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module Library.Command (
name,
number,
absTerm,
absThm,
appTerm,
appThm,
assume,
axiom,
betaConv,
constant,
constTerm,
deductAntisym,
defineConst,
defineTypeOp,
eqMp,
opType,
refl,
subst,
thm,
typeOp,
var,
varTerm,
varType
) where
-- deliberately not included:
-- cons, nil, def, ref, remove, pop
-- all functions here deal exclusively with arguments
-- and results from/to the stack
import Control.Monad
import Data.List
import Data.Maybe
import qualified Data.Set as Set
import qualified Data.Map as Map
import Library.TypeVar
import Library.Term
import Library.Theorem
import Library.Object
import Library.Parse
name :: String -> Maybe Name
name str =
do guard (isName str)
let wordlist = (separateBy '.') . removeEscChars . removeQuotes $ str
return (Name (init wordlist) (last wordlist))
number :: String -> Maybe Number
number num =
do guard (isNumber num)
return (read num)
absTerm :: Term -> Var -> Term
absTerm term var =
TAbs (TVar var) term
absThm :: Theorem -> Var -> Maybe Theorem
absThm thm var =
do guard (not (Set.member (TVar var) (thmHyp thm)))
return (Theorem (thmHyp thm) (mkEquals (TAbs (TVar var) (getlhs . thmCon $ thm))
(TAbs (TVar var) (getrhs . thmCon $ thm))))
appTerm :: Term -> Term -> Term
appTerm term1 term2 =
TApp term2 term1
appThm :: Theorem -> Theorem -> Theorem
appThm thm1 thm2 =
Theorem (Set.union (thmHyp thm1) (thmHyp thm2))
(mkEquals (TApp (getlhs . thmCon $ thm2) (getlhs . thmCon $ thm1))
(TApp (getrhs . thmCon $ thm2) (getrhs . thmCon $ thm1)))
assume :: Term -> Maybe Theorem
assume term =
do guard (typeOf term == typeBool)
return (Theorem (Set.singleton term) term)
axiom :: Term -> [Term] -> Maybe Theorem
axiom term termlist =
do guard (all ((== typeBool) . typeOf) termlist)
return (Theorem (Set.fromList termlist) term)
betaConv :: Term -> Theorem
betaConv term =
Theorem (Set.empty)
(mkEquals term
(substitute ([], [(tVar . tAbsVar . tAppLeft $ term, tAppRight $ term)])
(tAbsTerm . tAppLeft $ term)))
constant :: Name -> Const
constant name =
Const name
constTerm :: Type -> Const -> Term
constTerm ty c =
TConst c ty
deductAntisym :: Theorem -> Theorem -> Theorem
deductAntisym x y =
Theorem (Set.union (Set.delete (thmCon $ x) (thmHyp $ y))
(Set.delete (thmCon $ y) (thmHyp $ x)))
(mkEquals (thmCon $ y) (thmCon $ x))
defineConst :: Term -> Name -> Maybe (Theorem, Const)
defineConst term name =
do guard ((freeVars term == Set.empty) && (typeVarsInTerm term == typeVarsInType (typeOf term)))
let constant = Const name
constTerm = TConst constant (typeOf term)
theorem = Theorem Set.empty (mkEquals constTerm term)
return (theorem, constant)
defineTypeOp :: Theorem -> [Name] -> Name -> Name -> Name -> Maybe (Theorem, Theorem, Const, Const, TypeOp)
defineTypeOp thm namelist r a n =
do guard ((typeVarsInTerm . tAppLeft . thmCon $ thm) == (Set.fromList . map (TypeVar) $ namelist) &&
(length namelist) == (length . nub $ namelist))
let rep = Const r
abst = Const a
op = TypeOp n
rtype = typeOf . tAppRight . thmCon $ thm
atype = AType (map (TypeVar) namelist) op
r' = TVar (Var (Name [] "r'") rtype)
a' = TVar (Var (Name [] "a'") atype)
reptype = typeFunc atype rtype
abstype = typeFunc rtype atype
repTerm = TConst rep reptype
absTerm = TConst abst abstype
rthm = Theorem Set.empty
(mkEquals (TApp (tAppLeft . thmCon $ thm) r')
(mkEquals (TApp repTerm (TApp absTerm r')) r'))
athm = Theorem Set.empty
(mkEquals (TApp absTerm (TApp repTerm a')) a')
return (rthm, athm, rep, abst, op)
eqMp :: Theorem -> Theorem -> Maybe Theorem
eqMp thm1 thm2 =
do guard (thmCon thm1 == (getlhs . thmCon $ thm2))
return (Theorem (Set.union (thmHyp thm1) (thmHyp thm2))
(getrhs . thmCon $ thm2))
opType :: [Type] -> TypeOp -> Type
opType typelist tyOp =
AType typelist tyOp
refl :: Term -> Theorem
refl term =
Theorem Set.empty (mkEquals term term)
subst :: Theorem -> [Object] -> Maybe Theorem
subst thm list =
do s <- makeSubst list
return (Theorem (Set.map (substitute s) (thmHyp thm))
(substitute s (thmCon thm)))
thm :: Term -> [Term] -> Theorem -> Maybe Theorem
thm term termlist oldthm =
do guard ((term == thmCon oldthm) && (Set.fromList termlist == thmHyp oldthm))
return (Theorem (Set.fromList (alphaConvertList (Set.toList . thmHyp $ oldthm) termlist))
(alphaConvert (thmCon oldthm) term))
typeOp :: Name -> TypeOp
typeOp name =
TypeOp name
var :: Type -> Name -> Maybe Var
var ty name =
do guard ((nameSpace name) == [])
return (Var name ty)
varTerm :: Var -> Term
varTerm var =
TVar var
varType :: Name -> Maybe Type
varType name =
do guard ((nameSpace name) == [])
return (TypeVar name)
|
