Simplification of Common Lisp type specifiers.

simplified-types

#+TITLE: Simplified Types

Common Lisp has powerful facilities for reasoning about types, including
logical connectives, numeric intervals, and predicates involving arbitrary
functions.  A downside of this expressiveness is that the manipulation of
type specifiers is an arduous and error-prone task.  This library provides
functions to simplify type specifiers.

The API consists of two functions:

- =simplify-type= takes a type specifier and, optionally, an environment,
  and returns the corresponding simplified type.

- =simplified-type-of= takes an object and returns the simplified type of
  that object.

The simplified type hierarchy has been chosen to strike a balance between
simplicity and expressiveness.  The following simplified type specifiers
exist:

- The symbols =t= and =nil=.

- The symbols =function=, =character=, =symbol=, and =cons=.

- The symbols =short-float=, =single-float=, =double-float=, and =long-float=.

- The compound type specifier =(integer <lower-limit> <upper-limit>)=,
  where =<lower-limit= and =<upper-limit>= are either an integer, or the
  symbol =*=.

- The compound type specifier =(complex <float-type>)=, where
  =<float-type>= is one of the symbols =short-float=, =single-float=,
  =double-float=, or =long-float=.

A consequence of restricting all types this way is that the simplified type
lattice has only a single layer of disjoint types between =t= and =nil=.
That means that all types except =t= and =nil= are disjoint, that the join
of any of these disjoint types is =t=, and that the meet of any of these
disjoint types is =nil=.

Despite its simplicity, this set of types is expressive enough to help a
compiler generate fast code.  In particular, it covers all upgraded array
element types that are usually provided by an implementation.

The special variable =*precise-integer-types*= decides whether integer
types have a precise upper and lower limit, or whether the simplification
may also upgrade the bounds to the symbol =*=.  The advantage of the latter
approach is that type simplification will not cons.


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