work in the word piecewise (and add an example to explain why it is interesting)

closes #148

Author: rfindler

redex-doc/redex/scribblings/ref/languages.scrbl

@@ -46,7 +46,8 @@ side-condition @|pattern|s can restrict matches in complex ways.
 A @racket[non-terminal-def] comprises one or more non-terminal names
 (considered aliases) followed by one or more productions.
 
-For example, the following defines @deftech{@racket[_lc-lang]} as the
+@; this language is copied to other-relations.scrbl to be used in examples there, too
+ For example, the following defines @deftech{@racket[_lc-lang]} as the
 grammar of the λ-calculus:
 @examples[#:label #f #:eval redex-eval #:no-prompt #:no-result
 (define-language lc-lang

redex-doc/redex/scribblings/ref/other-relations.scrbl

@@ -11,7 +11,17 @@
                               vc-append hbl-append vl-append)
                      redex))
 
-@(define redex-eval (make-base-eval '(require redex/reduction-semantics)))
+@(define redex-eval (make-base-eval '(require redex/reduction-semantics redex/pict)))
+@; this definition is copied from languages.scrbl
+@(redex-eval
+  '(define-language lc-lang
+     (e ::= (e e ...)
+        x
+        (λ (x ...) e))
+     (v ::= (λ (x ...) e))
+     (E ::= (v ... E e ...)
+        hole)
+     (x y ::= variable-not-otherwise-mentioned)))
 
 @title{Other Relations}
 
@@ -99,8 +109,8 @@ clause to be taken.
 The @racket[clause-name] is used only when typesetting. See
 @racket[metafunction-cases].
 
-The @racket[or] clause is used to define a form of conditional
-right-hand side of a metafunction. In particular, if any of the
+The @racket[or] clause is used to define piecewise conditional
+metafunctions. In particular, if any of the
 @racket[where] or @racket[side-condition] clauses fail, then
 evaluation continues after an @racket[or] clause, treating the
 term that follows as the result (subject to any subsequent
@@ -110,6 +120,29 @@ clause, once for each @racket[or] expression, but signals to
 the typesetting library to use a large left curly brace to group
 the conditions in the @racket[or].
 
+ For example, here are two equivalent definitions of a @racket[biggest]
+ metafunction that typeset differently:
+
+ @examples[#:eval redex-eval
+           (define-metafunction lc-lang
+             biggest : natural natural -> natural
+             [(biggest natural_1 natural_2)
+              natural_2
+              (side-condition (< (term natural_1) (term natural_2)))]
+             [(biggest natural_1 natural_2)
+              natural_1])
+           (render-metafunction biggest)
+           (define-metafunction lc-lang
+             biggest : natural natural -> natural
+             [(biggest natural_1 natural_2)
+              natural_2
+              (side-condition (< (term natural_1) (term natural_2)))
+
+              or
+
+              natural_1])
+           (render-metafunction biggest)]
+
 Note that metafunctions are assumed to always return the same results
 for the same inputs, and their results are cached, unless
 @racket[caching-enabled?] is set to @racket[#f]. Accordingly, if a