Call-by-Name, Call-by-Value and the lambda-Calculus

This paper examines the old question of the relationship between ISWIM and the &calculus, using the distinction between call-by-value and call-by-name. It is held that the relationship should be mediated by a standardisation theorem. :3ince this leads to difficulties, a new &calcu%~s is introduced whose standardisation theorem gives a good correspondence with ISWIM a-; given by the SECT machine, but without the Zetrec feature. Next a call-by-name variant of ISWSM is introduced which i:; in an analogous corresponde nce with the usual kalculus. The relation between call-by-value and call-by-name is then studied I)y giving simulations elf each lauguage by tba other and irlteryretations of each calculus in the other. These are obtained as ication of the continuation technique. Some emphasis is placed throughout on the notion of opeiiational equality (or contextual equality). If terms c;tn :3e proved equal in a calculus they are operationally equal in the corresponding language. UnflDrtonatel y, operational Izquality is not preserved by either of the simulations. Our intention is tee, stu calculus which wzs first H-by-value and call-by-,,,, *TM in the setting of the kmbda-used to explicate progranting Language Ceatures by Latn