diff --git a/main.rkt b/main.rkt
index f06f306..471b30f 100644
--- a/main.rkt
+++ b/main.rkt
@@ -65,8 +65,8 @@
   )
 
 (define-syntax let/assert
-  (syntax-rules ()
-    ((_ fail ((v rest ...) ...) b1 ...)
+  (syntax-rules (fail)
+    ((_ ((v rest ...) ...) b1 ...)
      (call/cc
       (λ (fail)
         (let* ((v (assert-expr fail (rest ...)))
diff --git a/scrbl/let-assert.scrbl b/scrbl/let-assert.scrbl
index 57a9e6e..3971c29 100644
--- a/scrbl/let-assert.scrbl
+++ b/scrbl/let-assert.scrbl
@@ -3,196 +3,256 @@
 @(require (for-label racket/base
                      "../main.rkt"))
 
-@title{let-assert}
+@title{let/assert}
+
 @author[@author+email["Hans Dijkema" "hans@dijkewijk.nl"]]
 
 @defmodule[let-assert]
 
-This module provides @racket[let/assert], a small sequential binding form
-with local assertions.  It is useful for defensive programming around FFI
-bindings: checks for null pointers, exit codes, and similar failure values can
-be kept close to the binding that produced them, while the body stays on the
-happy path.  When an assertion fails, the whole @racket[let/assert] expression
-returns the associated fallback value.
+This module provides @racket[let/assert], a small sequential binding
+form for defensive programming. It is especially useful around FFI calls,
+where failure is often reported by ordinary values: @racket[#f] for a
+null pointer, a negative integer for an error code, or a non-zero integer
+for a failed C-style status result.
 
-@section{Binding with assertions}
+The form is implemented with @racket[call/cc]. A failed assertion does
+not raise an exception. Instead, it invokes an internal escape
+continuation and returns the supplied failure value as the result of the
+whole @racket[let/assert] expression.
 
 @defform[
-(let/assert (binding ...) body ...+)
-#:grammar
-([binding [id expr]
-          [id expr predicate-expr fallback-expr]])]{
+(let/assert
+  ((id expr)
+   (id expr assert-expr failure-expr)
+   ...)
+  body ...)
+]{
 
-The form expands to an internal @racket[let*] structure.  Bindings are
-therefore evaluated from left to right, and later bindings may refer to
-earlier ones.
-
-A binding of the form @racket[[id expr]] simply binds @racket[id] to
-@racket[expr].
+Evaluates the bindings from left to right, using @racket[let*]
+semantics. Later bindings may refer to earlier ones.
 
 A binding of the form
-@racket[[id expr predicate-expr fallback-expr]] evaluates @racket[expr] once,
-applies @racket[predicate-expr] to the result, and binds @racket[id] to that
-result when the predicate accepts it.  If the predicate returns @racket[#f],
-the body is not evaluated and the whole @racket[let/assert] form returns
-@racket[fallback-expr].
 
-The fallback expression is evaluated only when the assertion fails.  Internally,
-the failing assertion raises a private exception carrying that value; the
-exception is caught by @racket[let/assert] itself.
+@racketblock[
+(id expr)
+]
+
+is a plain sequential binding.
+
+A binding of the form
+
+@racketblock[
+(id expr assert-expr failure-expr)
+]
+
+evaluates @racket[expr] once and applies @racket[assert-expr] to the
+result. If the assertion succeeds, @racket[id] is bound to the original
+value. If the assertion fails, @racket[failure-expr] is returned as the
+result of the whole @racket[let/assert] form.
+
+The escape continuation is internal. It is not part of the surface syntax
+and is not visible in the body.
+
+@racketblock[
+(define (half-positive n)
+  (let/assert
+    ((x n a->0? 'not-positive))
+    (/ x 2)))
+]
+
+The result is @racket[5] for @racket[(half-positive 10)] and
+@racket['not-positive] for @racket[(half-positive 0)].
+
+Because @racket[let/assert] uses @racket[call/cc], failure is local
+control flow. There is no exception object, no exception handler, and no
+dynamic catching of unrelated failures.
 }
 
-@racketblock[
-(let/assert ([x 10 (a->? 0) 'too-small]
-             [y (+ x 2) (a-=? 12) 'wrong-value])
-  y)
-]
-
-The example returns @racket[12].  The second binding can use @racket[x],
-because @racket[let/assert] has @racket[let*] scoping.
-
-@section{FFI-style examples}
-
-FFI libraries often report errors by returning a null pointer or a negative
-integer status code.  With @racket[let/assert], those checks can be written
-next to the operation that may fail.
-
-@racketblock[
-(define (open-ffmpeg-instance)
-  (let/assert ([fh (fmpg-init) a-!nullptr? #f])
-    fh))
-]
-
-Here @racket[fmpg-init] is expected to return either a valid native handle or
-@racket[#f].  If the handle is @racket[#f], the complete
-@racket[let/assert] form returns @racket[#f].  Otherwise the valid handle is
-returned.
-
-A slightly larger example can combine a pointer check with an FFmpeg-style
-return-code check:
-
-@racketblock[
-(define (decode-next! ds)
-  (let/assert ([pkt (av-packet-alloc) a-!nullptr? 'packet-allocation-failed]
-               [ret (read-selected-audio-packet! ds pkt)
-                    (a->=? 0)
-                    'read-packet-failed]
-               [pcm (receive-available-frames! ds)
-                    bytes?
-                    'decode-failed])
-    pcm))
-]
-
-The body contains only the successful path.  If packet allocation fails, the
-result is @racket['packet-allocation-failed].  If reading the packet returns a
-negative status code, the result is @racket['read-packet-failed].  If decoding
-does not produce bytes, the result is @racket['decode-failed].
-
-@section{Creating assertion factories}
+@section{Assertion constructors}
 
 @defform[(make-assert name not-name pred)]{
 
-Defines two assertion factories in a definition context.
+Defines two assertion-constructor forms.
 
-The form @racket[(name constant)] expands to a unary predicate that applies
-@racket[pred] to the value being checked and @racket[constant].  The form
-@racket[(not-name constant)] expands to the negated variant.
-
-For example:
+The generated @racket[name] form creates a predicate that compares its
+argument with a constant using @racket[pred]:
 
 @racketblock[
-(make-assert a-eq? a-!eq? eq?)
+((name const) value)
 ]
 
-defines @racket[a-eq?] and @racket[a-!eq?].  Consequently,
-@racket[(a-eq? #f)] produces a predicate that accepts values that are
-@racket[eq?] to @racket[#f], while @racket[(a-!eq? #f)] accepts values that
-are not @racket[eq?] to @racket[#f].
+is equivalent to:
+
+@racketblock[
+(λ (x) (pred x const))
+]
+
+The generated @racket[not-name] form creates the negated predicate:
+
+@racketblock[
+(λ (x) (not (pred x const)))
+]
+
+For example, the module defines:
+
+@racketblock[
+(make-assert a-eq?  a-!eq?  eq?)
+(make-assert a->?   a-<=?   >)
+(make-assert a->=?  a-<?    >=)
+(make-assert a-=?   a-!=?   =)
+]
+
+The negated forms are logical negations of the positive predicate.
 }
 
-@section{Assertion factories}
-
-@defform[(a-eq? constant)]{
-Produces a unary predicate that accepts values for which
-@racket[(eq? value constant)] is true.
+@defform[(a-eq? const)]{
+Creates a predicate that accepts values @racket[eq?] to @racket[const].
 }
 
-@defform[(a-!eq? constant)]{
-Produces a unary predicate that accepts values for which
-@racket[(eq? value constant)] is false.
+@defform[(a-!eq? const)]{
+Creates a predicate that accepts values not @racket[eq?] to
+@racket[const].
 }
 
-@defform[(a->? constant)]{
-Produces a unary predicate that accepts values greater than
-@racket[constant].
+@defform[(a->? const)]{
+Creates a predicate that accepts values greater than @racket[const].
 }
 
-@defform[(a-<=? constant)]{
-Produces a unary predicate that rejects values greater than
-@racket[constant].
+@defform[(a-<=? const)]{
+Creates the negation of @racket[(a->? const)].
 }
 
-@defform[(a->=? constant)]{
-Produces a unary predicate that accepts values greater than or equal to
-@racket[constant].
+@defform[(a->=? const)]{
+Creates a predicate that accepts values greater than or equal to
+@racket[const].
 }
 
-@defform[(a-<? constant)]{
-Produces a unary predicate that rejects values greater than or equal to
-@racket[constant].
+@defform[(a-<? const)]{
+Creates the negation of @racket[(a->=? const)].
 }
 
-@defform[(a-=? constant)]{
-Produces a unary predicate that accepts values numerically equal to
-@racket[constant].
+@defform[(a-=? const)]{
+Creates a predicate that accepts values numerically equal to
+@racket[const].
 }
 
-@defform[(a-!=? constant)]{
-Produces a unary predicate that accepts values not numerically equal to
-@racket[constant].
+@defform[(a-!=? const)]{
+Creates the negation of @racket[(a-=? const)].
 }
 
-@section{Ready-made predicates}
+@section{Built-in predicates}
 
 @defproc[(a-=0? [x number?]) boolean?]{
-Returns @racket[#t] when @racket[x] is numerically equal to zero.
+Accepts values numerically equal to zero.
 }
 
 @defproc[(a-!=0? [x number?]) boolean?]{
-Returns @racket[#t] when @racket[x] is not numerically equal to zero.
+Accepts values not numerically equal to zero.
 }
 
 @defproc[(a->0? [x real?]) boolean?]{
-Returns @racket[#t] when @racket[x] is greater than zero.
+Accepts values greater than zero.
 }
 
 @defproc[(a->=0? [x real?]) boolean?]{
-Returns @racket[#t] when @racket[x] is greater than or equal to zero.
+Accepts values greater than or equal to zero.
 }
 
 @defproc[(a-<0? [x real?]) boolean?]{
-Returns @racket[#t] when @racket[x] is less than zero.
+Accepts values less than zero.
 }
 
 @defproc[(a-<=0? [x real?]) boolean?]{
-Returns @racket[#t] when @racket[x] is less than or equal to zero.
+Accepts values less than or equal to zero.
 }
 
 @defthing[a-true? procedure?]{
-A predicate equivalent to @racket[(a-eq? #t)].
+A predicate that accepts only @racket[#t].
 }
 
 @defthing[a-false? procedure?]{
-A predicate equivalent to @racket[(a-eq? #f)].
+A predicate that accepts only @racket[#f].
 }
 
 @defthing[a-nullptr? procedure?]{
-A predicate equivalent to @racket[(a-eq? #f)].  The name is intended for FFI
-code where @racket[#f] is used to represent a null pointer.
+A predicate that accepts @racket[#f]. This is intended for FFI bindings
+where a native null pointer is represented as @racket[#f].
 }
 
 @defthing[a-!nullptr? procedure?]{
-A predicate equivalent to @racket[(a-!eq? #f)].  It accepts values that are
-not @racket[#f], which is often the success case for pointer-returning FFI
-calls.
-}
\ No newline at end of file
+A predicate that accepts values that are not @racket[#f]. This is useful
+for checking successful pointer allocation in FFI code.
+}
+
+@section{Examples}
+
+A simple status-code check:
+
+@racketblock[
+(define (open-status r)
+  (let/assert
+    ((status r a-=0? 'open-failed))
+    'opened))
+]
+
+Here @racket[(open-status 0)] returns @racket['opened], while
+@racket[(open-status -1)] returns @racket['open-failed].
+
+A pointer-style check:
+
+@racketblock[
+(define (use-context maybe-ctx)
+  (let/assert
+    ((ctx maybe-ctx a-!nullptr? 'no-context))
+    ctx))
+]
+
+Here @racket[#f] is treated as a failed native pointer result.
+
+Plain bindings and asserted bindings may be mixed. Since the form uses
+@racket[let*] semantics, later expressions can refer to earlier values:
+
+@racketblock[
+(define (make-scaled-size width height scale)
+  (let/assert
+    ((w width  a->0? 'bad-width)
+     (h height a->0? 'bad-height)
+     (s scale  a->0? 'bad-scale)
+     (area (* w h)))
+    (* area s)))
+]
+
+The expression @racket[area] is only evaluated after @racket[w] and
+@racket[h] have passed their assertions.
+
+@subsection{FFmpeg-style null pointers}
+
+Many FFmpeg functions return a native pointer, where @racket[#f]
+represents a null pointer. Since @racket[let/assert] uses sequential
+@racket[let*] semantics, later bindings may depend on earlier checked
+pointer results.
+
+@racketblock[
+(define (make-stream-codec-context stream)
+  (let/assert
+    ((codecpar (AVStream-codecpar stream) a-!nullptr?
+               'missing-codec-parameters)
+
+     (codec    (avcodec-find-decoder
+                (AVCodecParameters-codec-id codecpar))
+               a-!nullptr?
+               'decoder-not-found)
+
+     (ctx      (avcodec-alloc-context3 codec) a-!nullptr?
+               'alloc-codec-context-failed))
+    ctx))
+]
+
+If @racket[avcodec-find-decoder] returns @racket[#f], the whole
+@racket[let/assert] expression returns @racket['decoder-not-found].
+The second binding is then not evaluated.
+
+If @racket[codec] is a valid pointer, it is used by the next binding.
+If @racket[avcodec-alloc-context3] returns @racket[#f], the expression
+returns @racket['alloc-codec-context-failed]. Otherwise @racket[ctx] is
+bound to the allocated context and returned by the body.
\ No newline at end of file