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%****************************************************************************%
% FILE : thm_convs.ml %
% DESCRIPTION : Conversions for rewriting with arithmetic theorems. %
% %
% READS FILES : <none> %
% WRITES FILES : <none> %
% %
% AUTHOR : R.J.Boulton %
% DATE : 4th March 1991 %
% %
% LAST MODIFIED : R.J.Boulton %
% DATE : 8th October 1992 %
%****************************************************************************%
%============================================================================%
% Conversions for rewriting Boolean terms %
%============================================================================%
CONJ_ASSOC_NORM_CONV := REWR_CONV (GSYM CONJ_ASSOC);;
DISJ_ASSOC_NORM_CONV := REWR_CONV (GSYM DISJ_ASSOC);;
EQ_EXPAND_CONV := REWR_CONV EQ_EXPAND;;
IMP_EXPAND_CONV := REWR_CONV IMP_DISJ_THM;;
IMP_F_EQ_F_CONV := REWR_CONV IMP_F_EQ_F;;
IMP_IMP_CONJ_IMP_CONV := REWR_CONV AND_IMP_INTRO;;
LEFT_DIST_NORM_CONV := REWR_CONV LEFT_AND_OVER_OR;;
NOT_CONJ_NORM_CONV :=
REWR_CONV
(GEN_ALL (CONJUNCT1 (SPECL ["t1:bool";"t2:bool"] DE_MORGAN_THM)));;
NOT_DISJ_NORM_CONV :=
REWR_CONV
(GEN_ALL (CONJUNCT2 (SPECL ["t1:bool";"t2:bool"] DE_MORGAN_THM)));;
NOT_NOT_NORM_CONV := REWR_CONV (CONJUNCT1 NOT_CLAUSES);;
OR_F_CONV := REWR_CONV (el 3 (CONJUNCTS (SPEC "x:bool" OR_CLAUSES)));;
RIGHT_DIST_NORM_CONV := REWR_CONV RIGHT_AND_OVER_OR;;
%============================================================================%
% Conversions for rewriting arithmetic terms %
%============================================================================%
ADD_ASSOC_CONV := REWR_CONV (theorem `arithmetic` `ADD_ASSOC`);;
ADD_SYM_CONV := REWR_CONV (theorem `arithmetic` `ADD_SYM`);;
GATHER_BOTH_CONV :=
REWR_CONV
(SYM (SPECL ["a:num";"b:num";"x:num"]
(theorem `arithmetic` `RIGHT_ADD_DISTRIB`)));;
GATHER_LEFT_CONV :=
REWR_CONV
(SUBS [el 3 (CONJUNCTS (SPECL ["x:num";"n:num"]
(theorem `arithmetic` `MULT_CLAUSES`)))]
(SYM (SPECL ["a:num";"1";"x:num"]
(theorem `arithmetic` `RIGHT_ADD_DISTRIB`))));;
GATHER_NEITHER_CONV := REWR_CONV (GSYM (theorem `arithmetic` `TIMES2`));;
GATHER_RIGHT_CONV :=
REWR_CONV
(SUBS [el 3 (CONJUNCTS (SPECL ["x:num";"n:num"]
(theorem `arithmetic` `MULT_CLAUSES`)))]
(SYM (SPECL ["1";"b:num";"x:num"]
(theorem `arithmetic` `RIGHT_ADD_DISTRIB`))));;
GEQ_NORM_CONV := REWR_CONV (theorem `arithmetic` `GREATER_EQ`);;
GREAT_NORM_CONV :=
REWR_CONV
(SUBS [SYM (SPECL ["m:num";"n:num"] (definition `arithmetic` `GREATER`));
SPEC "n:num" (theorem `arithmetic` `SUC_ONE_ADD`)]
(SPECL ["n:num";"m:num"] (theorem `arithmetic` `LESS_EQ`)));;
LEFT_ADD_DISTRIB_CONV := REWR_CONV (theorem `arithmetic` `LEFT_ADD_DISTRIB`);;
LESS_NORM_CONV :=
REWR_CONV
(SUBS [SPEC "m:num" (theorem `arithmetic` `SUC_ONE_ADD`)]
(SPECL ["m:num";"n:num"] (theorem `arithmetic` `LESS_EQ`)));;
MULT_ASSOC_CONV := REWR_CONV (theorem `arithmetic` `MULT_ASSOC`);;
MULT_COMM_CONV := REWR_CONV MULT_COMM;;
NOT_GEQ_NORM_CONV :=
REWR_CONV
(SUBS [SPEC "m:num" (theorem `arithmetic` `SUC_ONE_ADD`)]
(SPECL ["m:num";"n:num"] (theorem `arithmetic` `NOT_GREATER_EQ`)));;
NOT_GREAT_NORM_CONV := REWR_CONV (theorem `arithmetic` `NOT_GREATER`);;
NOT_LEQ_NORM_CONV :=
REWR_CONV
(SUBS [SPEC "n:num" (theorem `arithmetic` `SUC_ONE_ADD`)]
(SPECL ["m:num";"n:num"] (theorem `arithmetic` `NOT_LEQ`)));;
NOT_LESS_NORM_CONV := REWR_CONV (theorem `arithmetic` `NOT_LESS`);;
NOT_NUM_EQ_NORM_CONV :=
REWR_CONV
(SUBS [SPEC "m:num" (theorem `arithmetic` `SUC_ONE_ADD`);
SPEC "n:num" (theorem `arithmetic` `SUC_ONE_ADD`)]
(SPECL ["m:num";"n:num"] (theorem `arithmetic` `NOT_NUM_EQ`)));;
NUM_EQ_NORM_CONV := REWR_CONV (theorem `arithmetic` `EQ_LESS_EQ`);;
PLUS_ZERO_CONV := REWR_CONV PLUS_ZERO;;
SYM_ADD_ASSOC_CONV := REWR_CONV (GSYM (theorem `arithmetic` `ADD_ASSOC`));;
SYM_ONE_MULT_CONV := REWR_CONV (GEN_ALL (SYM (SPEC_ALL ONE_MULT)));;
ZERO_MULT_CONV := REWR_CONV ZERO_MULT;;
ZERO_MULT_PLUS_CONV :=
REWR_CONV
(SUBS [SYM (CONJUNCT1
(SPECL ["a:num";"b:num"] (theorem `arithmetic` `MULT_CLAUSES`)))]
(SPEC "b:num" (GEN_ALL (CONJUNCT1 (theorem `arithmetic` `ADD_CLAUSES`)))));;
ZERO_PLUS_CONV := REWR_CONV ZERO_PLUS;;
%============================================================================%
% Conversions for rewriting inequalities %
%============================================================================%
LEQ_PLUS_CONV := REWR_CONV (theorem `arithmetic` `ADD_MONO_LESS_EQ`);;
%============================================================================%
% Conversions for final simplification %
%============================================================================%
FORALL_SIMP_CONV := REWR_CONV FORALL_SIMP;;
%============================================================================%
% Conversions for normalising and eliminating subtraction %
%============================================================================%
NUM_COND_RATOR_CONV := REWR_CONV (INST_TYPE [":num",":*"] COND_RATOR);;
NUM_COND_RAND_CONV := REWR_CONV (INST_TYPE [":num",":*"] COND_RAND);;
SUB_NORM_CONV :=
let REWRITES_CONV thl =
let net = mk_conv_net thl
in \tm. FIRST_CONV (lookup_term net tm) tm
in
(REWRITES_CONV o (map (theorem `arithmetic`)))
[`SUB_LEFT_ADD`; `SUB_RIGHT_ADD`;
`SUB_LEFT_SUB`; `SUB_RIGHT_SUB`;
`LEFT_SUB_DISTRIB`; `RIGHT_SUB_DISTRIB`;
`SUB_LEFT_SUC`;
`SUB_LEFT_LESS_EQ`; `SUB_RIGHT_LESS_EQ`;
`SUB_LEFT_LESS`; `SUB_RIGHT_LESS`;
`SUB_LEFT_GREATER_EQ`; `SUB_RIGHT_GREATER_EQ`;
`SUB_LEFT_GREATER`; `SUB_RIGHT_GREATER`;
`SUB_LEFT_EQ`; `SUB_RIGHT_EQ`
];;
%============================================================================%
% Conversions for normalising and eliminating conditionals %
%============================================================================%
COND_RATOR_CONV := REWR_CONV COND_RATOR;;
COND_RAND_CONV := REWR_CONV COND_RAND;;
COND_EXPAND_CONV := REWR_CONV COND_EXPAND;;
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