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author | paulson |

Wed, 20 Mar 1996 18:42:31 +0100 | |

changeset 1593 | 69ed69a9c32a |

parent 1592 | d89d5ff2397f |

child 1594 | b776e3223dd6 |

New module for proof objects (deriviations)

src/Pure/deriv.ML | file | annotate | diff | comparison | revisions |

--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/src/Pure/deriv.ML Wed Mar 20 18:42:31 1996 +0100 @@ -0,0 +1,150 @@ +(* Title: Pure/deriv.ML + ID: $Id$ + Author: Lawrence C Paulson, Cambridge University Computer Laboratory + Copyright 1996 University of Cambridge + +Derivations (proof objects) and functions for examining them +*) + +signature DERIV = + sig + (*Object-level rules*) + datatype orule = Subgoal of cterm + | Asm of int + | Res of deriv + | Equal of deriv + | Thm of theory * string + | Other of deriv; + + val size : deriv -> int + val drop : 'a mtree * int -> 'a mtree + val linear : deriv -> deriv list + val tree : deriv -> orule mtree + end; + +structure Deriv : DERIV = +struct + +fun size (Join(Theorem _, _)) = 1 + | size (Join(_, ders)) = foldl op+ (1, map size ders); + +(*Conversion to linear format. Children of a node are the LIST of inferences + justifying ONE of the premises*) +fun rev_deriv (Join (rl, [])) = [Join(rl,[])] + | rev_deriv (Join (Theorem arg, _)) = [Join(Theorem arg, [])] + | rev_deriv (Join (Assumption arg, [der])) = + Join(Assumption arg,[]) :: rev_deriv der + | rev_deriv (Join (Bicompose arg, [rder, sder])) = + Join (Bicompose arg, linear rder) :: rev_deriv sder + | rev_deriv (Join (_, [der])) = rev_deriv der + | rev_deriv (Join (rl, der::ders)) = (*catch-all case; doubtful?*) + Join(rl, flat (map linear ders)) :: rev_deriv der +and linear der = rev (rev_deriv der); + + +(*** Conversion of object-level proof trees ***) + +(*Object-level rules*) +datatype orule = Subgoal of cterm + | Asm of int + | Res of deriv + | Equal of deriv + | Thm of theory * string + | Other of deriv; + +(*At position i, splice in value x, removing ngoal elements*) +fun splice (i,x,ngoal,prfs) = + let val prfs0 = take(i-1,prfs) + and prfs1 = drop(i-1,prfs) + val prfs2 = Join (x, take(ngoal, prfs1)) :: drop(ngoal, prfs1) + in prfs0 @ prfs2 end; + +(*Deletes trivial uses of Equal_elim; hides derivations of Theorems*) +fun simp_deriv (Join (Equal_elim, [Join (Rewrite_cterm _, []), der])) = + simp_deriv der + | simp_deriv (Join (Equal_elim, [Join (Reflexive _, []), der])) = + simp_deriv der + | simp_deriv (Join (rule as Theorem arg, [_])) = Join (rule, []) + | simp_deriv (Join (rule, ders)) = Join (rule, map simp_deriv ders); + +(*Proof term is an equality: first premise of equal_elim. + Attempt to decode proof terms made by Drule.goals_conv. + Subgoal numbers are returned; they are wrong if original subgoal + had flexflex pairs! + NEGATIVE i means "could affect all subgoals starting from i"*) +fun scan_equals (i, Join (Combination, + [Join (Combination, [_, der1]), der2])) = + (case der1 of (*ignore trivial cases*) + Join (Reflexive _, _) => scan_equals (i+1, der2) + | Join (Rewrite_cterm _, []) => scan_equals (i+1, der2) + | Join (Rewrite_cterm _, _) => (i,der1) :: scan_equals (i+1, der2) + | _ (*impossible in gconv*) => []) + | scan_equals (i, Join (Reflexive _, [])) = [] + | scan_equals (i, Join (Rewrite_cterm _, [])) = [] + (*Anything else could affect ALL following goals*) + | scan_equals (i, der) = [(~i,der)]; + +(*Record uses of equality reasoning on 1 or more subgoals*) +fun update_equals ((i,der), prfs) = + if i>0 then splice (i, Equal (simp_deriv der), 1, prfs) + else take (~i-1, prfs) @ + map (fn prf => Join (Equal (simp_deriv der), [prf])) + (drop (~i-1, prfs)); + +fun delift (Join (Lift_rule _, [der])) = der + | delift der = der; + +(*Conversion to an object-level proof tree. + Uses embedded Lift_rules to "annotate" the proof tree with subgoals; + -- assumes that Lift_rule never occurs except with resolution + -- may contain Vars that, in fact, are instantiated in that step*) +fun tree_aux (Join (Trivial ct, []), prfs) = Join(Subgoal ct, prfs) + | tree_aux (Join (Assumption(i,_), [der]), prfs) = + tree_aux (der, splice (i, Asm i, 0, prfs)) + | tree_aux (Join (Equal_elim, [der1,der2]), prfs) = + tree_aux (der2, foldr update_equals (scan_equals (1, der1), prfs)) + | tree_aux (Join (Bicompose (match,true,i,ngoal,env), ders), prfs) = + (*change eresolve_tac to proof by assumption*) + tree_aux (Join (Assumption(i, Some env), + [Join (Bicompose (match,false,i,ngoal,env), ders)]), + prfs) + | tree_aux (Join (Lift_rule (ct,i), [der]), prfs) = + tree_aux (der, splice (i, Subgoal ct, 1, prfs)) + | tree_aux (Join (Bicompose arg, + [Join (Instantiate _, [rder]), sder]), prfs) = + (*Ignore Instantiate*) + tree_aux (Join (Bicompose arg, [rder, sder]), prfs) + | tree_aux (Join (Bicompose arg, + [Join (Lift_rule larg, [rder]), sder]), prfs) = + (*Move Lift_rule: to make a Subgoal on the result*) + tree_aux (Join (Bicompose arg, [rder, + Join(Lift_rule larg, [sder])]), prfs) + | tree_aux (Join (Bicompose (match,ef,i,ngoal,env), + [Join (Bicompose (match',ef',i',ngoal',env'), + [der1,der2]), + der3]), prfs) = + (*associate resolutions to the right*) + tree_aux (Join (Bicompose (match', ef', i'+i-1, ngoal', env'), + [delift der1, (*This Lift_rule would be wrong!*) + Join (Bicompose (match, ef, i, ngoal-ngoal'+1, env), + [der2, der3])]), prfs) + | tree_aux (Join (Bicompose (arg as (_,_,i,ngoal,_)), + [rder, sder]), prfs) = + (*resolution with basic rule/assumption -- we hope!*) + tree_aux (sder, splice (i, Res (simp_deriv rder), ngoal, prfs)) + | tree_aux (Join (Theorem arg, _), prfs) = Join(Thm arg, prfs) + | tree_aux (Join (_, [der]), prfs) = tree_aux (der,prfs) + | tree_aux (der, prfs) = Join(Other (simp_deriv der), prfs); + + +fun tree der = tree_aux (der,[]); + +(*Currently declared at end, to avoid conflicting with library's drop + Can put it after "size" once we switch to List.drop*) +fun drop (der,0) = der + | drop (Join (_, der::_), n) = drop (der, n-1); + +end; + + +(*We do NOT open this structure*)