path: root/frontend/type.icl

implementation module type


import StdEnv
import syntax, typesupport, check, analtypes, overloading, unitype, refmark, predef, utilities, compare_constructor
import RWSDebug

::	TypeInput =
	{	ti_common_defs	:: {# CommonDefs }
	,	ti_functions	:: {# {# FunType }}
	}

::	FunctionType = CheckedType !SymbolType | SpecifiedType !SymbolType ![AType] !TempSymbolType
				 | UncheckedType !TempSymbolType | ExpandedType !SymbolType !TempSymbolType !TempSymbolType  | EmptyFunctionType

::	TypeState =
	{	ts_fun_env		:: !.{! FunctionType}
	,	ts_var_store	:: !Int
	,	ts_attr_store	:: !Int
	,	ts_var_heap		:: !.VarHeap 
	,	ts_type_heaps	:: !.TypeHeaps
	,	ts_expr_heap	:: !.ExpressionHeap 
	,	ts_td_infos		:: !.TypeDefInfos
	,	ts_error		:: !.ErrorAdmin
	}

::	TypeCoercion =
	{	tc_demanded		:: !AType
	,	tc_offered		:: !AType
	,	tc_position		:: !CoercionPosition
	,	tc_coercible	:: !Bool
	}

::	SharedAttribute = 
	{	sa_attr_nr	:: !Int
	,	sa_position	:: !Expression
	}

::	Requirements =
	{	req_overloaded_calls	:: ![ExprInfoPtr]
	,	req_type_coercions		:: ![TypeCoercion]
	,	req_attr_coercions		:: ![AttrCoercion]
	,	req_cons_variables		:: ![[TempVarId]]
	,	req_case_and_let_exprs	:: ![ExprInfoPtr]
	}
	
instance toString BoundVar
where
	toString varid = varid.var_name.id_name
	
class arraySubst type :: !type !u:{!Type} -> (!type, !u:{! Type})

instance arraySubst AType
where
	arraySubst atype=:{at_type} subst
		# (at_type, subst) = arraySubst at_type subst
		= ({ atype & at_type = at_type }, subst)
		
instance arraySubst Type
where
	arraySubst tv=:(TempV tv_number) subst
		#! type = subst.[tv_number]
		= case type of
			TE	-> (tv, subst)
			_	-> arraySubst type subst
	arraySubst (arg_type --> res_type) subst
		# (arg_type, subst) = arraySubst arg_type subst
		  (res_type, subst) = arraySubst res_type subst
		= (arg_type --> res_type, subst)
	arraySubst (TA cons_id cons_args) subst
		# (cons_args, subst) = arraySubst cons_args subst
		= (TA cons_id cons_args, subst) 
	arraySubst (TempCV tv_number :@: types) subst
		#! type = subst.[tv_number]
		= case type of
			TE
				# (types, subst) = arraySubst types subst
				-> (TempCV tv_number :@: types, subst)
			_
				# (type, subst) = arraySubst type subst
				  (types, subst) = arraySubst types subst
				-> (simplify_type_appl type types, subst)
	where
		simplify_type_appl :: !Type ![AType] -> Type
		simplify_type_appl (TA type_cons=:{type_arity} cons_args) type_args
			= TA { type_cons & type_arity = type_arity + length type_args } (cons_args ++ type_args)
		simplify_type_appl (cons_var :@: types) type_args
			= cons_var :@: (types ++ type_args)
		simplify_type_appl (TempV tv_number) type_args
			= TempCV tv_number :@: type_args
		simplify_type_appl (TempQV tv_number) type_args
			= TempQCV tv_number :@: type_args
	arraySubst type subst
		= (type, subst)

instance arraySubst [a] | arraySubst a
where
	arraySubst l subst
		= mapSt arraySubst l subst

instance arraySubst TempSymbolType
where
	arraySubst tst=:{tst_args,tst_result,tst_context} subst
		# (tst_args, subst) = arraySubst tst_args subst
		  (tst_result, subst) = arraySubst tst_result subst
		  (tst_context, subst) = arraySubst tst_context subst
		= ({tst & tst_args = tst_args,tst_result = tst_result,tst_context = tst_context}, subst)

instance arraySubst TypeContext
where
	arraySubst tc=:{tc_types} subst
		# (tc_types, subst) = arraySubst tc_types subst
		= ({ tc & tc_types = tc_types}, subst)

/*
instance arraySubst OverloadedCall
where
	arraySubst oc=:{oc_context} subst
		# (oc_context, subst) = arraySubst oc_context subst
		= ({ oc & oc_context = oc_context },  subst)
*/

instance arraySubst CaseType
where
	arraySubst ct=:{ct_pattern_type,ct_result_type,ct_cons_types} subst
		# (ct_pattern_type, subst) = arraySubst ct_pattern_type subst
		  (ct_result_type, subst) = arraySubst ct_result_type subst
		  (ct_cons_types, subst) = arraySubst ct_cons_types subst
		= ({ ct & ct_pattern_type = ct_pattern_type, ct_result_type = ct_result_type, ct_cons_types = ct_cons_types }, subst)

class contains_var a :: !Int !a -> Bool

instance contains_var [a] | contains_var a
where
	contains_var var_id [elem:list]
		= contains_var var_id elem || contains_var var_id list	
	contains_var var_id []
		= False

instance contains_var AType
where
	contains_var var_id {at_type} = contains_var var_id at_type

instance contains_var Type
where
	contains_var var_id (TempV tv_number) 
		= var_id == tv_number
	contains_var var_id (arg_type --> res_type) 
		= contains_var var_id arg_type || contains_var var_id res_type
	contains_var var_id (TA cons_id cons_args)
		= contains_var var_id cons_args
	contains_var var_id (type :@: types)
		= contains_var var_id type || contains_var var_id types
	contains_var _ _ 
		= False

instance contains_var ConsVariable
where
	contains_var var_id (TempCV tv_number) 
		= var_id == tv_number
	contains_var var_id _
		= False

cannotUnify t1 t2 position err 
	# err = errorHeading "Type error" err
	  format = { form_properties = cNoProperties, form_attr_position = No }
	= { err & ea_file = err.ea_file <<< " cannot unify " <:: (format, t1) <<< " with " <:: (format, t2)  <<< " near " <<< position <<< '\n' }


/*
simplifyType ta=:(type :@: type_args)
	# type = simplify_type type
	= case type of
		TA type_cons cons_args
			-> TA { type_cons & type_arity = type_cons.type_arity + length type_args } (cons_args ++ type_args)
	 	_ 	-> ta
simplifyType type
	= type
*/

class unify a :: !a !a !TypeInput !*{! Type} !*TypeHeaps -> (!Bool, !*{! Type}, !*TypeHeaps)

instance unify (a, b) | unify, arraySubst a & unify, arraySubst b
where
	unify (t1x, t1y) (t2x, t2y) modules subst heaps
		# (succ, subst, heaps) =  unify t1y t2y modules subst heaps
		| succ
	      # (t1x, subst) = arraySubst t1x subst
	        (t2x, subst) = arraySubst t2x subst
	      = unify t1x t2x modules subst heaps
	      = (False, subst, heaps)

instance unify [a] | unify, arraySubst a
where
	unify [t1 : ts1] [t2 : ts2] modules subst heaps
		= unify (t1,ts1) (t2,ts2) modules subst heaps
	unify [] [] modules subst heaps
		= (True, subst, heaps)
	unify _ _ modules subst heaps
		= (False, subst, heaps)

instance unify AType
where
	unify t1 t2 modules subst heaps = unifyTypes t1.at_type t1.at_attribute t2.at_type t2.at_attribute modules subst heaps


unifyTypes :: !Type !TypeAttribute !Type !TypeAttribute !TypeInput !*{! Type} !*TypeHeaps -> (!Bool, !*{! Type}, !*TypeHeaps)
unifyTypes (TempV tv_number1) attr1 tv=:(TempV tv_number2) attr2 modules subst heaps
	= unifyTempVarIds tv_number1 tv_number2 subst heaps
unifyTypes tv=:(TempV tv_number) attr1 type attr2 modules subst heaps
	| contains_var tv_number type
		= (False, subst, heaps)
		= (True, { subst & [tv_number] = type}, heaps)
unifyTypes type attr1 tv=:(TempV _) attr2 modules subst heaps
	= unifyTypes tv attr2 type attr1 modules subst heaps
unifyTypes t1=:(TB tb1) attr1 t2=:(TB tb2) attr2 modules subst heaps
	| tb1 == tb2
		= (True, subst, heaps)
		= (False, subst, heaps)
unifyTypes (arg_type1 --> res_type1) attr1 (arg_type2 --> res_type2) attr2 modules subst heaps
	= unify (arg_type1,res_type1) (arg_type2,res_type2) modules subst heaps
unifyTypes t1=:(TA cons_id1 cons_args1) attr1 t2=:(TA cons_id2 cons_args2) attr2 modules subst heaps
	| cons_id1 == cons_id2
		= unify cons_args1 cons_args2 modules subst heaps
		# (succ1, t1, heaps) = tryToExpand t1 attr1 modules heaps
		  (succ2, t2, heaps) = tryToExpand t2 attr2 modules heaps
		| succ1 || succ2
			= unifyTypes t1 attr1 t2 attr2 modules subst heaps
			= (False, subst, heaps)
unifyTypes (cons_var :@: types) attr1 type2 attr2 modules subst heaps
	# (_, type2, heaps) = tryToExpand type2 attr2 modules heaps
	= unifyTypeApplications cons_var types type2 modules subst heaps
unifyTypes type1 attr1 (cons_var :@: types) attr2 modules subst heaps
	# (_, type1, heaps) = tryToExpand type1 attr1 modules heaps
	= unifyTypeApplications cons_var types type1 modules subst heaps
unifyTypes t1=:(TempQV qv_number1) attr1 t2=:(TempQV qv_number2) attr2 modules subst heaps
	= (qv_number1 == qv_number2, subst, heaps)
unifyTypes (TempQV qv_number) attr1 type attr2 modules subst heaps
	= (False, subst, heaps)
unifyTypes type attr1 (TempQV qv_number1) attr2 modules subst heaps
	= (False, subst, heaps)
unifyTypes type1 attr1 type2 attr2 modules subst heaps
	# (succ1, type1, heaps) = tryToExpand type1 attr1 modules heaps
	  (succ2, type2, heaps) = tryToExpand type2 attr2 modules heaps
	| succ1 || succ2
		= unifyTypes type1 attr1 type2 attr2 modules subst heaps
		= (False, subst, heaps)

tryToExpand type=:(TA {type_index={glob_object,glob_module}} type_args) type_attr {ti_common_defs} type_heaps
	#! type_def = ti_common_defs.[glob_module].com_type_defs.[glob_object]
	= case type_def.td_rhs of
		SynType {at_type}
			# (res_type, type_heaps) = expandTypeApplication type_def.td_args type_def.td_attribute at_type type_args type_attr type_heaps
			-> (True, res_type, type_heaps)
		_
			-> (False, type, type_heaps)
tryToExpand type type_attr modules type_heaps
	= (False, type, type_heaps)

unifyConsVariables (TempCV tv_number1) (TempCV tv_number2) subst heaps
	= unifyTempVarIds tv_number1 tv_number2 subst heaps
unifyConsVariables (TempCV tv_number1) (TempQCV tv_number2) subst heaps
	= (True, { subst & [tv_number1] = TempQV tv_number2}, heaps)
unifyConsVariables (TempQCV tv_number1) (TempCV tv_number2) subst heaps
	= (True, { subst & [tv_number2] = TempQV tv_number1}, heaps)
unifyConsVariables (TempQCV tv_number1) (TempQCV tv_number2) subst heaps
	= (tv_number1 == tv_number2, subst, heaps)

unifyTempVarIds tv_number1 tv_number2 subst heaps
	| tv_number1 == tv_number2
		= (True, subst, heaps)
		= (True, { subst & [tv_number1] = TempV tv_number2}, heaps)

constructorVariableToTypeVariable (TempCV temp_var_id)
	= TempV temp_var_id
constructorVariableToTypeVariable (TempQCV temp_var_id)
	= TempQV temp_var_id

unifyTypeApplications cons_var type_args type=:(TA type_cons cons_args) modules subst heaps
	# diff = type_cons.type_arity - length type_args
	| diff >= 0 
		# (succ, subst, heaps) = unify type_args (drop diff cons_args) modules subst heaps
		| succ
			# (rest_args, subst) = arraySubst (take diff cons_args) subst
			= unifyTypes (constructorVariableToTypeVariable cons_var) TA_Multi (TA { type_cons & type_arity = diff } rest_args) TA_Multi modules subst heaps
		    = (False, subst, heaps)
		= (False, subst, heaps)
unifyTypeApplications cons_var1 type_args type=:(cons_var2 :@: types) modules subst heaps
	# arity1 = length type_args
	  arity2 = length types
	  diff = arity1 - arity2
	| diff == 0
		# (succ, subst, heaps) = unifyConsVariables cons_var1 cons_var2 subst heaps
		| succ
		    # (type_args, subst) = arraySubst type_args subst
		      (types, subst) = arraySubst types subst
		    = unify type_args types modules subst heaps
			= (False, subst, heaps)
	| diff < 0
		# diff = 0 - diff
		  (succ, subst, heaps) = unifyTypes (constructorVariableToTypeVariable cons_var1) TA_Multi (cons_var2 :@: take diff types) TA_Multi modules subst heaps
		| succ
		    # (type_args, subst) = arraySubst type_args subst
		      (types, subst) = arraySubst (drop diff types) subst
		    = unify type_args types modules subst heaps
			= (False, subst, heaps)
	| otherwise
		# (succ, subst, heaps) = unifyTypes (cons_var1 :@: take diff type_args) TA_Multi (constructorVariableToTypeVariable cons_var2) TA_Multi modules subst heaps
		| succ
		    # (type_args, subst) = arraySubst (drop diff type_args) subst
		      (types, subst) = arraySubst types subst
		    = unify type_args types modules subst heaps
			= (False, subst, heaps)
unifyTypeApplications cons_var type_args type modules subst heaps
	= (False, subst, heaps)


::	CopyState =
	{	copy_heaps		:: !.TypeHeaps
	}
	
instance fromInt TypeAttribute
where
	fromInt AttrUni		= TA_Unique
	fromInt AttrMulti	= TA_Multi
	fromInt av_number	= TA_TempVar av_number

class freshCopy a :: !a !*CopyState -> (!a, !*CopyState)

instance freshCopy [a] | freshCopy a
where
	freshCopy l ls = mapSt freshCopy l ls

/*
cDoExtendAttrEnv	:== True
cDontExtendAttrEnv	:== False

freshCopies :: !Bool ![a] !{# CommonDefs } !*CopyState -> (![a], !*CopyState) | freshCopy a
freshCopies extend_env [] modules cs
	= ([], [], cs)
freshCopies extend_env [t:ts] modules cs
	# (t, prop, cs) = freshCopy extend_env t modules cs
	  (ts, props, cs) = freshCopies extend_env ts modules cs
	= ([t:ts], [prop:props], cs)
*/

freshCopyOfAttributeVar {av_name,av_info_ptr} attr_var_heap
	# (av_info, attr_var_heap) = readPtr av_info_ptr attr_var_heap
	= case av_info of
		AVI_Attr attr
			-> (attr, attr_var_heap)
		_
			-> abort ("freshCopyOfAttributeVar (type,icl)" ---> av_name)


freshCopyOfTypeAttribute (TA_Var avar) attr_var_heap
	= freshCopyOfAttributeVar avar attr_var_heap

/* A temporary hack to handle the new Object IO lib */
/* Should be removed !!!!!!!!!! */

freshCopyOfTypeAttribute (TA_RootVar avar) attr_var_heap
//	= freshCopyOfAttributeVar avar attr_var_heap
	= (TA_TempExVar, attr_var_heap)
freshCopyOfTypeAttribute TA_None attr_var_heap
	= (TA_Multi, attr_var_heap)
freshCopyOfTypeAttribute TA_Unique attr_var_heap
	= (TA_Unique, attr_var_heap)
freshCopyOfTypeAttribute attr attr_var_heap
	= (attr, attr_var_heap)


cIsExistential 		:== True
cIsNotExistential	:== False

freshCopyOfTypeVariable {tv_name,tv_info_ptr} cs=:{copy_heaps}
	#! tv_info 	= sreadPtr tv_info_ptr copy_heaps.th_vars
	= case tv_info of
		 TVI_Type fresh_var
			-> (fresh_var, cs)

freshConsVariable {tv_info_ptr} type_var_heap
	#! tv_info 			= sreadPtr tv_info_ptr type_var_heap
	= (to_constructor_variable tv_info, type_var_heap)
	where
		to_constructor_variable (TVI_Type (TempV temp_var_id))
			= TempCV temp_var_id
		to_constructor_variable (TVI_Type (TempQV temp_var_id))
			= TempQCV temp_var_id

instance freshCopy AType
where 	
	freshCopy type=:{at_type = CV tv :@: types, at_attribute}  cs=:{copy_heaps}
		# (fresh_cons_var, th_vars)		= freshConsVariable tv copy_heaps.th_vars
		  (fresh_attribute, th_attrs)	= freshCopyOfTypeAttribute at_attribute copy_heaps.th_attrs
		  (types, cs)					= freshCopy types { cs & copy_heaps = { copy_heaps & th_attrs = th_attrs, th_vars = th_vars }}
		= ({type & at_type = fresh_cons_var :@: types, at_attribute = fresh_attribute }, cs)
	freshCopy type=:{at_type, at_attribute} cs=:{copy_heaps}
		# (fresh_attribute, th_attrs)	= freshCopyOfTypeAttribute at_attribute copy_heaps.th_attrs
		  (fresh_type, cs)				= freshCopy at_type { cs & copy_heaps = { copy_heaps & th_attrs = th_attrs }}
		= ({ type & at_type = fresh_type, at_attribute = fresh_attribute }, cs)
		
instance freshCopy Type
where
	freshCopy (TV tv) cs=:{copy_heaps}
		= freshCopyOfTypeVariable tv cs
	freshCopy (TA cons_id=:{type_index={glob_object,glob_module}} cons_args)  cs
		# (cons_args, cs) = freshCopy cons_args cs
		= (TA cons_id cons_args, cs)
	freshCopy (arg_type --> res_type) cs
		# (arg_type, cs) = freshCopy arg_type cs
		  (res_type, cs) = freshCopy res_type cs
		= (arg_type --> res_type, cs)
	freshCopy type cs
		= (type, cs)

freshExistentialVariables type_variables state
	= foldSt fresh_existential_variable type_variables state 
where
	fresh_existential_variable {atv_variable={tv_info_ptr}} (var_heap, var_store)
		= (var_heap <:= (tv_info_ptr, TVI_Type (TempQV var_store)), inc var_store)

freshAlgebraicType :: !(Global Int) ![AlgebraicPattern] !{#CommonDefs} !*TypeState -> (![[AType]],!AType,![AttrCoercion],!*TypeState)
freshAlgebraicType {glob_module, glob_object} patterns common_defs ts=:{ts_var_store,ts_attr_store,ts_type_heaps,ts_td_infos}
	# {td_rhs,td_args,td_attrs,td_name,td_attribute} = common_defs.[glob_module].com_type_defs.[glob_object]
	# (th_vars, ts_var_store)		= fresh_type_variables td_args (ts_type_heaps.th_vars, ts_var_store)
	  (th_attrs, ts_attr_store)		= fresh_attributes td_attrs (ts_type_heaps.th_attrs, ts_attr_store)
	  copy_heaps = { ts_type_heaps & th_vars = th_vars, th_attrs = th_attrs }
	  (cons_types, alg_type, ts_var_store, attr_env, copy_heaps)
	  		= fresh_symbol_types patterns common_defs.[glob_module].com_cons_defs ts_var_store copy_heaps
	= (cons_types, alg_type, attr_env, { ts & ts_var_store = ts_var_store, ts_attr_store = ts_attr_store, ts_type_heaps = copy_heaps })
//		---> ("freshAlgebraicType", alg_type, cons_types)
where
	fresh_symbol_types [{ap_symbol={glob_object}}] cons_defs var_store copy_heaps
		# {cons_type = {st_args,st_attr_env,st_result}, cons_index, cons_exi_vars, cons_exi_attrs} = cons_defs.[glob_object.ds_index]
		  (th_vars, var_store)		= freshExistentialVariables  cons_exi_vars (copy_heaps.th_vars, var_store)
	  	  (attr_env, th_attrs) 		= fresh_environment st_attr_env ([], copy_heaps.th_attrs)
	  	  (result_type, cs)			= freshCopy st_result { copy_heaps = { copy_heaps & th_attrs = th_attrs, th_vars = th_vars } }
	  	  (fresh_args, cs)			= freshCopy st_args cs
		= ([fresh_args], result_type, var_store, attr_env, cs.copy_heaps)
	fresh_symbol_types [{ap_symbol={glob_object}} : patterns] cons_defs var_store copy_heaps
		# (cons_types, result_type, var_store, attr_env, copy_heaps)
				= fresh_symbol_types patterns cons_defs var_store copy_heaps
		  {cons_type = {st_args,st_attr_env}, cons_index, cons_exi_vars} = cons_defs.[glob_object.ds_index]
		  (th_vars, var_store)		= freshExistentialVariables cons_exi_vars (copy_heaps.th_vars, var_store)
		  (attr_env, th_attrs) 		= fresh_environment st_attr_env (attr_env, copy_heaps.th_attrs)
	  	  (fresh_args, cs) 			= freshCopy st_args  { copy_heaps = { copy_heaps & th_attrs = th_attrs, th_vars = th_vars }}
		= ([fresh_args : cons_types], result_type, var_store, attr_env, cs.copy_heaps)

	
	fresh_type_variables type_variables state
		= foldSt (\{atv_variable={tv_info_ptr}} (var_heap, var_store) -> (var_heap <:= (tv_info_ptr, TVI_Type (TempV var_store)), inc var_store))
						type_variables state 
	fresh_attributes attributes state
		= foldSt (\{av_info_ptr} (attr_heap, attr_store) -> (attr_heap <:= (av_info_ptr, AVI_Attr (TA_TempVar attr_store)), inc attr_store))
						attributes state
	fresh_environment inequalities (attr_env, attr_heap)
		= foldSt fresh_inequality inequalities (attr_env, attr_heap)

	fresh_inequality {ai_demanded,ai_offered} (attr_env, attr_heap)
		# (AVI_Attr dem_temp_attr, attr_heap) = readPtr ai_demanded.av_info_ptr attr_heap
		  (AVI_Attr off_temp_attr, attr_heap) = readPtr ai_offered.av_info_ptr attr_heap
		= case dem_temp_attr of
			TA_TempVar dem_attr_var
				-> case off_temp_attr of
					TA_TempVar off_attr_var
						| is_new_ineqality  dem_attr_var off_attr_var attr_env
							-> ([{ac_demanded = dem_attr_var, ac_offered = off_attr_var} : attr_env ], attr_heap)
							-> (attr_env, attr_heap)
					_
						-> (attr_env, attr_heap)
			_
				-> (attr_env, attr_heap)
		
	is_new_ineqality dem_attr_var off_attr_var [{ac_demanded, ac_offered} : attr_env]
		= (dem_attr_var <> ac_demanded || off_attr_var <> ac_offered) && is_new_ineqality dem_attr_var off_attr_var  attr_env
	is_new_ineqality dem_attr_var off_attr_var []
		= True
		
freshSymbolType st=:{st_vars,st_args,st_result,st_context,st_attr_vars,st_attr_env,st_arity} common_defs
				ts=:{ts_var_store,ts_attr_store,ts_type_heaps,ts_td_infos}
	# (th_vars, ts_var_store)		= fresh_type_variables st_vars (ts_type_heaps.th_vars, ts_var_store)
	  (th_attrs, ts_attr_store)	= fresh_attributes st_attr_vars (ts_type_heaps.th_attrs, ts_attr_store)
	  (attr_env, th_attrs)		= freshEnvironment st_attr_env th_attrs 
	  cs = { copy_heaps = { ts_type_heaps & th_vars = th_vars, th_attrs = th_attrs }}
	  (tst_args, cs)				= freshCopy st_args  cs
	  (tst_result, cs)				= freshCopy st_result cs
	  (tst_context, {copy_heaps}) 	= freshTypeContexts st_context cs
	  cons_variables				= foldSt (collect_cons_variables_in_tc common_defs) tst_context []
	= ({ tst_args = tst_args, tst_result = tst_result, tst_context = tst_context, tst_attr_env = attr_env, tst_arity = st_arity, tst_lifted = 0 }, cons_variables,
	   { ts & ts_var_store = ts_var_store, ts_attr_store = ts_attr_store, ts_type_heaps = copy_heaps})
//		---> ("freshSymbolType", tst_args, tst_result)
	where
		fresh_type_variables type_variables state
			= foldr (\{tv_info_ptr} (var_heap, var_store) -> (writePtr tv_info_ptr (TVI_Type (TempV var_store)) var_heap, inc var_store))
							state type_variables
		fresh_attributes attributes state
			= foldr (\{av_info_ptr} (attr_heap, attr_store) -> (writePtr av_info_ptr (AVI_Attr (TA_TempVar attr_store)) attr_heap, inc attr_store))
							state attributes
		
		collect_cons_variables_in_tc common_defs tc=:{tc_class={glob_module,glob_object={ds_index}}, tc_types} collected_cons_vars
			# {class_cons_vars} = common_defs.[glob_module].com_class_defs.[ds_index]
			= collect_cons_variables tc_types class_cons_vars collected_cons_vars
		
		collect_cons_variables [] class_cons_vars collected_cons_vars
			= collected_cons_vars
		collect_cons_variables [type : tc_types] class_cons_vars collected_cons_vars
			| class_cons_vars bitand 1 == 0
				= collect_cons_variables tc_types (class_cons_vars >> 1) collected_cons_vars
				= case type of
					TempV temp_var_id 
						-> collect_cons_variables tc_types (class_cons_vars >> 1) (add_variable temp_var_id collected_cons_vars)
//							---> ("collect_cons_variables", temp_var_id)
					_
						-> collect_cons_variables tc_types (class_cons_vars >> 1) collected_cons_vars
						
		add_variable new_var_id []
			= [new_var_id]
		add_variable new_var_id vars=:[var_id : var_ids]
			| new_var_id == var_id
				= vars
				= [var_id : add_variable new_var_id var_ids]
		
			
freshInequality {ai_demanded,ai_offered} attr_heap
	# (av_dem_info, attr_heap) = readPtr ai_demanded.av_info_ptr attr_heap
	  (av_off_info, attr_heap) = readPtr ai_offered.av_info_ptr attr_heap
	  (AVI_Attr (TA_TempVar dem_attr_var)) = av_dem_info
	  (AVI_Attr (TA_TempVar off_attr_var)) = av_off_info
	= ({ac_demanded = dem_attr_var, ac_offered = off_attr_var}, attr_heap) // <<- (av_dem_info,av_off_info)
	
freshEnvironment [ineq : ineqs] attr_heap
	# (fresh_ineq, attr_heap) = freshInequality ineq attr_heap
	  (fresh_env, attr_heap) = freshEnvironment ineqs attr_heap
	= ([fresh_ineq : fresh_env], attr_heap)
freshEnvironment [] attr_heap
	= ([], attr_heap)

freshTypeContexts tcs cs
	= mapSt fresh_type_context tcs cs
where	
	fresh_type_context tc=:{tc_types} cs
		# (tc_types, cs) = mapSt fresh_context_type tc_types cs
		= ({ tc & tc_types = tc_types}, cs)

	fresh_context_type (CV tv :@: types) cs=:{copy_heaps}
		# (fresh_cons_var, th_vars)		= freshConsVariable tv copy_heaps.th_vars
		  (types, cs) = freshCopy types { cs & copy_heaps = { copy_heaps & th_vars = th_vars }}
		= (fresh_cons_var :@: types, cs)
	fresh_context_type type cs
		= freshCopy type cs

freshAttributedVariable :: !u:TypeState -> (!AType, !u:TypeState)
freshAttributedVariable ts=:{ts_var_store,ts_attr_store}
	= ({ at_attribute = TA_TempVar ts_attr_store, at_annotation = AN_None, at_type = TempV ts_var_store },
	     {ts & ts_var_store = inc ts_var_store, ts_attr_store = inc ts_attr_store})

freshNonUniqueVariable :: !u:TypeState -> (!AType, !u:TypeState)
freshNonUniqueVariable ts=:{ts_var_store}
	= ({ at_attribute = TA_Multi, at_annotation = AN_None, at_type = TempV ts_var_store },
	     {ts & ts_var_store = inc ts_var_store})

freshAttribute :: !u:TypeState -> (!TypeAttribute, !u:TypeState)
freshAttribute ts=:{ts_attr_store}
	= (TA_TempVar ts_attr_store, {ts & ts_attr_store = inc ts_attr_store})


::	PropState =
	{	prop_type_heaps	:: !.TypeHeaps
	,	prop_td_infos	:: !.TypeDefInfos
	,	prop_attr_vars	:: ![AttributeVar]
	,	prop_attr_env	:: ![AttrInequality]
	,	prop_error		:: !.ErrorAdmin
	}

attribute_error type_attr err
	# err = errorHeading "Type error" err
	= { err & ea_file = err.ea_file <<< "* attribute expected instead of " <<< type_attr <<< '\n' }

addPropagationAttributesToAType modules type=:{at_type = TA cons_id=:{type_index={glob_object,glob_module}} cons_args, at_attribute} ps
	# (cons_args, props, ps=:{prop_td_infos,prop_type_heaps,prop_attr_vars,prop_attr_env,prop_error})
			= add_propagation_attributes_to_atypes modules cons_args ps
	  (prop_class, th_vars, prop_td_infos) = propClassification glob_object glob_module props modules prop_type_heaps.th_vars prop_td_infos
	  (at_attribute, prop_class, th_attrs, prop_attr_vars, prop_attr_env, prop_error)
	  		= determine_attribute_of_cons modules at_attribute cons_args prop_class prop_type_heaps.th_attrs prop_attr_vars prop_attr_env prop_error
	= ({ type & at_type = TA cons_id cons_args, at_attribute = at_attribute }, prop_class,  { ps & prop_attr_vars = prop_attr_vars,
			prop_td_infos = prop_td_infos, prop_attr_env = prop_attr_env,
				prop_type_heaps = { prop_type_heaps & th_vars = th_vars, th_attrs = th_attrs}, prop_error = prop_error })
	where
		add_propagation_attributes_to_atypes modules [] ps
			= ([], [], ps) 
		add_propagation_attributes_to_atypes modules [atype : atypes] ps
			# (atype, prop_class, ps) = addPropagationAttributesToAType modules atype ps
			  (atypes, prop_classes, ps) = add_propagation_attributes_to_atypes modules atypes ps
			= ([atype : atypes], [prop_class : prop_classes], ps)
	
		determine_attribute_of_cons modules TA_Unique cons_args prop_class attr_var_heap attr_vars attr_env ps_error
			= (TA_Unique, prop_class >> length cons_args, attr_var_heap, attr_vars, attr_env, ps_error)
		determine_attribute_of_cons modules cons_attr cons_args prop_class attr_var_heap attr_vars attr_env ps_error
			# (cumm_attr, prop_attrs, prop_class) = determine_cummulative_attribute cons_args TA_Multi [] prop_class
			  (comb_attr, attr_var_heap, attr_vars, attr_env, ps_error)
			  		= combine_attributes cons_attr cumm_attr prop_attrs attr_var_heap attr_vars attr_env ps_error
			= (comb_attr, prop_class, attr_var_heap, attr_vars, attr_env, ps_error)
			  
		determine_cummulative_attribute [] cumm_attr attr_vars prop_class
			= (cumm_attr, attr_vars, prop_class)
		determine_cummulative_attribute [{at_attribute} : types ] cumm_attr attr_vars prop_class
			| prop_class bitand 1 == 0
				= determine_cummulative_attribute types cumm_attr attr_vars (prop_class >> 1)
				= case at_attribute of
					TA_Unique
						-> (TA_Unique, [], prop_class >> length types)
					TA_Multi
						-> determine_cummulative_attribute types cumm_attr attr_vars (prop_class >> 1)
					TA_Var attr_var
						-> determine_cummulative_attribute types at_attribute [attr_var : attr_vars] (prop_class >> 1)
		

		combine_attributes (TA_Var attr_var) cumm_attr prop_vars attr_var_heap attr_vars attr_env ps_error
			= case cumm_attr of
				TA_Unique
					-> (TA_Unique, attr_var_heap, attr_vars, attr_env, attribute_error attr_var ps_error)
				
				TA_Multi
					-> (TA_Var attr_var, attr_var_heap, attr_vars, attr_env, ps_error)
				TA_Var _
					-> (TA_Var attr_var, attr_var_heap, attr_vars, foldSt (new_inequality attr_var) prop_vars attr_env, ps_error)
		where
			new_inequality off_attr_var dem_attr_var [] 
				= [{ ai_demanded = dem_attr_var, ai_offered = off_attr_var }]
			new_inequality off_attr_var dem_attr_var ins=:[ inequal : iequals ]
				 | dem_attr_var.av_info_ptr == inequal.ai_demanded.av_info_ptr && off_attr_var.av_info_ptr == inequal.ai_offered.av_info_ptr
				 	= ins
				 	= [ inequal : new_inequality off_attr_var dem_attr_var iequals ]
	
		combine_attributes _ (TA_Var var) prop_vars attr_var_heap attr_vars attr_env ps_error
			# (new_attr_ptr, attr_var_heap) = newPtr AVI_Empty attr_var_heap
			  new_attr_var = { var & av_info_ptr = new_attr_ptr }
			= (TA_Var new_attr_var, attr_var_heap, [new_attr_var : attr_vars],
					mapAppend (\ai_demanded -> { ai_demanded = ai_demanded, ai_offered = new_attr_var }) prop_vars attr_env, ps_error)
		combine_attributes cons_attr TA_Unique _ attr_var_heap attr_vars attr_env ps_error
			= (TA_Unique, attr_var_heap, attr_vars, attr_env, ps_error)
		combine_attributes cons_attr _ _ attr_var_heap attr_vars attr_env ps_error
			= (cons_attr, attr_var_heap, attr_vars, attr_env, ps_error)

addPropagationAttributesToAType modules type=:{at_type} ps
	# (at_type, ps) = addPropagationAttributesToType modules at_type ps
	= ({ type & at_type = at_type }, NoPropClass, ps)

addPropagationAttributesToType modules (arg_type --> res_type) ps
	# (arg_type, prop_class, ps) = addPropagationAttributesToAType modules arg_type ps
	  (res_type, prop_class, ps) = addPropagationAttributesToAType modules res_type ps
	= (arg_type --> res_type, ps)
addPropagationAttributesToType modules (type_var :@: types) ps
	# (types, ps) = addPropagationAttributesToATypes modules types ps
	= (type_var :@: types, ps)
addPropagationAttributesToType modules type ps
	= (type, ps)

addPropagationAttributesToATypes modules types ps
	= mapSt (add_propagation_attributes_to_atype modules) types ps
where
	add_propagation_attributes_to_atype modules type ps
		# (type, prop_class, ps) = addPropagationAttributesToAType modules type ps
		= (type, ps)

:: Base :== {! AType}

currySymbolType st=:{tst_args,tst_arity,tst_result,tst_attr_env} req_arity ts=:{ts_attr_store}
	| tst_arity == req_arity
		= (st, ts)
	# (tst_args, rest_args, is_unique) = split_args req_arity tst_args 
	| is_unique
		# (type, _, _) = buildCurriedType rest_args tst_result TA_Unique [] 0
		= ({ st & tst_args = tst_args, tst_arity = req_arity, tst_result = type }, ts)
		# (type, tst_attr_env, ts_attr_store) = buildCurriedType rest_args tst_result (TA_TempVar ts_attr_store)
		  		(build_attr_env ts_attr_store tst_args tst_attr_env) (inc ts_attr_store)
		= ({ st & tst_args = tst_args, tst_arity = req_arity, tst_result = type, tst_attr_env = tst_attr_env }, { ts & ts_attr_store = ts_attr_store })
where
	split_args 0 args = ([], args, False)
	split_args n [atype=:{at_attribute} : args]
		# (left, right, is_unique) = split_args (dec n) args
		= ([ atype : left ], right, is_unique || attr_is_unique at_attribute)
	
	attr_is_unique TA_Unique = True
	attr_is_unique _ = False
	
	build_attr_env cum_attr_var [] attr_env
		= attr_env
	build_attr_env cum_attr_var [{at_attribute=(TA_TempVar attr_var)} : args] attr_env
		= build_attr_env cum_attr_var args [{ ac_demanded = attr_var, ac_offered = cum_attr_var } : attr_env]
	build_attr_env cum_attr_var [_ : args] attr_env
		= build_attr_env cum_attr_var args attr_env


emptyIdent =: { id_name = "", id_info = nilPtr }

buildCurriedType [] type cum_attr attr_env attr_store
	= (type, attr_env, attr_store)
buildCurriedType [at=:{at_attribute}:ats] type cum_attr attr_env attr_store
	# (next_cum_attr, attr_env, attr_store) = combine_attributes at_attribute cum_attr attr_env attr_store
	  (res_type, attr_env, attr_store) = buildCurriedType ats type next_cum_attr attr_env attr_store
	= ({at_annotation = AN_None, at_attribute = cum_attr , at_type = at --> res_type }, attr_env, attr_store)
where
	combine_attributes TA_Unique cum_attr attr_env attr_store
		= (TA_Unique, attr_env, attr_store)
	combine_attributes (TA_TempVar attr_var) (TA_TempVar cum_attr_var) attr_env attr_store
		= (TA_TempVar attr_store, [{ ac_demanded = cum_attr_var,ac_offered = attr_store },{ ac_demanded = attr_var,ac_offered = attr_store }:attr_env], inc attr_store)
	combine_attributes (TA_TempVar _) cum_attr attr_env attr_store
		= (cum_attr, attr_env, attr_store)
	combine_attributes _ (TA_TempVar cum_attr_var) attr_env attr_store
		= (TA_TempVar attr_store, [{ ac_demanded = cum_attr_var,ac_offered = attr_store }:attr_env], inc attr_store)
	combine_attributes _ cum_attr attr_env attr_store
		= (cum_attr, attr_env, attr_store)

determineSymbolTypeOfFunction ident act_arity st=:{st_args,st_result,st_attr_vars,st_attr_env} type_ptr common_defs ts=:{ts_var_heap}
	# (type_info, ts_var_heap) = readPtr type_ptr ts_var_heap
	  ts = { ts & ts_var_heap = ts_var_heap }
	= case type_info of
		VI_PropagationType symb_type
	   		# (copy_symb_type, cons_variables, ts) = freshSymbolType symb_type common_defs ts 
//				(ts  ---> ("determineSymbolTypeOfFunction1", ident, symb_type)) 
			  (curried_st, ts) = currySymbolType copy_symb_type act_arity ts
			-> (curried_st, cons_variables, ts)
//				 ---> ("determineSymbolTypeOfFunction", ident, curried_st)
		_	
			# (st_args, ps) = addPropagationAttributesToATypes common_defs st_args
					{ prop_type_heaps = ts.ts_type_heaps, prop_td_infos = ts.ts_td_infos,
					  prop_attr_vars = st_attr_vars, prop_attr_env = st_attr_env, prop_error = ts.ts_error}
			  (st_result, _, {prop_type_heaps,prop_td_infos,prop_attr_vars,prop_error,prop_attr_env})
			  			= addPropagationAttributesToAType common_defs st_result ps
			  st = { st & st_args = st_args, st_result = st_result, st_attr_vars = prop_attr_vars, st_attr_env = prop_attr_env }
	   		# (copy_symb_type, cons_variables, ts) = freshSymbolType st common_defs { ts &
	   										ts_type_heaps = prop_type_heaps, ts_td_infos = prop_td_infos, ts_error = prop_error,
											ts_var_heap = ts.ts_var_heap <:= (type_ptr, VI_PropagationType st) }
			  (curried_st, ts) = currySymbolType copy_symb_type act_arity ts
			-> (curried_st, cons_variables, ts)
//				 ---> ("determineSymbolTypeOfFunction", ident, st)

standardFieldSelectorType {glob_object={ds_ident,ds_index},glob_module} {ti_common_defs} ts=:{ts_var_store,ts_type_heaps}
	#! {sd_type,sd_exi_vars,sd_exi_attrs} = ti_common_defs.[glob_module].com_selector_defs.[ds_index]
	# (th_vars, ts_var_store) = freshExistentialVariables sd_exi_vars (ts_type_heaps.th_vars, ts_var_store)
	  (inst, cons_variables, ts) = freshSymbolType sd_type ti_common_defs { ts & ts_type_heaps = { ts_type_heaps & th_vars = th_vars }, ts_var_store = ts_var_store }
	= (inst, ts)
//		 ---> ("standardFieldSelectorType", ds_ident, inst)

standardTupleSelectorType {ds_index} arg_nr {ti_common_defs} ts
	#! {cons_type} = ti_common_defs.[cPredefinedModuleIndex].com_cons_defs.[ds_index]
	   (fresh_type, cons_variables, ts) = freshSymbolType { cons_type & st_args = [cons_type.st_result], st_result = cons_type.st_args !! arg_nr } ti_common_defs ts
	= (fresh_type, ts)

standardRhsConstructorType index mod arity {ti_common_defs} ts
	#! {cons_symb, cons_type, cons_exi_vars } = ti_common_defs.[mod].com_cons_defs.[index]
	# cons_type = { cons_type & st_vars = mapAppend (\{atv_variable} -> atv_variable) cons_exi_vars cons_type.st_vars }
	  (fresh_type, _, ts) = freshSymbolType cons_type ti_common_defs ts
	= currySymbolType fresh_type arity ts
//		 ---> ("standardRhsConstructorType", cons_symb, fresh_type)

standardLhsConstructorType index mod arity {ti_common_defs} ts=:{ts_var_store,ts_type_heaps}
	#! {cons_symb, cons_type, cons_exi_vars } = ti_common_defs.[mod].com_cons_defs.[index]
	# (th_vars, ts_var_store) = freshExistentialVariables cons_exi_vars (ts_type_heaps.th_vars, ts_var_store)
	  (fresh_type, _, ts) = freshSymbolType cons_type ti_common_defs { ts & ts_type_heaps = { ts_type_heaps & th_vars = th_vars }, ts_var_store = ts_var_store }
	= (fresh_type, ts)
//		 ---> ("standardLhsConstructorType", cons_symb, fresh_type)

:: ReferenceMarking :== Bool

cIsRecursive :== True
cIsNotRecursive :== False

storeAttribute (Yes expt_ptr) type_attribute symbol_heap
	= writePtr expt_ptr (EI_Attribute (toInt type_attribute)) symbol_heap
storeAttribute No type_attribute symbol_heap
	= symbol_heap

getSymbolType ti=:{ti_functions,ti_common_defs} {symb_kind = SK_Function {glob_module,glob_object}, symb_arity, symb_name} ts
	| glob_module == cIclModIndex
		# (fun_type, ts) = ts!ts_fun_env.[glob_object]
		= case fun_type of
			UncheckedType fun_type
				# (fun_type_copy, ts) = currySymbolType fun_type symb_arity ts
				-> (fun_type_copy, [], [], ts)
			SpecifiedType fun_type lifted_arg_types _ 
				# (fun_type_copy, cons_variables, ts) = freshSymbolType fun_type ti_common_defs ts
				  (fun_type_copy, ts) = currySymbolType { fun_type_copy & tst_args = lifted_arg_types ++ fun_type_copy.tst_args } symb_arity ts
				-> (fun_type_copy, cons_variables, [], ts)
			CheckedType fun_type
				# (fun_type_copy, cons_variables, ts) = freshSymbolType fun_type ti_common_defs ts
				  (fun_type_copy,ts) = currySymbolType fun_type_copy symb_arity ts
				-> (fun_type_copy, cons_variables, [], ts)
			_
				-> abort "getSymbolType (type.icl)" ---> (symb_name, fun_type)
		# {ft_type,ft_type_ptr,ft_specials} = ti_functions.[glob_module].[glob_object]
		  (fun_type_copy, cons_variables, ts) = determineSymbolTypeOfFunction symb_name symb_arity ft_type ft_type_ptr ti_common_defs ts
		= (fun_type_copy, cons_variables, get_specials ft_specials, ts)
	where
		get_specials (SP_ContextTypes specials) = specials
		get_specials SP_None 					= []
getSymbolType ti {symb_kind = SK_Constructor {glob_module,glob_object}, symb_arity} ts
	# (fresh_cons_type, ts) = standardRhsConstructorType glob_object glob_module symb_arity ti ts
	= (fresh_cons_type, [], [], ts) 
getSymbolType ti=:{ti_common_defs} {symb_kind = SK_OverloadedFunction {glob_module,glob_object}, symb_arity} ts
	# {me_symb, me_type,me_type_ptr} = ti_common_defs.[glob_module].com_member_defs.[glob_object]
	  (fun_type_copy, cons_variables, ts) = determineSymbolTypeOfFunction me_symb symb_arity me_type me_type_ptr ti_common_defs ts
	= (fun_type_copy, cons_variables, [], ts)

class requirements a :: !TypeInput !a !(!u:Requirements, !*TypeState) -> (!AType, !Optional ExprInfoPtr, !(!u:Requirements, !*TypeState))

instance requirements BoundVar
where
	requirements ti {var_name,var_info_ptr,var_expr_ptr} (reqs, ts)
		# (var_info, ts_var_heap) = readPtr var_info_ptr ts.ts_var_heap
		  ts = { ts & ts_var_heap = ts_var_heap }
		= case var_info of
			VI_Type type
				-> (type, Yes var_expr_ptr, (reqs, ts))
			_
				-> abort ("requirements BoundVar" ---> (var_name <<- var_info))

instance requirements App
where
	requirements ti {app_symb,app_args,app_info_ptr} (reqs=:{req_cons_variables, req_attr_coercions}, ts)
		# ({tst_attr_env,tst_args,tst_result,tst_context}, cons_variables, specials, ts) = getSymbolType ti app_symb ts
	  	  reqs = { reqs & req_attr_coercions = tst_attr_env ++ req_attr_coercions, req_cons_variables = [cons_variables : req_cons_variables] }
	      (reqs, ts) = requirements_of_args ti app_args tst_args (reqs, ts)
		| isEmpty tst_context
			= (tst_result, No, (reqs, ts))
			= (tst_result, No, ({ reqs & req_overloaded_calls = [app_info_ptr : reqs.req_overloaded_calls ]}, 
					{ ts & ts_expr_heap = ts.ts_expr_heap <:= (app_info_ptr,
							EI_Overloaded { oc_symbol = app_symb, oc_context = tst_context, oc_specials = specials })}))
	where
		requirements_of_args :: !TypeInput ![Expression] ![AType] !(!u:Requirements, !*TypeState) -> (!u:Requirements, !*TypeState)
		requirements_of_args ti [] [] reqs_ts
			= reqs_ts
		requirements_of_args ti [expr:exprs] [lt:lts] reqs_ts
			# (e_type, opt_expr_ptr, (reqs, ts)) = requirements ti expr reqs_ts
			  req_type_coercions = [{ tc_demanded = lt, tc_offered = e_type, tc_position = { cp_expression = expr }, tc_coercible = True } : reqs.req_type_coercions ]
			  ts_expr_heap = storeAttribute opt_expr_ptr lt.at_attribute ts.ts_expr_heap
			= requirements_of_args ti exprs lts ({ reqs & req_type_coercions = req_type_coercions}, { ts & ts_expr_heap = ts_expr_heap })

instance requirements Case
where
	requirements ti {case_expr,case_guards,case_default,case_info_ptr} reqs_ts
		# (expr_type, opt_expr_ptr, (reqs, ts)) = requirements ti case_expr reqs_ts
		  (fresh_v, ts) = freshAttributedVariable ts
		  (cons_types, reqs_ts) = requirements_of_guarded_expressions ti case_guards case_expr expr_type opt_expr_ptr fresh_v (reqs, ts)
		  (reqs, ts) = requirements_of_default ti case_default fresh_v reqs_ts
		  ts_expr_heap =  ts.ts_expr_heap <:= (case_info_ptr, EI_CaseType { ct_pattern_type = expr_type, ct_result_type = fresh_v, ct_cons_types = cons_types })
		= (fresh_v, No, ({ reqs & req_case_and_let_exprs = [case_info_ptr : reqs.req_case_and_let_exprs]},
				{ ts & ts_expr_heap = ts_expr_heap }))
	where
		requirements_of_guarded_expressions ti=:{ti_common_defs} (AlgebraicPatterns alg_type patterns) match_expr pattern_type opt_pattern_ptr
						goal_type (reqs, ts)
			# (cons_types, result_type, new_attr_env, ts) = freshAlgebraicType alg_type patterns ti_common_defs ts
			  (used_cons_types, (reqs, ts)) = requirements_of_algebraic_patterns ti patterns cons_types goal_type [] (reqs, ts)
			  ts_expr_heap = storeAttribute opt_pattern_ptr result_type.at_attribute ts.ts_expr_heap
			= (reverse used_cons_types,  ({ reqs & req_type_coercions = [{tc_demanded = result_type,tc_offered = pattern_type, tc_position = { cp_expression = match_expr },
					tc_coercible = True} : reqs.req_type_coercions],
						req_attr_coercions = new_attr_env ++ reqs.req_attr_coercions }, { ts & ts_expr_heap = ts_expr_heap }))
	
		requirements_of_guarded_expressions ti (BasicPatterns bas_type patterns) match_expr pattern_type opt_pattern_ptr goal_type (reqs, ts)
			# (attr_bas_type, ts) = attributedBasicType bas_type ts
			  (reqs, ts) = requirements_of_basic_patterns ti patterns goal_type (reqs, ts)
			  ts_expr_heap = storeAttribute opt_pattern_ptr attr_bas_type.at_attribute ts.ts_expr_heap
			= ([], ({ reqs & req_type_coercions = [{tc_demanded = attr_bas_type,tc_offered = pattern_type, tc_position = { cp_expression = match_expr }, tc_coercible = True} :
						reqs.req_type_coercions]}, { ts & ts_expr_heap = ts_expr_heap }))
		requirements_of_guarded_expressions ti (DynamicPatterns dynamic_patterns) match_expr pattern_type opt_pattern_ptr goal_type reqs_ts
			# dyn_type = { at_type = TB BT_Dynamic, at_attribute = TA_Multi, at_annotation = AN_None }
			  (used_dyn_types, (reqs, ts)) = requirements_of_dynamic_patterns ti goal_type dynamic_patterns [] reqs_ts
			  ts_expr_heap = storeAttribute opt_pattern_ptr TA_Multi ts.ts_expr_heap
			= (reverse used_dyn_types, ({ reqs & req_type_coercions = [{tc_demanded = dyn_type, tc_offered = pattern_type, tc_position = { cp_expression = match_expr }, tc_coercible = True} :
						reqs.req_type_coercions] }, { ts & ts_expr_heap = ts_expr_heap }))
	
		requirements_of_algebraic_patterns ti [] cons_types goal_type used_cons_types reqs_ts
			= (used_cons_types, reqs_ts)
		requirements_of_algebraic_patterns ti=:{ti_common_defs}[{ap_vars, ap_expr }:gs] [ cons_arg_types : cons_types] goal_type used_cons_types (reqs, ts)
			# (res_type, opt_expr_ptr, (reqs, ts)) = requirements ti ap_expr (reqs, { ts & ts_var_heap = makeBase ap_vars cons_arg_types ts.ts_var_heap})
			  ts_expr_heap = storeAttribute opt_expr_ptr res_type.at_attribute ts.ts_expr_heap
			= requirements_of_algebraic_patterns ti gs cons_types goal_type [ cons_arg_types : used_cons_types ]
				({ reqs & req_type_coercions = [ { tc_demanded = goal_type, tc_offered = res_type, tc_position = { cp_expression = ap_expr }, tc_coercible = True } : reqs.req_type_coercions] },
					  { ts & ts_expr_heap = ts_expr_heap })
	
		requirements_of_basic_patterns _ [] goal_type reqs_ts
			= reqs_ts
		requirements_of_basic_patterns ti=:{ti_common_defs} [{bp_expr }:gs] goal_type reqs_ts
		  	# (res_type, opt_expr_ptr, (reqs, ts)) = requirements ti bp_expr reqs_ts
			  ts_expr_heap = storeAttribute opt_expr_ptr res_type.at_attribute ts.ts_expr_heap
			= requirements_of_basic_patterns ti gs goal_type
				({ reqs & req_type_coercions = [ { tc_demanded = goal_type, tc_offered = res_type, tc_position = { cp_expression = bp_expr }, tc_coercible = True } : reqs.req_type_coercions] },
						 { ts & ts_expr_heap = ts_expr_heap })
	
		requirements_of_dynamic_patterns ti goal_type [{dp_var={fv_info_ptr},dp_type,dp_rhs} : dps] used_dyn_types (reqs, ts=:{ts_expr_heap, ts_var_heap})
			# (EI_TempDynamicPattern _ _ _ _ dyn_type dyn_context dyn_expr_ptr type_code_symbol, ts_expr_heap) = readPtr dp_type ts_expr_heap
			  ts_var_heap = ts_var_heap <:= (fv_info_ptr, VI_Type dyn_type)
			  (dp_rhs_type, opt_expr_ptr, (reqs, ts)) = requirements ti dp_rhs (reqs, { ts & ts_expr_heap = ts_expr_heap, ts_var_heap = ts_var_heap })
			  ts_expr_heap = storeAttribute opt_expr_ptr dp_rhs_type.at_attribute ts.ts_expr_heap
			  type_coercion = { tc_demanded = goal_type, tc_offered = dp_rhs_type, tc_position = { cp_expression = dp_rhs }, tc_coercible = True }
			| isEmpty dyn_context
				# reqs = {reqs & req_type_coercions = [ type_coercion : reqs.req_type_coercions]}
				= requirements_of_dynamic_patterns ti goal_type dps [ [dyn_type] : used_dyn_types ] (reqs, { ts &  ts_expr_heap = ts_expr_heap })
				# reqs = { reqs & req_type_coercions = [ type_coercion : reqs.req_type_coercions], req_overloaded_calls = [dyn_expr_ptr : reqs.req_overloaded_calls ]}
				= requirements_of_dynamic_patterns ti goal_type dps [ [dyn_type] : used_dyn_types ] (reqs, { ts & ts_expr_heap = ts_expr_heap <:=
						(dyn_expr_ptr,  EI_Overloaded {  oc_symbol = type_code_symbol, oc_context = dyn_context, oc_specials = [] }) })
		requirements_of_dynamic_patterns ti goal_type [] used_dyn_types reqs_ts
			= (used_dyn_types, reqs_ts)
	
	
		requirements_of_default ti (Yes expr) goal_type reqs_ts
			# (res_type, opt_expr_ptr, (reqs,  ts)) = requirements ti expr reqs_ts
			  ts_expr_heap = storeAttribute opt_expr_ptr res_type.at_attribute ts.ts_expr_heap
			= ({ reqs & req_type_coercions = [ { tc_demanded = goal_type, tc_offered = res_type, tc_position = { cp_expression = expr }, tc_coercible = True } : reqs.req_type_coercions] },
					{ ts & ts_expr_heap = ts_expr_heap })
		requirements_of_default ti No goal_type reqs_ts
			= reqs_ts

instance requirements Let
where
	requirements ti {let_lazy_binds, let_strict_binds, let_expr, let_info_ptr} (reqs, ts)
		# let_binds = let_strict_binds ++ let_lazy_binds
		  (rev_var_types, ts) = make_base let_binds [] ts
		  var_types = reverse rev_var_types
		  (res_type, opt_expr_ptr, reqs_ts) = requirements ti let_expr (reqs, ts)
		  (reqs, ts) = requirements_of_binds ti let_binds var_types reqs_ts
		  ts_expr_heap = writePtr let_info_ptr (EI_LetType var_types) ts.ts_expr_heap
		= ( res_type, opt_expr_ptr, ({ reqs & req_case_and_let_exprs = [let_info_ptr : reqs.req_case_and_let_exprs]},{ ts & ts_expr_heap = ts_expr_heap }))
	where
	
		make_base [{bind_dst={fv_info_ptr}}:bs] var_types ts=:{ts_var_heap}
			# (v, ts) = freshAttributedVariable ts
			= make_base bs [v:var_types] { ts & ts_var_heap = writePtr fv_info_ptr (VI_Type v) ts.ts_var_heap }
		make_base [] var_types ts
			= (var_types, ts)
	
		requirements_of_binds _ [] _ reqs_ts
			= reqs_ts
		requirements_of_binds ti [{bind_src}:bs] [b_type:bts] reqs_ts
			# (exp_type, opt_expr_ptr, (reqs, ts)) = requirements ti bind_src reqs_ts
			  ts_expr_heap = storeAttribute opt_expr_ptr b_type.at_attribute ts.ts_expr_heap
			  req_type_coercions = [ { tc_demanded = b_type, tc_offered = exp_type, tc_position = { cp_expression = bind_src }, tc_coercible = True }
			  		: reqs.req_type_coercions ]
			= requirements_of_binds ti bs bts ({ reqs & req_type_coercions = req_type_coercions }, { ts & ts_expr_heap = ts_expr_heap })

instance requirements DynamicExpr
where
	requirements ti {dyn_expr,dyn_info_ptr} (reqs, ts=:{ts_expr_heap})
		# (EI_TempDynamicType _ dyn_type dyn_context dyn_expr_ptr type_code_symbol, ts_expr_heap) = readPtr dyn_info_ptr ts_expr_heap
		  (dyn_expr_type, opt_expr_ptr, (reqs, ts)) = requirements ti dyn_expr (reqs, { ts & ts_expr_heap = ts_expr_heap })
		  ts_expr_heap = storeAttribute opt_expr_ptr dyn_expr_type.at_attribute ts.ts_expr_heap
		  type_coercion = { tc_demanded = dyn_type, tc_offered = dyn_expr_type, tc_position = { cp_expression = dyn_expr }, tc_coercible = True }
		| isEmpty dyn_context
			= ({ at_type = TB BT_Dynamic, at_attribute = TA_Multi, at_annotation = AN_None }, No, 
					({reqs & req_type_coercions = [ type_coercion : reqs.req_type_coercions]}, 
						{ ts &  ts_expr_heap = ts_expr_heap }))
			= ({ at_type = TB BT_Dynamic, at_attribute = TA_Multi, at_annotation = AN_None }, No,
					({ reqs & req_type_coercions = [ type_coercion : reqs.req_type_coercions], req_overloaded_calls = [dyn_expr_ptr : reqs.req_overloaded_calls ]},
						{ ts & ts_expr_heap = ts_expr_heap <:= (dyn_expr_ptr, EI_Overloaded {
								oc_symbol = type_code_symbol, oc_context = dyn_context, oc_specials = []}) }))

instance requirements Expression
where
	requirements ti (Var var) reqs_ts
		= requirements ti var reqs_ts
	requirements ti (App app) reqs_ts
		= requirements ti app reqs_ts

	requirements ti (function @ args) reqs_ts
		# (off_fun_type, opt_fun_expr_ptr, reqs_ts) = requirements ti function reqs_ts
		  (rev_off_arg_types, (reqs, ts)) = requirements_of_list ti args [] reqs_ts
		  (alpha, ts) = freshAttributedVariable ts
		  (fun_type, req_type_coercions, ts) = apply_type rev_off_arg_types alpha reqs.req_type_coercions function ts
		  ts_expr_heap = storeAttribute opt_fun_expr_ptr fun_type.at_attribute ts.ts_expr_heap
		= (alpha, No, ({ reqs & req_type_coercions = [{ tc_demanded = fun_type, tc_offered = off_fun_type, tc_position = { cp_expression = function }, tc_coercible = True } : req_type_coercions ]}, { ts & ts_expr_heap = ts_expr_heap }))
	where
		requirements_of_list _ [] rev_list_types reqs_ts
			= (rev_list_types, reqs_ts)
		requirements_of_list ti [expr:exprs] rev_list_types reqs_ts
			# (e_type, opt_expr_ptr, reqs_ts) = requirements ti expr reqs_ts
			= requirements_of_list ti exprs [(opt_expr_ptr,e_type) : rev_list_types] reqs_ts
	
		apply_type [] res_type type_coercions function ts
			= (res_type, type_coercions, ts)
		apply_type [(opt_expr_ptr,type) : types] res_type type_coercions function ts
			# (type, type_coercions, ts) = determine_demanded_type type opt_expr_ptr type_coercions function ts
			  (u, ts) = freshAttribute ts
			= apply_type types { at_annotation = AN_None, at_attribute = u, at_type = type --> res_type } type_coercions function ts
		
		determine_demanded_type :: !AType !(Optional ExprInfoPtr) ![TypeCoercion] !Expression !*TypeState
			-> (!AType, ![TypeCoercion], !*TypeState)
		determine_demanded_type type (Yes expr_ptr) type_coercions expr ts
			# (dem_type, ts) = freshAttributedVariable ts
			  ts_expr_heap = writePtr expr_ptr (EI_Attribute (toInt dem_type.at_attribute)) ts.ts_expr_heap
			= (dem_type, [ { tc_demanded = dem_type, tc_offered = type, tc_position = { cp_expression = expr }, tc_coercible = True } : type_coercions ],
				{ ts & ts_expr_heap = ts_expr_heap })
		determine_demanded_type type No type_coercions expr ts
			= (type, type_coercions, ts) 

	requirements ti (Case kees) reqs_ts
		= requirements ti kees reqs_ts
		
	requirements ti (Let lad) reqs_ts
		= requirements ti lad reqs_ts

	requirements ti (DynamicExpr dienamic) reqs_ts
		= requirements ti dienamic reqs_ts

	requirements ti (Selection result_type_symb expr selectors) reqs_ts
		# (expr_type, opt_expr_ptr, (reqs, ts)) = requirements ti expr reqs_ts
		= case result_type_symb of
			Yes {glob_object={ds_ident,ds_index,ds_arity}, glob_module}
				# (var, ts) = freshAttributedVariable ts
			  	  (result_type, (reqs, ts)) =  requirementsOfSelectors ti No expr selectors False var expr opt_expr_ptr (reqs, ts)
				  tuple_type = MakeTypeSymbIdent { glob_object = ds_index, glob_module = glob_module } ds_ident ds_arity
				  non_unique_type_var = { at_attribute = TA_Multi, at_annotation = AN_None, at_type = TempV ts.ts_var_store }
				  req_type_coercions
						= [ { tc_demanded = non_unique_type_var, tc_offered = result_type, tc_position = { cp_expression = expr }, tc_coercible = False },
							{ tc_demanded = var, tc_offered = expr_type, tc_position = { cp_expression = expr }, tc_coercible = True } :
	 								reqs.req_type_coercions]
				  result_type = { at_type = TA tuple_type [non_unique_type_var,var], at_attribute = TA_Unique, at_annotation = AN_None }
				-> (result_type, No, ({ reqs & req_type_coercions = req_type_coercions }, 
						{ts & ts_var_store = inc ts.ts_var_store, ts_expr_heap = storeAttribute opt_expr_ptr TA_Multi ts.ts_expr_heap}))
			_
			  	# (result_type, (reqs, ts)) =  requirementsOfSelectors ti No expr selectors True expr_type expr opt_expr_ptr (reqs, ts)
				-> ( result_type, No, (reqs, { ts & ts_expr_heap = storeAttribute opt_expr_ptr result_type.at_attribute ts.ts_expr_heap }))

	requirements ti (Update composite_expr selectors elem_expr) reqs_ts
		# (composite_expr_type, opt_composite_expr_ptr, reqs_ts) = requirements ti composite_expr reqs_ts
		  (result_type, reqs_ts) =  requirementsOfSelectors ti (Yes elem_expr) composite_expr selectors True composite_expr_type composite_expr opt_composite_expr_ptr reqs_ts
		= (composite_expr_type, No, reqs_ts)

	requirements ti (RecordUpdate {glob_module,glob_object={ds_index,ds_arity}} expression expressions) (reqs, ts)
		# (lhs, ts) = standardLhsConstructorType ds_index glob_module ds_arity ti ts	
		  (rhs, ts) = standardRhsConstructorType ds_index glob_module ds_arity ti ts	
		  (expression_type, opt_expr_ptr, reqs_ts) = requirements ti expression (reqs, ts)
		  (reqs, ts) = requirements_of_fields ti expression expressions rhs.tst_args lhs.tst_args reqs_ts
		  ts = { ts & ts_expr_heap = storeAttribute opt_expr_ptr lhs.tst_result.at_attribute ts.ts_expr_heap }
		  coercion = { tc_demanded = lhs.tst_result, tc_offered = expression_type, tc_position = { cp_expression = expression }, tc_coercible = True }
		= (rhs.tst_result, No, ({ reqs & req_attr_coercions = rhs.tst_attr_env ++ lhs.tst_attr_env ++ reqs.req_attr_coercions,
										 req_type_coercions = [ coercion : reqs.req_type_coercions ]}, ts))
	where 
		requirements_of_fields ti expression [] _ _ reqs_ts
			= reqs_ts
		requirements_of_fields ti expression [field : fields] [dem_type : dem_types] [off_type : off_types] reqs_ts
			# reqs_ts = requirements_of_field ti expression field dem_type off_type reqs_ts
			= requirements_of_fields ti expression fields dem_types off_types reqs_ts
	
		requirements_of_field ti expression {bind_src=EE} dem_field_type off_field_type (reqs=:{req_type_coercions}, ts)
			# coercion = { tc_demanded = dem_field_type, tc_offered = off_field_type, tc_position = { cp_expression = expression }, tc_coercible = True }
			= ({ reqs & req_type_coercions = [ coercion : req_type_coercions ]}, ts)
		requirements_of_field ti _ {bind_src} dem_field_type _ reqs_ts
			# (expr_type, opt_expr_ptr, (reqs, ts)) = requirements ti bind_src reqs_ts
			  ts = { ts & ts_expr_heap = storeAttribute opt_expr_ptr dem_field_type.at_attribute ts.ts_expr_heap }
			  coercion = { tc_demanded = dem_field_type, tc_offered = expr_type, tc_position = { cp_expression = bind_src }, tc_coercible = True }
			= ({ reqs & req_type_coercions = [ coercion : reqs.req_type_coercions ]}, ts)

	requirements ti (TupleSelect tuple_symbol arg_nr expr) (reqs=:{req_attr_coercions}, ts)
		# ({tst_args = [argtype:_], tst_result, tst_attr_env}, ts) = standardTupleSelectorType tuple_symbol arg_nr ti ts
		  (e_type, opt_expr_ptr, (reqs, ts)) = requirements ti expr ({ reqs & req_attr_coercions = tst_attr_env ++ req_attr_coercions }, ts)
		  req_type_coercions = [{ tc_demanded = argtype, tc_offered = e_type, tc_position = { cp_expression = expr }, tc_coercible = True } : reqs.req_type_coercions ]
		  ts_expr_heap = storeAttribute opt_expr_ptr argtype.at_attribute ts.ts_expr_heap
		= (tst_result, No, ({ reqs & req_type_coercions = req_type_coercions }, { ts & ts_expr_heap = ts_expr_heap }))
	
	
	requirements _ (BasicExpr basic_val basic_type) (reqs, ts)
		# (type, ts) = attributedBasicType basic_type ts
	 	= (type, No, (reqs, ts))


	requirements ti (MatchExpr opt_tuple_type {glob_object={ds_arity, ds_index},glob_module} expr) (reqs, ts)
		# ({tst_result,tst_args,tst_attr_env}, ts) = standardLhsConstructorType ds_index glob_module ds_arity ti ts	
		  (e_type, opt_expr_ptr, (reqs, ts)) = requirements ti expr (reqs, ts)
		  reqs = { reqs & req_attr_coercions =  tst_attr_env ++ reqs.req_attr_coercions,
		  				  req_type_coercions = [{ tc_demanded = tst_result, tc_offered = e_type, tc_position = { cp_expression = expr }, tc_coercible = True } : reqs.req_type_coercions ] }
		  ts = { ts & ts_expr_heap = storeAttribute opt_expr_ptr tst_result.at_attribute ts.ts_expr_heap }
		= case opt_tuple_type of
			Yes {glob_object={ds_ident,ds_index,ds_arity}, glob_module}
				# tuple_type = MakeTypeSymbIdent { glob_object = ds_index, glob_module = glob_module } ds_ident ds_arity
				-> ({ at_type = TA tuple_type tst_args, at_attribute = TA_Unique, at_annotation = AN_None }, No, (reqs, ts))
			No
				-> ( hd tst_args, No, (reqs, ts))
		
	requirements _ (AnyCodeExpr _ _ _) (reqs, ts)
		# (fresh_v, ts) = freshAttributedVariable ts
		= (fresh_v, No, (reqs, ts))
	requirements _ (ABCCodeExpr _ _) (reqs, ts)
		# (fresh_v, ts) = freshAttributedVariable ts
		= (fresh_v, No, (reqs, ts))
	
	requirements _ expr reqs_ts
		= (abort ("Error in requirements\n" ---> expr), No, reqs_ts)

requirementsOfSelectors ti opt_expr expr [selector] tc_coercible sel_expr_type sel_expr opt_expr_ptr (reqs, ts)
	# ts_expr_heap = storeAttribute opt_expr_ptr sel_expr_type.at_attribute ts.ts_expr_heap
	= requirementsOfSelector ti opt_expr expr selector tc_coercible sel_expr_type sel_expr (reqs, { ts & ts_expr_heap = ts_expr_heap })
requirementsOfSelectors ti opt_expr expr [selector : selectors] tc_coercible sel_expr_type sel_expr opt_expr_ptr (reqs, ts) 
	# ts_expr_heap = storeAttribute opt_expr_ptr sel_expr_type.at_attribute ts.ts_expr_heap
	  (result_type, reqs_ts) = requirementsOfSelector ti No expr selector tc_coercible sel_expr_type sel_expr (reqs, { ts & ts_expr_heap = ts_expr_heap })
	= requirements_of_remaining_selectors ti opt_expr expr selectors tc_coercible result_type expr reqs_ts
where
	requirements_of_remaining_selectors ti opt_expr expr [selector] tc_coercible sel_expr_type sel_expr reqs_ts 
		= requirementsOfSelector ti opt_expr expr selector tc_coercible sel_expr_type sel_expr reqs_ts 
	requirements_of_remaining_selectors ti opt_expr expr [selector : selectors] tc_coercible sel_expr_type sel_expr reqs_ts 
		# (result_type, reqs_ts) = requirementsOfSelector ti No expr selector tc_coercible sel_expr_type sel_expr reqs_ts 
		= requirements_of_remaining_selectors ti opt_expr expr selectors tc_coercible result_type sel_expr reqs_ts
		  
requirementsOfSelector ti _ expr (RecordSelection field filed_nr) tc_coercible sel_expr_type sel_expr (reqs, ts )
	# ({tst_args, tst_result, tst_attr_env}, ts) = standardFieldSelectorType field ti ts
	  req_type_coercions = [{ tc_demanded = sel_expr_type, tc_offered = hd tst_args, tc_position = { cp_expression = sel_expr }, tc_coercible = tc_coercible } : 
	  			reqs.req_type_coercions ]
	= (tst_result, ({ reqs & req_type_coercions = req_type_coercions }, ts))
requirementsOfSelector ti opt_expr expr (ArraySelection {glob_object = {ds_ident,ds_index,ds_arity},glob_module} expr_ptr index_expr) tc_coercible sel_expr_type sel_expr (reqs, ts) 
	# {me_type} = ti.ti_common_defs.[glob_module].com_member_defs.[ds_index]
	  ({tst_attr_env,tst_args,tst_result,tst_context}, cons_variables, ts) = freshSymbolType me_type ti.ti_common_defs ts
	  (dem_array_type, dem_index_type, rest_type) = array_and_index_type tst_args
	  reqs ={ reqs & req_attr_coercions = tst_attr_env ++ reqs.req_attr_coercions, req_cons_variables = [ cons_variables : reqs.req_cons_variables ]}
	  (index_type, opt_expr_ptr, (reqs, ts)) = requirements ti index_expr (reqs, ts)
      reqs = { reqs & req_type_coercions = [{ tc_demanded = dem_index_type, tc_offered = index_type, tc_position = { cp_expression = expr }, tc_coercible = True },
      			{ tc_demanded = dem_array_type, tc_offered = sel_expr_type, tc_position = { cp_expression = sel_expr }, tc_coercible = tc_coercible } : reqs.req_type_coercions ]}
	  (reqs, ts) = requirements_of_update ti opt_expr rest_type (reqs, ts)
	| isEmpty tst_context
		= (tst_result, (reqs, ts))
		= (tst_result, ({ reqs & req_overloaded_calls = [expr_ptr : reqs.req_overloaded_calls ]}, { ts & ts_expr_heap =
				ts.ts_expr_heap <:= (expr_ptr, EI_Overloaded { oc_symbol = 
					{ symb_name = ds_ident, symb_kind = SK_OverloadedFunction {glob_module = glob_module, glob_object = ds_index}, symb_arity = ds_arity },
						oc_context = tst_context, oc_specials = [] })}))
where
	array_and_index_type [array_type, index_type : rest_type ]
		= (array_type, index_type, rest_type)

	requirements_of_update ti No _ reqs_ts
		= reqs_ts
	requirements_of_update ti (Yes elem_expr) [ elem_type : _ ] reqs_ts
		# (elem_expr_type, opt_elem_expr_ptr, (reqs, ts)) = requirements ti elem_expr reqs_ts
		  ts = { ts & ts_expr_heap = storeAttribute opt_elem_expr_ptr elem_type.at_attribute ts.ts_expr_heap }
	      reqs = { reqs & req_type_coercions = [{ tc_demanded = elem_type, tc_offered = elem_expr_type,
						tc_position = { cp_expression = elem_expr }, tc_coercible = True } : reqs.req_type_coercions ]}
		= (reqs, ts)

makeBase vars types ts_var_heap
	= fold2St (\ {fv_info_ptr} type var_heap -> var_heap <:= (fv_info_ptr, VI_Type type)) vars types ts_var_heap

attributedBasicType (BT_String string_type) ts=:{ts_attr_store}
	= ({ at_annotation = AN_None, at_attribute = TA_TempVar ts_attr_store, at_type = string_type}, {ts & ts_attr_store = inc ts_attr_store})
attributedBasicType bas_type ts=:{ts_attr_store}
	= ({ at_annotation = AN_None, at_attribute = TA_TempVar ts_attr_store, at_type = TB bas_type}, {ts & ts_attr_store = inc ts_attr_store})

unify_coercions [{tc_demanded,tc_offered,tc_position}:coercions] modules subst heaps err
	# (subst, heaps, err) = unify_coercions coercions modules subst heaps err
	  (subst_demanded, subst) = arraySubst tc_demanded subst
	  (subst_offered, subst) = arraySubst tc_offered subst
	  (succ, subst, heaps) = unify subst_demanded subst_offered modules subst heaps
	| succ
		= (subst, heaps, err)
		= (subst, heaps, cannotUnify subst_demanded subst_offered tc_position err)
	
unify_coercions [] modules subst heaps err
	= (subst, heaps, err)

InitFunEnv :: !Int -> *{! FunctionType}
InitFunEnv nr_of_fun_defs
	= createArray nr_of_fun_defs EmptyFunctionType

//CreateInitialSymbolTypes :: ![Int] !u:{# FunDef} !{# CommonDefs } !*TypeState -> (!u:{# FunDef}, !*TypeState)
CreateInitialSymbolTypes common_defs [] defs_and_state
	= defs_and_state
CreateInitialSymbolTypes common_defs [fun : funs] (fun_defs, pre_def_symbols, req_cons_variables, ts)
	#! fd = fun_defs.[fun]
	# (pre_def_symbols, req_cons_variables, ts) = initial_symbol_type common_defs fd (pre_def_symbols, req_cons_variables, ts)
	= CreateInitialSymbolTypes common_defs funs (fun_defs, pre_def_symbols, req_cons_variables, ts)
where 
	initial_symbol_type common_defs {fun_type = Yes ft=:{st_arity,st_args,st_result,st_attr_vars,st_attr_env}, fun_lifted, fun_info = {fi_dynamics} }
				(pre_def_symbols, req_cons_variables, ts=:{ts_type_heaps,ts_expr_heap,ts_td_infos,ts_error})
		# (st_args, ps) = addPropagationAttributesToATypes common_defs st_args
				{ prop_type_heaps = ts_type_heaps, prop_td_infos = ts_td_infos,
				  prop_attr_vars = st_attr_vars, prop_attr_env = st_attr_env, prop_error = ts_error}
		  (st_result, _, {prop_type_heaps,prop_td_infos,prop_attr_vars,prop_error,prop_attr_env}) = addPropagationAttributesToAType common_defs st_result ps
		  ft = { ft & st_args = st_args, st_result = st_result, st_attr_vars = prop_attr_vars, st_attr_env = prop_attr_env }
		  (th_vars, ts_expr_heap) = clear_dynamics fi_dynamics (prop_type_heaps.th_vars, ts.ts_expr_heap)
		  (fresh_fun_type, cons_variables, ts) = freshSymbolType ft common_defs { ts & ts_type_heaps = { prop_type_heaps & th_vars = th_vars }, ts_expr_heap = ts_expr_heap,
		  		 ts_td_infos = prop_td_infos, ts_error = prop_error }
		  (lifted_args, ts) = fresh_non_unique_type_variables fun_lifted [] ts
		  (ts_var_store, ts_type_heaps, ts_var_heap, ts_expr_heap, pre_def_symbols)
		  		= fresh_dynamics fi_dynamics (ts.ts_var_store, ts.ts_type_heaps, ts.ts_var_heap, ts.ts_expr_heap, pre_def_symbols)
		= (pre_def_symbols, [ cons_variables : req_cons_variables],
				{ ts & ts_fun_env = { ts.ts_fun_env & [fun] = SpecifiedType ft lifted_args
					{ fresh_fun_type & tst_arity = st_arity + fun_lifted, tst_args = lifted_args ++ fresh_fun_type.tst_args, tst_lifted = fun_lifted }},
						ts_var_heap = ts_var_heap, ts_var_store = ts_var_store, ts_expr_heap = ts_expr_heap, ts_type_heaps = ts_type_heaps })
	initial_symbol_type common_defs {fun_arity, fun_lifted, fun_info = {fi_dynamics}} (pre_def_symbols, req_cons_variables, ts)
		# (st_gen, ts) = create_general_symboltype fun_arity fun_lifted ts
		  ts_type_heaps = ts.ts_type_heaps 
		  (th_vars, ts_expr_heap) = clear_dynamics fi_dynamics (ts_type_heaps.th_vars, ts.ts_expr_heap)
		  (ts_var_store, ts_type_heaps, ts_var_heap, ts_expr_heap, pre_def_symbols)
		  		= fresh_dynamics fi_dynamics (ts.ts_var_store, { ts_type_heaps & th_vars = th_vars },
		  				ts.ts_var_heap, ts_expr_heap, pre_def_symbols)
		= (pre_def_symbols, req_cons_variables, { ts & ts_fun_env = { ts.ts_fun_env & [fun] = UncheckedType st_gen }, ts_var_store = ts_var_store,
					ts_expr_heap = ts_expr_heap, ts_type_heaps = ts_type_heaps, ts_var_heap = ts_var_heap})


	create_general_symboltype :: !Int !Int !*TypeState -> (!TempSymbolType, !*TypeState)
	create_general_symboltype nr_of_args nr_of_lifted_args ts
		# (tst_args, ts) = fresh_attributed_type_variables nr_of_args [] ts
		  (tst_args, ts) = fresh_attributed_type_variables nr_of_lifted_args tst_args ts
		  (tst_result, ts) = freshAttributedVariable ts
		= ({ tst_args = tst_args, tst_arity = nr_of_args + nr_of_lifted_args, tst_result = tst_result, tst_context = [], tst_attr_env = [], tst_lifted = 0 }, ts)

	fresh_attributed_type_variables :: !Int ![AType] !*TypeState -> (![AType], !*TypeState)
	fresh_attributed_type_variables n vars ts
		| n == 0
			= (vars, ts)
			# (var, ts) = freshAttributedVariable ts
			= fresh_attributed_type_variables (dec n) [var : vars] ts

	fresh_non_unique_type_variables :: !Int ![AType] !*TypeState -> (![AType], !*TypeState)
	fresh_non_unique_type_variables n vars ts
		| n == 0
			= (vars, ts)
			# (var, ts) = freshNonUniqueVariable ts
			= fresh_non_unique_type_variables (dec n) [var : vars] ts

	fresh_dynamics dyn_ptrs state
		= foldSt fresh_dynamic dyn_ptrs state

	fresh_dynamic dyn_ptr (var_store, type_heaps, var_heap, expr_heap, predef_symbols)
		# (dyn_info, expr_heap) = readPtr dyn_ptr expr_heap
		= case dyn_info of
			EI_Dynamic opt_dyn_type=:(Yes {dt_uni_vars,dt_type,dt_global_vars})
				# (th_vars, var_store) = fresh_existential_attributed_variables dt_uni_vars (type_heaps.th_vars, var_store)
				  (th_vars, var_store) = fresh_type_variables dt_global_vars (th_vars, var_store)
				  (tdt_type, {copy_heaps}) = freshCopy dt_type { copy_heaps = { type_heaps & th_vars = th_vars }}
				  (contexts, expr_ptr, type_code_symbol, (var_heap, expr_heap, type_var_heap, predef_symbols))
				  		= determine_context_and_expr_ptr dt_global_vars (var_heap, expr_heap, copy_heaps.th_vars, predef_symbols)
				-> (var_store, { copy_heaps & th_vars = type_var_heap }, var_heap,
						expr_heap <:= (dyn_ptr, EI_TempDynamicType opt_dyn_type tdt_type contexts expr_ptr type_code_symbol), predef_symbols)
			EI_Dynamic No
				# fresh_var = TempV var_store
				  tdt_type = { at_attribute = TA_Multi, at_annotation = AN_None, at_type = fresh_var }

				# ({pds_ident,pds_module,pds_def},predef_symbols) = predef_symbols![PD_TypeCodeClass]
		  		  tc_class_symb = {glob_module = pds_module, glob_object = {ds_ident = pds_ident, ds_arity = 1, ds_index = pds_def }}
 				  (pds, predef_symbols) = predef_symbols![PD_TypeCodeMember]
		  		  ({pds_ident,pds_module,pds_def},predef_symbols) = predef_symbols![PD_TypeCodeMember]
				  tc_member_symb = { symb_name = pds_ident, symb_kind = SK_OverloadedFunction {glob_module = pds_module, glob_object = pds_def }, symb_arity = 0}
		 		  (new_var_ptr, var_heap) = newPtr VI_Empty var_heap
				  context = {tc_class = tc_class_symb, tc_types = [fresh_var], tc_var = new_var_ptr}
		  		  (expr_ptr, expr_heap) = newPtr EI_Empty expr_heap
				-> (inc var_store, type_heaps, var_heap,
						expr_heap <:= (dyn_ptr, EI_TempDynamicType No tdt_type [context] expr_ptr tc_member_symb), predef_symbols)
			EI_DynamicTypeWithVars loc_type_vars dt=:{dt_type,dt_global_vars} loc_dynamics
				# (fresh_vars, (th_vars, var_store)) = fresh_existential_variables loc_type_vars (type_heaps.th_vars, var_store)
				  (th_vars, var_store) = fresh_type_variables dt_global_vars (th_vars, var_store)
				  (tdt_type, {copy_heaps}) = freshCopy dt_type { copy_heaps = { type_heaps & th_vars = th_vars }}
				  (contexts, expr_ptr, type_code_symbol, (var_heap, expr_heap, type_var_heap, predef_symbols))
				  		= determine_context_and_expr_ptr dt_global_vars (var_heap, expr_heap, copy_heaps.th_vars, predef_symbols)
				-> fresh_local_dynamics loc_dynamics (var_store, { copy_heaps & th_vars = type_var_heap }, var_heap,
						expr_heap <:= (dyn_ptr, EI_TempDynamicPattern loc_type_vars dt loc_dynamics fresh_vars tdt_type contexts expr_ptr type_code_symbol), predef_symbols)

	fresh_local_dynamics loc_dynamics state
		= foldSt fresh_dynamic loc_dynamics state

	clear_dynamics dyn_ptrs heaps
		= foldSt clear_dynamic dyn_ptrs heaps
		
	clear_dynamic dyn_ptr (var_heap, expr_heap)
		# (dyn_info, expr_heap) = readPtr dyn_ptr expr_heap
		= case dyn_info of
			EI_Dynamic (Yes {dt_global_vars})
				-> (clear_type_vars dt_global_vars var_heap, expr_heap)
			EI_Dynamic No
				-> (var_heap, expr_heap)
			EI_DynamicTypeWithVars loc_type_vars {dt_global_vars} loc_dynamics
				-> clear_local_dynamics loc_dynamics (clear_type_vars dt_global_vars var_heap, expr_heap)

	clear_local_dynamics loc_dynamics state
		= foldSt clear_dynamic loc_dynamics state
		
	clear_type_vars type_vars var_heap
		= foldSt (\{tv_info_ptr} -> writePtr tv_info_ptr TVI_Empty) type_vars var_heap 
		
	fresh_existential_attributed_variables type_variables state
		= foldSt (\{atv_variable={tv_info_ptr}} (var_heap, var_store) -> (var_heap <:= (tv_info_ptr, TVI_Type (TempQV var_store)), inc var_store))
							type_variables state 
	fresh_existential_variables type_variables state
		= mapSt (\{tv_info_ptr} (var_heap, var_store) -> (var_store, (var_heap <:= (tv_info_ptr, TVI_Type (TempQV var_store)), inc var_store)))
							type_variables state 
	fresh_type_variables type_variables state
		= foldSt fresh_type_variable type_variables state 

	fresh_type_variable {tv_info_ptr} (var_heap, var_store)
		# (var_info, var_heap) = readPtr tv_info_ptr var_heap
		= case var_info of
			TVI_Empty
				-> (var_heap <:= (tv_info_ptr, TVI_Type (TempV var_store)), inc var_store)
			_
				-> (var_heap, var_store)
	
	determine_context_and_expr_ptr global_vars (var_heap, expr_heap, type_var_heap, predef_symbols)
		# ({pds_ident,pds_module,pds_def},predef_symbols) = predef_symbols![PD_TypeCodeClass]
		  tc_class_symb = {glob_module = pds_module, glob_object = {ds_ident = pds_ident, ds_arity = 1, ds_index = pds_def }}
		  ({pds_ident,pds_module,pds_def},predef_symbols) = predef_symbols![PD_TypeCodeMember]
		  tc_member_symb = { symb_name	= pds_ident, symb_kind = SK_TypeCode, symb_arity = 0}
		  (contexts, (var_heap, type_var_heap)) = mapSt (build_type_context tc_class_symb) global_vars (var_heap, type_var_heap)
		  (expr_ptr, expr_heap) = newPtr EI_Empty expr_heap
		= (contexts, expr_ptr, tc_member_symb, (var_heap, expr_heap, type_var_heap, predef_symbols))

	build_type_context tc_class_symb {tv_info_ptr} (var_heap, type_var_heap)
		# (TVI_Type fresh_var, type_var_heap) = readPtr tv_info_ptr type_var_heap
		  (new_var_ptr, var_heap) = newPtr VI_Empty var_heap
		= ({tc_class = tc_class_symb, tc_types = [fresh_var], tc_var = new_var_ptr}, (var_heap, type_var_heap))


specification_error type err
	# err = errorHeading "Type error" err
	  format = { form_properties = cAttributed, form_attr_position = No}
	= { err & ea_file = err.ea_file <<< " specified type conflicts with derived type " <:: (format, type) <<< '\n' }

cleanUpAndCheckFunctionTypes [] _ defs type_contexts coercion_env attr_partition type_var_env attr_var_env (fun_defs, ts)
	= (fun_defs, ts)
cleanUpAndCheckFunctionTypes [fun : funs] [ {fe_requirements = {req_case_and_let_exprs}} : reqs] defs type_contexts coercion_env
				attr_partition type_var_env attr_var_env (fun_defs, ts)
	#! fd = fun_defs.[fun]
	# (type_var_env, attr_var_env, ts) = clean_up_and_check_function_type fd fun defs type_contexts
				req_case_and_let_exprs coercion_env attr_partition type_var_env attr_var_env ts
	= cleanUpAndCheckFunctionTypes funs reqs defs type_contexts coercion_env attr_partition type_var_env attr_var_env (fun_defs, ts)
where
	clean_up_and_check_function_type {fun_symb,fun_pos,fun_type = opt_fun_type} fun defs type_contexts case_and_let_exprs
					coercion_env attr_partition type_var_env attr_var_env ts
		#! env_type = ts.ts_fun_env.[fun]
		# ts = { ts & ts_error = setErrorAdmin (newPosition fun_symb fun_pos) ts.ts_error}
		= case env_type of
			ExpandedType fun_type tmp_fun_type exp_fun_type
				# (clean_fun_type, type_var_env, attr_var_env, ts_type_heaps, ts_expr_heap, ts_error)
					= cleanUpSymbolType exp_fun_type type_contexts case_and_let_exprs coercion_env 
										attr_partition type_var_env attr_var_env ts.ts_type_heaps ts.ts_expr_heap ts.ts_error
				| ts_error.ea_ok
					# (ts_fun_env, attr_var_env, ts_type_heaps, ts_expr_heap, ts_error)
			  			= check_function_type fun_type tmp_fun_type clean_fun_type case_and_let_exprs defs ts.ts_fun_env attr_var_env ts_type_heaps ts_expr_heap ts_error
					-> (type_var_env, attr_var_env, { ts & ts_type_heaps = ts_type_heaps, ts_expr_heap = ts_expr_heap, ts_fun_env = ts_fun_env, ts_error = ts_error })
					-> (type_var_env, attr_var_env, { ts & ts_type_heaps = ts_type_heaps, ts_expr_heap = ts_expr_heap, ts_error = ts_error })
		  	UncheckedType exp_fun_type
				# (clean_fun_type, type_var_env, attr_var_env, ts_type_heaps, ts_expr_heap, ts_error)
					= cleanUpSymbolType exp_fun_type type_contexts case_and_let_exprs coercion_env
										attr_partition type_var_env attr_var_env ts.ts_type_heaps ts.ts_expr_heap ts.ts_error
				  ts_fun_env = { ts.ts_fun_env & [fun] = CheckedType clean_fun_type }
				-> (type_var_env, attr_var_env, { ts & ts_type_heaps = ts_type_heaps, ts_expr_heap = ts_expr_heap, ts_fun_env = ts_fun_env, ts_error = ts_error })

	check_function_type fun_type tmp_fun_type=:{tst_lifted} clean_fun_type=:{st_arity, st_args, st_vars, st_attr_vars} case_and_let_exprs
				defs fun_env attr_var_env type_heaps expr_heap error
		# (equi, attr_var_env, type_heaps) = equivalent clean_fun_type tmp_fun_type defs attr_var_env type_heaps
		| equi
			# type_with_lifted_arg_types = addLiftedArgumentsToSymbolType fun_type tst_lifted st_args st_vars st_attr_vars
			  (type_heaps, expr_heap) = updateExpressionTypes clean_fun_type type_with_lifted_arg_types case_and_let_exprs type_heaps expr_heap
			= ({ fun_env & [fun] = CheckedType type_with_lifted_arg_types}, attr_var_env, type_heaps, expr_heap, error)
//					---> ("check_function_type", clean_fun_type, fun_type, type_with_lifted_arg_types)
			= (fun_env, attr_var_env, type_heaps, expr_heap, specification_error clean_fun_type error)
	where
		add_lifted_arg_types arity_diff args1 args2
			| arity_diff > 0
				= take arity_diff args2 ++ args1
				= args1

addLiftedArgumentsToSymbolType st=:{st_arity,st_args,st_vars,st_attr_vars} nr_of_lifted_arguments new_args new_vars new_attrs
	= { st & st_args = take nr_of_lifted_arguments new_args ++ st_args, st_vars = st_vars ++ drop (length st_vars) new_vars,
			st_attr_vars = st_attr_vars ++ take (length new_attrs - length st_attr_vars) new_attrs, st_arity = st_arity + nr_of_lifted_arguments }


::	FunctionRequirements =
	{	fe_requirements	:: !Requirements
	,	fe_context		:: !Optional [TypeContext]
	,	fe_index		:: !Index
	,	fe_location		:: !IdentPos
	}

typeProgram ::!{! Group} !*{# FunDef} !IndexRange !CommonDefs ![Declaration] !{# DclModule} !*Heaps !*PredefinedSymbols !*File
	-> (!Bool, !*{# FunDef}, !IndexRange, {! GlobalTCType}, !{# CommonDefs}, !{# {# FunType} }, !*Heaps, !*PredefinedSymbols, !*File)
typeProgram comps fun_defs specials icl_defs imports modules {hp_var_heap, hp_expression_heap, hp_type_heaps} predef_symbols file
	#! fun_env_size = size fun_defs
	# ts_error = {ea_file = file, ea_loc = [], ea_ok = True }

	  ti_common_defs = {{dcl_common \\ {dcl_common} <-: modules } & [cIclModIndex] = icl_defs }
	  ti_functions	 = {dcl_functions \\ {dcl_functions} <-: modules }

	  type_def_sizes =  [ size com_type_defs \\ {com_type_defs} <-: ti_common_defs ]
	  class_def_sizes = [ size com_class_defs \\ {com_class_defs} <-: ti_common_defs ]
	  class_instances = { {  IT_Empty \\ i <- [0 .. dec size] } \\ size <- class_def_sizes }
	  
	  (td_infos, hp_type_heaps, ts_error) = analTypeDefs ti_common_defs hp_type_heaps ts_error

	  state = collect_imported_instances imports ti_common_defs {} ts_error class_instances hp_type_heaps.th_vars td_infos 
	  (_, ts_error, class_instances, th_vars, td_infos) = collect_and_check_instances (size icl_defs.com_instance_defs) ti_common_defs state
	  
	  ts = { ts_fun_env = InitFunEnv fun_env_size, ts_var_heap = hp_var_heap, ts_expr_heap = hp_expression_heap, ts_var_store = 0, ts_attr_store = FirstAttrVar,
	  		 ts_type_heaps = { hp_type_heaps & th_vars = th_vars }, ts_td_infos = td_infos, ts_error = ts_error }
	  ti = { ti_common_defs = ti_common_defs, ti_functions = ti_functions }
	  special_instances = { si_next_array_member_index = fun_env_size, si_array_instances = [], si_next_TC_member_index = 0, si_TC_instances = [] }
	# (type_error, fun_defs, predef_symbols, special_instances, ts) = type_components 0 comps  class_instances ti (False, fun_defs, predef_symbols, special_instances, ts)
	  (fun_defs,ts_fun_env) = update_function_types 0 comps ts.ts_fun_env fun_defs
	  (type_error, fun_defs, predef_symbols, special_instances, {ts_fun_env,ts_error,ts_var_heap, ts_expr_heap, ts_type_heaps})
			= type_instances specials.ir_from specials.ir_to class_instances ti (type_error, fun_defs, predef_symbols, special_instances,
				{ ts & ts_fun_env = ts_fun_env })
	  {si_array_instances, si_next_array_member_index, si_next_TC_member_index, si_TC_instances}= special_instances
	  (fun_defs, predef_symbols, ts_type_heaps) = convert_array_instances si_array_instances ti_common_defs fun_defs predef_symbols ts_type_heaps
	  type_code_instances = {createArray si_next_TC_member_index GTT_Function & [gtci_index] = gtci_type \\ {gtci_index, gtci_type} <- si_TC_instances}
	= (not type_error, fun_defs, { ir_from = fun_env_size, ir_to = si_next_array_member_index }, type_code_instances, ti_common_defs, ti_functions,
			{hp_var_heap = ts_var_heap, hp_expression_heap = ts_expr_heap, hp_type_heaps = ts_type_heaps }, predef_symbols, ts_error.ea_file)
where

	collect_imported_instances imports common_defs dummy error class_instances type_var_heap td_infos
		= foldSt (collect_imported_instance common_defs) imports (dummy, error, class_instances, type_var_heap, td_infos)

	collect_imported_instance common_defs {dcl_ident, dcl_kind = STE_Imported STE_Instance mod_index, dcl_index } state
		= update_instances_of_class common_defs mod_index dcl_index state
	collect_imported_instance common_defs _ state
		= state

	collect_and_check_instances nr_of_instances common_defs state
		= iFoldSt (update_instances_of_class common_defs cIclModIndex) 0 nr_of_instances state

	update_instances_of_class common_defs mod_index ins_index (dummy, error, class_instances, type_var_heap, td_infos)
		# {ins_class={glob_object={ds_index},glob_module},ins_type={it_types}} = common_defs.[mod_index].com_instance_defs.[ins_index]
		  (mod_instances, class_instances) = replace class_instances glob_module dummy
		  (instances, mod_instances) = replace mod_instances ds_index IT_Empty
		  (error, instances) = insert it_types ins_index mod_index common_defs error instances
		  (_, mod_instances) = replace mod_instances ds_index instances
		  (dummy, class_instances) = replace class_instances glob_module mod_instances
		  (error, type_var_heap, td_infos)
					= check_types_of_instances common_defs glob_module ds_index it_types (error, type_var_heap, td_infos)
		= (dummy, error, class_instances, type_var_heap, td_infos)

	check_types_of_instances common_defs class_module class_index types state
		# {class_arity,class_cons_vars} = common_defs.[class_module].com_class_defs.[class_index]
		= check_instances_of_constructor_variables common_defs class_cons_vars (dec class_arity) types state
	where
		check_instances_of_constructor_variables common_defs cons_vars arg_nr [type : types] state
			| cons_vars bitand (1 << arg_nr) <> 0
				# state = check_type_of_constructor_variable common_defs type state
				= check_instances_of_constructor_variables common_defs cons_vars (dec arg_nr) types state
				= check_instances_of_constructor_variables common_defs cons_vars (dec arg_nr) types state
		check_instances_of_constructor_variables common_defs cons_vars arg_nr [] state
			= state

		check_type_of_constructor_variable common_defs type=:(TA {type_index={glob_module,glob_object},type_arity} types) (error, type_var_heap, td_infos)
			# {td_arity} = common_defs.[glob_module].com_type_defs.[glob_object]
			  ({tdi_properties,tdi_cons_vars}, td_infos) = td_infos![glob_module].[glob_object]
			| tdi_properties bitand cIsNonCoercible == 0
				# ({sc_neg_vect}, type_var_heap, td_infos)
					= signClassification glob_object glob_module [TopSignClass \\ cv <- tdi_cons_vars ] common_defs type_var_heap td_infos
				= (check_sign type (sc_neg_vect >> type_arity) (td_arity - type_arity) error, type_var_heap, td_infos)			
				= (checkError type " instance type should be coercible" error, type_var_heap, td_infos)
		where
			check_sign type neg_signs arg_nr error
				| arg_nr == 0
					= error
					| neg_signs bitand 1 == 0
						= check_sign type (neg_signs >> 1) (dec arg_nr) error
						= checkError type " all arguments of an instance type should have a non-negative sign" error
		check_type_of_constructor_variable common_defs type=:(arg_type --> result_type) (error, type_var_heap, td_infos)
			= (checkError type " instance type should be coercible" error, type_var_heap, td_infos)
		check_type_of_constructor_variable common_defs type=:(cv :@: types) (error, type_var_heap, td_infos)
			= (checkError type " instance type should be coercible" error, type_var_heap, td_infos)
		check_type_of_constructor_variable common_defs type state
			= state
			
	insert ::  ![Type] !Index !Index !{# CommonDefs } !*ErrorAdmin !*InstanceTree -> (!*ErrorAdmin, !*InstanceTree)
	insert ins_types new_ins_index new_ins_module modules error IT_Empty
		=  (error, IT_Node {glob_object = new_ins_index,glob_module = new_ins_module}  IT_Empty IT_Empty)
	insert ins_types new_ins_index new_ins_module modules error (IT_Node ins=:{glob_object,glob_module} it_less it_greater)
		#! {ins_type={it_types}} = modules.[glob_module].com_instance_defs.[glob_object]
		# cmp = ins_types =< it_types
		| cmp == Smaller
			# (error, it_less) = insert ins_types new_ins_index new_ins_module modules error it_less
			= (error, IT_Node ins it_less it_greater)
		| cmp == Greater
			# (error, it_greater) = insert ins_types new_ins_index new_ins_module modules error it_greater
			= (error, IT_Node ins it_less it_greater)
			= (checkError ins_types " instance is overlapping" error, IT_Node ins it_less it_greater)

	type_instances ir_from ir_to class_instances ti funs_and_state
		| ir_from == ir_to
			= funs_and_state
			# funs_and_state = type_component [ir_from] class_instances ti funs_and_state
			= type_instances (inc ir_from) ir_to class_instances ti funs_and_state

	type_components group_index comps class_instances ti funs_and_state
		| group_index == size comps
			= funs_and_state
			#! comp = comps.[group_index]	
			# funs_and_state = type_component comp.group_members  class_instances ti funs_and_state
			= type_components (inc group_index) comps class_instances ti funs_and_state

	show_component comp fun_defs
		= foldSt show_fun comp ([], fun_defs)
	where
		show_fun fun_index (names, fun_defs)
			# ({fun_symb}, fun_defs) = fun_defs![fun_index]
			= ([fun_symb : names], fun_defs)
	

	type_component comp class_instances ti=:{ti_common_defs} (type_error, fun_defs, predef_symbols, special_instances, ts)
		# (fun_defs, predef_symbols, cons_variables, ts) = CreateInitialSymbolTypes ti_common_defs comp (fun_defs, predef_symbols, [], ts)
		  (names, fun_defs) = show_component comp fun_defs
		  (fun_reqs, (cons_variables, fun_defs, ts)) = type_functions comp ti cons_variables fun_defs ts /* (ts ---> names) */
		#! nr_of_type_variables = ts.ts_var_store
										
		# (subst, ts_type_heaps, ts_error)
		  		= unify_requirements_of_functions fun_reqs ti (createArray nr_of_type_variables TE) ts.ts_type_heaps ts.ts_error
		| not ts_error.ea_ok
			= (True, fun_defs, predef_symbols, special_instances, create_erroneous_function_types comp
				{ ts & ts_type_heaps = ts_type_heaps, ts_error = { ts_error & ea_ok = True }, ts_var_store = 0, ts_attr_store = FirstAttrVar})
		# {ts_attr_store,ts_var_heap,ts_var_store,ts_expr_heap,ts_td_infos} = ts
		  (cons_var_vects, subst) = determine_cons_variables cons_variables (createArray (inc (BITINDEX nr_of_type_variables)) 0, subst)
		  (subst, nr_of_attr_vars, th_vars, ts_td_infos) = liftSubstitution subst ti_common_defs cons_var_vects ts_attr_store ts_type_heaps.th_vars ts_td_infos
		  coer_demanded ={{ CT_Empty \\ i <- [0 .. nr_of_attr_vars - 1] } & [AttrUni] = CT_Unique }
		  coer_offered = {{ CT_Empty \\ i <- [0 .. nr_of_attr_vars - 1] } & [AttrMulti] = CT_NonUnique }
		  coercion_env = build_initial_coercion_env fun_reqs {coer_demanded = coer_demanded, coer_offered = coer_offered }
		  (over_info, (subst, ts_expr_heap)) = collect_and_expand_overloaded_calls fun_reqs [] (subst, ts_expr_heap)
		  (ts_expr_heap, subst) = expand_types_of_cases_and_lets fun_reqs (ts_expr_heap, subst)
		  (contexts, coercion_env, local_pattern_variables,
		  	{ os_type_heaps, os_var_heap, os_symbol_heap, os_predef_symbols, os_special_instances, os_error })
		  		= tryToSolveOverloading over_info ti_common_defs class_instances coercion_env
		  			{	os_type_heaps = {ts_type_heaps & th_vars = th_vars}, os_var_heap = ts_var_heap, os_symbol_heap = ts_expr_heap,
		  				os_predef_symbols = predef_symbols, os_error = ts_error, os_special_instances = special_instances }
		| not os_error.ea_ok
			= (True, fun_defs, os_predef_symbols, os_special_instances, create_erroneous_function_types comp { ts & ts_type_heaps = os_type_heaps,
					ts_error = { os_error & ea_ok = True }, ts_var_store = 0, ts_attr_store = FirstAttrVar, 
					ts_td_infos = ts_td_infos, ts_expr_heap = os_symbol_heap, ts_var_heap = os_var_heap })
		# (fun_defs, coercion_env, subst, os_var_heap, os_symbol_heap, os_error)
		  		= makeSharedReferencesNonUnique comp fun_defs coercion_env subst ti_common_defs os_var_heap os_symbol_heap os_error
		  (subst, {coer_offered,coer_demanded}, ts_td_infos, ts_type_heaps, ts_error)
		  		= build_coercion_env fun_reqs subst coercion_env ti_common_defs cons_var_vects ts_td_infos os_type_heaps os_error
		  (attr_partition, coer_demanded) = partitionateAttributes coer_offered coer_demanded
		  (subst, ts_fun_env) = expand_function_types comp subst ts.ts_fun_env
		  attr_var_env = createArray nr_of_attr_vars TA_None
		  var_env = { subst & [i] = TE \\ i <- [0..dec ts_var_store]}
		  (fun_defs, ts) = cleanUpAndCheckFunctionTypes comp fun_reqs ti_common_defs contexts coer_demanded attr_partition var_env attr_var_env
									(fun_defs,  { ts &	ts_error = ts_error, ts_fun_env = ts_fun_env, ts_type_heaps = ts_type_heaps,
		  												ts_td_infos = ts_td_infos, ts_var_heap = os_var_heap, ts_expr_heap = os_symbol_heap })
		| not ts.ts_error.ea_ok
			= (True, fun_defs, os_predef_symbols, os_special_instances, create_erroneous_function_types comp
					{ ts & ts_var_store = 0, ts_attr_store = FirstAttrVar, ts_error = { ts.ts_error & ea_ok = True } })
		| isEmpty over_info 
			# ts_type_heaps = ts.ts_type_heaps
			  type_code_info = {	tci_next_index = os_special_instances.si_next_TC_member_index, tci_instances = os_special_instances.si_TC_instances,
									tci_type_var_heap = ts_type_heaps.th_vars } 
			  (fun_defs, ts_expr_heap, {tci_next_index,tci_instances,tci_type_var_heap}, ts_var_heap, ts_error)
			  		= updateDynamics comp contexts local_pattern_variables fun_defs ts.ts_expr_heap type_code_info ts.ts_var_heap ts.ts_error
			= (	type_error || not ts_error.ea_ok, 
				fun_defs, os_predef_symbols, { os_special_instances & si_next_TC_member_index = tci_next_index, si_TC_instances = tci_instances },
				{ ts & ts_var_store = 0, ts_attr_store = FirstAttrVar, ts_expr_heap = ts_expr_heap, ts_error = { ts_error & ea_ok = True },
					  ts_var_heap = ts_var_heap, ts_type_heaps = { ts_type_heaps & th_vars =  tci_type_var_heap }})
			# ts_type_heaps = ts.ts_type_heaps
			  type_code_info = {	tci_next_index = os_special_instances.si_next_TC_member_index, tci_instances = os_special_instances.si_TC_instances,
									tci_type_var_heap = ts_type_heaps.th_vars } 
			  (fun_defs, ts_expr_heap, {tci_next_index,tci_instances,tci_type_var_heap}, ts_var_heap, ts_error)
			  		= removeOverloadedFunctions [(co, pos, index) \\ (co, _, pos, index) <- over_info]
			  			contexts local_pattern_variables fun_defs ts.ts_expr_heap type_code_info ts.ts_var_heap ts.ts_error
			= (	type_error || not ts_error.ea_ok,
				fun_defs, os_predef_symbols, { os_special_instances & si_next_TC_member_index = tci_next_index, si_TC_instances = tci_instances },
				{ ts & ts_var_store = 0, ts_attr_store = FirstAttrVar, ts_expr_heap = ts_expr_heap, ts_error = { ts_error & ea_ok = True },
					  ts_var_heap = ts_var_heap, ts_type_heaps = { ts_type_heaps & th_vars =  tci_type_var_heap }})

	unify_requirements_of_functions :: ![FunctionRequirements] !TypeInput !*{!Type} !*TypeHeaps !*ErrorAdmin -> (!*{!Type},!*TypeHeaps,!*ErrorAdmin)
	unify_requirements_of_functions [{fe_requirements={req_type_coercions},fe_location} : reqs_list] modules subst heaps ts_error
		# ts_error = setErrorAdmin fe_location ts_error
		  (subst, heaps, ts_error) = unify_coercions req_type_coercions modules subst heaps ts_error
		= unify_requirements_of_functions reqs_list modules subst heaps ts_error
	unify_requirements_of_functions [] modules subst heaps ts_error
		= (subst, heaps, ts_error)

	build_initial_coercion_env [{fe_requirements={req_attr_coercions},fe_location} : reqs_list] coercion_env
		= build_initial_coercion_env reqs_list (add_to_initial_coercion_env req_attr_coercions coercion_env)
	build_initial_coercion_env [] coercion_env
		= coercion_env

	add_to_initial_coercion_env [{ac_offered,ac_demanded} : attr_coercions] coercion_env
		= add_to_initial_coercion_env attr_coercions (newInequality ac_offered ac_demanded coercion_env)
	add_to_initial_coercion_env [] coercion_env
		= coercion_env

	determine_cons_variables variables vect_and_subst
		= foldSt (foldSt determine_cons_variable) variables vect_and_subst
		
	determine_cons_variable tv_number (bitvects, subst)
		# (type, subst) = subst![tv_number]
		= case type of
			TE
				-> (set_bit tv_number bitvects, subst)	// ---> ("determine_cons_variable1", tv_number)
			TempV var_number
				-> (set_bit var_number bitvects, subst)	// ---> ("determine_cons_variable2", var_number)
			_
				-> (bitvects, subst)
	where
		set_bit var_number bitvects
			# bit_index = BITINDEX var_number
			  (prev_vect, bitvects) = bitvects![bit_index]
			= { bitvects & [bit_index] = prev_vect bitor (1 << BITNUMBER var_number) }

	build_coercion_env [{fe_requirements={req_type_coercions},fe_location} : reqs_list] subst coercion_env common_defs cons_var_vects type_signs type_var_heap error
		# error = setErrorAdmin fe_location error
		  (subst, coercion_env, type_signs, type_var_heap, error)
			= add_to_coercion_env req_type_coercions subst coercion_env common_defs cons_var_vects type_signs type_var_heap error
		= build_coercion_env reqs_list subst coercion_env common_defs cons_var_vects  type_signs type_var_heap error
	build_coercion_env []  subst coercion_env common_defs cons_var_vects type_signs type_var_heap error
		= (subst, coercion_env, type_signs, type_var_heap, error)

	add_to_coercion_env [{tc_offered,tc_demanded,tc_coercible,tc_position} : attr_coercions] subst coercion_env common_defs cons_var_vects type_signs type_var_heap error
		# (subst, coercion_env, type_signs, type_var_heap, error)
				= determineAttributeCoercions tc_offered tc_demanded tc_coercible tc_position subst coercion_env common_defs cons_var_vects type_signs type_var_heap error
		= add_to_coercion_env attr_coercions subst coercion_env common_defs cons_var_vects type_signs type_var_heap error
	add_to_coercion_env []  subst coercion_env common_defs cons_var_vects type_signs type_var_heap error
		= (subst, coercion_env, type_signs, type_var_heap, error)

	collect_and_expand_overloaded_calls [] calls subst_and_heap
		= (calls, subst_and_heap)
	collect_and_expand_overloaded_calls [{ fe_context=Yes context, fe_requirements={req_overloaded_calls}, fe_location, fe_index}:reqs] calls (subst, expr_heap)
		# (context, subst) = arraySubst context subst
		= collect_and_expand_overloaded_calls reqs [(Yes context, req_overloaded_calls, fe_location, fe_index) : calls]
				(foldSt expand_type_contexts req_overloaded_calls (subst, expr_heap)) 	
	collect_and_expand_overloaded_calls [{fe_context, fe_requirements={req_overloaded_calls}, fe_location, fe_index}:reqs] calls (subst, expr_heap)
		= collect_and_expand_overloaded_calls reqs [(fe_context, req_overloaded_calls, fe_location, fe_index) : calls]
				(foldSt expand_type_contexts req_overloaded_calls (subst, expr_heap)) 	

	expand_type_contexts over_info_ptr (subst, expr_heap)
		# (EI_Overloaded info, expr_heap) = readPtr over_info_ptr expr_heap
		  (oc_context, subst) = arraySubst info.oc_context subst
		= (subst, expr_heap <:= (over_info_ptr, EI_Overloaded { info & oc_context = oc_context }))

	expand_types_of_cases_and_lets [] heap_and_subst
		= heap_and_subst
	expand_types_of_cases_and_lets [{fe_requirements={req_case_and_let_exprs}}:reqs] heap_and_subst
		= expand_types_of_cases_and_lets reqs (foldl expand_case_or_let_type heap_and_subst req_case_and_let_exprs)

	expand_case_or_let_type (expr_heap, subst) info_ptr
		#! info = sreadPtr info_ptr expr_heap
		= case info of
			EI_CaseType case_type
				# (case_type, subst) = arraySubst case_type subst
				-> (writePtr info_ptr (EI_CaseType case_type) expr_heap, subst)
			EI_LetType let_type
				# (let_type, subst) = arraySubst let_type subst
				-> (writePtr info_ptr (EI_LetType let_type) expr_heap, subst)

	expand_function_types :: ![Int] !*{!Type} *{! FunctionType} -> (!*{!Type}, *{! FunctionType})
	expand_function_types [fun : funs] subst ts_fun_env
		#! fun_type = ts_fun_env.[fun]
		= case fun_type of
			UncheckedType tst
				# (exp_tst, subst) = arraySubst tst subst
				-> expand_function_types funs subst { ts_fun_env & [fun] = UncheckedType exp_tst}
			SpecifiedType ft _ tst
				#  (exp_tst, subst) = arraySubst tst subst
				-> expand_function_types funs subst { ts_fun_env & [fun] = ExpandedType ft tst exp_tst}
	expand_function_types [] subst ts_fun_env
		= (subst, ts_fun_env)
			

	update_function_types :: !Index !{!Group} !*{!FunctionType} !*{#FunDef} -> (!*{#FunDef}, !*{!FunctionType})
	update_function_types group_index comps fun_env fun_defs
		| group_index == size comps
			= (fun_defs, fun_env)
			#! comp = comps.[group_index]	
			# (fun_defs, fun_env) = update_function_types_in_component comp.group_members fun_env fun_defs
			= update_function_types (inc group_index) comps fun_env fun_defs

	where
		update_function_types_in_component :: ![Index] !*{!FunctionType} !*{#FunDef} -> (!*{#FunDef}, !*{!FunctionType})
		update_function_types_in_component [ fun_index : funs ] fun_env fun_defs
			# (CheckedType checked_fun_type, fun_env) = fun_env![fun_index]
			#! fd = fun_defs.[fun_index]
			= case fd.fun_type of
				No
					-> update_function_types_in_component funs fun_env { fun_defs & [fun_index] = { fd & fun_type = Yes checked_fun_type }}
				Yes fun_type
					# nr_of_lifted_arguments = checked_fun_type.st_arity - fun_type.st_arity
					| nr_of_lifted_arguments > 0
						# fun_type = addLiftedArgumentsToSymbolType fun_type nr_of_lifted_arguments checked_fun_type.st_args checked_fun_type.st_vars checked_fun_type.st_attr_vars
						-> update_function_types_in_component funs fun_env { fun_defs & [fun_index] = { fd & fun_type = Yes fun_type }}
						-> update_function_types_in_component funs fun_env fun_defs
		update_function_types_in_component [] fun_env fun_defs
			= (fun_defs, fun_env)
	
	type_functions group ti cons_variables fun_defs ts
		= mapSt (type_function ti) group (cons_variables, fun_defs, ts) // ((cons_variables, fun_defs, ts) ---> "[(") ---> ")]"

	type_function ti fun_index (cons_variables, fun_defs, ts=:{ts_fun_env, ts_var_heap, ts_expr_heap, ts_error})
		#! fd = fun_defs.[fun_index]
		   type = ts_fun_env.[fun_index]
		# {fun_symb,fun_arity,fun_body=TransformedBody {tb_args,tb_rhs},fun_pos, fun_info, fun_type} = fd
		  temp_fun_type = type_of type
		  ts_var_heap = makeBase tb_args temp_fun_type.tst_args ts_var_heap
		  fe_location = newPosition fun_symb fun_pos
		  ts_error = setErrorAdmin fe_location ts_error
		  reqs = { req_overloaded_calls = [], req_type_coercions = [], req_attr_coercions = [], req_case_and_let_exprs = [], req_cons_variables = cons_variables }
		  ( rhs_type, rhs_expr_ptr, (rhs_reqs, ts)) = requirements ti tb_rhs (reqs, { ts & ts_var_heap = ts_var_heap, ts_expr_heap = ts_expr_heap, ts_error = ts_error })
		  req_type_coercions = [{tc_demanded = temp_fun_type.tst_result,tc_offered = rhs_type, tc_position = {cp_expression = tb_rhs }, tc_coercible = True} :
		  		rhs_reqs.req_type_coercions ]
		  ts_expr_heap = storeAttribute rhs_expr_ptr temp_fun_type.tst_result.at_attribute ts.ts_expr_heap
		= ({fe_location = fe_location, fe_context = if (has_option fun_type) (Yes temp_fun_type.tst_context) No, fe_index = fun_index,
			fe_requirements = { rhs_reqs & req_type_coercions = req_type_coercions, req_cons_variables = [] }}, (rhs_reqs.req_cons_variables, fun_defs,
				{ ts & ts_expr_heap = ts_expr_heap }))
//					 ---> ("type_function", fun_symb, tb_args, tb_rhs, fun_info.fi_local_vars)
	where
		has_option (Yes _)	= True
		has_option No 		= False
		 
		type_of (UncheckedType tst)		= tst
		type_of (SpecifiedType _ _ tst) = tst
			
	convert_array_instances si_array_instances common_defs fun_defs predef_symbols type_heaps
		| isEmpty si_array_instances
			= (fun_defs, predef_symbols, type_heaps)
			# ({pds_ident,pds_module,pds_def},predef_symbols) = predef_symbols![PD_UnboxedArrayType]
			  unboxed_array_type = TA (MakeTypeSymbIdent { glob_object = pds_def, glob_module = pds_module } pds_ident 0) []
			  ({pds_module,pds_def},predef_symbols) = predef_symbols![PD_ArrayClass]
			  {class_members} = common_defs.[pds_module].com_class_defs.[pds_def]
			  array_members = common_defs.[pds_module].com_member_defs
			  (offset_table, _, predef_symbols) = arrayFunOffsetToPD_IndexTable array_members predef_symbols
			  (rev_instances, type_heaps) = foldSt (convert_array_instance class_members array_members unboxed_array_type offset_table) si_array_instances
			  	([], type_heaps)
			= (arrayPlusRevList fun_defs rev_instances, predef_symbols, type_heaps)
	where
		convert_array_instance class_members array_members unboxed_array_type offset_table {ai_record} funs_and_heaps
			= iFoldSt (create_instance_type class_members array_members unboxed_array_type offset_table (TA ai_record [])) 0 (size class_members) funs_and_heaps

		create_instance_type members array_members unboxed_array_type offset_table record_type member_index (array_defs, type_heaps)
			# {me_type,me_symb,me_class_vars,me_pos} = array_members.[members.[member_index].ds_index]
			  (instance_type, _, type_heaps) = determineTypeOfMemberInstance me_type me_class_vars {it_vars = [], it_attr_vars = [], it_context = [],
													it_types = [unboxed_array_type, record_type]} SP_None type_heaps
			  instance_type = makeElemTypeOfArrayFunctionStrict instance_type member_index offset_table
			  fun = 
				{	fun_symb		= me_symb
				,	fun_arity		= me_type.st_arity
				,	fun_priority	= NoPrio
				,	fun_body		= NoBody
				,	fun_type		= Yes instance_type
				,	fun_pos			= me_pos
				,	fun_index		= member_index
				,	fun_kind		= FK_Unknown
				,	fun_lifted		= 0
				,	fun_info		= EmptyFunInfo
				}

			= ([fun : array_defs], type_heaps)
	
	create_erroneous_function_types group ts
		= foldSt create_erroneous_function_type group ts
		
	create_erroneous_function_type fun ts
		#! env_type = ts.ts_fun_env.[fun]
		= case env_type of
			ExpandedType fun_type tmp_fun_type exp_fun_type
				# (fun_type, ts_type_heaps) = extendSymbolType fun_type tmp_fun_type.tst_lifted ts.ts_type_heaps
				-> { ts & ts_type_heaps = ts_type_heaps, ts_fun_env = { ts.ts_fun_env & [fun] = CheckedType fun_type }}
		  	UncheckedType tmp_fun_type
		  		# (clean_fun_type, ts_type_heaps) = cleanSymbolType tmp_fun_type.tst_arity ts.ts_type_heaps
				-> { ts & ts_type_heaps = ts_type_heaps, ts_fun_env = { ts.ts_fun_env & [fun] = CheckedType clean_fun_type }}
			SpecifiedType fun_type _ tmp_fun_type
				# (fun_type, ts_type_heaps) = extendSymbolType fun_type tmp_fun_type.tst_lifted ts.ts_type_heaps
				-> { ts & ts_type_heaps = ts_type_heaps, ts_fun_env = { ts.ts_fun_env & [fun] = CheckedType fun_type }}
			CheckedType _
				-> ts

instance <<< AttrCoercion
where
	(<<<) file {ac_demanded,ac_offered} = file <<< ac_demanded <<< '~' <<< ac_offered

instance <<< FreeVar
where
	(<<<) file {fv_name} = file <<< fv_name

instance <<< TypeCoercion
where
	(<<<) file {tc_demanded,tc_offered} = file <<< tc_demanded <<< '~' <<< tc_offered

instance <<< TypeContext
where
	(<<<) file co = file <<< co.tc_class <<< " " <<< co.tc_types
	
instance <<< DefinedSymbol
where
	(<<<) file {ds_ident}
		= file <<< ds_ident

instance <<< FunctionType
where
	(<<<) file (CheckedType _)
		= file <<< "CheckedType"
	(<<<) file (SpecifiedType _ _ _)
		= file <<< "SpecifiedType"
	(<<<) file (UncheckedType _)
		= file <<< "UncheckedType"
	(<<<) file (ExpandedType _ _ _)
		= file <<< "ExpandedType"
	(<<<) file EmptyFunctionType
		= file <<< "EmptyFunctionType"