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module Encoding where
import Base
import Syntax.Internal
import Syntax.Lexicon
import Tptp.UnsortedFirstOrder qualified as Tptp
import Data.Text qualified as Text
import Bound
import Bound.Scope
encodeTask :: Lexicon -> Task -> Tptp.Task
encodeTask l (Task _isByContradiction hypos m conjecture) = Tptp.Task (conjecture' : hypos')
where
conjecture' = encodeConjecture l m conjecture
hypos' = encodeHypos l hypos
encodeConjecture :: Lexicon -> Marker -> Formula -> Tptp.AnnotatedFormula
encodeConjecture l (Marker str) f = Tptp.AnnotatedFormula (Tptp.NameAtomicWord (Tptp.AtomicWord str)) Tptp.Conjecture (encodeExpr l f)
-- NOTE: E's SInE will only filter out axioms and leave hypotheses fixed.
encodeHypos :: Lexicon -> [(Marker, Formula)] -> [Tptp.AnnotatedFormula]
encodeHypos l phis = [makeHypo m (encodeExpr l phi) | (m, phi) <- phis]
where
makeHypo :: Marker -> Tptp.Expr -> Tptp.AnnotatedFormula
makeHypo (Marker str) f' = Tptp.AnnotatedFormula (Tptp.NameAtomicWord (Tptp.AtomicWord str)) Tptp.Axiom f'
encodeWithRole :: Tptp.Role -> Lexicon -> [(Marker, Formula)] -> [Tptp.AnnotatedFormula]
encodeWithRole role l phis = [makeHypo m (encodeExpr l phi) | (m, phi) <- phis]
where
makeHypo :: Marker -> Tptp.Expr -> Tptp.AnnotatedFormula
makeHypo (Marker str) f' = Tptp.AnnotatedFormula (Tptp.NameAtomicWord (Tptp.AtomicWord str)) role f'
encodeExpr :: Lexicon -> Expr -> Tptp.Expr
encodeExpr l = go . (fmap encodeFreeVar)
where
go :: ExprOf Tptp.Expr -> Tptp.Expr
go = \case
e1 `Equals` e2 ->
Tptp.Eq (go e1) (go e2)
e1 `NotEquals` e2 ->
Tptp.NotEq (go e1) (go e2)
Atomic p es ->
let p' = encodePredicate l p
es' = go <$> toList es
in Tptp.Apply p' es'
PropositionalConstant IsBottom ->
Tptp.Bottom
PropositionalConstant IsTop ->
Tptp.Top
Not f ->
Tptp.Not (go f)
Connected Conjunction f1 f2 ->
Tptp.Conn Tptp.And (go f1) (go f2)
Connected Disjunction f1 f2 ->
Tptp.Conn Tptp.Or (go f1) (go f2)
Connected Implication f1 f2 ->
Tptp.Conn Tptp.Imply (go f1) (go f2)
Connected Equivalence f1 f2 ->
Tptp.Conn Tptp.Iff (go f1) (go f2)
Connected NegatedDisjunction f1 f2 ->
Tptp.Not (Tptp.Conn Tptp.Or (go f1) (go f2))
Connected ExclusiveOr f1 f2 ->
Tptp.Not (Tptp.Conn Tptp.Iff (go f1) (go f2))
Quantified quant scope ->
let phi = instantiate instantiator scope
xs = [encodeBoundVar x | x <- nubOrd (bindings scope)]
phi' = go phi
quant' = encodeQuant quant
in case xs of
[] -> phi'
y:ys -> Tptp.Quantified quant' (y:|ys) phi'
TermVar v ->
v
Apply e es -> case e of
TermVar (Tptp.Const x) -> Tptp.Apply x (go <$> toList es)
_ -> error ("encodeExpr: complex term as head of applicaition: " <> show e)
TermSymbol symb es ->
Tptp.Apply (encodeSymbol l symb) (go <$> es)
e@ReplaceFun{} ->
error ("Precondition failed in encodeTerm, cannot encode terms with comprehensions directly: " <> show e)
e@ReplacePred{} ->
error ("Precondition failed in encodeTerm, cannot encode terms with comprehensions directly: " <> show e)
e@TermSep{} ->
error ("Precondition failed in encodeTerm, cannot encode terms with comprehensions directly: " <> show e)
e@Iota{} ->
error ("Precondition failed in encodeTerm, cannot encode terms with descriptors directly: " <> show e)
TermSymbolStruct symb e -> case e of
Just e' ->
Tptp.Apply (Tptp.AtomicWord ("s__" <> (unStructSymbol symb))) [go e']
Nothing ->
error ("encodeExpr.go (precondition failed): unannotated struct symbol" <> show symb)
_ -> error "encodeExpr.go: missing case"
instantiator :: VarSymbol -> ExprOf Tptp.Expr
instantiator bv = TermVar (Tptp.Var (encodeBoundVar bv))
encodeQuant :: Quantifier -> Tptp.Quantifier
encodeQuant Universally = Tptp.Forall
encodeQuant Existentially = Tptp.Exists
encodeSymbol :: Lexicon -> Symbol -> Tptp.AtomicWord
encodeSymbol l symb = atomicWordFromRightMarker case symb of
SymbolMixfix op ->
lookupOp op (lexiconMixfix l)
SymbolFun fun ->
lookupLexicalItem fun (lexiconFuns l)
SymbolInteger n ->
Right (Marker (Text.pack (show n)))
SymbolPredicate _ ->
error "IMPOSSIBLE: predicates should already be translated"
encodePredicate :: Lexicon -> Predicate -> Tptp.AtomicWord
encodePredicate l p = atomicWordFromRightMarker case p of
PredicateAdj adj ->
lookupLexicalItem adj (lexiconAdjs l)
PredicateVerb verb ->
lookupLexicalItem verb (lexiconVerbs l)
PredicateNoun noun ->
lookupLexicalItem noun (lexiconNouns l)
PredicateRelation rel ->
lookupLexicalItem rel (lexiconRelationSymbols l)
PredicateNounStruct noun ->
lookupLexicalItem noun (lexiconStructNouns l)
PredicateSymbol symb ->
Right (Marker symb)
atomicWordFromRightMarker :: Either String Marker -> Tptp.AtomicWord
atomicWordFromRightMarker = \case
Right (Marker m) -> Tptp.AtomicWord m
Left a -> error ("symbol not in lexicon" <> a)
encodeFreeVar :: VarSymbol -> Tptp.Expr
encodeFreeVar fv = Tptp.Const fv'
where
fv' = Tptp.AtomicWord case fv of
NamedVar x -> Text.cons 'f' x
FreshVar n -> Text.cons 'y' (Text.pack (show n))
-- | Tptp variables must be "upper words", starting with an uppercase letter
-- and continuing with alphanumeric characters. We prefix all variables
-- with "X" to make them easy to decode.
encodeBoundVar :: VarSymbol -> Tptp.Variable
encodeBoundVar bv = Tptp.Variable $ Text.cons 'X' case bv of
NamedVar x -> x
FreshVar n -> Text.pack (show n)
|
