Group:
expression evaluation
Topic:
evaluate operator
Topic:
function call
Topic:
functional programming
Topic:
lambda calculus
Topic:
procedures as data
Topic:
reduction languages
Topic:
sequence reduction
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Summary
Unlike natural languages, programming languages consist of operators applied to operands. Operands may be evaluated and/or modified. In formal function theory, operators are literal lambda expressions indicating bound and free variables. Application unites literals, i.e., the operators, with values, the operands. The operands' values are substituted into the operator's semantic definition. (cbb 5/80)
Subtopic: function as operator over operands 
| Quote: the canonical form for a programming statement is operator, operand list; distinguishes programming language from natural language [»halpMI1_1968]
| | Quote: a programming language is essentially notation for the application of functions to their arguments [»leavBM4_1970]
| | Quote: an FP system has a single operation, application; in f:x, f is the operator and x is the operand [»backJ8_1978a]
| | Quote: only function application specifies computation [»backJ_1973, OK]
| | Quote: an application applies an operator to its operand; only one with a non-literal value [»backJ_1972]
| | Quote: an atom of FEA is a predicate applied to one or more terms; the syntax of a term depends on the base system [»postSW7_1978]
| | QuoteRef: landPJ_1966 ;;101 operator/operand form or expressions shows "applicative structure
| | Quote: applicative languages evaluate expressions within an environment; the environment binds variables to values [»reynJC8_1972]
| | Quote: algorithm for evaluating an applicative expression relative to an environment; first formalization of expression evaluation
| | Quote: a function is a value that can be "applied" to its arguments [»reynJC8_1972]
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Subtopic: non-termination
| Quote: function application and expression evaluation may never produce a result; never terminates or stops with an error [»reynJC8_1972]
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Subtopic: application syntax
| QuoteRef: mccaJ_1960 ;;187 LABEL (function-name, lambda-expressing) and APPLY (function, arg list
| | QuoteRef: leavBM4_1970 ;;2 function application (f x)
| | QuoteRef: landPJ_1966 ;;98 basic form: application expressions (AE)
| | QuoteRef: landPJ_1966 ;;103 (lambda arg list expression)(operand)
| | QuoteRef: landPJ_1966 ;;108 AE is an id, a lambda expression (bound variable part and lambda body-AE) or a combination (operator-AE and operand-AE parts)
| | QuoteRef: knowK8_1966 ;;618 general action (modified-arg, operation, parameters)
| Quote: with an applicative structure, practically all computable functions are one-liner expressible
[»liptRJ2_1977]
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Related Topics
Group: expression evaluation (5 topics, 97 quotes)
Topic: evaluate operator (7 items)
Topic: function call (28 items)
Topic: functional programming (45 items)
Topic: lambda calculus (16 items)
Topic: procedures as data (22 items)
Topic: reduction languages (17 items)
Topic: sequence reduction
(10 items)
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