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------------------------------------------------------------------------
--- A type is sensible if there exists at least one value of this type.
--- This module contains an analysis which associates to each type
--- constructor the following information:
--- * sensible, i.e., there is always some value of this type
--- * parametric sensible, i.e., it is sensible of all type arguments
---   are instantiated with sensible types
--- * not sensible, i.e., maybe not sensible
------------------------------------------------------------------------

module Analysis.SensibleTypes
  ( Sensible(..), showSensible, sensibleType )
 where

import Analysis.Types
import Analysis.ProgInfo
import FlatCurry.Types
import FlatCurry.Goodies
import Maybe

--- Datatype to represent sensible type information.
data Sensible = NotSensible | PSensible | Sensible

-- Show higher-order information as a string.
showSensible :: AOutFormat -> Sensible -> String
showSensible _ Sensible    = "sensible"
showSensible _ PSensible   = "parametric sensible"
showSensible _ NotSensible = "not sensible"

lubSens :: Sensible -> Sensible -> Sensible
lubSens Sensible    _           = Sensible
lubSens PSensible   Sensible    = Sensible
lubSens PSensible   PSensible   = PSensible
lubSens PSensible   NotSensible = PSensible
lubSens NotSensible x           = x

------------------------------------------------------------------------
-- Analysis of sensible types

sensibleType :: Analysis Sensible
sensibleType = dependencyTypeAnalysis "SensibleType" NotSensible sensOfType

-- predefined sensible data types
predefinedSensibles :: [QName]
predefinedSensibles = [pre "Int", pre "Float", pre "Char", pre "IO"]
 where pre tc = ("Prelude",tc)

sensOfType :: TypeDecl -> [(QName,Sensible)] -> Sensible
sensOfType (TypeSyn _ _ _ typeExpr) usedtypes =
  sensOfTypeExpr usedtypes typeExpr
sensOfType (Type tc _ _ conDecls) usedtypes
  | tc `elem` predefinedSensibles = Sensible
  | otherwise = foldr lubSens NotSensible (map sensOfConsDecl conDecls)
 where
   sensOfConsDecl (Cons _ _ _ typeExprs)
     | all (== Sensible)    senstargs = Sensible
     | all (/= NotSensible) senstargs = PSensible
     | otherwise                      = NotSensible
    where senstargs = map (sensOfTypeExpr usedtypes) typeExprs

-- Compute the sensibility of a type expression which depends on the
-- information about type cosntructors.
sensOfTypeExpr :: [(QName,Sensible)] -> TypeExpr -> Sensible
sensOfTypeExpr _ (TVar _)       = PSensible
sensOfTypeExpr _ (FuncType _ _) = NotSensible -- we do not know which functions
                                              -- of some type exists...
sensOfTypeExpr usedtypes (TCons tc typeExprs)
  | senstc == Sensible || (senstc == PSensible && all (==Sensible) senstargs)
  = Sensible
  | senstc == PSensible && all (/=NotSensible) senstargs
  = PSensible
  | otherwise
  = NotSensible
 where
  senstc    = maybe NotSensible id (lookup tc usedtypes)
  senstargs = map (sensOfTypeExpr usedtypes) typeExprs

-----------------------------------------------------------------------