hol88-contrib-source 2.02.19940316-35 / usr / share / hol88-2.02.19940316 / contrib / int / useful.ml

This file is indexed.

/usr/share/hol88-2.02.19940316/contrib/int/useful.ml is in hol88-contrib-source 2.02.19940316-35.

This file is owned by root:root, with mode 0o644.

The actual contents of the file can be viewed below. 

  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
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
%============================================================================%
% Various useful tactics, conversions etc.                                   %
%============================================================================%

timer true;;

%----------------------------------------------------------------------------%
% Applies a conversion to the left-hand operand of a binary operator         %
%----------------------------------------------------------------------------%

let LAND_CONV = RATOR_CONV o RAND_CONV;;

%----------------------------------------------------------------------------%
% Proves tautologies: handy for propositional lemmas                         %
%----------------------------------------------------------------------------%

let TAUT_CONV =
  let val w t = type_of t = ":bool" & can (find_term is_var) t & free_in t w in
  C (curry prove)
  (REPEAT GEN_TAC THEN (REPEAT o CHANGED_TAC o W)
   (C $THEN (REWRITE_TAC[]) o BOOL_CASES_TAC o hd o sort (uncurry free_in) o
    W(find_terms o val) o snd));;

%----------------------------------------------------------------------------%
% More concise way to get an AC rewrite lemma                                %
%----------------------------------------------------------------------------%

let AC thp tm = EQT_ELIM(AC_CONV thp tm);;

%----------------------------------------------------------------------------%
% GEN_PAIR_TAC - Like GEN_TAC but "pairs" the relevant variable              %
%----------------------------------------------------------------------------%

let GEN_PAIR_TAC =
  W($THEN GEN_TAC o SUBST1_TAC o SYM o
    C ISPEC PAIR o fst o dest_forall o snd);;

%----------------------------------------------------------------------------%
% MK_COMB_TAC - reduces ?- f x = g y to ?- f = g and ?- x = y                %
%----------------------------------------------------------------------------%

let MK_COMB_TAC : tactic (asl,w) =
  let l,r = dest_eq w in
  let l1,l2 = dest_comb l and r1,r2 = dest_comb r in
  ([(asl,mk_eq(l1,r1)); (asl,mk_eq(l2,r2))],end_itlist (curry MK_COMB));;

%----------------------------------------------------------------------------%
% BINOP_TAC - reduces "$op x y = $op u v" to "x = u" and "y = v"             %
%----------------------------------------------------------------------------%

let BINOP_TAC =
  MK_COMB_TAC THENL [AP_TERM_TAC; ALL_TAC];;

%----------------------------------------------------------------------------%
% SYM_CANON_CONV - Canonicalizes single application of symmetric operator    %
% Rewrites "so as to make fn true", e.g. fn = $<< or fn = curry$= "1" o fst  %
%----------------------------------------------------------------------------%

let SYM_CANON_CONV sym fn =
  REWR_CONV sym o assert ($not o fn o ((snd o dest_comb) # I) o dest_comb);;

%----------------------------------------------------------------------------%
% IMP_SUBST_TAC - Implicational substitution for deepest matchable term      %
%----------------------------------------------------------------------------%

let IMP_SUBST_TAC th :tactic (asl,w) =
  let tms = find_terms (can (PART_MATCH (lhs o snd o dest_imp) th)) w in
  let tm1 = hd (sort (uncurry free_in) tms) in
  let th1 = PART_MATCH (lhs o snd o dest_imp) th tm1 in
  let (a,(l,r)) = (I # dest_eq) (dest_imp (concl th1)) in
  let gv = genvar (type_of l) in
  let pat = subst[(gv,l)] w in
  ([(asl,a); (asl,subst[(r,gv)] pat)],
   \[t1;t2]. SUBST[(SYM(MP th1 t1),gv)] pat t2);;

%----------------------------------------------------------------------------%
% Tactic to introduce an abbreviation                                        %
%                                                                            %
% N.B. Just "ABBREV_TAC = CHOOSE_TAC o DEF_EXISTS_RULE" doesn't work if RHS  %
% has free variables.                                                        %
%----------------------------------------------------------------------------%

let ABBREV_TAC tm =
  let v,t = dest_eq tm in
  CHOOSE_THEN (\th. SUBST_ALL_TAC th THEN ASSUME_TAC th)
              (EXISTS(mk_exists(v,mk_eq(t,v)),t) (REFL t));;

%---------------------------------------------------------------%
% EXT_CONV "!x. f x = g x" = |- (!x. f x = g x) = (f = g)       %
%---------------------------------------------------------------%

let EXT_CONV =  SYM o uncurry X_FUN_EQ_CONV o
      (I # (mk_eq o (rator # rator) o dest_eq)) o dest_forall;;

%----------------------------------------------------------------------------%
%   (\x. s[x]) = (\y. t[y])                                                  %
%  ========================= ABS_TAC                                         %
%         s[x] = t[x]                                                        %
%----------------------------------------------------------------------------%

let ABS_TAC (asl,w) =
  (let l,r = dest_eq w in
   let v1,b1 = dest_abs l
   and v2,b2 = dest_abs r in
   let v = variant (freesl (w.asl)) v1 in
   let subg = mk_eq(subst[v,v1] b1,subst[v,v2] b2) in
   ([asl,subg],CONV_RULE(LAND_CONV(ALPHA_CONV v1)) o
               CONV_RULE(RAND_CONV(ALPHA_CONV v2)) o ABS v o hd))
  ? failwith `ABS_TAC`;;

%----------------------------------------------------------------------------%
% EQUAL_TAC - Strip down to unequal core (usually too enthusiastic)          %
%----------------------------------------------------------------------------%

let EQUAL_TAC = REPEAT(FIRST [AP_TERM_TAC; AP_THM_TAC; ABS_TAC]);;

%----------------------------------------------------------------------------%
% X_BETA_CONV "v" "tm[v]" = |- tm[v] = (\v. tm[v]) v                         %
%----------------------------------------------------------------------------%

let X_BETA_CONV v tm =
  SYM(BETA_CONV(mk_comb(mk_abs(v,tm),v)));;

%----------------------------------------------------------------------------%
% EXACT_CONV - Rewrite with theorem matching exactly one in a list           %
%----------------------------------------------------------------------------%

let EXACT_CONV =
  ONCE_DEPTH_CONV o FIRST_CONV o
  map (\t. K t o assert(curry$=(lhs(concl t))));;

%----------------------------------------------------------------------------%
% Rather ad-hoc higher-order fiddling conversion                             %
% |- (\x. f t1[x] ... tn[x]) = (\x. f ((\x. t1[x]) x) ... ((\x. tn[x]) x))   %
%----------------------------------------------------------------------------%

let HABS_CONV tm =
  let v,bod = dest_abs tm in
  let hop,pl = strip_comb bod in
  let eql = rev(map (X_BETA_CONV v) pl) in
  ABS v (itlist (C(curry MK_COMB)) eql (REFL hop));;

%----------------------------------------------------------------------------%
% autoload_definitions - Substitute for load_definitions                     %
%----------------------------------------------------------------------------%

let autoload_definitions thy =
  do map (\s. autoload_theory(`definition`,thy,fst s)) (definitions thy);;

%----------------------------------------------------------------------------%
% autoload_theorems - Substitute for load_theorems                           %
%----------------------------------------------------------------------------%

let autoload_theorems thy =
  do map (\s. autoload_theory(`theorem`,thy,fst s)) (theorems thy);;

%----------------------------------------------------------------------------%
% Expand an abbreviation                                                     %
%----------------------------------------------------------------------------%

let EXPAND_TAC s = FIRST_ASSUM(SUBST1_TAC o SYM o
  assert(curry$= s o fst o dest_var o rhs o concl)) THEN BETA_TAC;;

APT Browse - Built by Thomas Orozco.