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multi-methods are simplified variants of generic functions. They are procedures with state, i.e. closures. They are invoked like ordinary procedures, but that results in checking the arguments against predicates in the respective states and invoking the matching procedure, stored in the state as well. This state is implemented as a tree of tagged procedures, which makes searching of the multi-methods action comparatively fast.
Contrary to other implementations of generic functions, the state is accessible by the client. Hence the client has control over the place, where a method is to be inserted. This way there is no need to supply type hierarchies: Since more specific procedures are to be inserted before less specific ones, the former are found first.
Since trees of procedures are not really readable by humans, all of them are tagged by name symbols behind the scene, using the lolevel extend-procedure routine.
These symbols are compared against optional keys in the multi-method-insert! routine. No key means: insert at the end, and a key matching a symbol in the top level of tree: insert before the key, if that key doesn't also match the symbol of the method to be inserted, otherwise step down in the tree and recur.
multi-methods[procedure] (multi-methods [sym])
documentation procedure. Prints the list of exported symbols if called without an argument, or the signature of sym.
define-multi-method[syntax] (define-multi-method (name . vars)
constructor. Creates an empty multi-method, whose variadicity is determined by the signature (name . vars).
multi-method-insert![syntax] (multi-method-insert! multi proc* key ...)
updates multi's proc-tree at the appropriate argument level. For example, if no key (or a non-existent key) is given, proc* is iserted at the very end. If one key is given, proc* is inserted before that very key, provided, that key doesn't match multi's and meth's first predicate name. In that latter case, one recurs with appropriate subtrees. Keys are the tags of (possibly compound) type predicates, which are generated automatically from proc*.
proc* must be of one of the following forms
;; variadic, not unary (proc-name ((a a? a1? ...) (b b? b1? ...) ... : (cs cs? cs1? ...)) xpr . xprs) ;; variadic unary (proc-name (as as? as1? ...) xpr . xprs) ;; not variadic (proc-name ((a a? a1? ...) (b b? b1? ...) ...) xpr . xprs)
Note the colon to mark the variadic argument. Note also, that a variadic argument mustn't be empty, otherwise, there is nothing to dispatch on.
These expressions generate procedures proc-name
(lambda (a b ... . cs) xpr . xprs) (lambda as xpr . xprs) (lambda (a b ...) xpr . xprs)
respectively, check their arguments, for example a fixed argument
a by (conjoin a? a1? ...) named 'a?a1?...
and a variadic argument
cs by (conjoin (list-of? cs?) (list-of? cs1?) ...)
named 'list-of-cs?list-of-cs1? ...
Instead of variables, the predicates can also be named-lambda expressions. In any case, the tagging of the compound predicates is done completely behind the scene.
multi-method?[procedure] (multi-method? xpr)
multi-method-empty?[procedure] (multi-method-empty? xpr)
is xpr an empty multi-method?
multi-method-variadic?[procedure] (multi-method-variadic? xpr)
is xpr a varidic multi-method?
`==== multi-method-arity[procedure] (multi-method-arity multi)
returns the arity ot its multi-method argument.
multi-method-keys[procedure] (multi-method-keys multi key ...)
Inspect multi's tree vertically. Returs the list of predicate tags for checking nth argument, fullfilling key0 ... key(- n 1)
multi-method-tree[procedure] (multi-method-tree multi key ...)
Inspect multi's tree horizontally. With no key returns the whole tree of tags, with one key the subtree corresponding to key and so on.
nlambda[syntax] (nlambda name args xpr . xprs)
named lambda which can refer to name in its body and which is tagged by 'name.
tag[syntax] (tag proc [sym])
tags a procedure variable with its own name or a lambda expression with sym.
get-tag[procedure] (get-tag proc)
returns the tag of a tagged procedure.
tagged-procedure?[procedure] (tagged-procedure? xpr)
is xpr a tagged procedure?
pass[syntax] (pass ok? ok1? ...)
processes a fixed argument.
Returns a tagged procedure which checks, if its only fixed argument is accepted by each of the predicates ok? ok1? ... If so, returns the fixed argument, if not returns the failing predicate.
pass*[syntax] (pass* ok? ok1? ...)
processes the last variadic argument as a list.
Returns a tagged procedure which checks, if its only variadic argument is accepted by each of the predicates list-of- ok? ok1? ... If so, returns the variadic argument, if not returns the failing predicate. Note that the variadic argument mustn't be empty, otherwise there is nothing to dispatch on
;; not variadic, binary (define-multi-method (add a b)) (multi-method? add) ; -> #t (multi-method-arity add) ; -> 2 (multi-method-empty? add) ; -> #t (multi-method-variadic? add) ; -> #f (multi-method-insert! add (add-num?-num? ((a number?) (b number?)) (+ a b))) (multi-method-insert! add (add-str?-str? ((x string?) (y string?)) (string-append x y))) (multi-method-insert! add (add-fx?-fx? ((a fixnum?) (b fixnum?)) (fx+ a b)) 'number?) (multi-method-insert! add (add-num?-odd? ((a number?) (b integer? odd?)) (+ a b)) 'number? 'number?) (multi-method-keys add) ; -> '(fixnum? number? string?) (multi-method-keys add 'number?) ; -> '(integer?odd? number?) (multi-method-tree add) ; -> '((fixnum? ((fixnum? add-fx?-fx?))) ; (number? ((integer?odd? add-num?-odd?) ; (number? add-num?-num?))) ; (string? ((string? add-str?-str?)))) (add "a" "b") ; -> "ab" (add 1 2) ; -> 3 (add 1.5 3.0) ; -> 4.5 ;; variadic, unary (define-multi-method (mult . as)) (multi-method? mult) ; -> #t (multi-method-variadic? mult) ; -> #t (multi-method-empty? mult) ; -> #t (multi-method-insert! mult (mult-nums? (as number?) (apply * as))) (multi-method-insert! mult (mult-fxs? (as fixnum?) (let loop ((as as) (result 1)) (if (null? as) result (loop (cdr as) (fx* (car as) result))))) 'number?) (mult 1 2 3 4 5) ; -> 120 (mult 1.0 2.0 3.0 4.0 5.0) ; -> 120.0 (mult 1.5) ; -> 1.5 ;; variadic, arity 2 (define-multi-method (add* a . as)) (multi-method-variadic? add*) ; -> #t (multi-method-arity add*) ; -> 2 (multi-method-insert! add* (add*-str?-strs? ((a string?) : (as string?)) (apply string-append a as))) (multi-method-insert! add* (add*-fx?-strs? ((a fixnum?) : (as string?)) (apply string-append (->string a) as)) 'string?) (multi-method-insert! add* (add*-num?-nums? ((a number?) : (as number?)) (apply + a as))) (multi-method-keys add*) ; -> '(fixnum? string? number?) (multi-method-keys add* 'fixnum?) ; -> '(list-of-string?) (multi-method-tree add*) ; -> '((fixnum? ((list-of-string? add*-fx?-strs?))) ; (string? ((list-of-string? add*-str?-strs?))) ; (number? ((list-of-number? add*-num?-nums?)))) (multi-method-tree add* 'number?) ; -> '((list-of-number? add*-num?-nums?)) (add* "a" "b" "c") ; -> "abc" (add* 1 "b" "c") ; -> "1bc" (add* 1.0 2.0 3.0) ; -> 6.0 (add* 1.0) ; -> error: "variadic arguments mustn't be empty"
Apr 27, 2014
Copyright (c) 2013-2014, Juergen Lorenz All rights reserved.
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- new implementation with automatic tagging but without methods
- tests updated to new version of simple-tests, should have been numbered 0.7
- checkers now procedures, command-checker changed, docu-procedures only export symbols
- query-checker simplyfied
- method and the checkers changed
- syntax and implementation of query-checker changed
- no-checker added
- initial import