����; � TeX output 1995.07.01:1517� �����g�\����3��2�\����ܚ��\Np���K ff ff cmbx14�Bey���on�d�L�Prot��wot�yp�8�e�Imp���lem�en���t�a��>t�ions:���͍�f�>P���o���lymorphi��cc�L�Pro� �!ject�ion�An���alys�8�i�s���� �E.for�L�Glasgo���w�Hask�ell��"�%�� �3��"V cmbx10�Julian��TSew��9ard�� �� �����<x cmtt10�[email protected]���i�� �xz�%o��� cmr9�Depart��9m�en���t�Tof�Compu��t���e� �r�Science�� �� �%Vi���ct��or�'xia�TUniv��9e� �r��s� �it�y�of�Manc�h�e�A�s��t���e� �r���� ��ZOxford�TRoad,�Manc��9h�e�A�s��t���e� �r�TM13�9PL,�UK.��mk����Hs��&t�: cmbx9�A��h�b�Ks��tract.���x��Buildin��g�d�eect��9iv�e�a�b�Ns��tract�in���t���e� �rpret�e�r��s�d�require�A�s�careful�a���t-����Hs�t���en���t��9ion�R�t��o�b�A�ot��Th�t�h��9eory�an�d�en��gin�ee� �r�'xin�g�R�i� �s�Nsue�A�s.�Th�e�t��Th�eory�of�a�b�Ns��tract����Hs�in���t���e� �rpret��9a���t�ion���i� �s�w��9ell�d�؇ev�elo�p� �e�A�d,�bu��t�t��Th�e�en��gin�ee� �r�'xin�g���s� �id�؇e�h�as�f� �allen�b�e-����Hs�hin��9d�q�som�ewh�a���t,�an�u��nfort�u�n��a���t���e�q�ev�en���t�giv�en�t��Th�a���t�a�b�Ns��tract�in���t���e� �rpret�a���t�ion�i� �s����Hs�p�A�ot���en���t��9ially���a�k�ey�t���ec�hno��logy�for�d�؇eclara���t�iv�e�lan��guage�compila���t�ion.�Thi� �s����Hs�pap� �e� �r��sh��o��9ws�t��Th�e�t��Thinkin��g�b� �e��>hin�d�t��Th�e�d�؇e�A�s� �ign�an�d�imp��lem�en���t�a���t�ion�of�a����Hs�r��s�t-ord�؇e� �r,���p�A�o��lymorphi���c�pro� ��ject��9ion�an��alys�.e�r�for�Hask��9ell,�capa�b��le�of�d�؇e-����Hs�t���ect��9in��g���h�e�Nad�s��tr�'xi���ctn�e�A�s�Ns,�an�d�t��Th�e� �refore�suit�a�b��le�for�sup�p�A�ort�in��g�all�kno�wn����Hs�s��tr�'xi���ctn��9e�A�s�Ns-rela���t���e�d���transform��a�t��9ions.�Dev�elo�pm�en���t�culmin��a���t���e�A�d�in�a�su�cce�A�s�Ns-����Hs�ful�P�tr�'xial�ins��t��9alla���t�ion�P�in�v��9e� �r�s� �ion�0.19�of�t��Th��9e�Glasgo�w�Hask�ell�Compile� �r,����Hs�an��9d���t��Th�e�sys��t���em�h�as�b� �een�us�.e�A�d�t��o�an��alys�e�a�ran��ge�of�Hask��9ell�programs,����Hs�includin��g�Tan�e�Narlie� �r�v��9e�r��s� �ion�of�it��fs�.elf,�13000�lin��9e�A�s�lon��g.��"�Ѝ�, �(��N� cmbx12�1� � In��ftro�` d�� u�ct�ion��x��, �K�`y cmr10�Th���e�#�pas�t�d��Tecad�e�#�h�as�s�1�een�a�dram�Îa�� t�i���c�impro�v�em�en���t�in�t��Uh�e�p�#�e� �rform�Îance�of�lazy����, fu��rnct���ion�Îal���lan�guage�Gs,�not���a�b��ly�Hask�ell,�as�imp��lem�en���t��ror�s�h�a�v�e�d��Tev�elo�p�#�e�Gd�w�ays�t��ro����, m�Îap���su���c�h�lan��rguage�Gs�ecien���t��Uly�on�t��ro�s�t�o�Gc���k�arc�hit��Uect�ure�Gs.�Nev�e� �rt��Uh�ele�Gs�qs,�t��Uh�ey�s�t�ill����, ru��rn���an�ord��Te� �r�of�m�Îagnit���ud�e�slo���w�e� �r���t��Uh�an�t��Uh�e�Gir�imp�#�e� �ra�� t�iv�e�cou��rn���t��Ue� �rpart�� s,�an�d,�w�or�s�1�e,����, it��Qlo�Goks�lik���e�t��Uh�e�p�#�e� �rform�Îance�impro�v�em�en���t�� s�are�t�ailin��rg�o.�F��*�urt��Uh�e� �r�incre�qas�1�e�Gs�in����, p�#�e� �rform�Îance�V�d��Tep�en���d�on�n�din��rg�w�ays�t��ro�rep��lace�co�p�yin��rg�b�y�up�Gd��ra�� t��Ue-in-p��lace,�an�d����, lazy���ev��q�alua�� t���ion�b�y�s�tr�*�i���ct�ev��q�alua�� t�ion,�wh�en�p�Go�qs�s�#�ib��le.���A���cr�*�it�i���cal�elem�en���t�in�t��Uhi�#�s�i�s����, t��Uh���e�UUs�1�em�Îan���t�i���c�an�Îalys�1�e�Gs�whi�c���h�di�#�s��Tco�v�e� �r�wh�en�su�c�h�transform�Îa�� t�ions�are�v��q�alid.�� ��; Su���cce�Gs�qsful�PNus�1�e�of�s�tr�*�i���ctn�e�Gs�qs�an�d�sh�ar�*�in��rg�an�Îalys�1�e�Gs�in�compile� �r�s�d��Tem�an���ds�care-����, ful��cons�#�id��Te� �ra�� t���ion�of�t��Uh�e�en��rgin�ee� �r�*�in�g��cons�train���t�� s�imp�Go�qs�1�e�d��b�y�s�1�epara�� t��Ue�compila�t���ion,����, an���d�V�b�y�t��Uh�e�limit��Ue�Gd�compu��rt�in�g�V�re�Gsource�s�a���v��q�aila�b��le.�Sect�ion� 2�of�t��Uhi�#�s�pap�e� �r�exam-����, in���e�Gs�Y�su�c�h�cons�train���t�� s�in�d��Tet�ail,�as�a�w�ay�of�gen�e� �ra�� t�in��rg�us�1�eful�m�etr�*�i���cs�wit��Uh�whi�c���h����, t��ro��as�qs�1�e�Gs�s�p�Go�s�s�#�ibilit���ie�s��in�t��Uh���e�d��Te�s�#�ign�space.�Bas�1�e�d�on�t��Uhi�#�s,�w���e�ou��rt�lin���e�in�Sec-����, t���ion� 3�H�t��Uh�e�d��Te�Gs�#�ign�of�a�p�o��lymorphi���c,�bac���kw�ards�s�tr�*�i���ctn�e�Gs�qs�an�Îalys�1�e� �r�for�Hask�ell.����, Th���e���an�Îalys�1�e� �r�w�as�ins�t�alle�Gd�in�Glasgo�w�Hask�ell�0.19,�an�d�sh�Îo�ws�an�u��rnprece�Gd��Ten-����, t��Ue�Gd��1pr�*�i���ce-p�#�e� �rform�Îance�ra�� t���io.�Sect�ion� 4�pre�Gs�1�en���t�� s�t��Uh�e�re�Gsul��rt�� s�of�t��Uhi�#�s�exp�e� �r�*�im���en���t�an�d����, conclud��Te�Gs.�R�Al��rt��Uh�Îough�our�pr�*�im�ary�conce� �r�#�n�i�s�s�tr�*�i���ctn���e�Gs�qs�an�Îalys�i�s�of�Hask���ell,�t��Uh�e�Gs�1�e����, id��Te�qas�H=h���a�v�e�wid��Te� �r�ap�p��li���ca�bilit�y�t��ro�all�a�b�qs�tract-in���t��Ue� �rpret�a�� t�ion�bas�1�e�Gd�an�Îalys�e�Gs�for����� *�g�\����3��2�\����ܚ��R �fu��rnct���ion�Îal��olan�guage�Gs,�an���d�sh�Îould�in���t��Ue� �re�s�t�t��Uh�Îo�qs�1�e�conce� �r�#�n���e�d�b���y�t��Uh�e�s�1�eemin��rgly�large�� ��R gap�UUb�#�et���w�een�t��Uh�e�t��Uh�eory�an�d�pract�i���ce�of�a�b�qs�tract�in���t��Ue� �rpret�a�� t�ion.��w���a Re�qal,�)�usa���b��le�an�Îalys�1�e�Gs�die� �r�f�*�rom�prot��rot�yp�#�e�imp��lem�en���t�a�� t�ions�in�s�1�ev�e� �ral�w�ays.����R Th���e�N/an�Îalys�#�i�s�h���as�t��ro�ru�n�in�re�qason�Îa���b��le�t�im�e�an�d�m�emory��*�,�ev�en�wh�en�pre�Gs�1�en���t��Ue�d�wit��Uh����R u��rnre�qason�Îa���b��le�2oinpu�t�� s;�it�sh�Îould�\t"�pro���p�#�e� �rly�in���t�o�t��Uh���e�exi�#�s�t�in��rg�compile� �r�f�*�ram�e-����R w���or�� k,�x�vi�#�s-a-vi�s�s�1�epara�� t��Ue�compila�t���ion,�an�d�it�sh�Îould�do�a�go�Go�d�job�for�imp�ort���an���t����R lan��rguage�p-fe�qa�� t���ure�Gs,�part�i���cularly�su��rm-of-pro�Gd�u�ct�� s�t�yp�#�e�Gs,�p�o��lymorphi�#�sm�an���d�high�e� �r-����R ord��Te� �r�E�fu��rnct���ions.�W��*�e�sh�Îort��Uly�examin�e�t��Uh�e�cons�1�equence�Gs�of�t��Uh�e�Gs�1�e�cons�train���t�� s�in�som�e����R d��Tet���ail.����a Th���e�e�m�Îain�fo�Gcus�of�t��Uhi�#�s�pap�e� �r�i�s�on�global�d��Te�Gs�ign�trad��Teos.�Bas�1�e�Gd�on�t��Uh���a�� t����R di�#�s��Tcus�qs�ion,�g�w���e�ou��rt��Ulin�e�a�part�i���cularly�eect�iv�e�p�Go��lymorphi���c�pro� �8ject�ion�an�Îalys�1�e� �r����R for���Hask���ell,�an�d�sh�Îo�w�som�e�re�Gsul��rt�� s�f�*�rom�it.�Th�e�an�Îalys�1�e� �r's�d��Te�Gs�#�ign�d�et���ails�are����R b�Got��Uh���in���t��Ue� �re�s�t���in��rg�an�d�v�o��lu��rminous,�bu�t�not�ap���pro�pr�*�ia�� t��Ue�h�e� �re,�so�refe�rence�Gs�t��ro�more����R t��Uh�Îorough�A tre�qa�� t���m�en���t�� s�are�giv�en�t��Uhrough�Îou��rt�{�t�h���e�r�s�t�p�Gort�of�call�i�#�s�proba���b��ly�t��Uh�e����R a���u��rt��Uh�Îor's�UUPhD�t�h���e�Gs�#�i�s� [�Sew94��8�].�� U鍑R �Arc��9hit��"ect�ural��>Ov�e�Drview�-ȲThi�#�s�9�pap�e� �r�divid��Te�Gs�s�1�em�Îan���t���i���c�an�alys�#�i�s�sys�t��Uems�in���t��ro����R t���w�o�H�concept�ual�part�� s:�an�a�b�qs�tract�in���t��Ue� �rpret�e�r,�H�whi���c���h�gen�e� �ra�� t��Ue�Gs�recur�s�#�iv�e�equa�� t�ions����R o���v�e� �r�`�som�e�dom�Îains,�an�d�a�xp�Goin���t��Ue� �r,�whi���c�h�remo�v�e�Gs�recur�s�#�ion�f�*�rom�t��Uh�e�equa�� t�ions,����R t��Uh���e� �re��Tb�y��5m�Îakin��rg�t�h���em�us�1�eful�t��ro�compile� �r�s.�As�usual,�w�e�require�t��Uh�e�dom�Îains�t��ro�b�#�e����R of�6nit��Ue�h���e�Gigh�t�6t��ro�guaran���t�ee�t�e� �rmin�Îa�� t���ion�of�xp�Goin���t�in��rg,�an�d�furt��Uh�e� �r�re�Gs�tr�*�i���ct�t��Uh�em����R t��ro�UUb�#�e�di�s�tr�*�ibu��rt���iv�e�UUla�� t���t�i���ce�Gs�t��ro�m�Îak�e�xp�Goin���t�in��rg�e�qas�#�ie� �r.����a Sev���e� �ral��$die�ren���t�s��Tc���h�em�e�Gs�for�xp�oin���t���in��rg�h�a�v�e�b�#�een�pro�p�Go�qs�1�e�d.�Th���e�F��*�ron���t�ie� �r�s����R algor�*�it��Uhm�b'clev���e� �rly�exp��loit�� s�monot��roni���cit�y�t��ro�build�syn���t�act�i���cally�u��rnique�repre�Gs�1�en���t�a-����R t���ions,�� t��Uh�us�tr�*�iviali�#�s�in��rg�t��Uh���e�d��Tet��Uect�ion�of�xp�Goin���t�� s.�In�tro�Gd���u�ce�d�� b�y�Clac�k�an�d�P�eyt��ron����R Jon���e�Gs� [�PC87�� ],���t��Uh�e�algor�*�it��Uhm�h�as�b�#�een�m��Uu�c�h�t�u��rn�e�Gd�o�v�e� �r�t��Uh�e�y�e�qar�s� [�Mar92��Z,��Hu��rn91��o],����R an���d��sup�p�Gort�� s�high�e� �r�ord��Te�r�xp�Goin���t���in��rg.�A��s�1�econ�d�lin�e�of�enquiry�i�#�s�t��Uh�a�� t�of�lazy����R xp�Goin���t���in��rg,�6�wh�e� �re�t��Uh�e�xp�Goin���t�i�#�s�only�compu��rt��Ue�d�wh���e� �re�n�ee�Gd��Te�d,�on�d��Tem�Îan���d.�Th�e����R preci�#�s�1�e��1or�*�igins�of�lazy�xp�Goin���t���in��rg�are�d��Te�ba�� t�a�b��le,��1bu��rt�t�w�o�e�qarly�pre�Gs�1�en���t�a�� t�ions����R are���d���ue�t��ro�t��Uh�e�Cousot�� s� [�CC78��q�]�an�d�t��ro�Jon�e�Gs�an�d�Mycroft� [�JM86��N=].�Ext��Uens�#�ions����R t��ro��high���e� �r-ord��Te�r�xp�Goin���t���in��rg�are�sh�Îo�wn�b�y�F��*�e� �rguson�an�d�Hugh�e�Gs� [�FH93��!],�an�d�b�y����R Ro�qs�1�en���d��ra�hl� [�Ro�s93��j�].�ΆTh���e�w�or�� k�of�Hankin�an�d�Le�M���Get�ay�e� �r�on�\lazy�t�yp�#�e�Gs"� [�HM94����]����R i�#�s�UUalso�rela�� t��Ue�Gd.����a In�8�t��Uhi�#�s�pap�e� �r�w���e�t�ak�e�a�t��Uhird�ap�proac�h:�compu��rt�a�� t�ion�of�comp��let��Ue�xp�Goin���t�� s����R b���y�4�us�#�in��rg�a�t��Ue� �rm�rewr�*�it�e�sys�t�em�t��ro�transform�s�1�em�Îan���t���i���cally�equiv��q�alen�t�t��Ue� �rms�t��ro����R syn���t���act�i���cally�8|id��Ten�t�i���cal�8|norm�Îal�forms.�Cons�1�el�d��Te�Gs��Tcr�*�ib�#�e�s�8|a�s�imp��le�rewr�*�it��Ue� �r�for�t���w�o-����R p�Goin���t��ula�� t���t���i���ce�s�us�1�e�d�in�Y��*�ale�Hask���ell� [�Con91���!],�an�d�t��Uh�e�t��Uec�hnique�w�as�ext��Uen�d��Te�Gd�t��ro����R ot��Uh���e� �r���la�� t���t�i���ce�Gs�in� [�Sew94��8�],�Sect�ion�5.�Rewr�*�it��Ue-bas�1�e�Gd�xp�oin���t��Ue� �r�s�cannot,�in�gen���e�ral,����R so��lv���e�UUhigh�e� �r-ord��Te�r�equa�� t���ions,�bu��rt,�as�w�e�sh�all�s�1�ee,�t��Uhi�#�s�m�Îay�not�m�a�� t���t��Ue� �r�m��Uu���c�h.����a No�Gc���k�e� �r� [�No�c93��8�]�Ѷsh�Îo�ws�a�w�or�� kin��rg�an�Îalys�1�e� �r,�bas�e�Gd�on�\a���b�qs�tract�re�d���u�ct�ion",����R wh���e� �re��8t��Ue�rm-rewr�*�it�in��rg��8i�#�s�us�1�e�Gd�t�o�execu�t��Ue�t��Uh���e�program�us�#�in�g�som���e�a�b�qs�tract�s�1�e-����R m�Îan���t���i���cs.�dBy�compar�*�i�#�son,�our�t��Ue� �rm-rewr�it���in��rg�i�#�s�us�1�e�Gd�t�o�d��Tet��Uect�xp�Goin���t�� s,�an���d����R t��Uh���e� �re�-vi�#�s�a�cle�qar�di�s�t���inct�ion�-vb�et�w�een�-vt��Uh�e�a�b�qs�tract�in���t��Ue� �rpret�a�� t�ion�an�d�xp�Goin���t�in��rg����R act���ivit�ie�Gs.����a Th���e��preci�#�s�1�e�n�Îa�� t�ure�of�a�b�qs�tract�in���t��Ue� �rpret�a�� t�ions�i�#�s�d��Tet��Ue� �rmin�e�Gd,�n�Îa�� t�urally��*�,�b�y����� :�g�\����3��2�\����ܚ��, �t��Uh���e���transform�Îa�� t�ion�t��ro�b�#�e�sup�p�Gort��Ue�d.�On���e�part�i���cularly�imp�Gort�an���t�c�h�aract��Ue� �r�*�i�#�sa-�� ��, t���ion�Z�i�#�s�t��Uh�e�la�� t���t�i���ce�Gs�t��ro�whi�c���h�die� �ren���t�t�yp�#�e�Gs�are�m�Îap�p�#�e�Gd.�In�t��Uh�e�s�#�imp��le�Gs�t�cas�1�e,����, all�R�non-fu��rnct���ion�Îal�t�yp�#�e�Gs�could�b�e�m�Îap���p�e�Gd�t��ro�a�t���w�o-p�oin���t�R�la�� t���t�i���ce,�wit��Uh�t�h���e�p�Goin���t�� s����, repre�Gs�1�en���t���in��rg�Rpno�d��Tem�Îan�d�an�d�w�e�qak�h�e�qad�norm�Îal�form�(WHNF)�Rod��Tem�an���d�re�Gsp�#�ect-����, iv���ely���in�s�tr�*�i���ctn�e�Gs�qs�an�Îalys�#�i�s.���F��*�or�a�s�#�imp��le�sh�ar�*�in��rg�an�Îalys�#�i�s,���w�e�migh�t�us�1�e�a�3-����, p�Goin���t�!�c���h�ain,�d��Tenot�in��rg�no�refe� �rence�Gs,�exact��Uly�on�e�refe� �rence,�an�d�t�w�o�or�more����, refe� �rence�Gs.���Simp��le�a���b�qs�tract�ions���lik�e�t��Uh�e�Gs�1�e�are�rou��rt�in�ely�us�1�e�Gd�in�exi�#�s�t�in��rg�Hask�ell����, compile� �r�s� [�Con91���!,����PJ93����].���Th���e�s�#�imp��li���cit�y�of�t��Uh�e�a�b�qs�tract�ions�m�Îak�e�Gs�t��Uh�e�Gs�1�e�an�Îalys�e�Gs����, c���h�e�qap�UUan�d�relia�b��le,�so�w�e�sh�all�not�cons�#�id��Te� �r�t��Uh�em�furt��Uh�e� �r.��+���; A���more���p�Go���w�e� �rful�an�Îalys�#�i�s�migh���t�a�� t���t��Uempt�t��ro�giv�e�d��Tet�aile�Gd�inform�Îa�� t�ion�a�b�Gou��rt����, fu��rnct���ions��?d��Te�qalin�g�wit��Uh�s�tru���ct�ure�Gd�t�yp�#�e�Gs�su�c�h�as�li�#�s�t�� s,�tree�Gs,�or�wh�a�� t��Uev�e� �r�program-����, m���e� �r�s�7^care�t��ro�d��Ten�e.�La�� t���t�i���ce�Gs�a�b�qs�tract�in��rg�su�c�h�t�yp�#�e�Gs�gro�w�in�accord��rance�wit��Uh�t�h���e����, comp��lexit���y�apof�t��Uh�Îo�qs�1�e�t�yp�#�e�Gs,�so�t��Uh�e� �re�i�#�s�no�arbitrary�cu��rt�o�app�Goin���t�b�ey���on�d�apwhi���c�h����, all�LDd��Tet���ails�are�ignore�Gd.�In�ot��Uh�e� �r�w�ords,�t��Uh�e� �re�i�#�s�a�p�Go�qs�s�ibilit���y�LDof�s�1�ee�Gin��rg�arbitrar�*�ily����, f�#�ar���\ins�id��Te"�d��ra�� t���a�s�tru�ct�ure�Gs.�Th�e�do�wns�#�id��Te�i�s�t��Uh���a�� t�t�h���e�Gs�1�e�la�� t���t�i���ce�Gs�can�an�d�do�get����, v���e� �ry�&�large,�so�t��Uh�e�an�Îalys�#�i�s�&�b�ecom�e�Gs�&�exp�ens�iv�e.�&�In�t��Uhi�#�s�s�1�ens�e,�&�s�em�Îan���t�i���c�&�an�alys�#�i�s�i�s����, a��Qpart���i���cularly�in���tract�a�b��le�prob�lem,�b�#�eca���us�1�e�t��Uh���e�la�� t�t���i���ce�s�#�ize�Gs�an�d�t��Uh�us��Qamou��rn���t�of����, eort�*Krequire�Gd�can�gro���w�exp�on���en���t�ially�*Kwit��Uh�comp��lexit���y�of�t�yp�#�e�Gs.�F��*�or�examp��le,�if����, an�&�it��Uem�of�t���yp�#�e��(Int,�?�Int,�Int)�&��i�s�mo�Gd��Telle�d�&�b���y�a�9�p�Goin���t�la�� t���t�i���ce,�(2��W� !",� cmsy10���2����2)����O!� cmsy7�?����,����, addin��rg�B�jus�t�on���e�more��Int��t�o�t��Uh���e�t�up��le�eect�iv�ely�dou��Ub��le�Gs�t�h���e�la�� t���t�i���ce�s�#�ize,�giv-����, in��rg�[f(2�畸��2����2����2)����?����.�Th���e�co�qs�t�� s�of�high�e� �r�ord��Te�r�s�1�em�Îan���t���i���c�an�alys�1�e�Gs�are�almo�qs�t����, legen���d��rary��*�,�wkbu�t�ev���en�r�s�t�ord��Te� �r�an�Îalys�1�e�Gs�can�b�#�ecom���e�exce�s�qs�#�iv���ely�exp�ens�iv���e.�Get-����, t���in��rg��re�qason�Îa�b��le�p�#�e� �rform�Îance�som�et�im�e�Gs�require�s�\w���or�� k�limit�in��rg"�{�t��Uhro�win��rg�aw�ay����, d��Tet���ail�UUwhi���c�h�a�b�qs�tract�in���t��Ue� �rpret�a�� t�ion�w�ould�ot��Uh�e� �rwi�#�s�1�e�pi���c�k�up.��!@���, �2� � Cons� �train��ft���s�� on�via�� b�ٙle�d��fe�` s�0 igns���W��, �2.1��Separa��ft��"e��TCompila�t��9ion���W��, �Cur�*�iously���enough,�s�1�epara�� t��Ue�compila�t���ion�i�#�s�t��Uh�e�bigge�Gs�t�s�#�in��rgle�source�of�d��Te�s�#�ign����, cons�train���t�� s.�O�A�O�con���v�enien�t�O�w�ay�t��ro�view�a�m��Uul�t���i-mo�Gd�ule�program�i�#�s�as�a�direct��Ue�Gd,����, ro�Got��Ue�d,���p�o�qs�s�#�ib��ly�cycli���c�graph,�wit��Uh�arcs�re ect���in��rg�imp�Gort�d��Tep�en���d�encie�Gs,���t��Uh�e��Main����, �mo�Gd���ule�G�a�� t�t��Uh�e�\t��ro�p",�an�d�t��Uh�e�Hask�ell��Prelude��a�� t�t��Uh�e�b�Got���t��rom����^��ٓ�R cmr7�1���|s�.�Compila�� t�ion�of�a����, mo�Gd���ule��.�M���ca���us�1�e�s�t��Uh���e�compile� �r�t��ro�re�qad�t�h���e�source�t��Uext�of��M���an�d�in���t��Ue� �rf�#�ace�le�Gs�of����, mo�Gd���ule�s���imm�e�dia�� t��Uely���b�#�elo�w��M�,�an�d�emit�co�Gd��Te�an�d�in���t��Ue� �rf�#�ace�le�Gs�for��M�.�In�t��Ue� �rf�#�ace����, le�Gs��are�us�1�e�d�b���y�t��Uh�e�compile� �r�t��ro�comm��Uu�ni���ca�� t��Ue�re�Gsul�t�� s�of�s�1�em�Îan���t���i���c�an�alys�1�e�Gs�acro�qs�s����, mo�Gd���ule��b�ou��rn�d�ar�*�ie�Gs.��In�t��Uh�e�a�b�qs�1�ence�of�inform�Îa�� t�ion�a�b�Gou��rt�imp�ort��Ue�d�en���t���it�ie�s,��t��Uh�e� �re����, i�#�s���alw���ays�a�safe�as�qsu��rmpt�ion�whi���c�h�can�b�#�e�m�Îad��Te.�Thi�s�f�*�ram���ew�or�� k���imp�Go�qs�1�e�s�s�1�ev���e� �ral����, limit���a�� t�ions:���������2@�{����= �Th���e�tin���t��Ue� �rf�#�ace�le�Gs�ough�t�t��ro�b�#�e�limit��Ue�Gd�t�o�a�re�qason�Îa���b��le�s�#�ize,�ot��Uh�e� �rwi�#�s�1�e�t��Uh�e����= compile� �r�\fm�Îay�sp�#�en���d�a�lot�of�t�im�e�re�qadin��rg�t��Uh�em.�F��*�or�examp��le,�Glasgo�w�Hask�ell����= 0.19's��/�Prelude��in���t��Ue� �rf�#�ace�i�s�a���b�Gou��rt�100k�lon�g,�an���d�re�qadin�g�it�s�#�ignican���t��Uly�slo���ws����= compile� �r�UUs�t���art�up�for�sm�Îall�mo�Gd�ule�s.��, � ى ff 8�ϟ L͍��� ��-=�)�Aa� cmr6�1��� ?��It�Ti� �s�con��9v�enien���t�Tt��o�as�Nsu�m��9e�all�mo�A�d�ule�s�Timp�ort�t��Th��9e��1ߤN cmtt9�Prelude�.����� *^�g�\����3��2�\����ܚ�����X@�{����c �Inform�Îa�� t���ion���only� o�ws�up�w�ards,�t��ro�w�ards��Main�.�F��*�or�que�Gs�t�ions�of�t��Uh�e�form�� ��c \h�Îo���w�Q6i�#�s�en���t�it�y�X�P�goin��rg�t�o�b�#�e�us�1�e�Gd?",�w���e�also�n�ee�Gd�inform�Îa�� t�ion� o�ws�do�wn�w�ard����c f�*�rom�UU�Main�.�������X@�{����c �T��*�o���compile�a�mo�Gd���ule��M�,�it�sh�Îould�suce�t��ro�re�qad�t��Uh�e�in���t��Ue� �rf�#�ace�Gs�for�mo�d���ule�s����c imm���e�Gdia�� t��Uely���b�#�elo�w��M�.�W��*�e�ce� �rt�ainly�w�an���t�t��ro�a�v�oid�re�qadin��rg�all�t��Uh�e�in���t��Ue� �rf�#�ace�Gs����c in���t��Uh���e�do�wn�w�ard�clo�qsure�of��M�:�for��Main�,�t��Uh�a�� t�could�m�e�qan�re�adin��rg�t��Uh���e�en���t�ire����c s�1�et�UUof�in���t��Ue� �rf�#�ace�Gs.������R �Mu��t��9ually���recur�-s�(�iv�e�mo�Q�d�ule�s�<;�Exi�#�s�t���in��rg�D�imp��lem�en���t�a�� t�ions�d��Te�qal�wit��Uh�m�u��rt���ually����R recur�s�#�iv���e�c�mo�Gd�ule�s�c�in�t���w�o�c�w�ays.�On�e�i�#�s�t��ro�compile�all�mo�Gd�ule�s�c�in�a�group�t��ro-����R get��Uh���e� �r,��a�cle�qan�so��lu��rt�ion,�as�wit��Uh�Y��*�ale�Hask�ell's�\compila�� t�ion�u��rnit�� s".�Th�e�ot��Uh�e� �r����R i�#�s��pt��ro�compile�e�qac���h�mo�Gd�ule�in�t��Uh�e�group�s�1�epara�� t��Uely��*�,�u��rn���t�il�in���t��Ue� �rf�#�ace�le�Gs�s�t�a�bili�#�s�1�e,����R d��Tenot���in��rg��La�xe�Gd�p�oin���t.�Thi�#�s�m���e�qans�t��Uh�a�� t�a�t�le�qas�t�on���e�mo�Gd�ule�will�h�a�v�e�t��ro�b�#�e����R compile�Gd�?Nwit��Uh�ze� �ro�s�1�em�Îan���t���i���c�kno�wle�Gdge�of�t��Uh�e�ot��Uh�e� �r�s,�wit��Uh�t�h���e�compile� �r�m�Îak-����R in��rg��{w���or�s�t-cas�1�e�as�qsu��rmpt���ions.�Th�e�up�qsh�Îot�of�t��Uhi�#�s�i�s�t��Uh���a�� t,�for�s�1�em�Îan���t�i���c�an�Îalys�1�e�Gs����R in���v�o��lvin��rg�UUxp�Goin���t�in�g,�UUt��Uh�e�xp�Goin���t�� s�b�#�e�in��rg�compu�t��Ue�Gd�m�Îay�b�#�e�su��Ub�o���pt�im�Îal.����R �2.2��Comp��Jlet��"e��Tor�minim��}al�fu��nct��9ion�graphs?������R �Fixp�Goin���t���in��rg�1]b�y�minim�Îal�fu��rnct�ion�graphs����^��2��� �в(MF�Gs)�builds�t��Uh�e�minim�Îal�s�1�et�of����R argu��rm���en���t-re�Gsul�t�pair�s�� �b>