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% HOL 88 Version 2.0 %
% %
% FILE NAME: tacont.ml %
% %
% DESCRIPTION: Theorem continuations %
% AUTHOR: Larry Paulson %
% %
% USES FILES: basic-hol lisp files, bool.th, genfns.ml, hol-syn.ml, %
% hol-rule.ml, hol-drule.ml, drul.ml, tacticals.ml %
% %
% University of Cambridge %
% Hardware Verification Group %
% Computer Laboratory %
% New Museums Site %
% Pembroke Street %
% Cambridge CB2 3QG %
% England %
% %
% COPYRIGHT: University of Edinburgh %
% COPYRIGHT: University of Cambridge %
% COPYRIGHT: INRIA %
% %
% REVISION HISTORY: Revised for HOL by MJCG %
%=============================================================================%
% Many inference rules, particularly those involving disjunction and %
% existential quantifiers, produce intermediate results that are needed %
% only briefly. One approach is to treat the assumption list like a %
% stack, pushing and popping theorems from it. However, it is %
% traditional to regard the assumptions as unordered; also, stack %
% operations are crude. %
% %
% Instead, we adopt a continuation approach: a continuation is a %
% function that maps theorems to tactics. It can put the theorem on %
% the assumption list, produce a case split, throw it away, etc. The %
% text of a large theorem continuation should be a readable description %
% of the flow of inference. %
% %
% Must be compiled in the presence of the hol parser/pretty printer %
% This loads genfns.ml and hol-syn.ml too. %
% Also load hol-rule.ml, hol-drule.ml, drul.ml, tacticals.ml %
if compiling then (loadf `ml/hol-in-out`;
loadf `ml/hol-rule`;
loadf `ml/hol-drule`;
loadf `ml/drul`;
loadf `ml/tacticals`);;
lettype thm_tactic = thm -> tactic;;
lettype thm_tactical = thm_tactic -> thm_tactic;;
ml_curried_infix `THEN_TCL`;;
ml_curried_infix `ORELSE_TCL`;;
let $THEN_TCL (ttcl1: thm_tactical) (ttcl2: thm_tactical) ttac =
ttcl1 (ttcl2 ttac) ;;
let $ORELSE_TCL (ttcl1: thm_tactical) (ttcl2: thm_tactical) ttac th =
(ttcl1 ttac th) ? (ttcl2 ttac th);;
letrec REPEAT_TCL (ttcl: thm_tactical) ttac th =
((ttcl THEN_TCL (REPEAT_TCL ttcl)) ORELSE_TCL I) ttac th;;
% --------------------------------------------------------------------- %
% New version of REPEAT for ttcl's. Designed for use with IMP_RES_THEN.%
% TFM 91.01.20. %
% --------------------------------------------------------------------- %
letrec REPEAT_GTCL (ttcl: thm_tactical) ttac th (A,g) =
ttcl (REPEAT_GTCL ttcl ttac) th (A,g) ? ttac th (A,g);;
let ALL_THEN : thm_tactical = I;;
let NO_THEN : thm_tactical = \ttac th. failwith `NO_THEN`;;
%
Uses every theorem tactical.
EVERY_TCL [ttcl1;...;ttcln] = ttcl1 THEN_TCL ... THEN_TCL ttcln
%
let EVERY_TCL ttcll = itlist $THEN_TCL ttcll ALL_THEN;;
%
Uses first successful theorem tactical.
FIRST_TCL [ttcl1;...;ttcln] = ttcl1 ORELSE_TCL ... ORELSE_TCL ttcln
%
let FIRST_TCL ttcll = itlist $ORELSE_TCL ttcll NO_THEN;;
%
Conjunction elimination
C
============== |- A1 /\ A2
C
===== ttac1 |-A1
...
===== ttac2 |-A2
...
%
let CONJUNCTS_THEN2 (ttac1: thm_tactic) ttac2 cth : tactic =
let th1,th2 = CONJ_PAIR cth ? failwith `CONJUNCTS_THEN2` in
ttac1 th1 THEN ttac2 th2;;
let CONJUNCTS_THEN ttac = CONJUNCTS_THEN2 ttac ttac;;
%
Disjunction elimination
C
============================= |- A1 \/ A2
C C
===== ttac1 A1|-A1 ===== ttac2 A2|-A2
... ...
%
% -------------------------------------------------------------------------- %
% REVISED 22 Oct 1992 by TFM. Bugfix. %
% %
% The problem was, for example: %
% %
% th = |- ?n. ((?n. n = SUC 0) \/ F) /\ (n = 0) %
% set_goal ([], "F");; %
% expandf (STRIP_ASSUME_TAC th);; %
% OK.. %
% "F" %
% [ "n = SUC 0" ] (n.b. should be n') %
% [ "n = 0" ] %
% %
% let DISJ_CASES_THEN2 ttac1 ttac2 disth :tactic = %
% let a1,a2 = dest_disj (concl disth) ? failwith `DISJ_CASES_THEN2` in %
% \(asl,w). %
% let gl1,prf1 = ttac1 (ASSUME a1) (asl,w) %
% and gl2,prf2 = ttac2 (ASSUME a2) (asl,w) %
% in %
% gl1 @ gl2, %
% \thl. let thl1,thl2 = chop_list (length gl1) thl in %
% DISJ_CASES disth (prf1 thl1) (prf2 thl2);; %
% -------------------------------------------------------------------------- %
let DISJ_CASES_THEN2 ttac1 ttac2 disth :tactic =
let a1,a2 = dest_disj (concl disth) ? failwith `DISJ_CASES_THEN2` in
\(asl,w).
let gl1,prf1 = ttac1 (itlist ADD_ASSUM (hyp disth) (ASSUME a1)) (asl,w)
and gl2,prf2 = ttac2 (itlist ADD_ASSUM (hyp disth) (ASSUME a2)) (asl,w)
in
gl1 @ gl2,
\thl. let thl1,thl2 = chop_list (length gl1) thl in
DISJ_CASES disth (prf1 thl1) (prf2 thl2);;
%Single-, multi-tactic versions%
let DISJ_CASES_THEN ttac = DISJ_CASES_THEN2 ttac ttac;;
let DISJ_CASES_THENL = end_itlist DISJ_CASES_THEN2;;
%
Implication introduction
A ==> B
==============
B
============== ttac |-A
. . .
%
% DISCH changed to NEG_DISCH for HOL %
% Deleted: TFM 88.03.31 %
% %
% let DISCH_THEN ttac :tactic (asl,w) = %
% let ante,conc = dest_imp w ? failwith `DISCH_THEN` in %
% let gl,prf = ttac (ASSUME ante) (asl,conc) in %
% gl, (NEG_DISCH ante) o prf;; %
% Added: TFM 88.03.31 (bug fix) %
let DISCH_THEN ttac :tactic (asl,w) =
let ante,conc = dest_neg_imp w ? failwith `DISCH_THEN` in
let gl,prf = ttac (ASSUME ante) (asl,conc) in
gl, (if is_neg w then NEG_DISCH ante else DISCH ante) o prf;;
% --------------------------------------------------------------------- %
% If-and-only-iff elimination DELETED [TFM 91.01.20] %
% %
% C %
% ============== |- A1 <=> A2 %
% C %
% ===== ttac1 |-A1==>A2 %
% ... %
% ===== ttac2 |-A2==>A1 %
% ... %
% %
% let IFF_THEN2 (ttac1: thm_tactic) ttac2 iffth : tactic = %
% let th1,th2 = CONJ_PAIR (IFF_CONJ iffth) ? failwith `IFF_THEN2` in %
% ttac1 th1 THEN ttac2 th2;; %
% %
% let IFF_THEN ttac = IFF_THEN2 ttac ttac;; %
% --------------------------------------------------------------------- %
%
Existential elimination
B
================== |- ?x. A(x)
B
================== ttac A(y)
...
explicit version for tactic programming
%
let X_CHOOSE_THEN y ttac xth :tactic =
let x,body = dest_exists (concl xth) ? failwith `X_CHOOSE_THEN` in
\(asl,w).
let th = itlist ADD_ASSUM (hyp xth) (ASSUME (subst [y,x] body)) in
let gl,prf = ttac th (asl,w) in
gl, (CHOOSE (y, xth)) o prf;;
% chooses a variant for the user %
let CHOOSE_THEN ttac xth :tactic =
let x,body = dest_exists (concl xth) ? failwith `CHOOSE_THEN` in
\(asl,w).
let y = variant ((thm_frees xth) @ (freesl (w.asl))) x in
X_CHOOSE_THEN y ttac xth (asl,w);;
%Cases tactics%
%for a generalized disjunction |-(?xl1.B1(xl1)) \/...\/ (?xln.Bn(xln))
where the xl1...xln are vectors of zero or more variables,
and the variables in each of yl1...yln have the same types as the
corresponding xli do
A
=============================================
A A
======= ttac1 |-B1(yl1) ... ======= ttacn |-Bn(yln)
... ...
%
let X_CASES_THENL varsl ttacl =
DISJ_CASES_THENL
(map (\(vars,ttac). EVERY_TCL (map X_CHOOSE_THEN vars) ttac)
(varsl com ttacl));;
%needed??? = X_CASES_THENL varsl (map (K ttac) varsl) %
let X_CASES_THEN varsl ttac =
DISJ_CASES_THENL
(map (\vars. EVERY_TCL (map X_CHOOSE_THEN vars) ttac) varsl);;
%Version that chooses the y's as variants of the x's%
let CASES_THENL ttacl =
DISJ_CASES_THENL (map (REPEAT_TCL CHOOSE_THEN) ttacl);;
%Tactical to strip off ONE disjunction, conjunction, or existential%
let STRIP_THM_THEN =
FIRST_TCL [CONJUNCTS_THEN; DISJ_CASES_THEN; CHOOSE_THEN];;
|