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An assert macro with informative failure reports, as a syntax-rule or a defmacro. A concise definition form with optional arguments and default values MetaScheme, or untyped MetaOCaml and the underlying alpha-conversion macro Applicative syntax-rules: It is very difficult to write macros that compose, to assemble complex macros from already written and tested components.
The previous approaches to composable syntax-rules are heavy, notationally and computationally. This article presents an alternative, lightweight style of writing composable syntax-rules, based on the CK abstract machine.
We demonstrate recursive, higher-order applicative macros defined in the style that looks like that of ML or strict Haskell. We write composable, call-by-value--like macros without resorting to the continuation-passing-style and thus requiring no macro-level lambda.
The syntax remains direct-style, with nested applications. Syntax-rules are difficult to compose because of their evaluation order: That per se does not preclude functional composition since the normal-order lambda-calculus or non-strict languages like Haskell do not evaluate arguments of a function application either.
However, lambda-calculus has first-class anonymous abstractions; Haskell also has the case form that forces evaluation of an expression, to the extent needed to choose among the pattern-match clauses.
Syntax-rules have none of these compensating features. Generally, a syntax-rule cannot obtain the result of the expansion of its argument expression. The article on Systematic Macro Programming on this page explains the composability problem in detail. So far, the only way out has been to effectively change the evaluation order by writing macros in the continuation-passing style CPS.
However, CPS code is hard to read. Furthermore, building continuations requires the notation for first-class, preferably anonymous syntax-rule abstractions.
Although the latter are possible to emulate, the result is stylistically ugly and computationally expensive. Some macro expanders take the shocking amount of time and memory to expand CPS macros with anonymous abstractions.
This project was inspired by the question posed by Dan Friedman in March Write the macro permute that takes any number of arguments and returns the list of their permutations: One should write permute without resorting to CPS. Our answer is the transliteration of the standard Haskell code implementing the straightforward algorithm for all permutations: Our macros are written in a CK style.
We distinguish values, which are always quoted like ' 1 2 3from general applicative expressions such as c-append ' 1 c-cons '2 ' 3 4which may contain nested applications.
Values are regarded as results of the CK evaluation. Here is the first example, of the CK-style macro cons: The macro should never look at s, passing it to the macro ck described below.
All arguments of a CK-macro except for s are always values; the macro is free to pattern-match on them. A CK-macro always expands into the call to the macro ck, passing it the s argument followed by the produced value or by the expression that will produce the resulting value.
The macro c-cons produces a value, which is therefore quoted. We now demonstrate recursion and functional composition, or nested application. We define a macro c-append, using the just defined c-cons. The second clause yields an expression, with the nested application.
The machine is implemented as a syntax-rule ck. It operates on the stack the first argument to all CK macros built out of the frames op va Here op is the name of a CK-macro to do the reduction; zero or more va must all be values; zero or more ea are arbitrary expressions.
The Scheme expression ck c-append ' 1 2 3 ' 4 5 will hopefully macro-expands to 1 2 3 4 5which the Scheme expression evaluator will try to evaluate, reporting the error since 1 is not a procedure.
To see the result of just the macro-expansion, without any further evaluations, we should quote it: The code includes further examples, the indispensable factorial and a more practical example of deleting an element from an associative list.
The latter two examples are from the CPS Macros-talk. It is instructive to compare the direct-style applicative macros here with the CPS versions in that talk. Matthias Felleisen and Daniel P.Function Rule Calculator May a times in real life we have situations as follows, for example: In a theater showing a play, tickets are sold for dollars and tickets are sold for dollars.
Create functions that match one variable to the other in a two-variable equation. Functions are written using function notation. The Binary Slide Rule manufactured by Gilson in performed an addition and subtraction function limited to fractions.. Roots and powers. There are single-decade (C and D), double-decade (A and B), and triple-decade (K) scales.
Example 5: Calculate the first derivative of function f given by Solution to Example 5: Function f given above may be considered as the product of functions U = 1/x - 3 and V = (x 2 + 3)/(2x - 1), and function V may be considered as the quotient of two functions x 2 + 3 and 2x - 1.
We use the product rule for f and the quotient rule for V as follows. A function is the same: it produces one output for each individual input and the same input cannot produce two different outputs. For example, you cannot put strawberries into a blender and get both a smoothie and chopped carrots.
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