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|
{-# LANGUAGE OverloadedStrings #-}
module Felix.Test.Unit.Concrete (unitTests) where
import Base
import Felix.Report.Location
import Felix.Syntax.Abstract qualified as Raw
import Felix.Syntax.Concrete (grammar)
import Felix.Syntax.Lexicon (builtins)
import Felix.Syntax.Token (runLexer)
import Data.Text qualified as Text
import Test.Tasty
import Test.Tasty.HUnit
import Text.Earley (fullParses, parser)
import Text.Megaparsec (errorBundlePretty)
unitTests :: TestTree
unitTests =
testGroup "Parser"
[ testCase
"textual connectives follow symbolic precedence"
textualConnectivePrecedence
, testCase
"transfinite induction precedes its continuation"
transfiniteInductionContinuation
]
data StatementShape
= Truth
| Falsity
| Connected Raw.Connective StatementShape StatementShape
| Scoped StatementShape
deriving (Show, Eq)
textualConnectivePrecedence :: Assertion
textualConnectivePrecedence = do
for_ cases \(label, statement, expected) ->
assertEqual label (Right expected) (statementShape =<< parseStatement statement)
assertBool
"chained iff is rejected"
(case parseStatement "$\\top$ iff $\\bot$ iff $\\top$" of
Left _ -> True
Right _ -> False)
assertEqual
"textual and symbolic connective trees agree"
(statementShape
=<< parseStatement
"$\\top \\land \\bot \\lor \\top$")
(statementShape
=<< parseStatement
"$\\top$ and $\\bot$ or $\\top$")
where
cases =
[ ( "and binds tighter than following or"
, "$\\top$ and $\\bot$ or $\\top$"
, Connected Raw.Disjunction
(Connected Raw.Conjunction Truth Falsity)
Truth
)
, ( "and binds tighter than preceding or"
, "$\\top$ or $\\bot$ and $\\top$"
, Connected Raw.Disjunction
Truth
(Connected Raw.Conjunction Falsity Truth)
)
, ( "and associates left"
, "$\\top$ and $\\bot$ and $\\top$"
, Connected Raw.Conjunction
(Connected Raw.Conjunction Truth Falsity)
Truth
)
, ( "or associates left"
, "$\\top$ or $\\bot$ or $\\top$"
, Connected Raw.Disjunction
(Connected Raw.Disjunction Truth Falsity)
Truth
)
, ( "either is accepted after ordinary or"
, "$\\top$ or either $\\bot$ or $\\top$"
, Connected Raw.Disjunction
Truth
(Connected Raw.ExclusiveOr Falsity Truth)
)
, ( "implication associates right"
, "if $\\top$ then if $\\bot$ then $\\top$"
, Connected Raw.Implication
Truth
(Connected Raw.Implication Falsity Truth)
)
, ( "a quantified implication antecedent ends at then"
, "if for all $x$ we have $\\top$ then $\\bot$"
, Connected Raw.Implication
(Scoped Truth)
Falsity
)
, ( "parentheses override precedence"
, "($\\top$ or $\\bot$) and $\\top$"
, Connected Raw.Conjunction
(Connected Raw.Disjunction Truth Falsity)
Truth
)
, ( "a quantified right operand scopes over its continuation"
, "$\\top$ iff there exists $x$ such that $\\bot$ and $\\top$"
, Connected Raw.Equivalence
Truth
(Scoped
(Connected Raw.Conjunction Falsity Truth))
)
]
parseStatement :: Text -> Either String Raw.Stmt
parseStatement statement = do
chunks <- case runLexer
(FileId 46)
"textual-connectives.tex"
(Text.unlines
[ "\\begin{axiom}\\label{textual_connectives}"
, statement <> "."
, "\\end{axiom}"
]) of
Left err ->
Left (errorBundlePretty err)
Right (_imports, chunks') ->
Right chunks'
tokens <- case chunks of
[tokens'] ->
Right tokens'
_ ->
Left ("expected one source chunk, got " <> show (length chunks))
case fullParses (parser (grammar builtins)) tokens of
( [Raw.BlockAxiom
_location
_title
_marker
(Raw.Axiom [] statement')]
, _report
) ->
Right statement'
(blocks, report) ->
Left
( "expected one axiom, got "
<> show blocks
<> " with "
<> show report
)
statementShape :: Raw.Stmt -> Either String StatementShape
statementShape = \case
Raw.StmtConnected conn _ left right ->
Connected conn
<$> statementShape left
<*> statementShape right
Raw.StmtFormula formula ->
formulaShape formula
Raw.SymbolicQuantified _ _ _ _ _ statement ->
Scoped <$> statementShape statement
statement ->
Left ("unsupported statement in precedence test: " <> show statement)
formulaShape :: Raw.Formula -> Either String StatementShape
formulaShape = \case
Raw.PropositionalConstant _ Raw.IsTop ->
Right Truth
Raw.PropositionalConstant _ Raw.IsBottom ->
Right Falsity
Raw.Connected _ conn left right ->
Connected conn
<$> formulaShape left
<*> formulaShape right
formula ->
Left ("unsupported formula in precedence test: " <> show formula)
transfiniteInductionContinuation :: Assertion
transfiniteInductionContinuation =
case runLexer
(FileId 45)
"transfinite-induction.tex"
sourceText of
Left err ->
assertFailure (errorBundlePretty err)
Right (_imports, [tokens]) ->
case fullParses (parser (grammar builtins)) tokens of
( [ Raw.BlockProof
_start
(Raw.ByOrdInduction methodLocation
(Raw.Qed
(Just continuationLocation)
Raw.JustificationEmpty))
_end
]
, _report
) -> do
assertEqual
"method header line"
2
(locLine methodLocation)
assertEqual
"continuation line"
3
(locLine continuationLocation)
(blocks, report) ->
assertFailure
( "expected one transfinite-induction proof, got "
<> show blocks
<> " with "
<> show report
)
Right (_imports, chunks) ->
assertFailure
("expected one proof chunk, got " <> show (length chunks))
where
sourceText =
Text.unlines
[ "\\begin{proof}"
, "[proof by transfinite induction]"
, "Trivial."
, "\\end{proof}"
]
|
