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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

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cannotUnify t1 t2 position err 
	# err = errorHeading "Type error" err
	  format = { form_properties = cNoProperties, form_position = [] }
	= { err & ea_file = err.ea_file <<< " cannot unify " <:: (format, t1) <<< " with " <:: (format, t2)  <<< " near " <<< position <<< '\n' }

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/*
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
freshCopyOfTypeAttribute (TA_RootVar avar) attr_var_heap
	= freshCopyOfAttributeVar avar 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)
	  cs = { copy_heaps = { ts_type_heaps & th_vars = th_vars, th_attrs = th_attrs }}
	  (cons_types, alg_type, ts_var_store, ts_attr_store, attr_env, cs)
	  		= fresh_symbol_types patterns common_defs.[glob_module].com_cons_defs ts_var_store ts_attr_store cs
	= (cons_types, alg_type, attr_env, { ts & ts_var_store = ts_var_store, ts_attr_store = ts_attr_store, ts_type_heaps = cs.copy_heaps })
//		---> ("freshAlgebraicType", alg_type, cons_types)
where
	fresh_symbol_types [{ap_symbol={glob_object}}] cons_defs var_store attr_store cs=:{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)
//	  	  (th_attrs, attr_store)	= fresh_existential_attributes cons_exi_attrs (copy_heaps.th_attrs, attr_store)
	  	  (attr_env, th_attrs) 		= fresh_environment st_attr_env ([], copy_heaps.th_attrs)
	  	  (result_type, cs)			= freshCopy st_result { cs & 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_store, attr_env, cs)
	fresh_symbol_types [{ap_symbol={glob_object}} : patterns] cons_defs var_store attr_store cs
		# (cons_types, result_type, var_store, attr_store, attr_env, cs=:{copy_heaps})
				= fresh_symbol_types patterns cons_defs var_store attr_store cs
//		  {cons_type = {st_args,st_attr_env}, cons_index, cons_exi_vars, cons_exi_attrs} = cons_defs.[glob_object.ds_index]
		  {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)
//	  	  (th_attrs, attr_store)	= fresh_existential_attributes cons_exi_attrs (copy_heaps.th_attrs, attr_store)
		  (attr_env, th_attrs) 		= fresh_environment st_attr_env (attr_env, copy_heaps.th_attrs)
	  	  (fresh_args, cs) 			= freshCopy st_args { cs & copy_heaps = { copy_heaps & th_attrs = th_attrs, th_vars = th_vars }}
		= ([fresh_args : cons_types], result_type, var_store, attr_store, attr_env, cs)

	
	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_existential_attributes attributes state
		= foldSt (\{av_info_ptr} (attr_heap, attr_store) -> (attr_heap <:= (av_info_ptr, AVI_Attr (TA_TempExVar 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, var_store)		= fresh_type_variables st_vars (ts_type_heaps.th_vars, ts_var_store)
	  (th_attrs, 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 = var_store, ts_attr_store = 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
578
579
	# err = errorHeading "Type error" err
	= { err & ea_file = err.ea_file <<< "* attribute expected instead of " <<< type_attr <<< '\n' }
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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

requirementsOfApplication :: !App !TempSymbolType ![Special] !u:Requirements !TypeInput !*TypeState
	-> (!u:Requirements, !AType, !Optional ExprInfoPtr, !*TypeState)
requirementsOfApplication {app_symb,app_args,app_info_ptr}
		{tst_attr_env,tst_args,tst_result,tst_context} specials reqs=:{req_attr_coercions} ti ts
  	# reqs = { reqs & req_attr_coercions = tst_attr_env ++ req_attr_coercions }
	  (reqs, ts) = requirements_of_args app_args tst_args reqs ti ts
	| isEmpty tst_context
		= (reqs, tst_result, No, ts)
		= ({ reqs & req_overloaded_calls = [app_info_ptr : reqs.req_overloaded_calls ]}, tst_result, No,
				{ 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 :: ![Expression] ![AType] !u:Requirements !TypeInput !*TypeState
		-> (!u:Requirements,!*TypeState)
	requirements_of_args [] [] reqs ti ts
		= (reqs, ts)
	requirements_of_args [expr:exprs] [lt:lts] reqs ti ts
		# (reqs, e_type, opt_expr_ptr, ts) = requirements expr reqs ti 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 exprs lts { reqs & req_type_coercions = req_type_coercions} ti { ts & ts_expr_heap = ts_expr_heap }

requirements :: !Expression !u:Requirements !TypeInput !*TypeState -> (!u:Requirements, !AType, !Optional ExprInfoPtr, !*TypeState)
requirements (Var var=:{var_info_ptr,var_expr_ptr}) reqs ti ts=:{ts_var_store,ts_attr_store,ts_var_heap,ts_expr_heap}
	#! var_info = sreadPtr var_info_ptr ts_var_heap
	# (VI_Type type) = var_info
	= (reqs, type, Yes var_expr_ptr, ts)

requirements expr=:(App app=:{app_symb={symb_name,symb_kind = SK_Function {glob_module,glob_object}, symb_arity}}) reqs
		ti=:{ti_functions,ti_common_defs} ts=:{ts_fun_env,ts_var_heap}
	| glob_module == cIclModIndex
		#! fun_type = ts_fun_env.[glob_object]
		= case fun_type of
			UncheckedType fun_type
				# (fun_type_copy,ts) = currySymbolType fun_type symb_arity ts
				-> requirementsOfApplication app fun_type_copy [] reqs ti ts
			SpecifiedType fun_type lifted_arg_types _ 
				# (fun_type_copy, cons_variables, ts) = freshSymbolType fun_type ti_common_defs ts
//								---> ("requirements (App SpecifiedType)", symb_name, fun_type))
				  (fun_type_copy,ts) = currySymbolType { fun_type_copy & tst_args = lifted_arg_types ++ fun_type_copy.tst_args } symb_arity ts
				-> requirementsOfApplication app fun_type_copy [] { reqs & req_cons_variables = [ cons_variables : reqs.req_cons_variables ] } ti ts
			CheckedType fun_type
				# (fun_type_copy, cons_variables, ts) = freshSymbolType fun_type ti_common_defs ts
//								---> ("requirements (App CheckedType)", symb_name, fun_type))
				  (fun_type_copy,ts) = currySymbolType fun_type_copy symb_arity ts
				-> requirementsOfApplication app fun_type_copy [] { reqs & req_cons_variables = [ cons_variables : reqs.req_cons_variables ] } ti ts
			_
				-> abort "requirements (App)" ---> (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
		= requirementsOfApplication app fun_type_copy (get_specials ft_specials) { reqs & req_cons_variables = [ cons_variables : reqs.req_cons_variables ] } ti ts
where
	get_specials (SP_ContextTypes specials) = specials
	get_specials SP_None 					= []


requirements expr=:(App app=:{app_symb={symb_kind, symb_arity}}) reqs ti ts=:{ts_fun_env}
	# (fresh_type, cons_variables, ts) = standard_type symb_kind symb_arity ti ts
	= requirementsOfApplication app fresh_type [] { reqs & req_cons_variables = [ cons_variables : reqs.req_cons_variables ] } ti ts
where
	standard_type (SK_Constructor {glob_object,glob_module}) symb_arity ti ts
		# (fresh_cons_type, ts) = standardRhsConstructorType glob_object glob_module symb_arity ti ts
		= (fresh_cons_type, [], ts) 
	standard_type (SK_OverloadedFunction {glob_object,glob_module}) symb_arity {ti_common_defs} ts 
		#! {me_symb, me_type,me_type_ptr} = ti_common_defs.[glob_module].com_member_defs.[glob_object]
		= determineSymbolTypeOfFunction me_symb symb_arity me_type me_type_ptr ti_common_defs ts
requirements (function @ args) reqs ti ts
	# (reqs, off_fun_type, opt_fun_expr_ptr, ts) = requirements function reqs ti ts
	  (rev_off_arg_types, reqs, ts) = requirements_of_list args [] reqs ti 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
	= ({ reqs & req_type_coercions = [{ tc_demanded = fun_type, tc_offered = off_fun_type, tc_position = { cp_expression = function }, tc_coercible = True } : req_type_coercions ]},
		 alpha, No, { ts & ts_expr_heap = ts_expr_heap })
where
	requirements_of_list [] rev_list_types reqs ti ts
		= (rev_list_types, reqs, ts)
	requirements_of_list [expr:exprs] rev_list_types reqs ti ts
		# (reqs, e_type, opt_expr_ptr, ts) = requirements expr reqs ti ts
		= requirements_of_list exprs [(opt_expr_ptr,e_type) : rev_list_types] reqs ti 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 bind_expr=:(Let {let_binds, let_expr, let_info_ptr}) reqs ti ts
	# (rev_var_types, ts) = make_base let_binds [] ts
	  var_types = reverse rev_var_types
	  (reqs, res_type, opt_expr_ptr, ts) = requirements let_expr reqs ti ts
	  (reqs, ts) = requirements_of_binds let_binds var_types reqs ti ts
	  ts_expr_heap = writePtr let_info_ptr (EI_LetType var_types) ts.ts_expr_heap
	= ({ reqs & req_case_and_let_exprs = [let_info_ptr : reqs.req_case_and_let_exprs]}, res_type, opt_expr_ptr, { 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 ti ts
		= (reqs, ts)
	requirements_of_binds [{bind_src}:bs] [b_type:bts] reqs ti ts
		# (reqs, exp_type, opt_expr_ptr, ts) = requirements bind_src reqs ti 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 bs bts { reqs & req_type_coercions = req_type_coercions } ti { ts & ts_expr_heap = ts_expr_heap }

requirements (Case {case_expr,case_guards,case_default,case_info_ptr}) reqs ti ts
	# (reqs, expr_type, opt_expr_ptr, ts) = requirements case_expr reqs ti ts
	  (fresh_v, ts) = freshAttributedVariable ts
	  (reqs, cons_types, ts) = requirements_of_guarded_expressions case_guards case_expr expr_type opt_expr_ptr fresh_v reqs ti ts
	  (reqs, ts) = requirements_of_default case_default fresh_v reqs ti 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 })
	= ({ reqs & req_case_and_let_exprs = [case_info_ptr : reqs.req_case_and_let_exprs]}, fresh_v, No, { ts & ts_expr_heap = ts_expr_heap })
where
	requirements_of_guarded_expressions (AlgebraicPatterns alg_type patterns) match_expr pattern_type opt_pattern_ptr
					goal_type reqs ti=:{ti_common_defs} ts
		# (cons_types, result_type, new_attr_env, ts) = freshAlgebraicType alg_type patterns ti_common_defs ts
		  (reqs, used_cons_types, ts) = requirements_of_algebraic_patterns patterns cons_types goal_type [] reqs ti ts
		  ts_expr_heap = storeAttribute opt_pattern_ptr result_type.at_attribute ts.ts_expr_heap
		= ({ 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 }, reverse used_cons_types,
						{ ts & ts_expr_heap = ts_expr_heap })

	requirements_of_guarded_expressions (BasicPatterns bas_type patterns) match_expr pattern_type opt_pattern_ptr goal_type reqs ti ts
		# (attr_bas_type, ts) = attributedBasicType bas_type ts
		  (reqs, ts) = requirements_of_basic_patterns patterns goal_type reqs ti 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 (DynamicPatterns dynamic_patterns) match_expr pattern_type opt_pattern_ptr goal_type reqs ti ts
		# dyn_type = { at_type = TB BT_Dynamic, at_attribute = TA_Multi, at_annotation = AN_None }
		  (reqs, used_dyn_types, ts) = requirements_of_dynamic_patterns goal_type dynamic_patterns [] reqs ti ts
		  ts_expr_heap = storeAttribute opt_pattern_ptr TA_Multi ts.ts_expr_heap
		= ({ 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] }, reverse used_dyn_types, { ts & ts_expr_heap = ts_expr_heap })

	requirements_of_algebraic_patterns [] cons_types goal_type used_cons_types reqs ti ts
		= (reqs, used_cons_types, ts)
	requirements_of_algebraic_patterns [{ap_vars, ap_expr }:gs] [ cons_arg_types : cons_types] goal_type used_cons_types reqs ti=:{ti_common_defs} ts
		# (reqs, res_type, opt_expr_ptr, ts) = requirements ap_expr reqs ti { 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 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] }
				  ti { ts & ts_expr_heap = ts_expr_heap }

	requirements_of_basic_patterns [] goal_type reqs ti ts
		= (reqs, ts)
	requirements_of_basic_patterns [{bp_expr }:gs] goal_type reqs ti=:{ti_common_defs} ts
	  	# (reqs, res_type, opt_expr_ptr, ts) = requirements bp_expr reqs ti ts
		  ts_expr_heap = storeAttribute opt_expr_ptr res_type.at_attribute ts.ts_expr_heap
		= requirements_of_basic_patterns 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] }
					 ti { ts & ts_expr_heap = ts_expr_heap }

	requirements_of_dynamic_patterns goal_type [{dp_var={fv_info_ptr},dp_type,dp_rhs} : dps] used_dyn_types reqs ti 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)
		  (reqs, dp_rhs_type, opt_expr_ptr, ts) = requirements dp_rhs reqs ti { 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 goal_type dps [ [dyn_type] : used_dyn_types ] reqs ti { 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 goal_type dps [ [dyn_type] : used_dyn_types ] reqs ti { 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 goal_type [] used_dyn_types reqs ti ts
		= (reqs, used_dyn_types, ts)


	requirements_of_default (Yes expr) goal_type reqs ti ts
		# (reqs, res_type, opt_expr_ptr, ts) = requirements expr reqs ti 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 No goal_type reqs ti ts
		= (reqs, ts) 
requirements (DynamicExpr {dyn_expr,dyn_info_ptr}) reqs ti 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
	  (reqs, dyn_expr_type, opt_expr_ptr, ts) = requirements dyn_expr reqs ti { 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
		= ({reqs & req_type_coercions = [ type_coercion : reqs.req_type_coercions]}, 
				{ at_type = TB BT_Dynamic, at_attribute = TA_Multi, at_annotation = AN_None }, No, { ts &  ts_expr_heap = ts_expr_heap })
		= ({ reqs & req_type_coercions = [ type_coercion : reqs.req_type_coercions], req_overloaded_calls = [dyn_expr_ptr : reqs.req_overloaded_calls ]},
				{ at_type = TB BT_Dynamic, at_attribute = TA_Multi, at_annotation = AN_None }, No,
					{ ts & ts_expr_heap = ts_expr_heap <:= (dyn_expr_ptr, EI_Overloaded {
							oc_symbol = type_code_symbol, oc_context = dyn_context, oc_specials = []}) })

requirements (Selection result_type_symb expr selectors) reqs ti ts
	# (reqs, expr_type, opt_expr_ptr, ts) = requirements expr reqs ti ts
	= case result_type_symb of
		Yes {glob_object={ds_ident,ds_index,ds_arity}, glob_module}
			# (var, ts) = freshAttributedVariable ts
990
		  	  (result_type, reqs, ts) =  requirementsOfSelectors No expr selectors False var expr opt_expr_ptr reqs ti ts
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			  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 }
			-> ({ reqs & req_type_coercions = req_type_coercions }, result_type, No,
					{ts & ts_var_store = inc ts.ts_var_store, ts_expr_heap = storeAttribute opt_expr_ptr TA_Multi ts.ts_expr_heap})
		_