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|
Maude> fmod BAR is
inc FOO * (sort Foo to Baz, sort Bar to Quux) .
endfm
fmod BAR is
sorts Bool Baz Quux .
subsort Baz < Quux .
op if_then_else_fi : Bool Universal Universal -> Universal [poly (2 3 0) prec
0 gather (& & &) special (
id-hook BranchSymbol
term-hook 1 (true)
term-hook 2 (false))] .
op _==_ : Universal Universal -> Bool [poly (1 2) prec 51 gather (E E)
special (
id-hook EqualitySymbol
term-hook equalTerm (true)
term-hook notEqualTerm (false))] .
op _=/=_ : Universal Universal -> Bool [poly (1 2) prec 51 gather (E E)
special (
id-hook EqualitySymbol
term-hook equalTerm (false)
term-hook notEqualTerm (true))] .
op true : -> Bool [ctor special (
id-hook SystemTrue)] .
op false : -> Bool [ctor special (
id-hook SystemFalse)] .
op _and_ : Bool Bool -> Bool [assoc comm prec 55 gather (e E)] .
op _or_ : Bool Bool -> Bool [assoc comm prec 59 gather (e E)] .
op _xor_ : Bool Bool -> Bool [assoc comm prec 57 gather (e E)] .
op not_ : Bool -> Bool [prec 53 gather (E)] .
op _implies_ : Bool Bool -> Bool [prec 61 gather (e E)] .
eq true and A:Bool = A:Bool .
eq false and A:Bool = false .
eq A:Bool and A:Bool = A:Bool .
eq false xor A:Bool = A:Bool .
eq A:Bool xor A:Bool = false .
eq A:Bool and (B:Bool xor C:Bool) = A:Bool and B:Bool xor A:Bool and C:Bool .
eq not A:Bool = true xor A:Bool .
eq A:Bool or B:Bool = A:Bool and B:Bool xor A:Bool xor B:Bool .
eq A:Bool implies B:Bool = not (A:Bool xor A:Bool and B:Bool) .
endfm
fmod THREE is
inc TWO * (sort Foo to Foo', sort Baz to Baz', sort Quux to Quux') .
sorts Jaz .
subsorts Jaz < Baz' .
endfm
fmod THREE is
sorts Bool Baz' Bar Quux' Jaz .
subsorts Quux' Jaz < Baz' .
subsort Baz' < Bar .
op if_then_else_fi : Bool Universal Universal -> Universal [poly (2 3 0) prec
0 gather (& & &) special (
id-hook BranchSymbol
term-hook 1 (true)
term-hook 2 (false))] .
op _==_ : Universal Universal -> Bool [poly (1 2) prec 51 gather (E E)
special (
id-hook EqualitySymbol
term-hook equalTerm (true)
term-hook notEqualTerm (false))] .
op _=/=_ : Universal Universal -> Bool [poly (1 2) prec 51 gather (E E)
special (
id-hook EqualitySymbol
term-hook equalTerm (false)
term-hook notEqualTerm (true))] .
op true : -> Bool [ctor special (
id-hook SystemTrue)] .
op false : -> Bool [ctor special (
id-hook SystemFalse)] .
op _and_ : Bool Bool -> Bool [assoc comm prec 55 gather (e E)] .
op _or_ : Bool Bool -> Bool [assoc comm prec 59 gather (e E)] .
op _xor_ : Bool Bool -> Bool [assoc comm prec 57 gather (e E)] .
op not_ : Bool -> Bool [prec 53 gather (E)] .
op _implies_ : Bool Bool -> Bool [prec 61 gather (e E)] .
eq true and A:Bool = A:Bool .
eq false and A:Bool = false .
eq A:Bool and A:Bool = A:Bool .
eq false xor A:Bool = A:Bool .
eq A:Bool xor A:Bool = false .
eq A:Bool and (B:Bool xor C:Bool) = A:Bool and B:Bool xor A:Bool and C:Bool .
eq not A:Bool = true xor A:Bool .
eq A:Bool or B:Bool = A:Bool and B:Bool xor A:Bool xor B:Bool .
eq A:Bool implies B:Bool = not (A:Bool xor A:Bool and B:Bool) .
endfm
fmod BAR is
inc FOO * (sort Foo to Baz, op a to b) .
endfm
fmod BAR is
sorts Bool Baz Bar .
subsort Baz < Bar .
op if_then_else_fi : Bool Universal Universal -> Universal [poly (2 3 0) prec
0 gather (& & &) special (
id-hook BranchSymbol
term-hook 1 (true)
term-hook 2 (false))] .
op _==_ : Universal Universal -> Bool [poly (1 2) prec 51 gather (E E)
special (
id-hook EqualitySymbol
term-hook equalTerm (true)
term-hook notEqualTerm (false))] .
op _=/=_ : Universal Universal -> Bool [poly (1 2) prec 51 gather (E E)
special (
id-hook EqualitySymbol
term-hook equalTerm (false)
term-hook notEqualTerm (true))] .
op true : -> Bool [ctor special (
id-hook SystemTrue)] .
op false : -> Bool [ctor special (
id-hook SystemFalse)] .
op _and_ : Bool Bool -> Bool [assoc comm prec 55 gather (e E)] .
op _or_ : Bool Bool -> Bool [assoc comm prec 59 gather (e E)] .
op _xor_ : Bool Bool -> Bool [assoc comm prec 57 gather (e E)] .
op not_ : Bool -> Bool [prec 53 gather (E)] .
op _implies_ : Bool Bool -> Bool [prec 61 gather (e E)] .
op b : -> Baz .
eq true and A:Bool = A:Bool .
eq false and A:Bool = false .
eq A:Bool and A:Bool = A:Bool .
eq false xor A:Bool = A:Bool .
eq A:Bool xor A:Bool = false .
eq A:Bool and (B:Bool xor C:Bool) = A:Bool and B:Bool xor A:Bool and C:Bool .
eq not A:Bool = true xor A:Bool .
eq A:Bool or B:Bool = A:Bool and B:Bool xor A:Bool xor B:Bool .
eq A:Bool implies B:Bool = not (A:Bool xor A:Bool and B:Bool) .
endfm
fmod BAR' is
inc FOO' * (sort Foo to Quux, op _+_ : [Foo] [Foo] -> [Foo] to _*_ [prec 29
gather (E e)], op _+_ : [Baz] [Baz] -> [Foo] to _._ [prec 27 gather (E e)])
.
endfm
fmod BAR' is
sorts Bool Quux Bar Baz .
subsort Quux < Bar .
op if_then_else_fi : Bool Universal Universal -> Universal [poly (2 3 0) prec
0 gather (& & &) special (
id-hook BranchSymbol
term-hook 1 (true)
term-hook 2 (false))] .
op _==_ : Universal Universal -> Bool [poly (1 2) prec 51 gather (E E)
special (
id-hook EqualitySymbol
term-hook equalTerm (true)
term-hook notEqualTerm (false))] .
op _=/=_ : Universal Universal -> Bool [poly (1 2) prec 51 gather (E E)
special (
id-hook EqualitySymbol
term-hook equalTerm (false)
term-hook notEqualTerm (true))] .
op true : -> Bool [ctor special (
id-hook SystemTrue)] .
op false : -> Bool [ctor special (
id-hook SystemFalse)] .
op _and_ : Bool Bool -> Bool [assoc comm prec 55 gather (e E)] .
op _or_ : Bool Bool -> Bool [assoc comm prec 59 gather (e E)] .
op _xor_ : Bool Bool -> Bool [assoc comm prec 57 gather (e E)] .
op not_ : Bool -> Bool [prec 53 gather (E)] .
op _implies_ : Bool Bool -> Bool [prec 61 gather (e E)] .
op a : -> Baz .
op _*_ : Quux Quux -> Quux [assoc comm prec 29 gather (E e)] .
op _._ : Baz Baz -> Quux [prec 27 gather (E e)] .
eq true and A:Bool = A:Bool .
eq false and A:Bool = false .
eq A:Bool and A:Bool = A:Bool .
eq false xor A:Bool = A:Bool .
eq A:Bool xor A:Bool = false .
eq A:Bool and (B:Bool xor C:Bool) = A:Bool and B:Bool xor A:Bool and C:Bool .
eq not A:Bool = true xor A:Bool .
eq A:Bool or B:Bool = A:Bool and B:Bool xor A:Bool xor B:Bool .
eq A:Bool implies B:Bool = not (A:Bool xor A:Bool and B:Bool) .
endfm
==========================================
reduce in BAR' : a . a * a . a .
rewrites: 0
result Quux: a . a * a . a
fmod BAR'' is
inc FOO' * (sort Foo to Quux, op _+_ to _*_ [prec 29 gather (E E)]) .
endfm
fmod BAR'' is
sorts Bool Quux Bar Baz .
subsort Quux < Bar .
op if_then_else_fi : Bool Universal Universal -> Universal [poly (2 3 0) prec
0 gather (& & &) special (
id-hook BranchSymbol
term-hook 1 (true)
term-hook 2 (false))] .
op _==_ : Universal Universal -> Bool [poly (1 2) prec 51 gather (E E)
special (
id-hook EqualitySymbol
term-hook equalTerm (true)
term-hook notEqualTerm (false))] .
op _=/=_ : Universal Universal -> Bool [poly (1 2) prec 51 gather (E E)
special (
id-hook EqualitySymbol
term-hook equalTerm (false)
term-hook notEqualTerm (true))] .
op true : -> Bool [ctor special (
id-hook SystemTrue)] .
op false : -> Bool [ctor special (
id-hook SystemFalse)] .
op _and_ : Bool Bool -> Bool [assoc comm prec 55 gather (e E)] .
op _or_ : Bool Bool -> Bool [assoc comm prec 59 gather (e E)] .
op _xor_ : Bool Bool -> Bool [assoc comm prec 57 gather (e E)] .
op not_ : Bool -> Bool [prec 53 gather (E)] .
op _implies_ : Bool Bool -> Bool [prec 61 gather (e E)] .
op a : -> Baz .
op _*_ : Quux Quux -> Quux [assoc comm prec 29 gather (E E)] .
op _*_ : Baz Baz -> Quux [prec 29 gather (E E)] .
eq true and A:Bool = A:Bool .
eq false and A:Bool = false .
eq A:Bool and A:Bool = A:Bool .
eq false xor A:Bool = A:Bool .
eq A:Bool xor A:Bool = false .
eq A:Bool and (B:Bool xor C:Bool) = A:Bool and B:Bool xor A:Bool and C:Bool .
eq not A:Bool = true xor A:Bool .
eq A:Bool or B:Bool = A:Bool and B:Bool xor A:Bool xor B:Bool .
eq A:Bool implies B:Bool = not (A:Bool xor A:Bool and B:Bool) .
endfm
==========================================
reduce in BAR'' : a * a * a * a .
rewrites: 0
result Quux: a * a * a * a
==========================================
reduce in BAR'' : a * a * a * a .
rewrites: 0
result Quux: a * a * a * a
fmod TEST is
inc BASH * (op f : [Foo] -> [Foo] to g) .
endfm
fmod TEST is
sorts Bool Foo Bar .
subsort Foo < Bar .
op if_then_else_fi : Bool Universal Universal -> Universal [poly (2 3 0) prec
0 gather (& & &) special (
id-hook BranchSymbol
term-hook 1 (true)
term-hook 2 (false))] .
op _==_ : Universal Universal -> Bool [poly (1 2) prec 51 gather (E E)
special (
id-hook EqualitySymbol
term-hook equalTerm (true)
term-hook notEqualTerm (false))] .
op _=/=_ : Universal Universal -> Bool [poly (1 2) prec 51 gather (E E)
special (
id-hook EqualitySymbol
term-hook equalTerm (false)
term-hook notEqualTerm (true))] .
op true : -> Bool [ctor special (
id-hook SystemTrue)] .
op false : -> Bool [ctor special (
id-hook SystemFalse)] .
op _and_ : Bool Bool -> Bool [assoc comm prec 55 gather (e E)] .
op _or_ : Bool Bool -> Bool [assoc comm prec 59 gather (e E)] .
op _xor_ : Bool Bool -> Bool [assoc comm prec 57 gather (e E)] .
op not_ : Bool -> Bool [prec 53 gather (E)] .
op _implies_ : Bool Bool -> Bool [prec 61 gather (e E)] .
op g : Foo -> Foo .
op g : Bar -> Bar .
eq true and A:Bool = A:Bool .
eq false and A:Bool = false .
eq A:Bool and A:Bool = A:Bool .
eq false xor A:Bool = A:Bool .
eq A:Bool xor A:Bool = false .
eq A:Bool and (B:Bool xor C:Bool) = A:Bool and B:Bool xor A:Bool and C:Bool .
eq not A:Bool = true xor A:Bool .
eq A:Bool or B:Bool = A:Bool and B:Bool xor A:Bool xor B:Bool .
eq A:Bool implies B:Bool = not (A:Bool xor A:Bool and B:Bool) .
endfm
fmod BOOL
fmod TRUTH-VALUE
fmod BOOL-OPS
fmod TRUTH
fmod EXT-BOOL
fmod NAT
fmod INT
fmod RAT
fmod FLOAT
fmod STRING
fmod CONVERSION
fmod RANDOM
fmod QID
fth TRIV
fth STRICT-WEAK-ORDER
fth STRICT-TOTAL-ORDER
fth TOTAL-PREORDER
fth TOTAL-ORDER
fth DEFAULT
fmod LIST
fmod WEAKLY-SORTABLE-LIST
fmod SORTABLE-LIST
fmod WEAKLY-SORTABLE-LIST'
fmod SORTABLE-LIST'
fmod SET
fmod LIST-AND-SET
fmod SORTABLE-LIST-AND-SET
fmod SORTABLE-LIST-AND-SET'
fmod LIST*
fmod SET*
fmod MAP
fmod ARRAY
fmod NAT-LIST
fmod QID-LIST
fmod QID-SET
fmod META-TERM
fmod META-MODULE
fmod META-VIEW
fmod META-LEVEL
mod COUNTER
mod LOOP-MODE
mod CONFIGURATION
fmod FOO
fmod BAR
fmod ONE
fmod TWO
fmod THREE
fmod FOO'
fmod BAR'
fmod BAR''
fmod DIFF
fmod BASH
fmod TEST
fth X :: TRIV
fth X :: STRICT-WEAK-ORDER
fmod LIST{STRICT-WEAK-ORDER}
fmod LIST{STRICT-WEAK-ORDER}{[X]}
fmod LIST{STRICT-WEAK-ORDER}{[X]} * (sort NeList{STRICT-WEAK-ORDER}{X} to
NeList{X}, sort List{STRICT-WEAK-ORDER}{X} to List{X})
fth X :: STRICT-TOTAL-ORDER
fmod WEAKLY-SORTABLE-LIST{STRICT-TOTAL-ORDER}
fmod LIST{STRICT-WEAK-ORDER}{STRICT-TOTAL-ORDER}
fmod LIST{STRICT-WEAK-ORDER}{STRICT-TOTAL-ORDER}{[X]}
fmod LIST{STRICT-WEAK-ORDER}{STRICT-TOTAL-ORDER}{[X]} * (sort NeList{
STRICT-WEAK-ORDER}{STRICT-TOTAL-ORDER}{X} to NeList{STRICT-TOTAL-ORDER}{X},
sort List{STRICT-WEAK-ORDER}{STRICT-TOTAL-ORDER}{X} to List{
STRICT-TOTAL-ORDER}{X})
fmod WEAKLY-SORTABLE-LIST{STRICT-TOTAL-ORDER}{[X]}
fmod WEAKLY-SORTABLE-LIST{STRICT-TOTAL-ORDER}{[X]} * (sort NeList{
STRICT-TOTAL-ORDER}{X} to NeList{X}, sort List{STRICT-TOTAL-ORDER}{X} to
List{X})
fmod LIST{STRICT-WEAK-ORDER}{STRICT-TOTAL-ORDER}{[X]} * (sort NeList{
STRICT-WEAK-ORDER}{STRICT-TOTAL-ORDER}{X} to NeList{STRICT-TOTAL-ORDER}{X},
sort List{STRICT-WEAK-ORDER}{STRICT-TOTAL-ORDER}{X} to List{
STRICT-TOTAL-ORDER}{X}) * (sort NeList{STRICT-TOTAL-ORDER}{X} to NeList{X},
sort List{STRICT-TOTAL-ORDER}{X} to List{X})
fth X :: TOTAL-PREORDER
fmod LIST{TOTAL-PREORDER}
fmod LIST{TOTAL-PREORDER}{[X]}
fmod LIST{TOTAL-PREORDER}{[X]} * (sort NeList{TOTAL-PREORDER}{X} to NeList{X},
sort List{TOTAL-PREORDER}{X} to List{X})
fth X :: TOTAL-ORDER
fmod WEAKLY-SORTABLE-LIST'{TOTAL-ORDER}
fmod LIST{TOTAL-PREORDER}{TOTAL-ORDER}
fmod LIST{TOTAL-PREORDER}{TOTAL-ORDER}{[X]}
fmod LIST{TOTAL-PREORDER}{TOTAL-ORDER}{[X]} * (sort NeList{TOTAL-PREORDER}{
TOTAL-ORDER}{X} to NeList{TOTAL-ORDER}{X}, sort List{TOTAL-PREORDER}{
TOTAL-ORDER}{X} to List{TOTAL-ORDER}{X})
fmod WEAKLY-SORTABLE-LIST'{TOTAL-ORDER}{[X]}
fmod WEAKLY-SORTABLE-LIST'{TOTAL-ORDER}{[X]} * (sort NeList{TOTAL-ORDER}{X} to
NeList{X}, sort List{TOTAL-ORDER}{X} to List{X})
fmod LIST{TOTAL-PREORDER}{TOTAL-ORDER}{[X]} * (sort NeList{TOTAL-PREORDER}{
TOTAL-ORDER}{X} to NeList{TOTAL-ORDER}{X}, sort List{TOTAL-PREORDER}{
TOTAL-ORDER}{X} to List{TOTAL-ORDER}{X}) * (sort NeList{TOTAL-ORDER}{X} to
NeList{X}, sort List{TOTAL-ORDER}{X} to List{X})
fmod LIST{[X]}
fmod SET{[X]}
fmod SORTABLE-LIST{[X]}
fmod LIST-AND-SET{STRICT-WEAK-ORDER}
fmod SET{STRICT-WEAK-ORDER}
fmod SET{STRICT-WEAK-ORDER}{[X]}
fmod LIST-AND-SET{STRICT-WEAK-ORDER}{STRICT-TOTAL-ORDER}
fmod SET{STRICT-WEAK-ORDER}{STRICT-TOTAL-ORDER}
fmod SET{STRICT-WEAK-ORDER}{STRICT-TOTAL-ORDER}{[X]}
fmod LIST-AND-SET{STRICT-WEAK-ORDER}{STRICT-TOTAL-ORDER}{[X]}
fmod LIST-AND-SET{STRICT-WEAK-ORDER}{STRICT-TOTAL-ORDER}{[X]} * (sort NeList{
STRICT-WEAK-ORDER}{STRICT-TOTAL-ORDER}{X} to NeList{STRICT-TOTAL-ORDER}{X},
sort List{STRICT-WEAK-ORDER}{STRICT-TOTAL-ORDER}{X} to List{
STRICT-TOTAL-ORDER}{X})
fmod LIST-AND-SET{STRICT-WEAK-ORDER}{STRICT-TOTAL-ORDER}{[X]} * (sort NeList{
STRICT-WEAK-ORDER}{STRICT-TOTAL-ORDER}{X} to NeList{STRICT-TOTAL-ORDER}{X},
sort List{STRICT-WEAK-ORDER}{STRICT-TOTAL-ORDER}{X} to List{
STRICT-TOTAL-ORDER}{X}) * (sort NeList{STRICT-TOTAL-ORDER}{X} to NeList{X},
sort List{STRICT-TOTAL-ORDER}{X} to List{X}, sort NeSet{STRICT-WEAK-ORDER}{
STRICT-TOTAL-ORDER}{X} to NeSet{X}, sort Set{STRICT-WEAK-ORDER}{
STRICT-TOTAL-ORDER}{X} to Set{X})
fmod SET{STRICT-WEAK-ORDER}{STRICT-TOTAL-ORDER}{[X]} * (sort NeSet{
STRICT-WEAK-ORDER}{STRICT-TOTAL-ORDER}{X} to NeSet{X}, sort Set{
STRICT-WEAK-ORDER}{STRICT-TOTAL-ORDER}{X} to Set{X})
fmod SORTABLE-LIST'{[X]}
fmod LIST-AND-SET{TOTAL-PREORDER}
fmod SET{TOTAL-PREORDER}
fmod SET{TOTAL-PREORDER}{[X]}
fmod LIST-AND-SET{TOTAL-PREORDER}{TOTAL-ORDER}
fmod SET{TOTAL-PREORDER}{TOTAL-ORDER}
fmod SET{TOTAL-PREORDER}{TOTAL-ORDER}{[X]}
fmod LIST-AND-SET{TOTAL-PREORDER}{TOTAL-ORDER}{[X]}
fmod LIST-AND-SET{TOTAL-PREORDER}{TOTAL-ORDER}{[X]} * (sort NeList{
TOTAL-PREORDER}{TOTAL-ORDER}{X} to NeList{TOTAL-ORDER}{X}, sort List{
TOTAL-PREORDER}{TOTAL-ORDER}{X} to List{TOTAL-ORDER}{X})
fmod LIST-AND-SET{TOTAL-PREORDER}{TOTAL-ORDER}{[X]} * (sort NeList{
TOTAL-PREORDER}{TOTAL-ORDER}{X} to NeList{TOTAL-ORDER}{X}, sort List{
TOTAL-PREORDER}{TOTAL-ORDER}{X} to List{TOTAL-ORDER}{X}) * (sort NeList{
TOTAL-ORDER}{X} to NeList{X}, sort List{TOTAL-ORDER}{X} to List{X}, sort
NeSet{TOTAL-PREORDER}{TOTAL-ORDER}{X} to NeSet{X}, sort Set{
TOTAL-PREORDER}{TOTAL-ORDER}{X} to Set{X})
fmod SET{TOTAL-PREORDER}{TOTAL-ORDER}{[X]} * (sort NeSet{TOTAL-PREORDER}{
TOTAL-ORDER}{X} to NeSet{X}, sort Set{TOTAL-PREORDER}{TOTAL-ORDER}{X} to
Set{X})
fth Y :: TRIV
fth Y :: DEFAULT
fmod LIST{Nat}
fmod LIST{Nat} * (sort NeList{Nat} to NeNatList, sort List{Nat} to NatList)
fmod LIST{Qid}
fmod LIST{Qid} * (sort NeList{Qid} to NeQidList, sort List{Qid} to QidList)
fmod SET{Qid}
fmod SET{Qid} * (sort NeSet{Qid} to NeQidSet, sort Set{Qid} to QidSet)
fmod QID-SET * (op _`,_ to _;_ [prec 43], op empty to none)
fmod SET{Qid} * (sort NeSet{Qid} to NeQidSet, sort Set{Qid} to QidSet) * (op
_`,_ to _;_ [prec 43], op empty to none)
fmod ONE * (sort Foo to Baz)
fmod TWO * (sort Baz to Baz', sort Quux to Quux')
fmod ONE * (sort Foo to Baz) * (sort Baz to Baz')
fmod FOO * (sort Foo to Baz, op a to b)
fmod FOO' * (sort Foo to Quux, op _+_ : [Baz] [Baz] -> [Foo,Bar] to _._ [prec
27 gather (E e)], op _+_ : [Foo,Bar] [Foo,Bar] -> [Foo,Bar] to _*_ [prec 29
gather (E e)])
fmod FOO' * (sort Foo to Quux, op _+_ to _*_ [prec 29 gather (E E)])
fmod BASH * (op f : [Foo,Bar] -> [Foo,Bar] to g)
fmod DIFF * (op f : [Bar] -> [Bar] to g, op f : [Foo] -> [Foo] to g)
Maude> Bye.
|
