author | haftmann |
Tue, 03 Feb 2009 16:50:40 +0100 | |
changeset 29787 | 23bf900a21db |
parent 24584 | 01e83ffa6c54 |
child 29823 | 0ab754d13ccd |
permissions | -rw-r--r-- |
24584 | 1 |
(* Title: HOL/Tools/Qelim/generated_cooper.ML |
23689
0410269099dc
replaced code generator framework for reflected cooper
haftmann
parents:
23466
diff
changeset
|
2 |
|
29787 | 3 |
This file is generated from HOL/Reflection/Cooper.thy. DO NOT EDIT. |
23689
0410269099dc
replaced code generator framework for reflected cooper
haftmann
parents:
23466
diff
changeset
|
4 |
*) |
0410269099dc
replaced code generator framework for reflected cooper
haftmann
parents:
23466
diff
changeset
|
5 |
|
0410269099dc
replaced code generator framework for reflected cooper
haftmann
parents:
23466
diff
changeset
|
6 |
structure GeneratedCooper = |
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struct |
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type 'a eq = {eq : 'a -> 'a -> bool}; |
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fun eq (A_:'a eq) = #eq A_; |
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val eq_nat = {eq = (fn a => fn b => ((a : IntInf.int) = b))} : IntInf.int eq; |
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fun eqop A_ a b = eq A_ a b; |
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fun divmod n m = (if eqop eq_nat m 0 then (0, n) else IntInf.divMod (n, m)); |
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fun snd (a, y) = y; |
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fun mod_nat m n = snd (divmod m n); |
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fun gcd m n = (if eqop eq_nat n 0 then m else gcd n (mod_nat m n)); |
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fun fst (y, b) = y; |
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fun div_nat m n = fst (divmod m n); |
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fun lcm m n = div_nat (IntInf.* (m, n)) (gcd m n); |
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fun leta s f = f s; |
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fun suc n = IntInf.+ (n, 1); |
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datatype num = Mul of IntInf.int * num | Sub of num * num | Add of num * num | |
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Neg of num | Cn of IntInf.int * IntInf.int * num | Bound of IntInf.int | |
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C of IntInf.int; |
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||
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datatype fm = NClosed of IntInf.int | Closed of IntInf.int | A of fm | E of fm | |
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Iff of fm * fm | Imp of fm * fm | Or of fm * fm | And of fm * fm | Not of fm | |
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NDvd of IntInf.int * num | Dvd of IntInf.int * num | NEq of num | Eq of num | |
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Ge of num | Gt of num | Le of num | Lt of num | F | T; |
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fun abs_int i = (if IntInf.< (i, (0 : IntInf.int)) then IntInf.~ i else i); |
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fun zlcm i j = |
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(lcm (IntInf.max (0, (abs_int i))) (IntInf.max (0, (abs_int j)))); |
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fun map f [] = [] |
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| map f (x :: xs) = f x :: map f xs; |
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fun append [] y = y |
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| append (x :: xs) ys = x :: append xs ys; |
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fun disjuncts (Or (p, q)) = append (disjuncts p) (disjuncts q) |
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| disjuncts F = [] |
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| disjuncts T = [T] |
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| disjuncts (Lt u) = [Lt u] |
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| disjuncts (Le v) = [Le v] |
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| disjuncts (Gt w) = [Gt w] |
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| disjuncts (Ge x) = [Ge x] |
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| disjuncts (Eq y) = [Eq y] |
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| disjuncts (NEq z) = [NEq z] |
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| disjuncts (Dvd (aa, ab)) = [Dvd (aa, ab)] |
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| disjuncts (NDvd (ac, ad)) = [NDvd (ac, ad)] |
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| disjuncts (Not ae) = [Not ae] |
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| disjuncts (And (af, ag)) = [And (af, ag)] |
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| disjuncts (Imp (aj, ak)) = [Imp (aj, ak)] |
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| disjuncts (Iff (al, am)) = [Iff (al, am)] |
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| disjuncts (E an) = [E an] |
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| disjuncts (A ao) = [A ao] |
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| disjuncts (Closed ap) = [Closed ap] |
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| disjuncts (NClosed aq) = [NClosed aq]; |
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fun fm_case f1 f2 f3 f4 f5 f6 f7 f8 f9 f10 f11 f12 f13 f14 f15 f16 f17 f18 f19 |
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(NClosed nat) = f19 nat |
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| fm_case f1 f2 f3 f4 f5 f6 f7 f8 f9 f10 f11 f12 f13 f14 f15 f16 f17 f18 f19 |
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(Closed nat) = f18 nat |
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| fm_case f1 f2 f3 f4 f5 f6 f7 f8 f9 f10 f11 f12 f13 f14 f15 f16 f17 f18 f19 |
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(A fm) = f17 fm |
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| fm_case f1 f2 f3 f4 f5 f6 f7 f8 f9 f10 f11 f12 f13 f14 f15 f16 f17 f18 f19 |
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(E fm) = f16 fm |
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| fm_case f1 f2 f3 f4 f5 f6 f7 f8 f9 f10 f11 f12 f13 f14 f15 f16 f17 f18 f19 |
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(Iff (fm1, fm2)) = f15 fm1 fm2 |
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| fm_case f1 f2 f3 f4 f5 f6 f7 f8 f9 f10 f11 f12 f13 f14 f15 f16 f17 f18 f19 |
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(Imp (fm1, fm2)) = f14 fm1 fm2 |
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| fm_case f1 f2 f3 f4 f5 f6 f7 f8 f9 f10 f11 f12 f13 f14 f15 f16 f17 f18 f19 |
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(Or (fm1, fm2)) = f13 fm1 fm2 |
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| fm_case f1 f2 f3 f4 f5 f6 f7 f8 f9 f10 f11 f12 f13 f14 f15 f16 f17 f18 f19 |
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(And (fm1, fm2)) = f12 fm1 fm2 |
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| fm_case f1 f2 f3 f4 f5 f6 f7 f8 f9 f10 f11 f12 f13 f14 f15 f16 f17 f18 f19 |
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(Not fm) = f11 fm |
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| fm_case f1 f2 f3 f4 f5 f6 f7 f8 f9 f10 f11 f12 f13 f14 f15 f16 f17 f18 f19 |
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(NDvd (inta, num)) = f10 inta num |
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| fm_case f1 f2 f3 f4 f5 f6 f7 f8 f9 f10 f11 f12 f13 f14 f15 f16 f17 f18 f19 |
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(Dvd (inta, num)) = f9 inta num |
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| fm_case f1 f2 f3 f4 f5 f6 f7 f8 f9 f10 f11 f12 f13 f14 f15 f16 f17 f18 f19 |
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(NEq num) = f8 num |
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| fm_case f1 f2 f3 f4 f5 f6 f7 f8 f9 f10 f11 f12 f13 f14 f15 f16 f17 f18 f19 |
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(Eq num) = f7 num |
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| fm_case f1 f2 f3 f4 f5 f6 f7 f8 f9 f10 f11 f12 f13 f14 f15 f16 f17 f18 f19 |
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(Ge num) = f6 num |
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| fm_case f1 f2 f3 f4 f5 f6 f7 f8 f9 f10 f11 f12 f13 f14 f15 f16 f17 f18 f19 |
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(Gt num) = f5 num |
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| fm_case f1 f2 f3 f4 f5 f6 f7 f8 f9 f10 f11 f12 f13 f14 f15 f16 f17 f18 f19 |
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(Le num) = f4 num |
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| fm_case f1 f2 f3 f4 f5 f6 f7 f8 f9 f10 f11 f12 f13 f14 f15 f16 f17 f18 f19 |
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(Lt num) = f3 num |
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| fm_case f1 y f3 f4 f5 f6 f7 f8 f9 f10 f11 f12 f13 f14 f15 f16 f17 f18 f19 F |
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= y |
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| fm_case y f2 f3 f4 f5 f6 f7 f8 f9 f10 f11 f12 f13 f14 f15 f16 f17 f18 f19 T |
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= y; |
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fun eq_num (Mul (cb, dc)) (Sub (ae, be)) = false |
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| eq_num (Mul (cb, dc)) (Add (ae, be)) = false |
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| eq_num (Sub (cc, dc)) (Add (ae, be)) = false |
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| eq_num (Mul (bd, cc)) (Neg ae) = false |
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| eq_num (Sub (be, cc)) (Neg ae) = false |
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| eq_num (Add (be, cc)) (Neg ae) = false |
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| eq_num (Mul (db, ea)) (Cn (ac, bd, cc)) = false |
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| eq_num (Sub (dc, ea)) (Cn (ac, bd, cc)) = false |
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| eq_num (Add (dc, ea)) (Cn (ac, bd, cc)) = false |
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| eq_num (Neg dc) (Cn (ac, bd, cc)) = false |
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| eq_num (Mul (bd, cc)) (Bound ac) = false |
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| eq_num (Sub (be, cc)) (Bound ac) = false |
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| eq_num (Add (be, cc)) (Bound ac) = false |
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| eq_num (Neg be) (Bound ac) = false |
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| eq_num (Cn (bc, cb, dc)) (Bound ac) = false |
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| eq_num (Mul (bd, cc)) (C ad) = false |
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| eq_num (Sub (be, cc)) (C ad) = false |
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| eq_num (Add (be, cc)) (C ad) = false |
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| eq_num (Neg be) (C ad) = false |
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| eq_num (Cn (bc, cb, dc)) (C ad) = false |
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| eq_num (Bound bc) (C ad) = false |
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| eq_num (Sub (ab, bb)) (Mul (c, da)) = false |
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| eq_num (Add (ab, bb)) (Mul (c, da)) = false |
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| eq_num (Add (ab, bb)) (Sub (ca, da)) = false |
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| eq_num (Neg ab) (Mul (ba, ca)) = false |
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| eq_num (Neg ab) (Sub (bb, ca)) = false |
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| eq_num (Neg ab) (Add (bb, ca)) = false |
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| eq_num (Cn (a, ba, ca)) (Mul (d, e)) = false |
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| eq_num (Cn (a, ba, ca)) (Sub (da, e)) = false |
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| eq_num (Cn (a, ba, ca)) (Add (da, e)) = false |
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| eq_num (Cn (a, ba, ca)) (Neg da) = false |
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| eq_num (Bound a) (Mul (ba, ca)) = false |
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| eq_num (Bound a) (Sub (bb, ca)) = false |
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| eq_num (Bound a) (Add (bb, ca)) = false |
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| eq_num (Bound a) (Neg bb) = false |
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| eq_num (Bound a) (Cn (b, c, da)) = false |
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| eq_num (C aa) (Mul (ba, ca)) = false |
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| eq_num (C aa) (Sub (bb, ca)) = false |
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| eq_num (C aa) (Add (bb, ca)) = false |
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| eq_num (C aa) (Neg bb) = false |
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| eq_num (C aa) (Cn (b, c, da)) = false |
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| eq_num (C aa) (Bound b) = false |
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| eq_num (Mul (inta, num)) (Mul (int', num')) = |
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((inta : IntInf.int) = int') andalso eq_num num num' |
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| eq_num (Sub (num1, num2)) (Sub (num1', num2')) = |
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eq_num num1 num1' andalso eq_num num2 num2' |
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| eq_num (Add (num1, num2)) (Add (num1', num2')) = |
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eq_num num1 num1' andalso eq_num num2 num2' |
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| eq_num (Neg num) (Neg num') = eq_num num num' |
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| eq_num (Cn (nat, inta, num)) (Cn (nat', int', num')) = |
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((nat : IntInf.int) = nat') andalso |
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(((inta : IntInf.int) = int') andalso eq_num num num') |
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| eq_num (Bound nat) (Bound nat') = ((nat : IntInf.int) = nat') |
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| eq_num (C inta) (C int') = ((inta : IntInf.int) = int'); |
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fun eq_fm (NClosed bd) (Closed ad) = false |
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| eq_fm (NClosed bd) (A af) = false |
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| eq_fm (Closed bd) (A af) = false |
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| eq_fm (NClosed bd) (E af) = false |
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| eq_fm (Closed bd) (E af) = false |
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| eq_fm (A bf) (E af) = false |
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| eq_fm (NClosed cd) (Iff (af, bf)) = false |
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| eq_fm (Closed cd) (Iff (af, bf)) = false |
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| eq_fm (A cf) (Iff (af, bf)) = false |
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| eq_fm (E cf) (Iff (af, bf)) = false |
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| eq_fm (NClosed cd) (Imp (af, bf)) = false |
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| eq_fm (Closed cd) (Imp (af, bf)) = false |
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| eq_fm (A cf) (Imp (af, bf)) = false |
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| eq_fm (E cf) (Imp (af, bf)) = false |
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| eq_fm (Iff (cf, db)) (Imp (af, bf)) = false |
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| eq_fm (NClosed cd) (Or (af, bf)) = false |
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| eq_fm (Closed cd) (Or (af, bf)) = false |
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| eq_fm (A cf) (Or (af, bf)) = false |
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| eq_fm (E cf) (Or (af, bf)) = false |
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| eq_fm (Iff (cf, db)) (Or (af, bf)) = false |
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| eq_fm (Imp (cf, db)) (Or (af, bf)) = false |
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| eq_fm (NClosed cd) (And (af, bf)) = false |
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| eq_fm (Closed cd) (And (af, bf)) = false |
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| eq_fm (A cf) (And (af, bf)) = false |
|
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| eq_fm (E cf) (And (af, bf)) = false |
|
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| eq_fm (Iff (cf, db)) (And (af, bf)) = false |
|
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| eq_fm (Imp (cf, db)) (And (af, bf)) = false |
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| eq_fm (Or (cf, db)) (And (af, bf)) = false |
|
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| eq_fm (NClosed bd) (Not af) = false |
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| eq_fm (Closed bd) (Not af) = false |
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| eq_fm (A bf) (Not af) = false |
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| eq_fm (E bf) (Not af) = false |
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| eq_fm (Iff (bf, cf)) (Not af) = false |
|
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| eq_fm (Imp (bf, cf)) (Not af) = false |
|
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| eq_fm (Or (bf, cf)) (Not af) = false |
|
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| eq_fm (And (bf, cf)) (Not af) = false |
|
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| eq_fm (NClosed cd) (NDvd (ae, bg)) = false |
|
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| eq_fm (Closed cd) (NDvd (ae, bg)) = false |
|
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| eq_fm (A cf) (NDvd (ae, bg)) = false |
|
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| eq_fm (E cf) (NDvd (ae, bg)) = false |
|
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| eq_fm (Iff (cf, db)) (NDvd (ae, bg)) = false |
|
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| eq_fm (Imp (cf, db)) (NDvd (ae, bg)) = false |
|
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| eq_fm (Or (cf, db)) (NDvd (ae, bg)) = false |
|
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| eq_fm (And (cf, db)) (NDvd (ae, bg)) = false |
|
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| eq_fm (Not cf) (NDvd (ae, bg)) = false |
|
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| eq_fm (NClosed cd) (Dvd (ae, bg)) = false |
|
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| eq_fm (Closed cd) (Dvd (ae, bg)) = false |
|
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| eq_fm (A cf) (Dvd (ae, bg)) = false |
|
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| eq_fm (E cf) (Dvd (ae, bg)) = false |
|
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| eq_fm (Iff (cf, db)) (Dvd (ae, bg)) = false |
|
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| eq_fm (Imp (cf, db)) (Dvd (ae, bg)) = false |
|
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| eq_fm (Or (cf, db)) (Dvd (ae, bg)) = false |
|
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| eq_fm (And (cf, db)) (Dvd (ae, bg)) = false |
|
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| eq_fm (Not cf) (Dvd (ae, bg)) = false |
|
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| eq_fm (NDvd (ce, dc)) (Dvd (ae, bg)) = false |
|
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| eq_fm (NClosed bd) (NEq ag) = false |
|
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| eq_fm (Closed bd) (NEq ag) = false |
|
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| eq_fm (A bf) (NEq ag) = false |
|
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| eq_fm (E bf) (NEq ag) = false |
|
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| eq_fm (Iff (bf, cf)) (NEq ag) = false |
|
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| eq_fm (Imp (bf, cf)) (NEq ag) = false |
|
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| eq_fm (Or (bf, cf)) (NEq ag) = false |
|
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| eq_fm (And (bf, cf)) (NEq ag) = false |
|
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| eq_fm (Not bf) (NEq ag) = false |
|
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| eq_fm (NDvd (be, cg)) (NEq ag) = false |
|
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| eq_fm (Dvd (be, cg)) (NEq ag) = false |
|
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| eq_fm (NClosed bd) (Eq ag) = false |
|
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| eq_fm (Closed bd) (Eq ag) = false |
|
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| eq_fm (A bf) (Eq ag) = false |
|
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| eq_fm (E bf) (Eq ag) = false |
|
238 |
| eq_fm (Iff (bf, cf)) (Eq ag) = false |
|
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| eq_fm (Imp (bf, cf)) (Eq ag) = false |
|
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| eq_fm (Or (bf, cf)) (Eq ag) = false |
|
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| eq_fm (And (bf, cf)) (Eq ag) = false |
|
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| eq_fm (Not bf) (Eq ag) = false |
|
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| eq_fm (NDvd (be, cg)) (Eq ag) = false |
|
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| eq_fm (Dvd (be, cg)) (Eq ag) = false |
|
245 |
| eq_fm (NEq bg) (Eq ag) = false |
|
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| eq_fm (NClosed bd) (Ge ag) = false |
|
247 |
| eq_fm (Closed bd) (Ge ag) = false |
|
248 |
| eq_fm (A bf) (Ge ag) = false |
|
249 |
| eq_fm (E bf) (Ge ag) = false |
|
250 |
| eq_fm (Iff (bf, cf)) (Ge ag) = false |
|
251 |
| eq_fm (Imp (bf, cf)) (Ge ag) = false |
|
252 |
| eq_fm (Or (bf, cf)) (Ge ag) = false |
|
253 |
| eq_fm (And (bf, cf)) (Ge ag) = false |
|
254 |
| eq_fm (Not bf) (Ge ag) = false |
|
255 |
| eq_fm (NDvd (be, cg)) (Ge ag) = false |
|
256 |
| eq_fm (Dvd (be, cg)) (Ge ag) = false |
|
257 |
| eq_fm (NEq bg) (Ge ag) = false |
|
258 |
| eq_fm (Eq bg) (Ge ag) = false |
|
259 |
| eq_fm (NClosed bd) (Gt ag) = false |
|
260 |
| eq_fm (Closed bd) (Gt ag) = false |
|
261 |
| eq_fm (A bf) (Gt ag) = false |
|
262 |
| eq_fm (E bf) (Gt ag) = false |
|
263 |
| eq_fm (Iff (bf, cf)) (Gt ag) = false |
|
264 |
| eq_fm (Imp (bf, cf)) (Gt ag) = false |
|
265 |
| eq_fm (Or (bf, cf)) (Gt ag) = false |
|
266 |
| eq_fm (And (bf, cf)) (Gt ag) = false |
|
267 |
| eq_fm (Not bf) (Gt ag) = false |
|
268 |
| eq_fm (NDvd (be, cg)) (Gt ag) = false |
|
269 |
| eq_fm (Dvd (be, cg)) (Gt ag) = false |
|
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| eq_fm (NEq bg) (Gt ag) = false |
|
271 |
| eq_fm (Eq bg) (Gt ag) = false |
|
272 |
| eq_fm (Ge bg) (Gt ag) = false |
|
273 |
| eq_fm (NClosed bd) (Le ag) = false |
|
274 |
| eq_fm (Closed bd) (Le ag) = false |
|
275 |
| eq_fm (A bf) (Le ag) = false |
|
276 |
| eq_fm (E bf) (Le ag) = false |
|
277 |
| eq_fm (Iff (bf, cf)) (Le ag) = false |
|
278 |
| eq_fm (Imp (bf, cf)) (Le ag) = false |
|
279 |
| eq_fm (Or (bf, cf)) (Le ag) = false |
|
280 |
| eq_fm (And (bf, cf)) (Le ag) = false |
|
281 |
| eq_fm (Not bf) (Le ag) = false |
|
282 |
| eq_fm (NDvd (be, cg)) (Le ag) = false |
|
283 |
| eq_fm (Dvd (be, cg)) (Le ag) = false |
|
284 |
| eq_fm (NEq bg) (Le ag) = false |
|
285 |
| eq_fm (Eq bg) (Le ag) = false |
|
286 |
| eq_fm (Ge bg) (Le ag) = false |
|
287 |
| eq_fm (Gt bg) (Le ag) = false |
|
288 |
| eq_fm (NClosed bd) (Lt ag) = false |
|
289 |
| eq_fm (Closed bd) (Lt ag) = false |
|
290 |
| eq_fm (A bf) (Lt ag) = false |
|
291 |
| eq_fm (E bf) (Lt ag) = false |
|
292 |
| eq_fm (Iff (bf, cf)) (Lt ag) = false |
|
293 |
| eq_fm (Imp (bf, cf)) (Lt ag) = false |
|
294 |
| eq_fm (Or (bf, cf)) (Lt ag) = false |
|
295 |
| eq_fm (And (bf, cf)) (Lt ag) = false |
|
296 |
| eq_fm (Not bf) (Lt ag) = false |
|
297 |
| eq_fm (NDvd (be, cg)) (Lt ag) = false |
|
298 |
| eq_fm (Dvd (be, cg)) (Lt ag) = false |
|
299 |
| eq_fm (NEq bg) (Lt ag) = false |
|
300 |
| eq_fm (Eq bg) (Lt ag) = false |
|
301 |
| eq_fm (Ge bg) (Lt ag) = false |
|
302 |
| eq_fm (Gt bg) (Lt ag) = false |
|
303 |
| eq_fm (Le bg) (Lt ag) = false |
|
304 |
| eq_fm (NClosed ad) F = false |
|
305 |
| eq_fm (Closed ad) F = false |
|
306 |
| eq_fm (A af) F = false |
|
307 |
| eq_fm (E af) F = false |
|
308 |
| eq_fm (Iff (af, bf)) F = false |
|
309 |
| eq_fm (Imp (af, bf)) F = false |
|
310 |
| eq_fm (Or (af, bf)) F = false |
|
311 |
| eq_fm (And (af, bf)) F = false |
|
312 |
| eq_fm (Not af) F = false |
|
313 |
| eq_fm (NDvd (ae, bg)) F = false |
|
314 |
| eq_fm (Dvd (ae, bg)) F = false |
|
315 |
| eq_fm (NEq ag) F = false |
|
316 |
| eq_fm (Eq ag) F = false |
|
317 |
| eq_fm (Ge ag) F = false |
|
318 |
| eq_fm (Gt ag) F = false |
|
319 |
| eq_fm (Le ag) F = false |
|
320 |
| eq_fm (Lt ag) F = false |
|
321 |
| eq_fm (NClosed ad) T = false |
|
322 |
| eq_fm (Closed ad) T = false |
|
323 |
| eq_fm (A af) T = false |
|
324 |
| eq_fm (E af) T = false |
|
325 |
| eq_fm (Iff (af, bf)) T = false |
|
326 |
| eq_fm (Imp (af, bf)) T = false |
|
327 |
| eq_fm (Or (af, bf)) T = false |
|
328 |
| eq_fm (And (af, bf)) T = false |
|
329 |
| eq_fm (Not af) T = false |
|
330 |
| eq_fm (NDvd (ae, bg)) T = false |
|
331 |
| eq_fm (Dvd (ae, bg)) T = false |
|
332 |
| eq_fm (NEq ag) T = false |
|
333 |
| eq_fm (Eq ag) T = false |
|
334 |
| eq_fm (Ge ag) T = false |
|
335 |
| eq_fm (Gt ag) T = false |
|
336 |
| eq_fm (Le ag) T = false |
|
337 |
| eq_fm (Lt ag) T = false |
|
338 |
| eq_fm F T = false |
|
339 |
| eq_fm (Closed a) (NClosed b) = false |
|
340 |
| eq_fm (A ab) (NClosed b) = false |
|
341 |
| eq_fm (A ab) (Closed b) = false |
|
342 |
| eq_fm (E ab) (NClosed b) = false |
|
343 |
| eq_fm (E ab) (Closed b) = false |
|
344 |
| eq_fm (E ab) (A bb) = false |
|
345 |
| eq_fm (Iff (ab, bb)) (NClosed c) = false |
|
346 |
| eq_fm (Iff (ab, bb)) (Closed c) = false |
|
347 |
| eq_fm (Iff (ab, bb)) (A cb) = false |
|
348 |
| eq_fm (Iff (ab, bb)) (E cb) = false |
|
349 |
| eq_fm (Imp (ab, bb)) (NClosed c) = false |
|
350 |
| eq_fm (Imp (ab, bb)) (Closed c) = false |
|
351 |
| eq_fm (Imp (ab, bb)) (A cb) = false |
|
352 |
| eq_fm (Imp (ab, bb)) (E cb) = false |
|
353 |
| eq_fm (Imp (ab, bb)) (Iff (cb, d)) = false |
|
354 |
| eq_fm (Or (ab, bb)) (NClosed c) = false |
|
355 |
| eq_fm (Or (ab, bb)) (Closed c) = false |
|
356 |
| eq_fm (Or (ab, bb)) (A cb) = false |
|
357 |
| eq_fm (Or (ab, bb)) (E cb) = false |
|
358 |
| eq_fm (Or (ab, bb)) (Iff (cb, d)) = false |
|
359 |
| eq_fm (Or (ab, bb)) (Imp (cb, d)) = false |
|
360 |
| eq_fm (And (ab, bb)) (NClosed c) = false |
|
361 |
| eq_fm (And (ab, bb)) (Closed c) = false |
|
362 |
| eq_fm (And (ab, bb)) (A cb) = false |
|
363 |
| eq_fm (And (ab, bb)) (E cb) = false |
|
364 |
| eq_fm (And (ab, bb)) (Iff (cb, d)) = false |
|
365 |
| eq_fm (And (ab, bb)) (Imp (cb, d)) = false |
|
366 |
| eq_fm (And (ab, bb)) (Or (cb, d)) = false |
|
367 |
| eq_fm (Not ab) (NClosed b) = false |
|
368 |
| eq_fm (Not ab) (Closed b) = false |
|
369 |
| eq_fm (Not ab) (A bb) = false |
|
370 |
| eq_fm (Not ab) (E bb) = false |
|
371 |
| eq_fm (Not ab) (Iff (bb, cb)) = false |
|
372 |
| eq_fm (Not ab) (Imp (bb, cb)) = false |
|
373 |
| eq_fm (Not ab) (Or (bb, cb)) = false |
|
374 |
| eq_fm (Not ab) (And (bb, cb)) = false |
|
375 |
| eq_fm (NDvd (aa, bc)) (NClosed c) = false |
|
376 |
| eq_fm (NDvd (aa, bc)) (Closed c) = false |
|
377 |
| eq_fm (NDvd (aa, bc)) (A cb) = false |
|
378 |
| eq_fm (NDvd (aa, bc)) (E cb) = false |
|
379 |
| eq_fm (NDvd (aa, bc)) (Iff (cb, d)) = false |
|
380 |
| eq_fm (NDvd (aa, bc)) (Imp (cb, d)) = false |
|
381 |
| eq_fm (NDvd (aa, bc)) (Or (cb, d)) = false |
|
382 |
| eq_fm (NDvd (aa, bc)) (And (cb, d)) = false |
|
383 |
| eq_fm (NDvd (aa, bc)) (Not cb) = false |
|
384 |
| eq_fm (Dvd (aa, bc)) (NClosed c) = false |
|
385 |
| eq_fm (Dvd (aa, bc)) (Closed c) = false |
|
386 |
| eq_fm (Dvd (aa, bc)) (A cb) = false |
|
387 |
| eq_fm (Dvd (aa, bc)) (E cb) = false |
|
388 |
| eq_fm (Dvd (aa, bc)) (Iff (cb, d)) = false |
|
389 |
| eq_fm (Dvd (aa, bc)) (Imp (cb, d)) = false |
|
390 |
| eq_fm (Dvd (aa, bc)) (Or (cb, d)) = false |
|
391 |
| eq_fm (Dvd (aa, bc)) (And (cb, d)) = false |
|
392 |
| eq_fm (Dvd (aa, bc)) (Not cb) = false |
|
393 |
| eq_fm (Dvd (aa, bc)) (NDvd (ca, da)) = false |
|
394 |
| eq_fm (NEq ac) (NClosed b) = false |
|
395 |
| eq_fm (NEq ac) (Closed b) = false |
|
396 |
| eq_fm (NEq ac) (A bb) = false |
|
397 |
| eq_fm (NEq ac) (E bb) = false |
|
398 |
| eq_fm (NEq ac) (Iff (bb, cb)) = false |
|
399 |
| eq_fm (NEq ac) (Imp (bb, cb)) = false |
|
400 |
| eq_fm (NEq ac) (Or (bb, cb)) = false |
|
401 |
| eq_fm (NEq ac) (And (bb, cb)) = false |
|
402 |
| eq_fm (NEq ac) (Not bb) = false |
|
403 |
| eq_fm (NEq ac) (NDvd (ba, cc)) = false |
|
404 |
| eq_fm (NEq ac) (Dvd (ba, cc)) = false |
|
405 |
| eq_fm (Eq ac) (NClosed b) = false |
|
406 |
| eq_fm (Eq ac) (Closed b) = false |
|
407 |
| eq_fm (Eq ac) (A bb) = false |
|
408 |
| eq_fm (Eq ac) (E bb) = false |
|
409 |
| eq_fm (Eq ac) (Iff (bb, cb)) = false |
|
410 |
| eq_fm (Eq ac) (Imp (bb, cb)) = false |
|
411 |
| eq_fm (Eq ac) (Or (bb, cb)) = false |
|
412 |
| eq_fm (Eq ac) (And (bb, cb)) = false |
|
413 |
| eq_fm (Eq ac) (Not bb) = false |
|
414 |
| eq_fm (Eq ac) (NDvd (ba, cc)) = false |
|
415 |
| eq_fm (Eq ac) (Dvd (ba, cc)) = false |
|
416 |
| eq_fm (Eq ac) (NEq bc) = false |
|
417 |
| eq_fm (Ge ac) (NClosed b) = false |
|
418 |
| eq_fm (Ge ac) (Closed b) = false |
|
419 |
| eq_fm (Ge ac) (A bb) = false |
|
420 |
| eq_fm (Ge ac) (E bb) = false |
|
421 |
| eq_fm (Ge ac) (Iff (bb, cb)) = false |
|
422 |
| eq_fm (Ge ac) (Imp (bb, cb)) = false |
|
423 |
| eq_fm (Ge ac) (Or (bb, cb)) = false |
|
424 |
| eq_fm (Ge ac) (And (bb, cb)) = false |
|
425 |
| eq_fm (Ge ac) (Not bb) = false |
|
426 |
| eq_fm (Ge ac) (NDvd (ba, cc)) = false |
|
427 |
| eq_fm (Ge ac) (Dvd (ba, cc)) = false |
|
428 |
| eq_fm (Ge ac) (NEq bc) = false |
|
429 |
| eq_fm (Ge ac) (Eq bc) = false |
|
430 |
| eq_fm (Gt ac) (NClosed b) = false |
|
431 |
| eq_fm (Gt ac) (Closed b) = false |
|
432 |
| eq_fm (Gt ac) (A bb) = false |
|
433 |
| eq_fm (Gt ac) (E bb) = false |
|
434 |
| eq_fm (Gt ac) (Iff (bb, cb)) = false |
|
435 |
| eq_fm (Gt ac) (Imp (bb, cb)) = false |
|
436 |
| eq_fm (Gt ac) (Or (bb, cb)) = false |
|
437 |
| eq_fm (Gt ac) (And (bb, cb)) = false |
|
438 |
| eq_fm (Gt ac) (Not bb) = false |
|
439 |
| eq_fm (Gt ac) (NDvd (ba, cc)) = false |
|
440 |
| eq_fm (Gt ac) (Dvd (ba, cc)) = false |
|
441 |
| eq_fm (Gt ac) (NEq bc) = false |
|
442 |
| eq_fm (Gt ac) (Eq bc) = false |
|
443 |
| eq_fm (Gt ac) (Ge bc) = false |
|
444 |
| eq_fm (Le ac) (NClosed b) = false |
|
445 |
| eq_fm (Le ac) (Closed b) = false |
|
446 |
| eq_fm (Le ac) (A bb) = false |
|
447 |
| eq_fm (Le ac) (E bb) = false |
|
448 |
| eq_fm (Le ac) (Iff (bb, cb)) = false |
|
449 |
| eq_fm (Le ac) (Imp (bb, cb)) = false |
|
450 |
| eq_fm (Le ac) (Or (bb, cb)) = false |
|
451 |
| eq_fm (Le ac) (And (bb, cb)) = false |
|
452 |
| eq_fm (Le ac) (Not bb) = false |
|
453 |
| eq_fm (Le ac) (NDvd (ba, cc)) = false |
|
454 |
| eq_fm (Le ac) (Dvd (ba, cc)) = false |
|
455 |
| eq_fm (Le ac) (NEq bc) = false |
|
456 |
| eq_fm (Le ac) (Eq bc) = false |
|
457 |
| eq_fm (Le ac) (Ge bc) = false |
|
458 |
| eq_fm (Le ac) (Gt bc) = false |
|
459 |
| eq_fm (Lt ac) (NClosed b) = false |
|
460 |
| eq_fm (Lt ac) (Closed b) = false |
|
461 |
| eq_fm (Lt ac) (A bb) = false |
|
462 |
| eq_fm (Lt ac) (E bb) = false |
|
463 |
| eq_fm (Lt ac) (Iff (bb, cb)) = false |
|
464 |
| eq_fm (Lt ac) (Imp (bb, cb)) = false |
|
465 |
| eq_fm (Lt ac) (Or (bb, cb)) = false |
|
466 |
| eq_fm (Lt ac) (And (bb, cb)) = false |
|
467 |
| eq_fm (Lt ac) (Not bb) = false |
|
468 |
| eq_fm (Lt ac) (NDvd (ba, cc)) = false |
|
469 |
| eq_fm (Lt ac) (Dvd (ba, cc)) = false |
|
470 |
| eq_fm (Lt ac) (NEq bc) = false |
|
471 |
| eq_fm (Lt ac) (Eq bc) = false |
|
472 |
| eq_fm (Lt ac) (Ge bc) = false |
|
473 |
| eq_fm (Lt ac) (Gt bc) = false |
|
474 |
| eq_fm (Lt ac) (Le bc) = false |
|
475 |
| eq_fm F (NClosed a) = false |
|
476 |
| eq_fm F (Closed a) = false |
|
477 |
| eq_fm F (A ab) = false |
|
478 |
| eq_fm F (E ab) = false |
|
479 |
| eq_fm F (Iff (ab, bb)) = false |
|
480 |
| eq_fm F (Imp (ab, bb)) = false |
|
481 |
| eq_fm F (Or (ab, bb)) = false |
|
482 |
| eq_fm F (And (ab, bb)) = false |
|
483 |
| eq_fm F (Not ab) = false |
|
484 |
| eq_fm F (NDvd (aa, bc)) = false |
|
485 |
| eq_fm F (Dvd (aa, bc)) = false |
|
486 |
| eq_fm F (NEq ac) = false |
|
487 |
| eq_fm F (Eq ac) = false |
|
488 |
| eq_fm F (Ge ac) = false |
|
489 |
| eq_fm F (Gt ac) = false |
|
490 |
| eq_fm F (Le ac) = false |
|
491 |
| eq_fm F (Lt ac) = false |
|
492 |
| eq_fm T (NClosed a) = false |
|
493 |
| eq_fm T (Closed a) = false |
|
494 |
| eq_fm T (A ab) = false |
|
495 |
| eq_fm T (E ab) = false |
|
496 |
| eq_fm T (Iff (ab, bb)) = false |
|
497 |
| eq_fm T (Imp (ab, bb)) = false |
|
498 |
| eq_fm T (Or (ab, bb)) = false |
|
499 |
| eq_fm T (And (ab, bb)) = false |
|
500 |
| eq_fm T (Not ab) = false |
|
501 |
| eq_fm T (NDvd (aa, bc)) = false |
|
502 |
| eq_fm T (Dvd (aa, bc)) = false |
|
503 |
| eq_fm T (NEq ac) = false |
|
504 |
| eq_fm T (Eq ac) = false |
|
505 |
| eq_fm T (Ge ac) = false |
|
506 |
| eq_fm T (Gt ac) = false |
|
507 |
| eq_fm T (Le ac) = false |
|
508 |
| eq_fm T (Lt ac) = false |
|
509 |
| eq_fm T F = false |
|
510 |
| eq_fm (NClosed nat) (NClosed nat') = ((nat : IntInf.int) = nat') |
|
511 |
| eq_fm (Closed nat) (Closed nat') = ((nat : IntInf.int) = nat') |
|
512 |
| eq_fm (A fm) (A fm') = eq_fm fm fm' |
|
513 |
| eq_fm (E fm) (E fm') = eq_fm fm fm' |
|
514 |
| eq_fm (Iff (fm1, fm2)) (Iff (fm1', fm2')) = |
|
515 |
eq_fm fm1 fm1' andalso eq_fm fm2 fm2' |
|
516 |
| eq_fm (Imp (fm1, fm2)) (Imp (fm1', fm2')) = |
|
517 |
eq_fm fm1 fm1' andalso eq_fm fm2 fm2' |
|
518 |
| eq_fm (Or (fm1, fm2)) (Or (fm1', fm2')) = |
|
519 |
eq_fm fm1 fm1' andalso eq_fm fm2 fm2' |
|
520 |
| eq_fm (And (fm1, fm2)) (And (fm1', fm2')) = |
|
521 |
eq_fm fm1 fm1' andalso eq_fm fm2 fm2' |
|
522 |
| eq_fm (Not fm) (Not fm') = eq_fm fm fm' |
|
523 |
| eq_fm (NDvd (inta, num)) (NDvd (int', num')) = |
|
524 |
((inta : IntInf.int) = int') andalso eq_num num num' |
|
525 |
| eq_fm (Dvd (inta, num)) (Dvd (int', num')) = |
|
526 |
((inta : IntInf.int) = int') andalso eq_num num num' |
|
527 |
| eq_fm (NEq num) (NEq num') = eq_num num num' |
|
528 |
| eq_fm (Eq num) (Eq num') = eq_num num num' |
|
529 |
| eq_fm (Ge num) (Ge num') = eq_num num num' |
|
530 |
| eq_fm (Gt num) (Gt num') = eq_num num num' |
|
531 |
| eq_fm (Le num) (Le num') = eq_num num num' |
|
532 |
| eq_fm (Lt num) (Lt num') = eq_num num num' |
|
533 |
| eq_fm F F = true |
|
534 |
| eq_fm T T = true; |
|
535 |
||
536 |
val eq_fma = {eq = eq_fm} : fm eq; |
|
537 |
||
538 |
fun djf f p q = |
|
539 |
(if eqop eq_fma q T then T |
|
540 |
else (if eqop eq_fma q F then f p |
|
541 |
else let |
|
542 |
val a = f p; |
|
543 |
in |
|
544 |
(case a of T => T | F => q | Lt num => Or (f p, q) |
|
545 |
| Le num => Or (f p, q) | Gt num => Or (f p, q) |
|
546 |
| Ge num => Or (f p, q) | Eq num => Or (f p, q) |
|
547 |
| NEq num => Or (f p, q) | Dvd (inta, num) => Or (f p, q) |
|
548 |
| NDvd (inta, num) => Or (f p, q) | Not fm => Or (f p, q) |
|
549 |
| And (fm1, fm2) => Or (f p, q) |
|
550 |
| Or (fm1, fm2) => Or (f p, q) |
|
551 |
| Imp (fm1, fm2) => Or (f p, q) |
|
552 |
| Iff (fm1, fm2) => Or (f p, q) | E fm => Or (f p, q) |
|
553 |
| A fm => Or (f p, q) | Closed nat => Or (f p, q) |
|
554 |
| NClosed nat => Or (f p, q)) |
|
555 |
end)); |
|
556 |
||
557 |
fun foldr f [] y = y |
|
558 |
| foldr f (x :: xs) a = f x (foldr f xs a); |
|
559 |
||
560 |
fun evaldjf f ps = foldr (djf f) ps F; |
|
561 |
||
562 |
fun dj f p = evaldjf f (disjuncts p); |
|
563 |
||
564 |
fun disj p q = |
|
565 |
(if eqop eq_fma p T orelse eqop eq_fma q T then T |
|
566 |
else (if eqop eq_fma p F then q |
|
567 |
else (if eqop eq_fma q F then p else Or (p, q)))); |
|
568 |
||
569 |
fun minus_nat n m = IntInf.max (0, (IntInf.- (n, m))); |
|
570 |
||
571 |
fun decrnum (Bound n) = Bound (minus_nat n 1) |
|
572 |
| decrnum (Neg a) = Neg (decrnum a) |
|
573 |
| decrnum (Add (a, b)) = Add (decrnum a, decrnum b) |
|
574 |
| decrnum (Sub (a, b)) = Sub (decrnum a, decrnum b) |
|
575 |
| decrnum (Mul (c, a)) = Mul (c, decrnum a) |
|
576 |
| decrnum (Cn (n, i, a)) = Cn (minus_nat n 1, i, decrnum a) |
|
577 |
| decrnum (C u) = C u; |
|
578 |
||
579 |
fun decr (Lt a) = Lt (decrnum a) |
|
580 |
| decr (Le a) = Le (decrnum a) |
|
581 |
| decr (Gt a) = Gt (decrnum a) |
|
582 |
| decr (Ge a) = Ge (decrnum a) |
|
583 |
| decr (Eq a) = Eq (decrnum a) |
|
584 |
| decr (NEq a) = NEq (decrnum a) |
|
585 |
| decr (Dvd (i, a)) = Dvd (i, decrnum a) |
|
586 |
| decr (NDvd (i, a)) = NDvd (i, decrnum a) |
|
587 |
| decr (Not p) = Not (decr p) |
|
588 |
| decr (And (p, q)) = And (decr p, decr q) |
|
589 |
| decr (Or (p, q)) = Or (decr p, decr q) |
|
590 |
| decr (Imp (p, q)) = Imp (decr p, decr q) |
|
591 |
| decr (Iff (p, q)) = Iff (decr p, decr q) |
|
592 |
| decr T = T |
|
593 |
| decr F = F |
|
594 |
| decr (E ao) = E ao |
|
595 |
| decr (A ap) = A ap |
|
596 |
| decr (Closed aq) = Closed aq |
|
597 |
| decr (NClosed ar) = NClosed ar; |
|
598 |
||
599 |
fun concat [] = [] |
|
600 |
| concat (x :: xs) = append x (concat xs); |
|
601 |
||
602 |
fun split f (a, b) = f a b; |
|
603 |
||
604 |
fun numsubst0 t (C c) = C c |
|
605 |
| numsubst0 t (Bound n) = (if eqop eq_nat n 0 then t else Bound n) |
|
606 |
| numsubst0 t (Neg a) = Neg (numsubst0 t a) |
|
607 |
| numsubst0 t (Add (a, b)) = Add (numsubst0 t a, numsubst0 t b) |
|
608 |
| numsubst0 t (Sub (a, b)) = Sub (numsubst0 t a, numsubst0 t b) |
|
609 |
| numsubst0 t (Mul (i, a)) = Mul (i, numsubst0 t a) |
|
610 |
| numsubst0 ta (Cn (v, ia, aa)) = |
|
611 |
(if eqop eq_nat v 0 then Add (Mul (ia, ta), numsubst0 ta aa) |
|
612 |
else Cn (suc (minus_nat v 1), ia, numsubst0 ta aa)); |
|
613 |
||
614 |
fun subst0 t T = T |
|
615 |
| subst0 t F = F |
|
616 |
| subst0 t (Lt a) = Lt (numsubst0 t a) |
|
617 |
| subst0 t (Le a) = Le (numsubst0 t a) |
|
618 |
| subst0 t (Gt a) = Gt (numsubst0 t a) |
|
619 |
| subst0 t (Ge a) = Ge (numsubst0 t a) |
|
620 |
| subst0 t (Eq a) = Eq (numsubst0 t a) |
|
621 |
| subst0 t (NEq a) = NEq (numsubst0 t a) |
|
622 |
| subst0 t (Dvd (i, a)) = Dvd (i, numsubst0 t a) |
|
623 |
| subst0 t (NDvd (i, a)) = NDvd (i, numsubst0 t a) |
|
624 |
| subst0 t (Not p) = Not (subst0 t p) |
|
625 |
| subst0 t (And (p, q)) = And (subst0 t p, subst0 t q) |
|
626 |
| subst0 t (Or (p, q)) = Or (subst0 t p, subst0 t q) |
|
627 |
| subst0 t (Imp (p, q)) = Imp (subst0 t p, subst0 t q) |
|
628 |
| subst0 t (Iff (p, q)) = Iff (subst0 t p, subst0 t q) |
|
629 |
| subst0 t (Closed p) = Closed p |
|
630 |
| subst0 t (NClosed p) = NClosed p; |
|
631 |
||
632 |
fun minusinf (And (p, q)) = And (minusinf p, minusinf q) |
|
633 |
| minusinf (Or (p, q)) = Or (minusinf p, minusinf q) |
|
634 |
| minusinf T = T |
|
635 |
| minusinf F = F |
|
636 |
| minusinf (Lt (C bo)) = Lt (C bo) |
|
637 |
| minusinf (Lt (Bound bp)) = Lt (Bound bp) |
|
638 |
| minusinf (Lt (Neg bt)) = Lt (Neg bt) |
|
639 |
| minusinf (Lt (Add (bu, bv))) = Lt (Add (bu, bv)) |
|
640 |
| minusinf (Lt (Sub (bw, bx))) = Lt (Sub (bw, bx)) |
|
641 |
| minusinf (Lt (Mul (by, bz))) = Lt (Mul (by, bz)) |
|
642 |
| minusinf (Le (C co)) = Le (C co) |
|
643 |
| minusinf (Le (Bound cp)) = Le (Bound cp) |
|
644 |
| minusinf (Le (Neg ct)) = Le (Neg ct) |
|
645 |
| minusinf (Le (Add (cu, cv))) = Le (Add (cu, cv)) |
|
646 |
| minusinf (Le (Sub (cw, cx))) = Le (Sub (cw, cx)) |
|
647 |
| minusinf (Le (Mul (cy, cz))) = Le (Mul (cy, cz)) |
|
648 |
| minusinf (Gt (C doa)) = Gt (C doa) |
|
649 |
| minusinf (Gt (Bound dp)) = Gt (Bound dp) |
|
650 |
| minusinf (Gt (Neg dt)) = Gt (Neg dt) |
|
651 |
| minusinf (Gt (Add (du, dv))) = Gt (Add (du, dv)) |
|
652 |
| minusinf (Gt (Sub (dw, dx))) = Gt (Sub (dw, dx)) |
|
653 |
| minusinf (Gt (Mul (dy, dz))) = Gt (Mul (dy, dz)) |
|
654 |
| minusinf (Ge (C eo)) = Ge (C eo) |
|
655 |
| minusinf (Ge (Bound ep)) = Ge (Bound ep) |
|
656 |
| minusinf (Ge (Neg et)) = Ge (Neg et) |
|
657 |
| minusinf (Ge (Add (eu, ev))) = Ge (Add (eu, ev)) |
|
658 |
| minusinf (Ge (Sub (ew, ex))) = Ge (Sub (ew, ex)) |
|
659 |
| minusinf (Ge (Mul (ey, ez))) = Ge (Mul (ey, ez)) |
|
660 |
| minusinf (Eq (C fo)) = Eq (C fo) |
|
661 |
| minusinf (Eq (Bound fp)) = Eq (Bound fp) |
|
662 |
| minusinf (Eq (Neg ft)) = Eq (Neg ft) |
|
663 |
| minusinf (Eq (Add (fu, fv))) = Eq (Add (fu, fv)) |
|
664 |
| minusinf (Eq (Sub (fw, fx))) = Eq (Sub (fw, fx)) |
|
665 |
| minusinf (Eq (Mul (fy, fz))) = Eq (Mul (fy, fz)) |
|
666 |
| minusinf (NEq (C go)) = NEq (C go) |
|
667 |
| minusinf (NEq (Bound gp)) = NEq (Bound gp) |
|
668 |
| minusinf (NEq (Neg gt)) = NEq (Neg gt) |
|
669 |
| minusinf (NEq (Add (gu, gv))) = NEq (Add (gu, gv)) |
|
670 |
| minusinf (NEq (Sub (gw, gx))) = NEq (Sub (gw, gx)) |
|
671 |
| minusinf (NEq (Mul (gy, gz))) = NEq (Mul (gy, gz)) |
|
672 |
| minusinf (Dvd (aa, ab)) = Dvd (aa, ab) |
|
673 |
| minusinf (NDvd (ac, ad)) = NDvd (ac, ad) |
|
674 |
| minusinf (Not ae) = Not ae |
|
675 |
| minusinf (Imp (aj, ak)) = Imp (aj, ak) |
|
676 |
| minusinf (Iff (al, am)) = Iff (al, am) |
|
677 |
| minusinf (E an) = E an |
|
678 |
| minusinf (A ao) = A ao |
|
679 |
| minusinf (Closed ap) = Closed ap |
|
680 |
| minusinf (NClosed aq) = NClosed aq |
|
681 |
| minusinf (Lt (Cn (cm, c, e))) = |
|
682 |
(if eqop eq_nat cm 0 then T else Lt (Cn (suc (minus_nat cm 1), c, e))) |
|
683 |
| minusinf (Le (Cn (dm, c, e))) = |
|
684 |
(if eqop eq_nat dm 0 then T else Le (Cn (suc (minus_nat dm 1), c, e))) |
|
685 |
| minusinf (Gt (Cn (em, c, e))) = |
|
686 |
(if eqop eq_nat em 0 then F else Gt (Cn (suc (minus_nat em 1), c, e))) |
|
687 |
| minusinf (Ge (Cn (fm, c, e))) = |
|
688 |
(if eqop eq_nat fm 0 then F else Ge (Cn (suc (minus_nat fm 1), c, e))) |
|
689 |
| minusinf (Eq (Cn (gm, c, e))) = |
|
690 |
(if eqop eq_nat gm 0 then F else Eq (Cn (suc (minus_nat gm 1), c, e))) |
|
691 |
| minusinf (NEq (Cn (hm, c, e))) = |
|
692 |
(if eqop eq_nat hm 0 then T else NEq (Cn (suc (minus_nat hm 1), c, e))); |
|
23689
0410269099dc
replaced code generator framework for reflected cooper
haftmann
parents:
23466
diff
changeset
|
693 |
|
23466 | 694 |
fun adjust b = |
23689
0410269099dc
replaced code generator framework for reflected cooper
haftmann
parents:
23466
diff
changeset
|
695 |
(fn a as (q, r) => |
0410269099dc
replaced code generator framework for reflected cooper
haftmann
parents:
23466
diff
changeset
|
696 |
(if IntInf.<= ((0 : IntInf.int), IntInf.- (r, b)) |
0410269099dc
replaced code generator framework for reflected cooper
haftmann
parents:
23466
diff
changeset
|
697 |
then (IntInf.+ (IntInf.* ((2 : IntInf.int), q), (1 : IntInf.int)), |
0410269099dc
replaced code generator framework for reflected cooper
haftmann
parents:
23466
diff
changeset
|
698 |
IntInf.- (r, b)) |
0410269099dc
replaced code generator framework for reflected cooper
haftmann
parents:
23466
diff
changeset
|
699 |
else (IntInf.* ((2 : IntInf.int), q), r))); |
23466 | 700 |
|
701 |
fun negDivAlg a b = |
|
23689
0410269099dc
replaced code generator framework for reflected cooper
haftmann
parents:
23466
diff
changeset
|
702 |
(if IntInf.<= ((0 : IntInf.int), IntInf.+ (a, b)) orelse |
0410269099dc
replaced code generator framework for reflected cooper
haftmann
parents:
23466
diff
changeset
|
703 |
IntInf.<= (b, (0 : IntInf.int)) |
0410269099dc
replaced code generator framework for reflected cooper
haftmann
parents:
23466
diff
changeset
|
704 |
then ((~1 : IntInf.int), IntInf.+ (a, b)) |
0410269099dc
replaced code generator framework for reflected cooper
haftmann
parents:
23466
diff
changeset
|
705 |
else adjust b (negDivAlg a (IntInf.* ((2 : IntInf.int), b)))); |
0410269099dc
replaced code generator framework for reflected cooper
haftmann
parents:
23466
diff
changeset
|
706 |
|
29787 | 707 |
fun apsnd f (x, y) = (x, f y); |
708 |
||
709 |
val eq_int = {eq = (fn a => fn b => ((a : IntInf.int) = b))} : IntInf.int eq; |
|
23466 | 710 |
|
711 |
fun posDivAlg a b = |
|
23689
0410269099dc
replaced code generator framework for reflected cooper
haftmann
parents:
23466
diff
changeset
|
712 |
(if IntInf.< (a, b) orelse IntInf.<= (b, (0 : IntInf.int)) |
0410269099dc
replaced code generator framework for reflected cooper
haftmann
parents:
23466
diff
changeset
|
713 |
then ((0 : IntInf.int), a) |
0410269099dc
replaced code generator framework for reflected cooper
haftmann
parents:
23466
diff
changeset
|
714 |
else adjust b (posDivAlg a (IntInf.* ((2 : IntInf.int), b)))); |
0410269099dc
replaced code generator framework for reflected cooper
haftmann
parents:
23466
diff
changeset
|
715 |
|
29787 | 716 |
fun divmoda a b = |
717 |
(if IntInf.<= ((0 : IntInf.int), a) |
|
718 |
then (if IntInf.<= ((0 : IntInf.int), b) then posDivAlg a b |
|
719 |
else (if eqop eq_int a (0 : IntInf.int) |
|
720 |
then ((0 : IntInf.int), (0 : IntInf.int)) |
|
721 |
else apsnd IntInf.~ (negDivAlg (IntInf.~ a) (IntInf.~ b)))) |
|
722 |
else (if IntInf.< ((0 : IntInf.int), b) then negDivAlg a b |
|
723 |
else apsnd IntInf.~ (posDivAlg (IntInf.~ a) (IntInf.~ b)))); |
|
23689
0410269099dc
replaced code generator framework for reflected cooper
haftmann
parents:
23466
diff
changeset
|
724 |
|
29787 | 725 |
fun mod_int a b = snd (divmoda a b); |
23714 | 726 |
|
29787 | 727 |
fun num_case f1 f2 f3 f4 f5 f6 f7 (Mul (inta, num)) = f7 inta num |
728 |
| num_case f1 f2 f3 f4 f5 f6 f7 (Sub (num1, num2)) = f6 num1 num2 |
|
729 |
| num_case f1 f2 f3 f4 f5 f6 f7 (Add (num1, num2)) = f5 num1 num2 |
|
730 |
| num_case f1 f2 f3 f4 f5 f6 f7 (Neg num) = f4 num |
|
731 |
| num_case f1 f2 f3 f4 f5 f6 f7 (Cn (nat, inta, num)) = f3 nat inta num |
|
732 |
| num_case f1 f2 f3 f4 f5 f6 f7 (Bound nat) = f2 nat |
|
733 |
| num_case f1 f2 f3 f4 f5 f6 f7 (C inta) = f1 inta; |
|
23689
0410269099dc
replaced code generator framework for reflected cooper
haftmann
parents:
23466
diff
changeset
|
734 |
|
29787 | 735 |
fun nummul i (C j) = C (IntInf.* (i, j)) |
736 |
| nummul i (Cn (n, c, t)) = Cn (n, IntInf.* (c, i), nummul i t) |
|
737 |
| nummul i (Bound v) = Mul (i, Bound v) |
|
738 |
| nummul i (Neg v) = Mul (i, Neg v) |
|
739 |
| nummul i (Add (v, va)) = Mul (i, Add (v, va)) |
|
740 |
| nummul i (Sub (v, va)) = Mul (i, Sub (v, va)) |
|
741 |
| nummul i (Mul (v, va)) = Mul (i, Mul (v, va)); |
|
23689
0410269099dc
replaced code generator framework for reflected cooper
haftmann
parents:
23466
diff
changeset
|
742 |
|
29787 | 743 |
fun numneg t = nummul (IntInf.~ (1 : IntInf.int)) t; |
23689
0410269099dc
replaced code generator framework for reflected cooper
haftmann
parents:
23466
diff
changeset
|
744 |
|
29787 | 745 |
fun numadd (Cn (n1, c1, r1), Cn (n2, c2, r2)) = |
746 |
(if eqop eq_nat n1 n2 |
|
747 |
then let |
|
748 |
val c = IntInf.+ (c1, c2); |
|
749 |
in |
|
750 |
(if eqop eq_int c (0 : IntInf.int) then numadd (r1, r2) |
|
751 |
else Cn (n1, c, numadd (r1, r2))) |
|
752 |
end |
|
753 |
else (if IntInf.<= (n1, n2) |
|
754 |
then Cn (n1, c1, numadd (r1, Add (Mul (c2, Bound n2), r2))) |
|
755 |
else Cn (n2, c2, numadd (Add (Mul (c1, Bound n1), r1), r2)))) |
|
756 |
| numadd (Cn (n1, c1, r1), C dd) = Cn (n1, c1, numadd (r1, C dd)) |
|
757 |
| numadd (Cn (n1, c1, r1), Bound de) = Cn (n1, c1, numadd (r1, Bound de)) |
|
758 |
| numadd (Cn (n1, c1, r1), Neg di) = Cn (n1, c1, numadd (r1, Neg di)) |
|
759 |
| numadd (Cn (n1, c1, r1), Add (dj, dk)) = |
|
760 |
Cn (n1, c1, numadd (r1, Add (dj, dk))) |
|
761 |
| numadd (Cn (n1, c1, r1), Sub (dl, dm)) = |
|
762 |
Cn (n1, c1, numadd (r1, Sub (dl, dm))) |
|
763 |
| numadd (Cn (n1, c1, r1), Mul (dn, doa)) = |
|
764 |
Cn (n1, c1, numadd (r1, Mul (dn, doa))) |
|
765 |
| numadd (C w, Cn (n2, c2, r2)) = Cn (n2, c2, numadd (C w, r2)) |
|
766 |
| numadd (Bound x, Cn (n2, c2, r2)) = Cn (n2, c2, numadd (Bound x, r2)) |
|
767 |
| numadd (Neg ac, Cn (n2, c2, r2)) = Cn (n2, c2, numadd (Neg ac, r2)) |
|
768 |
| numadd (Add (ad, ae), Cn (n2, c2, r2)) = |
|
769 |
Cn (n2, c2, numadd (Add (ad, ae), r2)) |
|
770 |
| numadd (Sub (af, ag), Cn (n2, c2, r2)) = |
|
771 |
Cn (n2, c2, numadd (Sub (af, ag), r2)) |
|
772 |
| numadd (Mul (ah, ai), Cn (n2, c2, r2)) = |
|
773 |
Cn (n2, c2, numadd (Mul (ah, ai), r2)) |
|
774 |
| numadd (C b1, C b2) = C (IntInf.+ (b1, b2)) |
|
775 |
| numadd (C aj, Bound bi) = Add (C aj, Bound bi) |
|
776 |
| numadd (C aj, Neg bm) = Add (C aj, Neg bm) |
|
777 |
| numadd (C aj, Add (bn, bo)) = Add (C aj, Add (bn, bo)) |
|
778 |
| numadd (C aj, Sub (bp, bq)) = Add (C aj, Sub (bp, bq)) |
|
779 |
| numadd (C aj, Mul (br, bs)) = Add (C aj, Mul (br, bs)) |
|
780 |
| numadd (Bound ak, C cf) = Add (Bound ak, C cf) |
|
781 |
| numadd (Bound ak, Bound cg) = Add (Bound ak, Bound cg) |
|
782 |
| numadd (Bound ak, Neg ck) = Add (Bound ak, Neg ck) |
|
783 |
| numadd (Bound ak, Add (cl, cm)) = Add (Bound ak, Add (cl, cm)) |
|
784 |
| numadd (Bound ak, Sub (cn, co)) = Add (Bound ak, Sub (cn, co)) |
|
785 |
| numadd (Bound ak, Mul (cp, cq)) = Add (Bound ak, Mul (cp, cq)) |
|
786 |
| numadd (Neg ao, C en) = Add (Neg ao, C en) |
|
787 |
| numadd (Neg ao, Bound eo) = Add (Neg ao, Bound eo) |
|
788 |
| numadd (Neg ao, Neg es) = Add (Neg ao, Neg es) |
|
789 |
| numadd (Neg ao, Add (et, eu)) = Add (Neg ao, Add (et, eu)) |
|
790 |
| numadd (Neg ao, Sub (ev, ew)) = Add (Neg ao, Sub (ev, ew)) |
|
791 |
| numadd (Neg ao, Mul (ex, ey)) = Add (Neg ao, Mul (ex, ey)) |
|
792 |
| numadd (Add (ap, aq), C fl) = Add (Add (ap, aq), C fl) |
|
793 |
| numadd (Add (ap, aq), Bound fm) = Add (Add (ap, aq), Bound fm) |
|
794 |
| numadd (Add (ap, aq), Neg fq) = Add (Add (ap, aq), Neg fq) |
|
795 |
| numadd (Add (ap, aq), Add (fr, fs)) = Add (Add (ap, aq), Add (fr, fs)) |
|
796 |
| numadd (Add (ap, aq), Sub (ft, fu)) = Add (Add (ap, aq), Sub (ft, fu)) |
|
797 |
| numadd (Add (ap, aq), Mul (fv, fw)) = Add (Add (ap, aq), Mul (fv, fw)) |
|
798 |
| numadd (Sub (ar, asa), C gj) = Add (Sub (ar, asa), C gj) |
|
799 |
| numadd (Sub (ar, asa), Bound gk) = Add (Sub (ar, asa), Bound gk) |
|
800 |
| numadd (Sub (ar, asa), Neg go) = Add (Sub (ar, asa), Neg go) |
|
801 |
| numadd (Sub (ar, asa), Add (gp, gq)) = Add (Sub (ar, asa), Add (gp, gq)) |
|
802 |
| numadd (Sub (ar, asa), Sub (gr, gs)) = Add (Sub (ar, asa), Sub (gr, gs)) |
|
803 |
| numadd (Sub (ar, asa), Mul (gt, gu)) = Add (Sub (ar, asa), Mul (gt, gu)) |
|
804 |
| numadd (Mul (at, au), C hh) = Add (Mul (at, au), C hh) |
|
805 |
| numadd (Mul (at, au), Bound hi) = Add (Mul (at, au), Bound hi) |
|
806 |
| numadd (Mul (at, au), Neg hm) = Add (Mul (at, au), Neg hm) |
|
807 |
| numadd (Mul (at, au), Add (hn, ho)) = Add (Mul (at, au), Add (hn, ho)) |
|
808 |
| numadd (Mul (at, au), Sub (hp, hq)) = Add (Mul (at, au), Sub (hp, hq)) |
|
809 |
| numadd (Mul (at, au), Mul (hr, hs)) = Add (Mul (at, au), Mul (hr, hs)); |
|
23714 | 810 |
|
29787 | 811 |
val eq_numa = {eq = eq_num} : num eq; |
23689
0410269099dc
replaced code generator framework for reflected cooper
haftmann
parents:
23466
diff
changeset
|
812 |
|
29787 | 813 |
fun numsub s t = |
814 |
(if eqop eq_numa s t then C (0 : IntInf.int) else numadd (s, numneg t)); |
|
23689
0410269099dc
replaced code generator framework for reflected cooper
haftmann
parents:
23466
diff
changeset
|
815 |
|
29787 | 816 |
fun simpnum (C j) = C j |
817 |
| simpnum (Bound n) = Cn (n, (1 : IntInf.int), C (0 : IntInf.int)) |
|
818 |
| simpnum (Neg t) = numneg (simpnum t) |
|
819 |
| simpnum (Add (t, s)) = numadd (simpnum t, simpnum s) |
|
820 |
| simpnum (Sub (t, s)) = numsub (simpnum t) (simpnum s) |
|
821 |
| simpnum (Mul (i, t)) = |
|
822 |
(if eqop eq_int i (0 : IntInf.int) then C (0 : IntInf.int) |
|
823 |
else nummul i (simpnum t)) |
|
824 |
| simpnum (Cn (v, va, vb)) = Cn (v, va, vb); |
|
23714 | 825 |
|
29787 | 826 |
fun nota (Not y) = y |
827 |
| nota T = F |
|
828 |
| nota F = T |
|
829 |
| nota (Lt vc) = Not (Lt vc) |
|
830 |
| nota (Le vc) = Not (Le vc) |
|
831 |
| nota (Gt vc) = Not (Gt vc) |
|
832 |
| nota (Ge vc) = Not (Ge vc) |
|
833 |
| nota (Eq vc) = Not (Eq vc) |
|
834 |
| nota (NEq vc) = Not (NEq vc) |
|
835 |
| nota (Dvd (va, vab)) = Not (Dvd (va, vab)) |
|
836 |
| nota (NDvd (va, vab)) = Not (NDvd (va, vab)) |
|
837 |
| nota (And (vb, vaa)) = Not (And (vb, vaa)) |
|
838 |
| nota (Or (vb, vaa)) = Not (Or (vb, vaa)) |
|
839 |
| nota (Imp (vb, vaa)) = Not (Imp (vb, vaa)) |
|
840 |
| nota (Iff (vb, vaa)) = Not (Iff (vb, vaa)) |
|
841 |
| nota (E vb) = Not (E vb) |
|
842 |
| nota (A vb) = Not (A vb) |
|
843 |
| nota (Closed v) = Not (Closed v) |
|
844 |
| nota (NClosed v) = Not (NClosed v); |
|
23714 | 845 |
|
29787 | 846 |
fun iffa p q = |
847 |
(if eqop eq_fma p q then T |
|
848 |
else (if eqop eq_fma p (nota q) orelse eqop eq_fma (nota p) q then F |
|
849 |
else (if eqop eq_fma p F then nota q |
|
850 |
else (if eqop eq_fma q F then nota p |
|
851 |
else (if eqop eq_fma p T then q |
|
852 |
else (if eqop eq_fma q T then p |
|
853 |
else Iff (p, q))))))); |
|
23466 | 854 |
|
29787 | 855 |
fun impa p q = |
856 |
(if eqop eq_fma p F orelse eqop eq_fma q T then T |
|
857 |
else (if eqop eq_fma p T then q |
|
858 |
else (if eqop eq_fma q F then nota p else Imp (p, q)))); |
|
23714 | 859 |
|
29787 | 860 |
fun conj p q = |
861 |
(if eqop eq_fma p F orelse eqop eq_fma q F then F |
|
862 |
else (if eqop eq_fma p T then q |
|
863 |
else (if eqop eq_fma q T then p else And (p, q)))); |
|
23714 | 864 |
|
29787 | 865 |
fun simpfm (And (p, q)) = conj (simpfm p) (simpfm q) |
866 |
| simpfm (Or (p, q)) = disj (simpfm p) (simpfm q) |
|
867 |
| simpfm (Imp (p, q)) = impa (simpfm p) (simpfm q) |
|
868 |
| simpfm (Iff (p, q)) = iffa (simpfm p) (simpfm q) |
|
869 |
| simpfm (Not p) = nota (simpfm p) |
|
870 |
| simpfm (Lt a) = |
|
871 |
let |
|
872 |
val a' = simpnum a; |
|
873 |
in |
|
874 |
(case a' of C v => (if IntInf.< (v, (0 : IntInf.int)) then T else F) |
|
875 |
| Bound nat => Lt a' | Cn (nat, inta, num) => Lt a' | Neg num => Lt a' |
|
876 |
| Add (num1, num2) => Lt a' | Sub (num1, num2) => Lt a' |
|
877 |
| Mul (inta, num) => Lt a') |
|
878 |
end |
|
879 |
| simpfm (Le a) = |
|
880 |
let |
|
881 |
val a' = simpnum a; |
|
882 |
in |
|
883 |
(case a' of C v => (if IntInf.<= (v, (0 : IntInf.int)) then T else F) |
|
884 |
| Bound nat => Le a' | Cn (nat, inta, num) => Le a' | Neg num => Le a' |
|
885 |
| Add (num1, num2) => Le a' | Sub (num1, num2) => Le a' |
|
886 |
| Mul (inta, num) => Le a') |
|
887 |
end |
|
888 |
| simpfm (Gt a) = |
|
889 |
let |
|
890 |
val a' = simpnum a; |
|
891 |
in |
|
892 |
(case a' of C v => (if IntInf.< ((0 : IntInf.int), v) then T else F) |
|
893 |
| Bound nat => Gt a' | Cn (nat, inta, num) => Gt a' | Neg num => Gt a' |
|
894 |
| Add (num1, num2) => Gt a' | Sub (num1, num2) => Gt a' |
|
895 |
| Mul (inta, num) => Gt a') |
|
896 |
end |
|
897 |
| simpfm (Ge a) = |
|
898 |
let |
|
899 |
val a' = simpnum a; |
|
900 |
in |
|
901 |
(case a' of C v => (if IntInf.<= ((0 : IntInf.int), v) then T else F) |
|
902 |
| Bound nat => Ge a' | Cn (nat, inta, num) => Ge a' | Neg num => Ge a' |
|
903 |
| Add (num1, num2) => Ge a' | Sub (num1, num2) => Ge a' |
|
904 |
| Mul (inta, num) => Ge a') |
|
905 |
end |
|
906 |
| simpfm (Eq a) = |
|
907 |
let |
|
908 |
val a' = simpnum a; |
|
909 |
in |
|
910 |
(case a' of C v => (if eqop eq_int v (0 : IntInf.int) then T else F) |
|
911 |
| Bound nat => Eq a' | Cn (nat, inta, num) => Eq a' | Neg num => Eq a' |
|
912 |
| Add (num1, num2) => Eq a' | Sub (num1, num2) => Eq a' |
|
913 |
| Mul (inta, num) => Eq a') |
|
914 |
end |
|
915 |
| simpfm (NEq a) = |
|
916 |
let |
|
917 |
val a' = simpnum a; |
|
918 |
in |
|
919 |
(case a' of C v => (if not (eqop eq_int v (0 : IntInf.int)) then T else F) |
|
920 |
| Bound nat => NEq a' | Cn (nat, inta, num) => NEq a' |
|
921 |
| Neg num => NEq a' | Add (num1, num2) => NEq a' |
|
922 |
| Sub (num1, num2) => NEq a' | Mul (inta, num) => NEq a') |
|
923 |
end |
|
924 |
| simpfm (Dvd (i, a)) = |
|
925 |
(if eqop eq_int i (0 : IntInf.int) then simpfm (Eq a) |
|
926 |
else (if eqop eq_int (abs_int i) (1 : IntInf.int) then T |
|
927 |
else let |
|
928 |
val a' = simpnum a; |
|
929 |
in |
|
930 |
(case a' |
|
931 |
of C v => |
|
932 |
(if eqop eq_int (mod_int v i) (0 : IntInf.int) then T |
|
933 |
else F) |
|
934 |
| Bound nat => Dvd (i, a') |
|
935 |
| Cn (nat, inta, num) => Dvd (i, a') |
|
936 |
| Neg num => Dvd (i, a') |
|
937 |
| Add (num1, num2) => Dvd (i, a') |
|
938 |
| Sub (num1, num2) => Dvd (i, a') |
|
939 |
| Mul (inta, num) => Dvd (i, a')) |
|
940 |
end)) |
|
941 |
| simpfm (NDvd (i, a)) = |
|
942 |
(if eqop eq_int i (0 : IntInf.int) then simpfm (NEq a) |
|
943 |
else (if eqop eq_int (abs_int i) (1 : IntInf.int) then F |
|
944 |
else let |
|
945 |
val a' = simpnum a; |
|
946 |
in |
|
947 |
(case a' |
|
948 |
of C v => |
|
949 |
(if not (eqop eq_int (mod_int v i) (0 : IntInf.int)) |
|
950 |
then T else F) |
|
951 |
| Bound nat => NDvd (i, a') |
|
952 |
| Cn (nat, inta, num) => NDvd (i, a') |
|
953 |
| Neg num => NDvd (i, a') |
|
954 |
| Add (num1, num2) => NDvd (i, a') |
|
955 |
| Sub (num1, num2) => NDvd (i, a') |
|
956 |
| Mul (inta, num) => NDvd (i, a')) |
|
957 |
end)) |
|
958 |
| simpfm T = T |
|
959 |
| simpfm F = F |
|
960 |
| simpfm (E v) = E v |
|
961 |
| simpfm (A v) = A v |
|
962 |
| simpfm (Closed v) = Closed v |
|
963 |
| simpfm (NClosed v) = NClosed v; |
|
23466 | 964 |
|
29787 | 965 |
fun iupt i j = |
966 |
(if IntInf.< (j, i) then [] |
|
967 |
else i :: iupt (IntInf.+ (i, (1 : IntInf.int))) j); |
|
968 |
||
969 |
fun mirror (And (p, q)) = And (mirror p, mirror q) |
|
970 |
| mirror (Or (p, q)) = Or (mirror p, mirror q) |
|
971 |
| mirror T = T |
|
972 |
| mirror F = F |
|
973 |
| mirror (Lt (C bo)) = Lt (C bo) |
|
974 |
| mirror (Lt (Bound bp)) = Lt (Bound bp) |
|
975 |
| mirror (Lt (Neg bt)) = Lt (Neg bt) |
|
976 |
| mirror (Lt (Add (bu, bv))) = Lt (Add (bu, bv)) |
|
977 |
| mirror (Lt (Sub (bw, bx))) = Lt (Sub (bw, bx)) |
|
978 |
| mirror (Lt (Mul (by, bz))) = Lt (Mul (by, bz)) |
|
979 |
| mirror (Le (C co)) = Le (C co) |
|
980 |
| mirror (Le (Bound cp)) = Le (Bound cp) |
|
981 |
| mirror (Le (Neg ct)) = Le (Neg ct) |
|
982 |
| mirror (Le (Add (cu, cv))) = Le (Add (cu, cv)) |
|
983 |
| mirror (Le (Sub (cw, cx))) = Le (Sub (cw, cx)) |
|
984 |
| mirror (Le (Mul (cy, cz))) = Le (Mul (cy, cz)) |
|
985 |
| mirror (Gt (C doa)) = Gt (C doa) |
|
986 |
| mirror (Gt (Bound dp)) = Gt (Bound dp) |
|
987 |
| mirror (Gt (Neg dt)) = Gt (Neg dt) |
|
988 |
| mirror (Gt (Add (du, dv))) = Gt (Add (du, dv)) |
|
989 |
| mirror (Gt (Sub (dw, dx))) = Gt (Sub (dw, dx)) |
|
990 |
| mirror (Gt (Mul (dy, dz))) = Gt (Mul (dy, dz)) |
|
991 |
| mirror (Ge (C eo)) = Ge (C eo) |
|
992 |
| mirror (Ge (Bound ep)) = Ge (Bound ep) |
|
993 |
| mirror (Ge (Neg et)) = Ge (Neg et) |
|
994 |
| mirror (Ge (Add (eu, ev))) = Ge (Add (eu, ev)) |
|
995 |
| mirror (Ge (Sub (ew, ex))) = Ge (Sub (ew, ex)) |
|
996 |
| mirror (Ge (Mul (ey, ez))) = Ge (Mul (ey, ez)) |
|
997 |
| mirror (Eq (C fo)) = Eq (C fo) |
|
998 |
| mirror (Eq (Bound fp)) = Eq (Bound fp) |
|
999 |
| mirror (Eq (Neg ft)) = Eq (Neg ft) |
|
1000 |
| mirror (Eq (Add (fu, fv))) = Eq (Add (fu, fv)) |
|
1001 |
| mirror (Eq (Sub (fw, fx))) = Eq (Sub (fw, fx)) |
|
1002 |
| mirror (Eq (Mul (fy, fz))) = Eq (Mul (fy, fz)) |
|
1003 |
| mirror (NEq (C go)) = NEq (C go) |
|
1004 |
| mirror (NEq (Bound gp)) = NEq (Bound gp) |
|
1005 |
| mirror (NEq (Neg gt)) = NEq (Neg gt) |
|
1006 |
| mirror (NEq (Add (gu, gv))) = NEq (Add (gu, gv)) |
|
1007 |
| mirror (NEq (Sub (gw, gx))) = NEq (Sub (gw, gx)) |
|
1008 |
| mirror (NEq (Mul (gy, gz))) = NEq (Mul (gy, gz)) |
|
1009 |
| mirror (Dvd (aa, C ho)) = Dvd (aa, C ho) |
|
1010 |
| mirror (Dvd (aa, Bound hp)) = Dvd (aa, Bound hp) |
|
1011 |
| mirror (Dvd (aa, Neg ht)) = Dvd (aa, Neg ht) |
|
1012 |
| mirror (Dvd (aa, Add (hu, hv))) = Dvd (aa, Add (hu, hv)) |
|
1013 |
| mirror (Dvd (aa, Sub (hw, hx))) = Dvd (aa, Sub (hw, hx)) |
|
1014 |
| mirror (Dvd (aa, Mul (hy, hz))) = Dvd (aa, Mul (hy, hz)) |
|
1015 |
| mirror (NDvd (ac, C io)) = NDvd (ac, C io) |
|
1016 |
| mirror (NDvd (ac, Bound ip)) = NDvd (ac, Bound ip) |
|
1017 |
| mirror (NDvd (ac, Neg it)) = NDvd (ac, Neg it) |
|
1018 |
| mirror (NDvd (ac, Add (iu, iv))) = NDvd (ac, Add (iu, iv)) |
|
1019 |
| mirror (NDvd (ac, Sub (iw, ix))) = NDvd (ac, Sub (iw, ix)) |
|
1020 |
| mirror (NDvd (ac, Mul (iy, iz))) = NDvd (ac, Mul (iy, iz)) |
|
1021 |
| mirror (Not ae) = Not ae |
|
1022 |
| mirror (Imp (aj, ak)) = Imp (aj, ak) |
|
1023 |
| mirror (Iff (al, am)) = Iff (al, am) |
|
1024 |
| mirror (E an) = E an |
|
1025 |
| mirror (A ao) = A ao |
|
1026 |
| mirror (Closed ap) = Closed ap |
|
1027 |
| mirror (NClosed aq) = NClosed aq |
|
1028 |
| mirror (Lt (Cn (cm, c, e))) = |
|
1029 |
(if eqop eq_nat cm 0 then Gt (Cn (0, c, Neg e)) |
|
1030 |
else Lt (Cn (suc (minus_nat cm 1), c, e))) |
|
1031 |
| mirror (Le (Cn (dm, c, e))) = |
|
1032 |
(if eqop eq_nat dm 0 then Ge (Cn (0, c, Neg e)) |
|
1033 |
else Le (Cn (suc (minus_nat dm 1), c, e))) |
|
1034 |
| mirror (Gt (Cn (em, c, e))) = |
|
1035 |
(if eqop eq_nat em 0 then Lt (Cn (0, c, Neg e)) |
|
1036 |
else Gt (Cn (suc (minus_nat em 1), c, e))) |
|
1037 |
| mirror (Ge (Cn (fm, c, e))) = |
|
1038 |
(if eqop eq_nat fm 0 then Le (Cn (0, c, Neg e)) |
|
1039 |
else Ge (Cn (suc (minus_nat fm 1), c, e))) |
|
1040 |
| mirror (Eq (Cn (gm, c, e))) = |
|
1041 |
(if eqop eq_nat gm 0 then Eq (Cn (0, c, Neg e)) |
|
1042 |
else Eq (Cn (suc (minus_nat gm 1), c, e))) |
|
1043 |
| mirror (NEq (Cn (hm, c, e))) = |
|
1044 |
(if eqop eq_nat hm 0 then NEq (Cn (0, c, Neg e)) |
|
1045 |
else NEq (Cn (suc (minus_nat hm 1), c, e))) |
|
1046 |
| mirror (Dvd (i, Cn (im, c, e))) = |
|
1047 |
(if eqop eq_nat im 0 then Dvd (i, Cn (0, c, Neg e)) |
|
1048 |
else Dvd (i, Cn (suc (minus_nat im 1), c, e))) |
|
1049 |
| mirror (NDvd (i, Cn (jm, c, e))) = |
|
1050 |
(if eqop eq_nat jm 0 then NDvd (i, Cn (0, c, Neg e)) |
|
1051 |
else NDvd (i, Cn (suc (minus_nat jm 1), c, e))); |
|
1052 |
||
1053 |
fun size_list [] = 0 |
|
1054 |
| size_list (a :: lista) = IntInf.+ (size_list lista, suc 0); |
|
23466 | 1055 |
|
29787 | 1056 |
fun alpha (And (p, q)) = append (alpha p) (alpha q) |
1057 |
| alpha (Or (p, q)) = append (alpha p) (alpha q) |
|
1058 |
| alpha T = [] |
|
1059 |
| alpha F = [] |
|
1060 |
| alpha (Lt (C bo)) = [] |
|
1061 |
| alpha (Lt (Bound bp)) = [] |
|
1062 |
| alpha (Lt (Neg bt)) = [] |
|
1063 |
| alpha (Lt (Add (bu, bv))) = [] |
|
1064 |
| alpha (Lt (Sub (bw, bx))) = [] |
|
1065 |
| alpha (Lt (Mul (by, bz))) = [] |
|
1066 |
| alpha (Le (C co)) = [] |
|
1067 |
| alpha (Le (Bound cp)) = [] |
|
1068 |
| alpha (Le (Neg ct)) = [] |
|
1069 |
| alpha (Le (Add (cu, cv))) = [] |
|
1070 |
| alpha (Le (Sub (cw, cx))) = [] |
|
1071 |
| alpha (Le (Mul (cy, cz))) = [] |
|
1072 |
| alpha (Gt (C doa)) = [] |
|
1073 |
| alpha (Gt (Bound dp)) = [] |
|
1074 |
| alpha (Gt (Neg dt)) = [] |
|
1075 |
| alpha (Gt (Add (du, dv))) = [] |
|
1076 |
| alpha (Gt (Sub (dw, dx))) = [] |
|
1077 |
| alpha (Gt (Mul (dy, dz))) = [] |
|
1078 |
| alpha (Ge (C eo)) = [] |
|
1079 |
| alpha (Ge (Bound ep)) = [] |
|
1080 |
| alpha (Ge (Neg et)) = [] |
|
1081 |
| alpha (Ge (Add (eu, ev))) = [] |
|
1082 |
| alpha (Ge (Sub (ew, ex))) = [] |
|
1083 |
| alpha (Ge (Mul (ey, ez))) = [] |
|
1084 |
| alpha (Eq (C fo)) = [] |
|
1085 |
| alpha (Eq (Bound fp)) = [] |
|
1086 |
| alpha (Eq (Neg ft)) = [] |
|
1087 |
| alpha (Eq (Add (fu, fv))) = [] |
|
1088 |
| alpha (Eq (Sub (fw, fx))) = [] |
|
1089 |
| alpha (Eq (Mul (fy, fz))) = [] |
|
1090 |
| alpha (NEq (C go)) = [] |
|
1091 |
| alpha (NEq (Bound gp)) = [] |
|
1092 |
| alpha (NEq (Neg gt)) = [] |
|
1093 |
| alpha (NEq (Add (gu, gv))) = [] |
|
1094 |
| alpha (NEq (Sub (gw, gx))) = [] |
|
1095 |
| alpha (NEq (Mul (gy, gz))) = [] |
|
1096 |
| alpha (Dvd (aa, ab)) = [] |
|
1097 |
| alpha (NDvd (ac, ad)) = [] |
|
1098 |
| alpha (Not ae) = [] |
|
1099 |
| alpha (Imp (aj, ak)) = [] |
|
1100 |
| alpha (Iff (al, am)) = [] |
|
1101 |
| alpha (E an) = [] |
|
1102 |
| alpha (A ao) = [] |
|
1103 |
| alpha (Closed ap) = [] |
|
1104 |
| alpha (NClosed aq) = [] |
|
1105 |
| alpha (Lt (Cn (cm, c, e))) = (if eqop eq_nat cm 0 then [e] else []) |
|
1106 |
| alpha (Le (Cn (dm, c, e))) = |
|
1107 |
(if eqop eq_nat dm 0 then [Add (C (~1 : IntInf.int), e)] else []) |
|
1108 |
| alpha (Gt (Cn (em, c, e))) = (if eqop eq_nat em 0 then [] else []) |
|
1109 |
| alpha (Ge (Cn (fm, c, e))) = (if eqop eq_nat fm 0 then [] else []) |
|
1110 |
| alpha (Eq (Cn (gm, c, e))) = |
|
1111 |
(if eqop eq_nat gm 0 then [Add (C (~1 : IntInf.int), e)] else []) |
|
1112 |
| alpha (NEq (Cn (hm, c, e))) = (if eqop eq_nat hm 0 then [e] else []); |
|
1113 |
||
1114 |
fun beta (And (p, q)) = append (beta p) (beta q) |
|
1115 |
| beta (Or (p, q)) = append (beta p) (beta q) |
|
1116 |
| beta T = [] |
|
1117 |
| beta F = [] |
|
1118 |
| beta (Lt (C bo)) = [] |
|
1119 |
| beta (Lt (Bound bp)) = [] |
|
1120 |
| beta (Lt (Neg bt)) = [] |
|
1121 |
| beta (Lt (Add (bu, bv))) = [] |
|
1122 |
| beta (Lt (Sub (bw, bx))) = [] |
|
1123 |
| beta (Lt (Mul (by, bz))) = [] |
|
1124 |
| beta (Le (C co)) = [] |
|
1125 |
| beta (Le (Bound cp)) = [] |
|
1126 |
| beta (Le (Neg ct)) = [] |
|
1127 |
| beta (Le (Add (cu, cv))) = [] |
|
1128 |
| beta (Le (Sub (cw, cx))) = [] |
|
1129 |
| beta (Le (Mul (cy, cz))) = [] |
|
1130 |
| beta (Gt (C doa)) = [] |
|
1131 |
| beta (Gt (Bound dp)) = [] |
|
1132 |
| beta (Gt (Neg dt)) = [] |
|
1133 |
| beta (Gt (Add (du, dv))) = [] |
|
1134 |
| beta (Gt (Sub (dw, dx))) = [] |
|
1135 |
| beta (Gt (Mul (dy, dz))) = [] |
|
1136 |
| beta (Ge (C eo)) = [] |
|
1137 |
| beta (Ge (Bound ep)) = [] |
|
1138 |
| beta (Ge (Neg et)) = [] |
|
1139 |
| beta (Ge (Add (eu, ev))) = [] |
|
1140 |
| beta (Ge (Sub (ew, ex))) = [] |
|
1141 |
| beta (Ge (Mul (ey, ez))) = [] |
|
1142 |
| beta (Eq (C fo)) = [] |
|
1143 |
| beta (Eq (Bound fp)) = [] |
|
1144 |
| beta (Eq (Neg ft)) = [] |
|
1145 |
| beta (Eq (Add (fu, fv))) = [] |
|
1146 |
| beta (Eq (Sub (fw, fx))) = [] |
|
1147 |
| beta (Eq (Mul (fy, fz))) = [] |
|
1148 |
| beta (NEq (C go)) = [] |
|
1149 |
| beta (NEq (Bound gp)) = [] |
|
1150 |
| beta (NEq (Neg gt)) = [] |
|
1151 |
| beta (NEq (Add (gu, gv))) = [] |
|
1152 |
| beta (NEq (Sub (gw, gx))) = [] |
|
1153 |
| beta (NEq (Mul (gy, gz))) = [] |
|
1154 |
| beta (Dvd (aa, ab)) = [] |
|
1155 |
| beta (NDvd (ac, ad)) = [] |
|
1156 |
| beta (Not ae) = [] |
|
1157 |
| beta (Imp (aj, ak)) = [] |
|
1158 |
| beta (Iff (al, am)) = [] |
|
1159 |
| beta (E an) = [] |
|
1160 |
| beta (A ao) = [] |
|
1161 |
| beta (Closed ap) = [] |
|
1162 |
| beta (NClosed aq) = [] |
|
1163 |
| beta (Lt (Cn (cm, c, e))) = (if eqop eq_nat cm 0 then [] else []) |
|
1164 |
| beta (Le (Cn (dm, c, e))) = (if eqop eq_nat dm 0 then [] else []) |
|
1165 |
| beta (Gt (Cn (em, c, e))) = (if eqop eq_nat em 0 then [Neg e] else []) |
|
1166 |
| beta (Ge (Cn (fm, c, e))) = |
|
1167 |
(if eqop eq_nat fm 0 then [Sub (C (~1 : IntInf.int), e)] else []) |
|
1168 |
| beta (Eq (Cn (gm, c, e))) = |
|
1169 |
(if eqop eq_nat gm 0 then [Sub (C (~1 : IntInf.int), e)] else []) |
|
1170 |
| beta (NEq (Cn (hm, c, e))) = (if eqop eq_nat hm 0 then [Neg e] else []); |
|
1171 |
||
1172 |
fun member A_ x [] = false |
|
1173 |
| member A_ x (y :: ys) = eqop A_ x y orelse member A_ x ys; |
|
1174 |
||
1175 |
fun remdups A_ [] = [] |
|
1176 |
| remdups A_ (x :: xs) = |
|
1177 |
(if member A_ x xs then remdups A_ xs else x :: remdups A_ xs); |
|
1178 |
||
1179 |
fun delta (And (p, q)) = zlcm (delta p) (delta q) |
|
1180 |
| delta (Or (p, q)) = zlcm (delta p) (delta q) |
|
1181 |
| delta T = (1 : IntInf.int) |
|
1182 |
| delta F = (1 : IntInf.int) |
|
1183 |
| delta (Lt u) = (1 : IntInf.int) |
|
1184 |
| delta (Le v) = (1 : IntInf.int) |
|
1185 |
| delta (Gt w) = (1 : IntInf.int) |
|
1186 |
| delta (Ge x) = (1 : IntInf.int) |
|
1187 |
| delta (Eq ya) = (1 : IntInf.int) |
|
1188 |
| delta (NEq z) = (1 : IntInf.int) |
|
1189 |
| delta (Dvd (aa, C bo)) = (1 : IntInf.int) |
|
1190 |
| delta (Dvd (aa, Bound bp)) = (1 : IntInf.int) |
|
1191 |
| delta (Dvd (aa, Neg bt)) = (1 : IntInf.int) |
|
1192 |
| delta (Dvd (aa, Add (bu, bv))) = (1 : IntInf.int) |
|
1193 |
| delta (Dvd (aa, Sub (bw, bx))) = (1 : IntInf.int) |
|
1194 |
| delta (Dvd (aa, Mul (by, bz))) = (1 : IntInf.int) |
|
1195 |
| delta (NDvd (ac, C co)) = (1 : IntInf.int) |
|
1196 |
| delta (NDvd (ac, Bound cp)) = (1 : IntInf.int) |
|
1197 |
| delta (NDvd (ac, Neg ct)) = (1 : IntInf.int) |
|
1198 |
| delta (NDvd (ac, Add (cu, cv))) = (1 : IntInf.int) |
|
1199 |
| delta (NDvd (ac, Sub (cw, cx))) = (1 : IntInf.int) |
|
1200 |
| delta (NDvd (ac, Mul (cy, cz))) = (1 : IntInf.int) |
|
1201 |
| delta (Not ae) = (1 : IntInf.int) |
|
1202 |
| delta (Imp (aj, ak)) = (1 : IntInf.int) |
|
1203 |
| delta (Iff (al, am)) = (1 : IntInf.int) |
|
1204 |
| delta (E an) = (1 : IntInf.int) |
|
1205 |
| delta (A ao) = (1 : IntInf.int) |
|
1206 |
| delta (Closed ap) = (1 : IntInf.int) |
|
1207 |
| delta (NClosed aq) = (1 : IntInf.int) |
|
1208 |
| delta (Dvd (b, Cn (cm, c, e))) = |
|
1209 |
(if eqop eq_nat cm 0 then b else (1 : IntInf.int)) |
|
1210 |
| delta (NDvd (b, Cn (dm, c, e))) = |
|
1211 |
(if eqop eq_nat dm 0 then b else (1 : IntInf.int)); |
|
1212 |
||
1213 |
fun div_int a b = fst (divmoda a b); |
|
23689
0410269099dc
replaced code generator framework for reflected cooper
haftmann
parents:
23466
diff
changeset
|
1214 |
|
29787 | 1215 |
fun a_beta (And (p, q)) = (fn k => And (a_beta p k, a_beta q k)) |
1216 |
| a_beta (Or (p, q)) = (fn k => Or (a_beta p k, a_beta q k)) |
|
1217 |
| a_beta T = (fn k => T) |
|
1218 |
| a_beta F = (fn k => F) |
|
1219 |
| a_beta (Lt (C bo)) = (fn k => Lt (C bo)) |
|
1220 |
| a_beta (Lt (Bound bp)) = (fn k => Lt (Bound bp)) |
|
1221 |
| a_beta (Lt (Neg bt)) = (fn k => Lt (Neg bt)) |
|
1222 |
| a_beta (Lt (Add (bu, bv))) = (fn k => Lt (Add (bu, bv))) |
|
1223 |
| a_beta (Lt (Sub (bw, bx))) = (fn k => Lt (Sub (bw, bx))) |
|
1224 |
| a_beta (Lt (Mul (by, bz))) = (fn k => Lt (Mul (by, bz))) |
|
1225 |
| a_beta (Le (C co)) = (fn k => Le (C co)) |
|
1226 |
| a_beta (Le (Bound cp)) = (fn k => Le (Bound cp)) |
|
1227 |
| a_beta (Le (Neg ct)) = (fn k => Le (Neg ct)) |
|
1228 |
| a_beta (Le (Add (cu, cv))) = (fn k => Le (Add (cu, cv))) |
|
1229 |
| a_beta (Le (Sub (cw, cx))) = (fn k => Le (Sub (cw, cx))) |
|
1230 |
| a_beta (Le (Mul (cy, cz))) = (fn k => Le (Mul (cy, cz))) |
|
1231 |
| a_beta (Gt (C doa)) = (fn k => Gt (C doa)) |
|
1232 |
| a_beta (Gt (Bound dp)) = (fn k => Gt (Bound dp)) |
|
1233 |
| a_beta (Gt (Neg dt)) = (fn k => Gt (Neg dt)) |
|
1234 |
| a_beta (Gt (Add (du, dv))) = (fn k => Gt (Add (du, dv))) |
|
1235 |
| a_beta (Gt (Sub (dw, dx))) = (fn k => Gt (Sub (dw, dx))) |
|
1236 |
| a_beta (Gt (Mul (dy, dz))) = (fn k => Gt (Mul (dy, dz))) |
|
1237 |
| a_beta (Ge (C eo)) = (fn k => Ge (C eo)) |
|
1238 |
| a_beta (Ge (Bound ep)) = (fn k => Ge (Bound ep)) |
|
1239 |
| a_beta (Ge (Neg et)) = (fn k => Ge (Neg et)) |
|
1240 |
| a_beta (Ge (Add (eu, ev))) = (fn k => Ge (Add (eu, ev))) |
|
1241 |
| a_beta (Ge (Sub (ew, ex))) = (fn k => Ge (Sub (ew, ex))) |
|
1242 |
| a_beta (Ge (Mul (ey, ez))) = (fn k => Ge (Mul (ey, ez))) |
|
1243 |
| a_beta (Eq (C fo)) = (fn k => Eq (C fo)) |
|
1244 |
| a_beta (Eq (Bound fp)) = (fn k => Eq (Bound fp)) |
|
1245 |
| a_beta (Eq (Neg ft)) = (fn k => Eq (Neg ft)) |
|
1246 |
| a_beta (Eq (Add (fu, fv))) = (fn k => Eq (Add (fu, fv))) |
|
1247 |
| a_beta (Eq (Sub (fw, fx))) = (fn k => Eq (Sub (fw, fx))) |
|
1248 |
| a_beta (Eq (Mul (fy, fz))) = (fn k => Eq (Mul (fy, fz))) |
|
1249 |
| a_beta (NEq (C go)) = (fn k => NEq (C go)) |
|
1250 |
| a_beta (NEq (Bound gp)) = (fn k => NEq (Bound gp)) |
|
1251 |
| a_beta (NEq (Neg gt)) = (fn k => NEq (Neg gt)) |
|
1252 |
| a_beta (NEq (Add (gu, gv))) = (fn k => NEq (Add (gu, gv))) |
|
1253 |
| a_beta (NEq (Sub (gw, gx))) = (fn k => NEq (Sub (gw, gx))) |
|
1254 |
| a_beta (NEq (Mul (gy, gz))) = (fn k => NEq (Mul (gy, gz))) |
|
1255 |
| a_beta (Dvd (aa, C ho)) = (fn k => Dvd (aa, C ho)) |
|
1256 |
| a_beta (Dvd (aa, Bound hp)) = (fn k => Dvd (aa, Bound hp)) |
|
1257 |
| a_beta (Dvd (aa, Neg ht)) = (fn k => Dvd (aa, Neg ht)) |
|
1258 |
| a_beta (Dvd (aa, Add (hu, hv))) = (fn k => Dvd (aa, Add (hu, hv))) |
|
1259 |
| a_beta (Dvd (aa, Sub (hw, hx))) = (fn k => Dvd (aa, Sub (hw, hx))) |
|
1260 |
| a_beta (Dvd (aa, Mul (hy, hz))) = (fn k => Dvd (aa, Mul (hy, hz))) |
|
1261 |
| a_beta (NDvd (ac, C io)) = (fn k => NDvd (ac, C io)) |
|