An injective finite mapping is an abstraction common to many
programs.  We describe the design of an injective finite mapping
and its implementation in Curry, a functional logic language.
Curry supports the concurrent asynchronous execution of distinct
portions of a program.  This condition prevents passing from one
portion to another a structure containing a partially constructed
mapping to ensure that a new choice does not violate the
injectivity condition.  We present some motivating problems and we
show fragments of programs that solve these problems using our
design and implementation.