## type-i

2019-12-27

Type Inference Utility on Fundamentally 1-arg Predicates

# 1Type-I : type-inference from a predicate

This library tries to provide a way to detect what kind of type the given
predicate is trying to check. **This is different from inferring the return
type of a function.** For example,

```
(eq 'null (test-type '(eql nil ?)))
(eq 'string (test-type '(stringp ?)))
```

The inference is done on form basis, and the equivalence of predicates are
determined by `#'equal`

. To simplify the design, the argument to check
should be a symbol `?`

, exported in package `type-i`

.

Function `test-type`

returns the inferred type. In contrast, `type-tests`

returns a list of all possible test predicates that returns true when `?`

is bound to the object of interest.

```
(is (subset '((TYPEP ? 'integer)
(integerp ?))
(type-tests 'integer)))
;; more inference on integers, e.g., (< 0 ? 4), should be added
(is (subset '((TYPEP ? '(mod 5))
(TYPEP ? '(integer 0 4)))
(type-tests '(mod 5))))
```

This library is extensible. with `define-inference-rule`

macro, you can add
more inferers to improve this library. Each inference rule is a unary
function that takes a predicate form, then returns a list of more
forms.

The `test-type`

searches in the form space, adding the results of each
inference rule, until a form `(typep ? X)`

is found (where X is
unknown). If it fails to find such a form even if the maximal set
is obtained, then the `test-type`

returns nil. `type-tests`

just returns
the maximal set.

I currently implemented the following inference rules:

- typep --
`(typep ? 'array)`

->`(arrayp ?)`

etc. - unary --
`(arrayp ?)`

-> =(typep ? 'array) (typep ? '(array)) (typep ?'(array *))= ... - null --
`(null ?) (typep ? null) (eql ? nil) (eql nil ?) (eq ? nil)`

... - derived -- call
`typexpand`

Inference on exhaustive partitions, e.g., `(typep ? 'list)`

-> ```
(typep ?
'(or cons null))
```

is planned.

## 1.1Dependencies

This library is at least tested on implementation listed below:

- SBCL 1.2.8 on X86-64 Linux 3.13.0-46-generic (author's environment)

Also, it depends on the following libraries:

- Trivia by Masataro Asai
- NON-Optimized Pattern Matching Library
- alexandria by
- Alexandria is a collection of portable public domain utilities.
- iterate by
- Jonathan Amsterdam's iterator/gatherer/accumulator facility
- introspect-environment by Bike <aeshtaer@gmail.com>
- Small interface to portable but nonstandard introspection of CL environments.

## 1.2Author

- Masataro Asai (guicho2.71828@gmail.com)

# 2Copyright

Copyright (c) 2015 Masataro Asai (guicho2.71828@gmail.com)

# 3License

Licensed under the LLGPL License.