PSEUDO-TERMP.html -- ACL2 Version 6.3

### PSEUDO-TERMP

a predicate for recognizing term-like s-expressions

    Major Section:  ACL2-BUILT-INS

    Example Forms:
    (pseudo-termp '(car (cons x 'nil)))      ; has value t
    (pseudo-termp '(car x y z))              ; also has value t!
    (pseudo-termp '(delta (h x)))            ; has value t
    (pseudo-termp '(delta (h x) . 7))        ; has value nil (not a true-listp)
    (pseudo-termp '((lambda (x) (car x)) b)) ; has value t
    (pseudo-termp '(if x y 123))             ; has value nil (123 is not quoted)
    (pseudo-termp '(if x y '123))            ; has value t

If `x` is the quotation of a term, then `(pseudo-termp x)` is `t`. However, if `x` is not the quotation of a term it is not necessarily the case that `(pseudo-termp x)` is `nil`.

See term for a discussion of the various meanings of the word ``term'' in ACL2. In its most strict sense, a term is either a legal variable symbol, a quoted constant, or the application of an `n`-ary function symbol or closed `lambda`-expression to `n` terms. By ``legal variable symbol'' we exclude constant symbols, such as `t`, `nil`, and `*ts-rational*`. By ``quoted constants'' we include `'t` (aka `(quote t)`), `'nil`, `'31`, etc., and exclude constant names such as `t`, `nil` and `*ts-rational*`, unquoted constants such as `31` or `1/2`, and ill-formed `quote` expressions such as `(quote 3 4)`. By ``closed lambda expression'' we exclude expressions, such as `(lambda (x) (cons x y))`, containing free variables in their bodies. Terms typed by the user are translated into strict terms for internal use in ACL2.

The predicate `termp` checks this strict sense of ``term'' with respect to a given ACL2 logical world; See world. Many ACL2 functions, such as the rewriter, require certain of their arguments to satisfy `termp`. However, as of this writing, `termp` is in `:``program` mode and thus cannot be used effectively in conjectures to be proved. Furthermore, if regarded simply from the perspective of an effective guard for a term-processing function, `termp` checks many irrelevant things. (Does it really matter that the variable symbols encountered never start and end with an asterisk?) For these reasons, we have introduced the notion of a ``pseudo-term'' and embodied it in the predicate `pseudo-termp`, which is easier to check, does not require the logical world as input, has `:``logic` mode, and is often perfectly suitable as a guard on term-processing functions.

A `pseudo-termp` is either a symbol, a true list of length 2 beginning with the word `quote`, the application of an `n`-ary pseudo-`lambda` expression to a true list of `n` pseudo-terms, or the application of a symbol to a true list of `n` `pseudo-termp`s. By an ```n`-ary pseudo-`lambda` expression'' we mean an expression of the form `(lambda (v1 ... vn) pterm)`, where the `vi` are symbols (but not necessarily distinct legal variable symbols) and `pterm` is a `pseudo-termp`.

Metafunctions may use `pseudo-termp` as a guard.