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\DOC mk_gabs
\TYPE {mk_gabs : term * term -> term}
\SYNOPSIS
Constructs a generalized abstraction.
\DESCRIBE
Given a pair of terms {s} and {t}, the call {mk_gabs(s,t)} constructs a
canonical `generalized abstraction' that is thought of as `some function that
always maps {s} to {t}'. In the case where {s} is a variable, the result is an
ordinary abstraction as constructed by {mk_abs}. In other cases, the canonical
composite structure is created. Note that the logical construct is welldefined
even if there is no function mapping {s} to {t}, and this function will
always succeed, even if the resulting structure is not really useful.
\FAILURE
Never fails.
\EXAMPLE
Here is a simple abstraction:
{
# mk_gabs(`x:bool`,`~x`);;
val it : term = `\x. ~x`
}
\noindent and here are a couple of potentially useful generalized ones:
{
# mk_gabs(`(x:num,y:num)`,`x + y + 1`);;
val it : term = `\(x,y). x + y + 1`
# mk_gabs(`CONS (h:num) t`,`if h = 0 then t else CONS h t`);;
val it : term = `\CONS h t. if h = 0 then t else CONS h t`
}
\noindent while here is a vacuous one about which nothing interesting will be
proved, because there is no welldefined function that always maps {x + y} to
{x}:
{
# mk_gabs(`x + y:num`,`x:num`);;
val it : term = `\(x + y). x`
}
\SEEALSO
dest_gabs, GEN_BETA_CONV, is_gabs, list_mk_gabs.
\ENDDOC
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