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lemma_calc_script.n
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lemma_calc_script.n
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% loading file /home/dream3/air/clam/clam.v3.2/make/clam.v3.2.qui
% foreign file /disk/local/src/quintus3/generic/qplib3.1.4/library/sun4-4/libpl.so loaded
% clam.v3.2.qui loaded in module user, 0.733 sec 664,220 bytes
CLaM Proof Planner: Critics Version (v3.2) (29/1/96 10:56)
% compiling file /home/dream3/air/clam/clam.v3.2/lib/needs.pl
% needs.pl compiled in module user, 0.667 sec 324 bytes
Quintus Prolog Release 3.1.4 (Sun-4, SunOS 4.1)
Copyright (C) 1993, Quintus Corporation. All rights reserved.
2100 Geng Road, Palo Alto, California U.S.A. (415) 813-3800
CLaM Proof Planner (v3.2) -- libraries only (29/1/96 10:55)
CLaM Proof Planner: Critics Version (v3.2) (29/1/96 10:56)
| ?- plan(doubleplus).
loading def(double)...done
loading eqn(double1)...done
loading eqn(double2)...done
adding wave-rules for double1:..done
adding wave-rules for double2:..............done
adding defeqn-record for double1...done
adding defeqn-record for double2...done
loading def(plus)...done
loading eqn(plus1)...done
loading eqn(plus2)...done
adding wave-rules for plus1:..done
adding wave-rules for plus2:.................done
adding defeqn-record for plus1...done
adding defeqn-record for plus2...done
loading thm(doubleplus)...done
doubleplus([])
==>x:pnat=>double(x)=plus(x,x)in pnat
SELECTED METHOD at depth 0: induction([s(x)],[x:pnat])
|doubleplus([2])
|x:pnat
|v0:ih(double(x)=plus(x,x)in pnat)
|==>double(``s({x})''<out>)=plus(``s({x})''<out>,``s({x})''<out>)in pnat
|SELECTED METHOD at depth 1: wave([1,1],[double2,equ(left)])
||doubleplus([1,2])
||x:pnat
||v0:ih(double(x)=plus(x,x)in pnat)
||==>``s({``s({double(x)})''<out>})''<out> =plus(``s({x})''<out>,``s({x})''<out>)in pnat
||SELECTED METHOD at depth 2: wave([2,1],[plus2,equ(left)])
|||doubleplus([1,1,2])
|||x:pnat
|||v0:ih(double(x)=plus(x,x)in pnat)
|||==>``s({``s({double(x)})''<out>})''<out> =``s({plus(x,``s({x})''<out>)})''<out>in pnat
>>>>> INVOKING lemma-calculation CRITIC <<<<<
------------------------------------------------------------
lemma1:
[v0:pnat,x:pnat]
|- plus(v0,s(x))=s(plus(v0,x))in pnat
saving thm(lemma1)...done
lemma1([])
==>v0:pnat=>x:pnat=>plus(v0,s(x))=s(plus(v0,x))in pnat
SELECTED METHOD at depth 0: induction([s(v0)],[v0:pnat])
|lemma1([2])
|v0:pnat
|v1:ih(x:pnat=>plus(v0,s(x))=s(plus(v0,x))in pnat)
|==>x:pnat=>plus(``s({v0})''<out>,s(\x/))=s(plus(``s({v0})''<out>,\x/))in pnat
|SELECTED METHOD at depth 1: wave([1,2,1],[plus2,equ(left)])
||lemma1([1,2])
||v0:pnat
||v1:ih(x:pnat=>plus(v0,s(x))=s(plus(v0,x))in pnat)
||==>x:pnat=>plus(``s({v0})''<out>,s(\x/))=s(``s({plus(v0,\x/)})''<out>)in pnat
||SELECTED METHOD at depth 2: wave([1,1],[plus2,equ(left)])
|||lemma1([1,1,2])
|||v0:pnat
|||v1:ih(x:pnat=>plus(v0,s(x))=s(plus(v0,x))in pnat)
|||==>x:pnat=>``s({plus(v0,s(\x/))})''<out> =s(``s({plus(v0,\x/)})''<out>)in pnat
>>>>> INVOKING meta-ripple-position CRITIC <<<<<
|||lemma1([1,1,2])
|||v0:pnat
|||v1:ih(x:pnat=>plus(v0,s(x))=s(plus(v0,x))in pnat)
|||==>x:pnat=>``s({plus(v0,s(\x/))})''<out> =``s({s(plus(v0,\x/))})''<out>in pnat
|||SELECTED METHOD at depth 3: fertilize(weak(v1))
||||lemma1([1,1,1,2])
||||v0:pnat
||||v1:ih(x:pnat=>plus(v0,s(x))=s(plus(v0,x))in pnat)
||||==>x:pnat=>s(plus(v0,s(x)))=s(plus(v0,s(x)))in pnat
||||TERMINATING METHOD at depth 4: elementary(...)
|lemma1([1])
|v0:pnat
|==>x:pnat=>plus(0,s(x))=s(plus(0,x))in pnat
|SELECTED METHOD at depth 1: eval_def([1,1],plus1)
||lemma1([1,1])
||v0:pnat
||==>x:pnat=>s(x)=s(plus(0,x))in pnat
||SELECTED METHOD at depth 2: eval_def([1,2,1],plus1)
|||lemma1([1,1,1])
|||v0:pnat
|||==>x:pnat=>s(x)=s(x)in pnat
|||TERMINATING METHOD at depth 3: elementary(...)
adding wave-rules for lemma1:.................done
|||doubleplus([1,1,2])
|||x:pnat
|||v0:ih(double(x)=plus(x,x)in pnat)
|||==>``s({``s({double(x)})''<out>})''<out> =``s({plus(x,``s({x})''<out>)})''<out>in pnat
|||SELECTED METHOD at depth 3: wave([1,2,1],[lemma1,equ(left)])
||||doubleplus([1,1,1,2])
||||x:pnat
||||v0:ih(double(x)=plus(x,x)in pnat)
||||==>``s({``s({double(x)})''<out>})''<out> =``s({``s({plus(x,x)})''<out>})''<out>in pnat
||||SELECTED METHOD at depth 4: fertilize(weak(v0))
|||||doubleplus([1,1,1,1,2])
|||||x:pnat
|||||v0:ih(double(x)=plus(x,x)in pnat)
|||||==>s(s(double(x)))=s(s(double(x)))in pnat
|||||TERMINATING METHOD at depth 5: elementary(...)
|doubleplus([1])
|x:pnat
|==>double(0)=plus(0,0)in pnat
|SELECTED METHOD at depth 1: eval_def([2,1],plus1)
||doubleplus([1,1])
||x:pnat
||==>double(0)=0 in pnat
||SELECTED METHOD at depth 2: eval_def([1,1],double1)
|||doubleplus([1,1,1])
|||x:pnat
|||==>0=0 in pnat
|||TERMINATING METHOD at depth 3: elementary(...)
Planning complete for doubleplus
------------------------------------------------------------
doubleplus:
[x:pnat]
|- double(x)=plus(x,x)in pnat
induction([s(x)],[x:pnat]) then
[eval_def([2,1],plus1) then
eval_def([1,1],double1) then
elementary(...),
wave([1,1],[double2,equ(left)]) then
wave([2,1],[plus2,equ(left)]) then
wave([1,2,1],[lemma1,equ(left)]) then
fertilize(weak(v0)) then
elementary(...)
]
------------------------------------------------------------
lemma1:
[v0:pnat,x:pnat]
|- plus(v0,s(x))=s(plus(v0,x))in pnat
induction([s(v0)],[v0:pnat]) then
[eval_def([1,1],plus1) then
eval_def([1,2,1],plus1) then
elementary(...),
wave([1,2,1],[plus2,equ(left)]) then
wave([1,1],[plus2,equ(left)]) then
fertilize(weak(v1)) then
elementary(...)
]
yes
| ?- dt.
------------------------------------------------------------
Plan node: lemma1([])
Status: closed
Hypotheses: []
Quantifiers: [v0:pnat,x:pnat]
Conclusion: plus(v0,s(x))=s(plus(v0,x))in pnat
Method: induction([s(v0)],[v0:pnat])
Substitutions: []
Preconds: 0
Subgoals: 2
------------------------------------------------------------
yes
| ?- sg(doubleplus).
yes
| ?- dt.
------------------------------------------------------------
Plan node: doubleplus([])
Status: closed
Hypotheses: []
Quantifiers: [x:pnat]
Conclusion: double(x)=plus(x,x)in pnat
Method: induction([s(x)],[x:pnat])
Substitutions: []
Preconds: 0
Subgoals: 2
------------------------------------------------------------
yes
| ?- dd(2).
------------------------------------------------------------
Plan node: doubleplus([2])
Status: closed
Hypotheses: [x:pnat,v0:ih(double(x)=plus(x,x)in pnat)]
Quantifiers: []
Conclusion: double(``s({x})''<out>)=plus(``s({x})''<out>,``s({x})''<out>)in pnat
Method: wave([1,1],[double2,equ(left)])
Substitutions: []
Preconds: 7
Subgoals: 1
------------------------------------------------------------
yes
| ?- dd.
------------------------------------------------------------
Plan node: doubleplus([1,2])
Status: closed
Hypotheses: [x:pnat,v0:ih(double(x)=plus(x,x)in pnat)]
Quantifiers: []
Conclusion: ``s({``s({double(x)})''<out>})''<out> =plus(``s({x})''<out>,``s({x})''<out>)in pnat
Method: wave([2,1],[plus2,equ(left)])
Substitutions: []
Preconds: 5
Subgoals: 1
------------------------------------------------------------
yes
| ?- dd.
------------------------------------------------------------
Plan node: doubleplus([1,1,2])
Status: closed
Hypotheses: [x:pnat,v0:ih(double(x)=plus(x,x)in pnat)]
Quantifiers: []
Conclusion: ``s({``s({double(x)})''<out>})''<out> =``s({plus(x,``s({x})''<out>)})''<out>in pnat
Method: wave([1,2,1],[lemma1,equ(left)])
Substitutions: []
Preconds: 6
Subgoals: 1
------------------------------------------------------------
yes
| ?- cp.
wave_occ_at(``s({``s({double(x)})''<out>})''<out> =``s({plus(x,``s({x})''<out>)})''<out>in pnat,[1,2,1],plus(x,``s({x})''<out>))
false
false
-------------
wave_occ_at(``s({``s({double(x)})''<out>})''<out> =``s({plus(x,``s({x})''<out>)})''<out>in pnat,[1,2,1],plus(x,``s({x})''<out>))
false
false
false
-------------
wave_occ_at(``s({``s({double(x)})''<out>})''<out> =``s({plus(x,``s({x})''<out>)})''<out>in pnat,[1],``s({``s({double(x)})''<out>})''<out> =``s({plus(x,``s({x})''<out>)})''<out>)
false
false
false
-------------
wave_occ_at(``s({``s({double(x)})''<out>})''<out> =``s({plus(x,``s({x})''<out>)})''<out>in pnat,[],``s({``s({double(x)})''<out>})''<out> =``s({plus(x,``s({x})''<out>)})''<out>in pnat)
false
false
false
-------------
wave_occ_at(``s({``s({double(x)})''<out>})''<out> =``s({plus(x,``s({x})''<out>)})''<out>in pnat,[1],``s({``s({double(x)})''<out>})''<out> =``s({plus(x,``s({x})''<out>)})''<out>)
false
false
-------------
wave_occ_at(``s({``s({double(x)})''<out>})''<out> =``s({plus(x,``s({x})''<out>)})''<out>in pnat,[],``s({``s({double(x)})''<out>})''<out> =``s({plus(x,``s({x})''<out>)})''<out>in pnat)
false
false
-------------
yes
| ?- current_goal(Goal).
Goal = ``s({``s({double(x)})''<out>})''<out> =``s({plus(x,``s({x})''<out>)})''<out>in pnat
| ?- current_goal(Goal),construct_lemma_lhs(Goal,LHS,Typ).
no
| ?- current_sequent(H).
H = [x:pnat,v0:ih(double(x)=plus(x,x)in pnat)]==>``s({``s({double(x)})''<out>})''<out> =``s({plus(x,``s({x})''<out>)})''<out>in pnat
| ?- current_sequent(Seq),construct_lemma_lhs(Seq,LHS,Typ).
current_sequent(Seq),construct_lemma_lhs(Seq,LHS,Typ).
Seq = [x:pnat,v0:ih(double(x)=plus(x,x)in pnat)]==>``s({``s({double(x)})''<out>})''<out> =``s({plus(x,``s({x})''<out>)})''<out>in pnat,
LHS = ``s({plus(x,``s({x})''<out>)})''<out>,
Typ = equ(pnat) ;
no
| ?- current_sequent(Seq),construct_lemma_lhs(Seq,LHS,Typ),construct_lemma_rhs(Seq,RHS,Typ).
current_sequent(Seq),construct_lemma_lhs(Seq,LHS,Typ),construct_lemma_rhs(Seq,RHS,Typ).
Seq = [x:pnat,v0:ih(double(x)=plus(x,x)in pnat)]==>``s({``s({double(x)})''<out>})''<out> =``s({plus(x,``s({x})''<out>)})''<out>in pnat,
LHS = ``s({plus(x,``s({x})''<out>)})''<out>,
Typ = equ(pnat),
RHS = ``s(s({plus(x,x)}))''<in> ;
Seq = [x:pnat,v0:ih(double(x)=plus(x,x)in pnat)]==>``s({``s({double(x)})''<out>})''<out> =``s({plus(x,``s({x})''<out>)})''<out>in pnat,
LHS = ``s({plus(x,``s({x})''<out>)})''<out>,
Typ = equ(pnat),
RHS = plus(x,x) ;
Seq = [x:pnat,v0:ih(double(x)=plus(x,x)in pnat)]==>``s({``s({double(x)})''<out>})''<out> =``s({plus(x,``s({x})''<out>)})''<out>in pnat,
LHS = ``s({plus(x,``s({x})''<out>)})''<out>,
Typ = equ(pnat),
RHS = plus(x,x) ;
no
| ?- current_sequent(H==>G),construct_context(H,G,Context),construct_lemma_lhs(H==>G,LHS,Typ),construct_lemma_rhs(H==>G,RHS,Typ),construct_generalized_lemma(LHS,RHS,Typ,Context,Na:Lemma).
current_sequent(H==>G),construct_context(H,G,Context),construct_lemma_lhs(H==>G,LHS,Typ),construct_lemma_rhs(H==>G,RHS,Typ),construct_generalized_lemma(LHS,RHS,Typ,Context,Na:Lemma).
H = Context = [x:pnat,v0:ih(double(x)=plus(x,x)in pnat)],
G = ``s({``s({double(x)})''<out>})''<out> =``s({plus(x,``s({x})''<out>)})''<out>in pnat,
LHS = ``s({plus(x,``s({x})''<out>)})''<out>,
Typ = equ(pnat),
RHS = ``s(s({plus(x,x)}))''<in>,
Na = lemma2,
Lemma = []==>x:pnat=>plus(x,s(x))=s(plus(x,x))in pnat ;
no
| ?-