/usr/share/hol88-2.02.19940316/contrib/convert/unwind.ml is in hol88-contrib-source 2.02.19940316-14.
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---------------------------------
new-unwind library
unwind.ml
based on HOL88 unwind library
Rules for unwinding
this file uses mk_thm !!
---------------------------------
>%
let REWRITES_CONV net = \tm. FIRST_CONV (lookup_term net tm) tm;;
%< some useful conversions for getting things into right form for unwinding >%
%<
AND_FORALL_CONV -- move universal quantification out of a conjunction
"(!x. t1) /\ ... /\ (!x. tn)" --->
|- (!x. t1) /\ ... /\ (!x. tn) = !x. t1 /\ ... /\ tn
>%
%< now we remove the mk_thm ones and use binary conversions for left, right and both
conversions as in exists_and (?) ones >%
let AND_FORALL_LEFT_CONV t =
(let xt1,xt2 = dest_conj t
in
let x = fst(dest_forall xt1)
in
let (th1,th2) = CONJ_PAIR(ASSUME t)
in
let th3 = DISCH_ALL(GEN x (CONJ(SPEC x th1)th2))
in
let (th4,th5) =
CONJ_PAIR
(SPEC x
(ASSUME
(mk_forall(x,(mk_conj((snd o dest_forall o concl)th1,
concl th2))))))
in
let th6 = DISCH_ALL(CONJ(GEN x th4)th5)
in
IMP_ANTISYM_RULE th3 th6
) ? failwith `AND_FORALL_LEFT_CONV`;;
%( test AND_FORALL_LEFT_CONV "(! (x:*). T) /\ T";;)%
let AND_FORALL_RIGHT_CONV t =
(let xt1,xt2 = dest_conj t
in
let x = fst(dest_forall xt2)
in
let (th1,th2) = CONJ_PAIR(ASSUME t)
in
let th3 = DISCH_ALL(GEN x (CONJ th1(SPEC x th2)))
in
let (th4,th5) =
CONJ_PAIR
(SPEC x
(ASSUME
(mk_forall(x,(mk_conj(concl th1,
(snd o dest_forall o concl)th2))))))
in
let th6 = DISCH_ALL(CONJ th4(GEN x th5))
in
IMP_ANTISYM_RULE th3 th6
) ? failwith `AND_FORALL_RIGHT_CONV`;;
%( test AND_FORALL_RIGHT_CONV "T /\ (! (x:*). T)";;)%
let AND_FORALL_BOTH_CONV t =
(let xt1,xt2 = dest_conj t
in
let x = fst(dest_forall xt2)
in
let (th1,th2) = CONJ_PAIR(ASSUME t)
in
let th3 = DISCH_ALL(GEN x (CONJ (SPEC x th1)(SPEC x th2)))
in
let (th4,th5) =
CONJ_PAIR
(SPEC x
(ASSUME
(mk_forall(x,(mk_conj((snd o dest_forall o concl)th1,
(snd o dest_forall o concl)th2))))))
in
let th6 = DISCH_ALL(CONJ (GEN x th4)(GEN x th5))
in
IMP_ANTISYM_RULE th3 th6
) ? failwith `AND_FORALL_BOTH_CONV`;;
%( test
AND_FORALL_BOTH_CONV "(! (x:*). T) /\ (! (x:*). T)";;
)%
let AND_FORALL_CONV = AND_FORALL_BOTH_CONV ORELSEC
AND_FORALL_LEFT_CONV ORELSEC
AND_FORALL_RIGHT_CONV;;
%( test
AND_FORALL_CONV "(! (x:*). T) /\ (! (x:*). T)";;
)%
%< mk_thm version eliminated [DES] 31jul90
% "(!x. t1) /\ ... /\ (!x. tn)" ---> ("x", ["t1"; ... ;"tn"]) %
letrec dest_andl t =
((let x1,t1 = dest_forall t
in
(x1,[t1])
)
?
(let first,rest = dest_conj t
in
let x1,l1 = dest_andl first
and x2,l2 = dest_andl rest
in
if x1=x2 then (x1, l1@l2) else fail)
) ? failwith `dest_andl`;;
% Version of AND_FORALL_CONV below will pull quantifiers out and flatten an
arbitrary tree of /\s, not just a linear list. %
let AND_FORALL_CONV t =
(let x,l = dest_andl t
in
mk_thm([], mk_eq(t,mk_forall(x,list_mk_conj l)))
) ? failwith `AND_FORALL_CONV`;;
>%
%<
FORALL_AND_CONV -- inverse of above
"!x. t1 /\ ... /\ tn" --->
|- !x. t1 /\ ... /\ tn = (!x. t1) /\ ... /\ (!x. tn)
>%
%< superceded by mk_thm version
let FORALL_AND_CONV t =
(let x,l = ((I # conjuncts) o dest_forall) t
in
SYM(AND_FORALL_CONV(list_mk_conj(map(curry mk_forall x)l)))
) ? failwith `AND_FORALL_CONV`;;
>%
let FORALL_AND_CONV t =
(let x,l = ((I # conjuncts) o dest_forall) t
in
mk_thm([],mk_eq(t, list_mk_conj(map(curry mk_forall x)l)))
) ? failwith `FORALL_AND_CONV`;;
%< [DES] 27apr89
EXISTS_FORALL_CONV
? s . ! t . ....(s t).... = ! t . ? st . ....st....
used after unfolding to bring ! t's to outside
s and t and unprimed then reprimed to be unique in body
(avoids ?s'!t'.bdy ===> !t'?s't'.bdy problem as s't' not "legal" var name)
>%
let unprime s = implode(filter (\c.not(c=`'`)) (explode s));;
let EXISTS_FORALL_CONV t =
let ex,t0 = dest_exists t
in let un,t1 = dest_forall t0
in let unty = snd(dest_var un)
in let newname = mk_var(unprime(fst(dest_var ex))^unprime(fst(dest_var un)),type_of"^ex ^un")
in let new = variant (frees t1) newname
in let t2 = subst [new,"^ex ^un"] t1
in let t3 = mk_forall (un,mk_exists (new,t2))
in let t4 = mk_eq (t,t3)
in TAC_PROOF(([],t4),
EQ_TAC THEN REPEAT STRIP_TAC
THENL [ EXISTS_TAC "^ex ^un" THEN
POP_ASSUM (ACCEPT_TAC o SPEC "^un")
;EXISTS_TAC "\ ^un . @ ^new . ^t2"
THEN BETA_TAC
THEN POP_ASSUM (ACCEPT_TAC o (GEN "^un")
o SELECT_RULE o (SPEC "^un"))
]);;
% line_var "!v1 ... vn. f v1 ... vn = t" ====> "f" %
let line_var tm = fst(strip_comb(lhs(snd(strip_forall tm))));;
% var_name "var" ====> `var` %
let var_name = fst o dest_var;;
% line_name "!v1 ... vn. f v1 ... vn = t" ====> `f` %
let line_name = var_name o line_var;;
% UNWIND CONVERSIONS -------------------------------------------------- %
% UNWIND_ONCE_CONV - Basic conversion for parallel unwinding of lines. %
% %
% DESCRIPTION: tm should be a conjunction, t1 /\ t2 ... /\ tn. %
% p:term->bool is a function which is used to partition the%
% terms (ti) into two sets. Those ti which p is true of %
% are then used as a set of rewrite rules (thus they must %
% be equations) to do a top-down one-step parallel rewrite %
% of the conjunction of the remaining terms. I.e. %
% %
% t1 /\ ... /\ eqn1 /\ ... /\ eqni /\ ... /\ tn %
% --------------------------------------------- %
% |- t1 /\ ... /\ eqn1 /\ ... /\ eqni /\ ... /\ tn %
% = %
% eqn1 /\ ... /\ eqni /\ ... /\ t1' /\ ... /\ tn' %
% %
% where tj' is tj rewritten with the equations eqnx %
let UNWIND_ONCE_CONV p tm =
let eqns = conjuncts tm in
let eq1,eq2 = partition (\tm. ((p tm) ? false)) eqns in
if (null eq1) or (null eq2)
then REFL tm
else let thm = CONJ_DISCHL eq1
(ONCE_DEPTH_CONV
(REWRITES_CONV (mk_conv_net (map ASSUME eq1)))
(list_mk_conj eq2)) in
let re = CONJUNCTS_CONV(tm,(lhs(concl thm))) in
re TRANS thm;;
% Unwind until no change using equations selected by p. %
% WARNING -- MAY LOOP! %
letrec UNWIND_CONV p tm =
let th = UNWIND_ONCE_CONV p tm in
if lhs(concl th)=rhs(concl th)
then th
else th TRANS (UNWIND_CONV p (rhs(concl th)));;
%< [DES] 27apr89
UNWIND_EXISTS_ONCE_CONV and UNWIND_EXISTS_CONV
? l1 ... ln . eqn1 /\ ... /\ eqnm
----------------------------------------
|- (? l1 ... ln . eqn1 /\ ... /\ eqnm) =
(? l1 ... ln . eqn1'/\ ... /\ eqnm')
where any eqs (li = ti) are used as rewrites
>%
let UNWIND_EXISTS_ONCE_CONV t =
(let exs,bdy = strip_exists t in
let th1 = UNWIND_ONCE_CONV (\t.mem (line_var t) exs ? false) bdy in
LIST_MK_EXISTS exs th1) ? failwith `UNWIND_EXISTS_ONCE_CONV`;;
let UNWIND_EXISTS_CONV t =
(let exs,bdy = strip_exists t in
let th1 = UNWIND_CONV (\t.mem (line_var t) exs ? false) bdy in
LIST_MK_EXISTS exs th1) ? failwith `UNWIND_EXISTS_ONCE_CONV`;;
% UNWIND CONVERSIONS -------------------------------------------------- %
% One-step unwinding of device behaviour with hidden lines using line %
% equations selected by p. %
let UNWIND_ONCE_RULE p th =
let rhs_conv = \rhs. (let lines,eqs = strip_exists rhs in
LIST_MK_EXISTS lines (UNWIND_ONCE_CONV p eqs)) in
RIGHT_CONV_RULE rhs_conv th ? failwith `UNWIND_ONCE_RULE`;;
% Unwind device behaviour using line equations selected by p until no %
% change. WARNING --- MAY LOOP! %
let UNWIND_RULE p th =
let rhs_conv = \rhs. (let lines,eqs = strip_exists rhs in
LIST_MK_EXISTS lines (UNWIND_CONV p eqs)) in
RIGHT_CONV_RULE rhs_conv th ? failwith `UNWIND_RULE`;;
% Unwind all lines (except those in the list l) as much as possible. %
let UNWIND_ALL_RULE l th =
let rhs_conv =
\rh. (let lines,eqs = strip_exists rh in
let eqns = filter (can line_name) (conjuncts eqs) in
let line_names = subtract (map line_name eqns) l in
let p = \line. \tm. (line_name tm) = line in
let itfn = \line. \th. th TRANS
UNWIND_CONV (p line) (rhs(concl th)) in
LIST_MK_EXISTS lines (itlist itfn line_names (REFL eqs))) in
RIGHT_CONV_RULE rhs_conv th ? failwith `UNWIND_ALL_RULE`;;
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