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module Megalodon where
import Base hiding (null)
import Syntax.Internal
import Syntax.Lexicon
import Checking (makeReplacementIff)
import Bound.Scope
import Bound.Var
import Data.HashMap.Strict qualified as HM
import Data.List.NonEmpty qualified as NonEmpty
import Text.Builder
import Data.List qualified as List
import Data.Text qualified as Text
encodeBlocks :: Lexicon -> [Block] -> Text
encodeBlocks lexi blocks = run (preamble <> buildBlocks lexi blocks)
closure :: [ExprOf VarSymbol] -> ExprOf VarSymbol -> Formula
closure asms stmt = contraction (forallClosure mempty (makeConjunction asms `Implies` stmt))
unAsm :: Asm -> Formula
unAsm (Asm phi )= phi
unAsm (AsmStruct x sp) = TermSymbol (SymbolPredicate (PredicateNounStruct sp)) [TermVar x]
buildBlocks :: Lexicon -> [Block] -> Builder
buildBlocks lexi = \case
BlockAxiom _pos lbl (Axiom asms stmt) : blocks ->
let phi = closure (unAsm <$> asms) stmt
in text "Fact " <> buildMarker lbl <> text " : " <> buildFormula lexi phi <> text ".\nAdmitted.\n" <> buildBlocks lexi blocks
BlockLemma _pos lbl (Lemma asms stmt) : BlockProof _ _ : blocks ->
let phi = closure (unAsm <$> asms) stmt
in text "Theorem " <> buildMarker lbl <> text " : " <> buildFormula lexi phi <> text ".\nAdmitted.\n" <> buildBlocks lexi blocks
BlockLemma _pos lbl (Lemma asms stmt) : blocks ->
let phi = closure (unAsm <$> asms) stmt
in text "Theorem " <> buildMarker lbl <> text " : " <> buildFormula lexi phi <> text ".\nAdmitted.\n" <> buildBlocks lexi blocks
BlockDefn _pos _lbl defn : blocks->
buildDefn lexi defn <> buildBlocks lexi blocks
BlockAbbr _pos _lbl abbr : blocks->
buildAbbr lexi abbr <> buildBlocks lexi blocks
[] ->
mempty
block : _ ->
_TODO ("builBlocks" <> show block)
buildDefn :: Lexicon -> Defn -> Builder
buildDefn lexi = \case
DefnPredicate [] predi xs phi ->
"Definition " <> buildSymbol lexi (SymbolPredicate predi) <> " := " <>
"fun " <> buildVarSymbols xs <> ": set => " <> buildFormula lexi phi <> ".\n"
DefnFun [] f xs phi ->
"Definition " <> buildSymbol lexi (SymbolFun f) <> " := " <>
buildSetFunIfNonEmpty (buildVarSymbols xs) (buildFormula lexi phi) <> ".\n"
DefnOp f xs phi ->
"Definition " <> buildSymbol lexi (SymbolMixfix f) <> " := " <>
buildSetFunIfNonEmpty (buildVarSymbols xs) (buildFormula lexi phi) <> ".\n"
_ ->
error "assumptions in definition, deprecated"
buildAbbr :: Lexicon -> Abbreviation -> Builder
buildAbbr lexi (Abbreviation f body) =
"Definition " <> buildSymbol lexi f <> " := " <>
buildSetFunIfNonEmpty buildBindings' (buildFormula lexi ((instantiate (TermVar . FreshVar) (fmap absurd body)))) <> ".\n"
where
buildBindings' :: Builder
buildBindings' = intercalate (char ' ') (buildVarSymbol . FreshVar <$> List.sort (List.nub (bindings body)))
buildSetFunIfNonEmpty :: Builder -> Builder -> Builder
buildSetFunIfNonEmpty xs b = if null xs then b else "fun " <> xs <> " : set => " <> b
buildFormula :: Lexicon -> Formula -> Builder
buildFormula lexi = \case
TermVar x -> buildVarSymbol x
-- We handle eq in a special manner to avoid having to specify the type of the equality.
TermSymbol f [x,y] | isEqSymbol f ->
char '(' <> buildFormula lexi x <> text " = " <> buildFormula lexi y <> char ')'
TermSymbol f [x,y] | isDiseqSymbol f ->
char '(' <> buildFormula lexi x <> text " <> " <> buildFormula lexi y <> char ')'
TermSymbol f es ->
let es' = buildSymbol lexi f : (buildFormula lexi <$> es)
in char '(' <> intercalate (char ' ') es' <> char ')'
Apply e es ->
let es' = NonEmpty.cons (buildFormula lexi e) (buildFormula lexi <$> es)
in char '(' <> intercalate (char ' ') es' <> char ')'
Not e -> text "~(" <> buildFormula lexi e <> char ')'
Connected conn e1 e2 ->
char '(' <> buildConn conn (buildFormula lexi e1) (buildFormula lexi e2) <> char ')'
Quantified quant body ->
char '(' <> buildQuant quant <> char ' ' <> buildBindings body <> text ",(" <> buildFormula lexi (instantiate TermVar body) <> text "))"
TermSep x bound phi ->
char '{' <> buildVarSymbol x <> " :e (" <> buildFormula lexi bound <> text ")|" <> buildFormula lexi (instantiate1 (TermVar x) phi) <> char '}'
Iota _ _ -> error "TODO buildFormula Iota"
ReplacePred y x xB body ->
let x' = buildVarSymbol x
y' = buildVarSymbol y
fromReplacementVar = \case
ReplacementDomVar -> TermVar x
ReplacementRangeVar -> TermVar y
body' = buildFormula lexi (instantiate fromReplacementVar body)
in "let MkReplFun := fun " <> x' <> " : set => (Eps_i (fun " <> y' <> "=>" <> body' <> ")) in {MkReplFun " <> x' <> "|" <> x' <> " :e (" <> buildFormula lexi xB <> ")}"
ReplaceFun ((x, xB) :| []) lhs cond ->
let x' = buildVarSymbol x
xB' = "(" <> buildFormula lexi xB <> ")" -- parens probably not needed
lhs' = "(fun " <> x' <> " => " <> buildFormula lexi (instantiate TermVar lhs) <> ")"
cond' = "(fun " <> x' <> " => " <> buildFormula lexi (instantiate TermVar cond) <> ")"
-- Using "ReplSep : set->(set->prop)->(set->set)->set"
in "ReplSep " <> xB' <> cond' <> lhs'
ReplaceFun ((x, xB) :| (y, yB) : []) lhs cond ->
let x' = buildVarSymbol x
xB' = "(" <> buildFormula lexi xB <> ")"
y' = buildVarSymbol y
yB' = "(fun dummyVar => " <> buildFormula lexi yB <> ")"
lhs' = "(fun " <> x' <> " " <> y' <> " => " <> buildFormula lexi (instantiate TermVar lhs) <> ")"
cond' = "(fun " <> x' <> " " <> y' <> " => " <> buildFormula lexi (instantiate TermVar cond) <> ")"
-- Using "ReplSep2 : set -> (set -> set) -> (set -> set -> prop) -> (set -> set -> set) -> set"
in "ReplSep2 " <> xB' <> yB' <> cond' <> lhs'
ReplaceFun bounds lhs cond ->
-- Silly placeholder translation for now
let iff = makeReplacementIff (TermVar (F "frs")) bounds lhs cond
in "Eps_i (fun frs : set => " <> buildFormula lexi iff <> ")"
Lambda _ -> text "TODO_buildFormula_Lambda"
PropositionalConstant IsTop -> "True"
PropositionalConstant IsBottom -> "False"
TermSymbolStruct f me ->
let f' = buildMarker ((?? error "unrecognized symbol") (HM.lookup f (lexiconStructFun lexi)))
e = me ?? error "unannotated struct op"
in char '(' <> f' <> buildFormula lexi e <> char ')'
buildMarker :: Marker -> Builder
buildMarker (Marker m)= text m
buildQuant :: Quantifier -> Builder
buildQuant = \case
Universally -> "forall"
Existentially -> "exists"
buildBindings :: Scope VarSymbol ExprOf a -> Builder
buildBindings body = intercalate (char ' ') (buildVarSymbol <$> List.nub (bindings body))
buildBounds :: Lexicon -> NonEmpty (VarSymbol, ExprOf VarSymbol) -> Builder
buildBounds l (bound :| bounds) = foldr (\b bs -> buildBound b <> "/\\ " <> bs) (buildBound bound) bounds
where
buildBound (y, yB) = buildVarSymbol y <> " :e (" <> buildFormula l yB <> ")"
buildConn :: Connective -> (Builder -> Builder -> Builder)
buildConn conn = \p q -> case conn of
Conjunction -> p <> text "/\\" <> q
Disjunction -> p <> text "\\/" <> q
Implication -> p <> text "->" <> q
Equivalence -> p <> text "<->" <> q
ExclusiveOr -> text "xor" <> p <> char ' ' <> q
NegatedDisjunction -> text "nor" <> p <> char ' ' <> q
buildVarSymbol :: VarSymbol -> Builder
buildVarSymbol = \case
NamedVar x -> text x
FreshVar i -> char 'x' <> decimal i
buildVarSymbols :: (Functor t, Foldable t) => t VarSymbol -> Builder
buildVarSymbols xs = intercalate (char ' ') (fmap buildVarSymbol xs)
buildSymbol :: Lexicon -> Symbol -> Builder
buildSymbol _ (SymbolInteger i) = decimal i
buildSymbol lexi symb = fromRightMarker case symb of
SymbolMixfix f ->
lookupOp f (lexiconMixfix lexi)
SymbolFun f -> lookupLexicalItem f (lexiconFuns lexi)
SymbolPredicate (PredicateAdj f) -> lookupLexicalItem f (lexiconAdjs lexi)
SymbolPredicate (PredicateVerb f) -> lookupLexicalItem f (lexiconVerbs lexi)
SymbolPredicate (PredicateNoun f) -> lookupLexicalItem f (lexiconNouns lexi)
SymbolPredicate (PredicateRelation f) ->lookupLexicalItem f (lexiconRelationSymbols lexi)
SymbolPredicate (PredicateNounStruct f) -> lookupLexicalItem f (lexiconStructNouns lexi)
SymbolPredicate (PredicateSymbol f) -> Right (Marker f) -- HM.lookup f (lexiconPrefixPredicates lexi)
fromRightMarker :: Either String Marker -> Builder
fromRightMarker = \case
Right (Marker m) -> text m
Left a -> error ("symbol not in lexicon" <> a)
isEqSymbol :: Symbol -> Bool
isEqSymbol = \case
SymbolPredicate (PredicateRelation (Symbol "=")) -> True
SymbolPredicate (PredicateVerb f) | f == (unsafeReadPhraseSgPl "equal[s/] ?") -> True
SymbolPredicate (PredicateAdj f) | f == (unsafeReadPhrase "equal to ?") -> True
_ -> False
isDiseqSymbol :: Symbol -> Bool
isDiseqSymbol = \case
SymbolPredicate (PredicateRelation (Command "neq")) -> True
SymbolPredicate (PredicateAdj f) | f == (unsafeReadPhrase "distinct from ?") -> True
_ -> False
preamble :: Builder
preamble = text $ Text.unlines
[ "Let emptyset : set := Empty."
, "Let elem : set->set->prop := In."
, "Let notelem : set->set->prop := fun a A => ~(In a A)."
, "Let pow : set->set := Power."
, "Let unions : set->set := Union."
, "Let union : set->set->set := binunion."
, "Let cons : set -> set -> set := fun x X => binunion {x} X."
, "Let xor : prop -> prop -> prop := fun p q => (p \\/ q) /\\ ~(p /\\ q)."
, "Let pair : set -> set -> set := fun a b => {{a}, {a, b}}."
, "Let fst : set -> set := fun p => Eps_i (fun a => exists b, p = pair a b)."
, "Let snd : set -> set := fun p => Eps_i (fun b => exists a, p = pair a b)."
, "Let nor : prop -> prop -> prop := fun p q => ~(p \\/ q) ."
]
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