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Programming Language Theory: Difference between revisions
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* Applicative state transition system (<tt>ast</tt>): <tt>ffp</tt> plus mutable state and coarse-grained operations thereupon | * Applicative state transition system (<tt>ast</tt>): <tt>ffp</tt> plus mutable state and coarse-grained operations thereupon | ||
===Untyped λ-calculus=== | ===Untyped λ-calculus=== | ||
Two operators (function ''definition'' and ''application'') upon one operand type (λ-expression). | |||
* Function definition: <tt>(λ''formalparam'' . body)</tt> | |||
* Function application: <tt>function(''actualparam'')</tt> | |||
Common syntactic sugar: | |||
* Left-associative application as implicit parentheses | |||
* Use of definitions (allowing identifiers to stand in as λ-expressions) | |||
* Currying: <tt>(λx, y . x + y)</tt> rather than <tt>(λx . (λy . x + y))</tt> | |||
Revision as of 05:38, 7 December 2009
Applicative/Functional Programming
Expressions compose functions rather than values. Backus proposed three tiers of complexity in his Turing Award lecture:
- Simply functional language (fp): No state, limited names, finitely many functional forms, simple substitution semantics, algebraic laws
- Formal functional system (ffp): Extensible functional forms, functions represented by objects, translation of object representation to applicable form, formal semantics
- Applicative state transition system (ast): ffp plus mutable state and coarse-grained operations thereupon
Untyped λ-calculus
Two operators (function definition and application) upon one operand type (λ-expression).
- Function definition: (λformalparam . body)
- Function application: function(actualparam)
Common syntactic sugar:
- Left-associative application as implicit parentheses
- Use of definitions (allowing identifiers to stand in as λ-expressions)
- Currying: (λx, y . x + y) rather than (λx . (λy . x + y))
