Difference between revisions of "Table/Lambda Calculus abstractions"
Jump to navigation
Jump to search
| (2 intermediate revisions by the same user not shown) | |||
| Line 1: | Line 1: | ||
{| class="wikitable" | {| class="wikitable" | ||
|+ A Table representing [[Lambda calculus]] and its abstraction types. | |||
|- | |- | ||
! Admissible data types !! Symbolic representation !! Description | ! Admissible data types !! Symbolic representation !! Description | ||
|- | |- | ||
| Variable (<math>\alpha</math> conversion)|| ''x'' || A character or string representing a parameter or mathematical/logical value. | | Variable ([[alpha-conversion|<math>\alpha</math>-conversion]])|| ''x'' || A character or string representing a parameter or mathematical/logical value. | ||
|- | |- | ||
| Substitution (<math>\beta</math> reduction)|| (λ''x''.''M'')(value to be [[Free variables and bound variables|bound]] to x) || This expression specifies how function is defined by replacing values of [[Free variables and bound variables|bound variable]] ''x'' in the lambda (λ) expression ''M''. | | Substitution ([[beta-reduction|<math>\beta</math> reduction]])|| (λ''x''.''M'')(value to be [[Free variables and bound variables|bound]] to x) || This expression specifies how function is defined by replacing values of [[Free variables and bound variables|bound variable]] ''x'' in the lambda (λ) expression ''M''. | ||
|- | |- | ||
| Composition (<math>\eta</math> reduction)|| (''M'' ''N'') || Specifying the sequential composition of multiple lambda expressions such as ''M'' and ''N'' | | Composition ([[eta-reduction|<math>\eta</math>-reduction]])|| (''M'' ''N'') || Specifying the sequential composition of multiple lambda expressions such as ''M'' and ''N''. | ||
|} | |} | ||
Latest revision as of 13:36, 19 May 2022
| Admissible data types | Symbolic representation | Description |
|---|---|---|
| Variable (-conversion) | x | A character or string representing a parameter or mathematical/logical value. |
| Substitution ( reduction) | (λx.M)(value to be bound to x) | This expression specifies how function is defined by replacing values of bound variable x in the lambda (λ) expression M. |
| Composition (-reduction) | (M N) | Specifying the sequential composition of multiple lambda expressions such as M and N. |
