tendermint/tendermint/pull/4209#discussion_r365171847

It will be handled by the above switch.

* verifyCommitBasic does not depend on vals

Co-authored-by: Marko <marbar3778@yahoo.com>

Refs #1771

ADR: https://github.com/tendermint/tendermint/blob/master/docs/architecture/adr-044-lite-client-with-weak-subjectivity.md

## Commits:

* add Verifier and VerifyCommitTrusting

* add two more checks

make trustLevel an option

* float32 for trustLevel

* check newHeader time

* started writing lite Client

* unify Verify methods

* ensure h2.Header.bfttime < h1.Header.bfttime + tp

* move trust checks into Verify function

* add more comments

* more docs

* started writing tests

* unbonding period failures

* tests are green

* export ErrNewHeaderTooFarIntoFuture

* make golangci happy

* test for non-adjusted headers

* more precision

* providers and stores

* VerifyHeader and VerifyHeaderAtHeight funcs

* fix compile errors

* remove lastVerifiedHeight, persist new trusted header

* sequential verification

* remove TrustedStore option

* started writing tests for light client

* cover basic cases for linear verification

* bisection tests PASS

* rename BisectingVerification to SkippingVerification

* refactor the code

* add TrustedHeader method

* consolidate sequential verification tests

* consolidate skipping verification tests

* rename trustedVals to trustedNextVals

* start writing docs

* ValidateTrustLevel func and ErrOldHeaderExpired error

* AutoClient and example tests

* fix errors

* update doc

* remove ErrNewHeaderTooFarIntoFuture

This check is unnecessary given existing a) ErrOldHeaderExpired b)
h2.Time > now checks.

* return an error if we're at more recent height

* add comments

* add LastSignedHeaderHeight method to Store

I think it's fine if Store tracks last height

* copy over proxy from old lite package

* make TrustedHeader return latest if height=0

* modify LastSignedHeaderHeight to return an error if no headers exist

* copy over proxy impl

* refactor proxy and start http lite client

* Tx and BlockchainInfo methods

* Block method

* commit method

* code compiles again

* lite client compiles

* extract updateLiteClientIfNeededTo func

* move final parts

* add placeholder for tests

* force usage of lite http client in proxy

* comment out query tests for now

* explicitly mention tp: trusting period

* verify nextVals in VerifyHeader

* refactor bisection

* move the NextValidatorsHash check into updateTrustedHeaderAndVals

+ update the comment

* add ConsensusParams method to RPC client

* add ConsensusParams to rpc/mock/client

* change trustLevel type to a new cmn.Fraction type

+ update SkippingVerification comment

* stress out trustLevel is only used for non-adjusted headers

* fixes after Fede's review

Co-authored-by: Federico Kunze <31522760+fedekunze@users.noreply.github.com>

* compare newHeader with a header from an alternative provider

* save pivot header

Refs https://github.com/tendermint/tendermint/pull/3989#discussion_r349122824

* check header can still be trusted in TrustedHeader

Refs https://github.com/tendermint/tendermint/pull/3989#discussion_r349101424

* lite: update Validators and Block endpoints

- Block no longer contains BlockMeta
- Validators now accept two additional params: page and perPage

* make linter happy