Datasets:
Tasks:
Text Generation
Modalities:
Text
Sub-tasks:
language-modeling
Languages:
English
Size:
100K - 1M
License:
File size: 5,149 Bytes
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(* ---------------------------------------------------------------------- *)
(* Simplification *)
(* ---------------------------------------------------------------------- *)
(*
let psimplify1 fm =
match fm with
Not False -> True
| Not True -> False
| And(False,q) -> False
| And(p,False) -> False
| And(True,q) -> q
| And(p,True) -> p
| Or(False,q) -> q
| Or(p,False) -> p
| Or(True,q) -> True
| Or(p,True) -> True
| Imp(False,q) -> True
| Imp(True,q) -> q
| Imp(p,True) -> True
| Imp(p,False) -> Not p
| Iff(True,q) -> q
| Iff(p,True) -> p
| Iff(False,q) -> Not q
| Iff(p,False) -> Not p
| _ -> fm;;
*)
let PSIMPLIFY1_CONV =
let nt = `~T`
and t = `T`
and f = `F`
and nf = `~F` in
fun fm ->
try
let fm' =
if fm = nt then f
else if fm = nf then t
else if is_conj fm then
let l,r = dest_conj fm in
if l = f || r = f then f
else if l = t then r
else if r = t then l
else fm
else if is_disj fm then
let l,r = dest_disj fm in
if l = t || r = t then t
else if l = f then r
else if r = f then l
else fm
else if is_imp fm then
let l,r = dest_imp fm in
if l = f then t
else if r = t then t
else if l = t then r
else if r = f then mk_neg l
else fm
else if is_iff fm then
let l,r = dest_beq fm in
if l = f then mk_neg r
else if l = t then r
else if r = t then l
else if r = f then mk_neg l
else fm
else failwith "PSIMPLIFY: 0" in
let fm'' = mk_eq(fm,fm') in
prove(fm'',REWRITE_TAC[])
with _ -> REFL fm;;
(*
let fm = `T /\ T`
PSIMPLIFY1_CONV `T /\ A`
let simplify1 fm =
match fm with
Forall(x,p) -> if mem x (fv p) then fm else p
| Exists(x,p) -> if mem x (fv p) then fm else p
| _ -> psimplify1 fm;;
*)
let SIMPLIFY1_CONV fm =
if is_forall fm || is_exists fm then
let x,p = dest_forall fm in
if mem x (frees p) then REFL fm
else prove(mk_eq(fm,p),REWRITE_TAC[])
else PSIMPLIFY1_CONV fm;;
(*
let rec simplify fm =
match fm with
Not p -> simplify1 (Not(simplify p))
| And(p,q) -> simplify1 (And(simplify p,simplify q))
| Or(p,q) -> simplify1 (Or(simplify p,simplify q))
| Imp(p,q) -> simplify1 (Imp(simplify p,simplify q))
| Iff(p,q) -> simplify1 (Iff(simplify p,simplify q))
| Forall(x,p) -> simplify1(Forall(x,simplify p))
| Exists(x,p) -> simplify1(Exists(x,simplify p))
| _ -> fm;;
*)
let rec SIMPLIFY_CONV =
let not_tm = `(~)`
and ex_tm = `(?)` in
fun fm ->
if is_neg fm then
let thm1 = SIMPLIFY_CONV (dest_neg fm) in
let thm2 = AP_TERM not_tm thm1 in
let l,r = dest_eq (concl thm2) in
let thm3 = SIMPLIFY1_CONV r in
TRANS thm2 thm3
else if is_conj fm || is_disj fm || is_imp fm || is_iff fm then
let op,l,r = get_binop fm in
let l_thm = SIMPLIFY_CONV l in
let r_thm = SIMPLIFY_CONV r in
let a_thm = (curry MK_COMB) (AP_TERM op l_thm) r_thm in
let al,ar = dest_eq (concl a_thm) in
let thm = SIMPLIFY1_CONV ar in
TRANS a_thm thm
else if is_forall fm || is_exists fm then
let x,bod = dest_quant fm in
let bod_thm = SIMPLIFY_CONV bod in
let lam_thm = ABS x bod_thm in
let q_thm = AP_TERM ex_tm lam_thm in
let l,r = dest_eq (concl q_thm) in
let thm = SIMPLIFY1_CONV r in
TRANS q_thm thm
else REFL fm;;
(*
SIMPLIFY_CONV `T /\ T \/ F`
let operations =
["=",(=/); "<",(</); ">",(>/); "<=",(<=/); ">=",(>=/);
"divides",(fun x y -> mod_num y x =/ Int 0)];;
let evalc_atom at =
match at with
R(p,[s;t]) ->
(try if assoc p operations (dest_numeral s) (dest_numeral t)
then True else False
with Failure _ -> Atom at)
| _ -> Atom at;;
let evalc = onatoms evalc_atom;;
*)
let REAL_LEAF_CONV fm =
let op,l,r = get_binop fm in
if op = rlt then
REAL_RAT_LT_CONV fm
else if op = rgt then
REAL_RAT_GT_CONV fm
else if op = rle then
REAL_RAT_LE_CONV fm
else if op = rge then
REAL_RAT_GE_CONV fm
else if op = req then
REAL_RAT_EQ_CONV fm
else failwith "REAL_LEAF_CONV";;
let EVALC_CONV = DEPTH_CONV REAL_LEAF_CONV;;
(*
EVALC_CONV `x < &0 /\ &1 < &2`
(EVALC_CONV THENC SIMPLIFY_CONV) `(&0 + a * &1 = &0) /\
((&0 + b * &1 = &0) /\
((&0 + c * &1 = &0) /\ T \/
&0 + c * &1 < &0 /\ F \/
&0 + c * &1 > &0 /\ F) \/
&0 + b * &1 < &0 /\ T \/
&0 + b * &1 > &0 /\ T) \/
&0 + a * &1 < &0 /\
((&0 + a * ((&0 + b * (&0 + b * -- &1)) + a * (&0 + c * &4)) = &0) /\ T \/
&0 + a * ((&0 + b * (&0 + b * -- &1)) + a * (&0 + c * &4)) < &0 /\ F \/
&0 + a * ((&0 + b * (&0 + b * -- &1)) + a * (&0 + c * &4)) > &0 /\ T) \/
&0 + a * &1 > &0 /\
((&0 + a * ((&0 + b * (&0 + b * -- &1)) + a * (&0 + c * &4)) = &0) /\ T \/
&0 + a * ((&0 + b * (&0 + b * -- &1)) + a * (&0 + c * &4)) < &0 /\ T \/
&0 + a * ((&0 + b * (&0 + b * -- &1)) + a * (&0 + c * &4)) > &0 /\ &1 < &2)`
*)
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