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src/Pure/deriv.ML

author | paulson |

Fri, 21 Feb 1997 15:31:47 +0100 | |

changeset 2672 | 85d7e800d754 |

parent 2042 | 33b4c1624e26 |

child 6085 | 3d8dcb09dbfb |

permissions | -rw-r--r-- |

Replaced "flat" by the Basis Library function List.concat

(* 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 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 name, _)) = [Join(Theorem name, [])] | 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, List.concat (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 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 name, [_])) = 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 name, _), prfs) = Join(Thm name, 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) | drop (der,_) = der; end; (*We do NOT open this structure*)