Datasets:
Tasks:
Text Generation
Modalities:
Text
Sub-tasks:
language-modeling
Languages:
English
Size:
100K - 1M
License:
File size: 3,606 Bytes
4365a98 |
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 |
(* miscellaneous useful stuff that doesn't fit in anywhere else *)
let pair_map f (x,y) = (f x,f y)
(* module for maps keyed on terms *)
module Termmap = Map.Make (struct type t = term let compare = Pervasives.compare end)
module Litset = Set.Make (struct type t = bool * int let compare = Pervasives.compare end)
let tm_listItems m = List.rev (Termmap.fold (fun k v l -> (k,v)::l) m [])
let print_term t = print_string (string_of_term t)
let print_type ty = print_string (string_of_type ty)
(*FIXME: inefficient to read chars one by one; 1024 can be improved upon*)
let input_all in_ch =
let rec loop b =
match
(try Some (input_char in_ch)
with End_of_file -> None)
with
Some c -> (Buffer.add_char b c; loop b)
| None -> () in
let b = Buffer.create 1024 in
let _ = loop b in
Buffer.contents b
let QUANT_CONV conv = RAND_CONV(ABS_CONV conv)
let BINDER_CONV conv = ABS_CONV conv ORELSEC QUANT_CONV conv
let rec LAST_FORALL_CONV c tm =
if is_forall (snd (dest_forall tm))
then
BINDER_CONV (LAST_FORALL_CONV c) tm
else c tm
let FORALL_IMP_CONV tm =
let (bvar,bbody) = dest_forall tm in
let (ant,conseq) = dest_imp bbody in
let fant = free_in bvar ant in
let fconseq = free_in bvar conseq in
let ant_thm = ASSUME ant in
let tm_thm = ASSUME tm in
if (fant && fconseq)
then failwith("FORALL_IMP_CONV"^
("`"^(fst(dest_var bvar))^"` free on both sides of `==>`"))
else
if fant
then
let asm = mk_exists(bvar,ant) in
let th1 = CHOOSE(bvar,ASSUME asm) (UNDISCH(SPEC bvar tm_thm)) in
let imp1 = DISCH tm (DISCH asm th1) in
let cncl = rand(concl imp1) in
let th2 = MP (ASSUME cncl) (EXISTS (asm,bvar) ant_thm) in
let imp2 = DISCH cncl (GEN bvar (DISCH ant th2)) in
IMP_ANTISYM_RULE imp1 imp2
else
if fconseq
then
let imp1 = DISCH ant(GEN bvar(UNDISCH(SPEC bvar tm_thm))) in
let cncl = concl imp1 in
let imp2 = GEN bvar(DISCH ant(SPEC bvar(UNDISCH(ASSUME cncl)))) in
IMP_ANTISYM_RULE (DISCH tm imp1) (DISCH cncl imp2)
else
let asm = mk_exists(bvar,ant) in
let tmp = UNDISCH (SPEC bvar tm_thm) in
let th1 = GEN bvar (CHOOSE(bvar,ASSUME asm) tmp) in
let imp1 = DISCH tm (DISCH asm th1) in
let cncl = rand(concl imp1) in
let th2 = SPEC bvar (MP(ASSUME cncl) (EXISTS (asm,bvar) ant_thm)) in
let imp2 = DISCH cncl (GEN bvar (DISCH ant th2)) in
IMP_ANTISYM_RULE imp1 imp2
let LEFT_IMP_EXISTS_CONV tm =
let ant, _ = dest_imp tm in
let bvar,bdy = dest_exists ant in
let x' = variant (frees tm) bvar in
let t' = subst [x',bvar] bdy in
let th1 = GEN x' (DISCH t'(MP(ASSUME tm)(EXISTS(ant,x')(ASSUME t')))) in
let rtm = concl th1 in
let th2 = CHOOSE (x',ASSUME ant) (UNDISCH(SPEC x'(ASSUME rtm))) in
IMP_ANTISYM_RULE (DISCH tm th1) (DISCH rtm (DISCH ant th2))
(*********** terms **************)
let lrand x = rand (rator x)
let t_tm = `T`;;
let f_tm = `F`;;
let is_T tm = (tm = t_tm)
let is_F tm = (tm = f_tm)
(************ HOL **************)
let rec ERC lt tm =
if is_comb lt
then
let ((ltl,ltr),(tml,tmr)) =
pair_map dest_comb (lt,tm) in
(ERC ltl tml)@(ERC ltr tmr)
else
if is_var lt
then [(tm,lt)]
else []
(* easier REWR_CONV which assumes that the supplied theorem is ground and quantifier free,
so type instantiation and var capture checks are not needed *)
(* no restrictions on the term argument *)
let EREWR_CONV th tm =
let lt = lhs(concl th) in
let il = ERC lt tm in
INST il th
|