diff options
| -rw-r--r-- | proofs/signatures/Makefile.am | 7 | ||||
| -rwxr-xr-x | proofs/signatures/th_arrays.plf | 103 | ||||
| -rwxr-xr-x | proofs/signatures/th_quant.plf | 164 |
3 files changed, 138 insertions, 136 deletions
diff --git a/proofs/signatures/Makefile.am b/proofs/signatures/Makefile.am index 610990ba2..42ba48262 100644 --- a/proofs/signatures/Makefile.am +++ b/proofs/signatures/Makefile.am @@ -3,7 +3,7 @@ # add support for more theories, just list them here in the same order # you would to the LFSC proof-checker binary. # -CORE_PLFS = sat.plf smt.plf th_base.plf +CORE_PLFS = sat.plf smt.plf th_base.plf th_arrays.plf noinst_LTLIBRARIES = libsignatures.la @@ -31,4 +31,7 @@ signatures.cpp: $(CORE_PLFS) ) > $@ EXTRA_DIST = \ - example.plf + example.plf \ + example-arrays.plf \ + example-quant.plf \ + th_quant.plf diff --git a/proofs/signatures/th_arrays.plf b/proofs/signatures/th_arrays.plf index edb6dc96e..0c6b16048 100755 --- a/proofs/signatures/th_arrays.plf +++ b/proofs/signatures/th_arrays.plf @@ -1,52 +1,51 @@ -;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
-;
-; Theory of Arrays
-;
-;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
-; depdends on : th_base.plf
-
-; sorts
-
-(declare array (! s1 sort (! s2 sort sort))) ; s1 is index, s2 is element
-
-; functions
-(declare write (! s1 sort
- (! s2 sort
- (term (arrow (array s1 s2)
- (arrow s1
- (arrow s2 (array s1 s2))))))))
-
-(declare read (! s1 sort
- (! s2 sort
- (term (arrow (array s1 s2)
- (arrow s1 s2))))))
-
-; inference rules
-(declare row1 (! s1 sort
- (! s2 sort
- (! t1 (term (array s1 s2))
- (! t2 (term s1)
- (! t3 (term s2)
- (th_holds (= _ (apply _ _ (apply _ _ (read s1 s2) (apply _ _ (apply _ _ (apply _ _ (write s1 s2) t1) t2) t3)) t2)
- t3))))))))
-
-
-(declare row (! s1 sort
- (! s2 sort
- (! t2 (term s1)
- (! t3 (term s1)
- (! t1 (term (array s1 s2))
- (! t4 (term s2)
- (! u (th_holds (not (= _ t2 t3)))
- (th_holds (= _ (apply _ _ (apply _ _ (read s1 s2) (apply _ _ (apply _ _ (apply _ _ (write s1 s2) t1) t2) t4)) t3)
- (apply _ _ (apply _ _ (read s1 s2) t1) t3)))))))))))
-
-(declare ext (! s1 sort
- (! s2 sort
- (! t1 (term (array s1 s2))
- (! t2 (term (array s1 s2))
- (! u1 (! k (term s1)
- (! u2 (th_holds (or (= _ t1 t2) (not (= _ (apply _ _ (apply _ _ (read s1 s2) t1) k) (apply _ _ (apply _ _ (read s1 s2) t2) k)))))
- (holds cln)))
- (holds cln)))))))
-
\ No newline at end of file +;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; +; +; Theory of Arrays +; +;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; +; depdends on : th_base.plf + +; sorts + +(declare array (! s1 sort (! s2 sort sort))) ; s1 is index, s2 is element + +; functions +(declare write (! s1 sort + (! s2 sort + (term (arrow (array s1 s2) + (arrow s1 + (arrow s2 (array s1 s2)))))))) + +(declare read (! s1 sort + (! s2 sort + (term (arrow (array s1 s2) + (arrow s1 s2)))))) + +; inference rules +(declare row1 (! s1 sort + (! s2 sort + (! t1 (term (array s1 s2)) + (! t2 (term s1) + (! t3 (term s2) + (th_holds (= _ (apply _ _ (apply _ _ (read s1 s2) (apply _ _ (apply _ _ (apply _ _ (write s1 s2) t1) t2) t3)) t2) + t3)))))))) + + +(declare row (! s1 sort + (! s2 sort + (! t2 (term s1) + (! t3 (term s1) + (! t1 (term (array s1 s2)) + (! t4 (term s2) + (! u (th_holds (not (= _ t2 t3))) + (th_holds (= _ (apply _ _ (apply _ _ (read s1 s2) (apply _ _ (apply _ _ (apply _ _ (write s1 s2) t1) t2) t4)) t3) + (apply _ _ (apply _ _ (read s1 s2) t1) t3))))))))))) + +(declare ext (! s1 sort + (! s2 sort + (! t1 (term (array s1 s2)) + (! t2 (term (array s1 s2)) + (! u1 (! k (term s1) + (! u2 (th_holds (or (= _ t1 t2) (not (= _ (apply _ _ (apply _ _ (read s1 s2) t1) k) (apply _ _ (apply _ _ (read s1 s2) t2) k))))) + (holds cln))) + (holds cln))))))) diff --git a/proofs/signatures/th_quant.plf b/proofs/signatures/th_quant.plf index 98b53e43d..d85b2115c 100755 --- a/proofs/signatures/th_quant.plf +++ b/proofs/signatures/th_quant.plf @@ -1,82 +1,82 @@ -(declare forall (! s sort
- (! t (term s)
- (! f formula
- formula))))
-
-(program eqterm ((n1 term) (n2 term)) bool
- (do (markvar n1)
- (let s (ifmarked n2 tt ff)
- (do (markvar n1) s))))
-
-(program is_inst_t ((ti term) (t term) (k term)) bool
- (match t
- ((apply s1 s2 t1 t2)
- (match ti
- ((apply si1 si2 ti1 ti2) (match (is_inst_t ti1 t1 k) (tt (is_inst_t ti2 t2 k)) (ff ff)))
- (default ff)))
- (default
- (match ti
- ((apply si1 si2 ti1 ti2) ff)
- (default (eqterm ti (ifmarked t k t)))))))
-
-(program is_inst_f ((fi formula) (f formula) (k term)) bool
- (match f
- ((and f1 f2) (match fi
- ((and fi1 fi2) (match (is_inst_f fi1 f1 k) (tt (is_inst_f fi2 f2 k)) (ff ff)))
- (default ff)))
- ((or f1 f2) (match fi
- ((or fi1 fi2) (match (is_inst_f fi1 f1 k) (tt (is_inst_f fi2 f2 k)) (ff ff)))
- (default ff)))
- ((impl f1 f2) (match fi
- ((impl fi1 fi2) (match (is_inst_f fi1 f1 k) (tt (is_inst_f fi2 f2 k)) (ff ff)))
- (default ff)))
- ((not f1) (match fi
- ((not fi1) (is_inst_f fi1 f1 k))
- (default ff)))
- ((iff f1 f2) (match fi
- ((iff fi1 fi2) (match (is_inst_f fi1 f1 k) (tt (is_inst_f fi2 f2 k)) (ff ff)))
- (default ff)))
- ((xor f1 f2) (match fi
- ((xor fi1 fi2) (match (is_inst_f fi1 f1 k) (tt (is_inst_f fi2 f2 k)) (ff ff)))
- (default ff)))
- ((ifte f1 f2 f3) (match fi
- ((ifte fi1 fi2 fi3) (match (is_inst_f fi1 f1 k)
- (tt (match (is_inst_f fi2 f2 k) (tt (is_inst_f fi3 f3 k)) (ff ff)))
- (ff ff)))
- (default ff)))
- ((= s t1 t2) (match fi
- ((= s ti1 ti2) (match (is_inst_t ti1 t1 k) (tt (is_inst_t ti2 t2 k)) (ff ff)))
- (default ff)))
- ((forall s t1 f1) (match fi
- ((forall s ti1 fi1) (is_inst_f fi1 f1 k))
- (default ff)))
- (default ff)))
-
-(program is_inst ((fi formula) (f formula) (t term) (k term)) bool
- (do (markvar t)
- (let f1 (is_inst_f fi f k)
- (do (markvar t) f1))))
-
-(declare skolem
- (! s sort
- (! t (term s)
- (! f formula
- (! p (th_holds (not (forall s t f)))
- (! u (! k (term s)
- (! fi formula
- (! p1 (th_holds (not fi))
- (! r (^ (is_inst fi f t k) tt)
- (holds cln)))))
- (holds cln)))))))
-
-(declare inst
- (! s sort
- (! t (term s)
- (! f formula
- (! k (term s)
- (! fi formula
- (! p (th_holds (forall s t f))
- (! r (^ (is_inst fi f t k) tt)
- (! u (! p1 (th_holds fi)
- (holds cln))
- (holds cln))))))))))
\ No newline at end of file +(declare forall (! s sort + (! t (term s) + (! f formula + formula)))) + +(program eqterm ((n1 term) (n2 term)) bool + (do (markvar n1) + (let s (ifmarked n2 tt ff) + (do (markvar n1) s)))) + +(program is_inst_t ((ti term) (t term) (k term)) bool + (match t + ((apply s1 s2 t1 t2) + (match ti + ((apply si1 si2 ti1 ti2) (match (is_inst_t ti1 t1 k) (tt (is_inst_t ti2 t2 k)) (ff ff))) + (default ff))) + (default + (match ti + ((apply si1 si2 ti1 ti2) ff) + (default (eqterm ti (ifmarked t k t))))))) + +(program is_inst_f ((fi formula) (f formula) (k term)) bool + (match f + ((and f1 f2) (match fi + ((and fi1 fi2) (match (is_inst_f fi1 f1 k) (tt (is_inst_f fi2 f2 k)) (ff ff))) + (default ff))) + ((or f1 f2) (match fi + ((or fi1 fi2) (match (is_inst_f fi1 f1 k) (tt (is_inst_f fi2 f2 k)) (ff ff))) + (default ff))) + ((impl f1 f2) (match fi + ((impl fi1 fi2) (match (is_inst_f fi1 f1 k) (tt (is_inst_f fi2 f2 k)) (ff ff))) + (default ff))) + ((not f1) (match fi + ((not fi1) (is_inst_f fi1 f1 k)) + (default ff))) + ((iff f1 f2) (match fi + ((iff fi1 fi2) (match (is_inst_f fi1 f1 k) (tt (is_inst_f fi2 f2 k)) (ff ff))) + (default ff))) + ((xor f1 f2) (match fi + ((xor fi1 fi2) (match (is_inst_f fi1 f1 k) (tt (is_inst_f fi2 f2 k)) (ff ff))) + (default ff))) + ((ifte f1 f2 f3) (match fi + ((ifte fi1 fi2 fi3) (match (is_inst_f fi1 f1 k) + (tt (match (is_inst_f fi2 f2 k) (tt (is_inst_f fi3 f3 k)) (ff ff))) + (ff ff))) + (default ff))) + ((= s t1 t2) (match fi + ((= s ti1 ti2) (match (is_inst_t ti1 t1 k) (tt (is_inst_t ti2 t2 k)) (ff ff))) + (default ff))) + ((forall s t1 f1) (match fi + ((forall s ti1 fi1) (is_inst_f fi1 f1 k)) + (default ff))) + (default ff))) + +(program is_inst ((fi formula) (f formula) (t term) (k term)) bool + (do (markvar t) + (let f1 (is_inst_f fi f k) + (do (markvar t) f1)))) + +(declare skolem + (! s sort + (! t (term s) + (! f formula + (! p (th_holds (not (forall s t f))) + (! u (! k (term s) + (! fi formula + (! p1 (th_holds (not fi)) + (! r (^ (is_inst fi f t k) tt) + (holds cln))))) + (holds cln))))))) + +(declare inst + (! s sort + (! t (term s) + (! f formula + (! k (term s) + (! fi formula + (! p (th_holds (forall s t f)) + (! r (^ (is_inst fi f t k) tt) + (! u (! p1 (th_holds fi) + (holds cln)) + (holds cln)))))))))) |