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Merge pull request #17 from mio-19/main

equation with schematic

authored by

Liam O'Connor and committed by
GitHub
f0ba546d 8f7759d5

+680 -538
+10
index.html
··· 339 339 (= a b) (f a) 340 340 -------- eq-ap 341 341 (f b) 342 + 343 + a. 344 + -------- eqab 345 + (= (A a) (B a)) 342 346 </hol-comp> 343 347 <hol-config id="index.html/myconfig">Gentzen</hol-config> 344 348 <hol-proof id="index.html/prooftest" deps="index.html/myconfig index.html/baz index.html/nat"> ··· 367 371 (= a c) 368 372 369 373 a. b. c. ab bc |- ? 374 + </hol-proof> 375 + <hol-proof id="index.html/eq-high" deps="index.html/myconfig index.html/baz index.html/nat"> 376 + ------- A0B0 377 + (= (A 0) (B 0)) 378 + 379 + |- ? 370 380 </hol-proof> 371 381 <h1>String</h1> 372 382 <h2>Basic</h2>
+490 -466
package-lock.json
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+23 -2
src/HOTerm.res
··· 155 155 switch term { 156 156 | App({func, arg}) => 157 157 App({func: discharge(subst, func, ~prune), arg: discharge(subst, arg, ~prune)}) 158 - // Lam case is not actually needed by FCU but needed by rewriting 158 + // Lam case is not actually needed by FCU 159 159 | Lam({name, body}) => Lam({name, body: discharge(upshift_tt(subst), body, ~prune)}) 160 160 | Var(_) if prune => Unallowed 161 161 | Var(_) | Schematic(_) | Symbol(_) | Unallowed => term ··· 189 189 | Var(_) | Unallowed | Symbol(_) => term 190 190 } 191 191 192 - // TODO: check how will this interact with meta variables (schematics) and check if it is needed to have a subst parameter - it should not be needed for subst produced by pattern unification 193 192 let rec substDeBruijn = (term: t, substs: array<t>, ~from: int=0) => 194 193 switch term { 195 194 | Symbol(_) => term ··· 470 469 | UnifyFail(_) => [] 471 470 }, 472 471 ) 472 + let rec rewrite = (term: t, from: t, to: t, ~subst: subst, ~gen: option<gen>): (subst, t) => { 473 + try { 474 + let subst1 = unifyTerm(term, from, subst, ~gen) 475 + (subst1, to) 476 + } catch { 477 + | UnifyFail(_) => 478 + switch term { 479 + | Schematic({schematic}) if subst->substHas(schematic) => 480 + rewrite(subst->substGet(schematic)->Option.getExn, from, to, ~subst, ~gen) 481 + | Var(_) | Unallowed | Symbol(_) | Schematic(_) => (subst, term) 482 + | Lam({name, body}) => { 483 + let (subst1, body1) = rewrite(body, from, to, ~subst, ~gen) 484 + (subst1, Lam({name, body: body1})) 485 + } 486 + | App({func, arg}) => { 487 + let (subst1, func') = rewrite(func, from, to, ~subst, ~gen) 488 + let (subst2, arg') = rewrite(arg, from, to, ~subst=subst1, ~gen) 489 + (subst2, App({func: func', arg: arg'})) 490 + } 491 + } 492 + } 493 + } 473 494 let place = (x: int, ~scope: array<string>) => 474 495 app( 475 496 Schematic({
+1 -2
src/HOTerm.resi
··· 22 22 let substAdd: (subst, schematic, t) => subst 23 23 let unifyTerm: (t, t, subst, ~gen: option<gen>) => subst 24 24 let reduceSubst: subst => subst 25 - let discharge: (array<(t, t)>, t, ~prune: bool) => t 26 - let upshift_tt: (array<(t, t)>, ~amount: int=?) => array<(t, t)> 25 + let rewrite: (t, t, t, ~subst: subst, ~gen: option<gen>) => (subst, t)
+147 -65
src/Method.res
··· 491 491 } 492 492 493 493 module MakeRewriteHOTerm = ( 494 - Judgment: JUDGMENT with module Term := HOTerm, 494 + Judgment: JUDGMENT with module Term := HOTerm and type subst = HOTerm.subst and type t = HOTerm.t, 495 495 Config: { 496 496 let keyword: string 497 497 let reversed: bool ··· 501 501 module Rule = Rule.Make(HOTerm, Judgment) 502 502 module Context = Context(HOTerm, Judgment) 503 503 504 - let isEqualityRule = (rule: Rule.t): bool => { 505 - Array.length(rule.vars) == 0 && Array.length(rule.premises) == 0 506 - } 507 - 508 - let extractEqualityTerms = (judgment: Judgment.t): option<(HOTerm.t, HOTerm.t)> => { 509 - let term: HOTerm.t = Obj.magic(judgment) 504 + let extractEqualityTermsFromJudgment = (judgment: Judgment.t): option<(HOTerm.t, HOTerm.t)> => { 505 + let term: HOTerm.t = judgment 510 506 switch HOTerm.strip(term) { 511 507 | (HOTerm.Symbol({name: "="}), args) if Array.length(args) == 2 => 512 508 Some((args->Array.getUnsafe(0), args->Array.getUnsafe(1))) ··· 514 510 } 515 511 } 516 512 513 + let extractEqualityTerms = (rule: Rule.t): option<(HOTerm.t, HOTerm.t)> => { 514 + if Array.length(rule.premises) != 0 { 515 + None 516 + } else { 517 + extractEqualityTermsFromJudgment(rule.conclusion) 518 + } 519 + } 520 + 521 + let extractEqualityTermsFromBare = (rule: Rule.bare): option<(HOTerm.t, HOTerm.t)> => { 522 + if Array.length(rule.premises) != 0 { 523 + None 524 + } else { 525 + extractEqualityTermsFromJudgment(rule.conclusion) 526 + } 527 + } 528 + 529 + let isEqualityRule = (rule: Rule.t): bool => { 530 + extractEqualityTerms(rule)->Option.isSome 531 + } 532 + 517 533 type t<'a> = { 518 534 equalityName: string, 535 + instantiation: array<Judgment.substCodom>, 519 536 subgoal: 'a, 520 537 } 521 538 ··· 524 541 let map = (it: t<'a>, f) => { 525 542 { 526 543 equalityName: it.equalityName, 544 + instantiation: it.instantiation, 527 545 subgoal: f(it.subgoal), 528 546 } 529 547 } 530 548 531 - let substitute = (it: t<'a>, _subst: Judgment.subst) => { 532 - // Rewrite method itself doesn't contain terms that need substitution 533 - it 549 + let substitute = (it: t<'a>, subst: Judgment.subst) => { 550 + { 551 + equalityName: it.equalityName, 552 + instantiation: it.instantiation->Array.map(t => t->Judgment.substituteSubstCodom(subst)), 553 + subgoal: it.subgoal, 554 + } 534 555 } 535 556 536 557 let prettyPrint = ( ··· 540 561 ~subprinter: ('a, ~scope: array<HOTerm.meta>, ~indentation: int=?) => string, 541 562 ) => { 542 563 let ind = String.repeat(" ", indentation) 543 - `${ind}${Config.keyword} ${it.equalityName} {\n` 564 + let args = it.instantiation->Array.map(t => Judgment.prettyPrintSubstCodom(t, ~scope)) 565 + let argsStr = if Array.length(args) > 0 { 566 + " " ++ Array.join(args, " ") 567 + } else { 568 + "" 569 + } 570 + `${ind}${Config.keyword} (${it.equalityName}${argsStr}) {\n` 544 571 ->String.concat(subprinter(it.subgoal, ~scope, ~indentation=indentation + 2)) 545 572 ->String.concat("\n") 546 573 ->String.concat(ind) ··· 552 579 let parse = (input, ~keyword as _, ~scope, ~gen, ~subparser) => { 553 580 let cur = ref(String.trim(input)) 554 581 555 - switch Rule.parseRuleName(cur.contents) { 556 - | Error(e) => Error(e) 557 - | Ok((equalityName, rest)) => { 558 - cur := String.trim(rest) 582 + if cur.contents->String.get(0) == Some("(") { 583 + switch Rule.parseRuleName(cur.contents->String.sliceToEnd(~start=1)) { 584 + | Error(e) => Error(e) 585 + | Ok((equalityName, rest)) => { 586 + cur := rest 587 + let instantiation = [] 588 + let it = ref(Error("")) 589 + while { 590 + it := Judgment.parseSubstCodom(cur.contents, ~scope, ~gen) 591 + it.contents->Result.isOk 592 + } { 593 + let (val, rest) = it.contents->Result.getExn 594 + Array.push(instantiation, val) 595 + cur := String.trim(rest) 596 + } 597 + if cur.contents->String.get(0) == Some(")") { 598 + cur := String.trim(cur.contents->String.sliceToEnd(~start=1)) 559 599 560 - if cur.contents->String.get(0) == Some("{") { 561 - cur := String.trim(String.sliceToEnd(cur.contents, ~start=1)) 600 + if cur.contents->String.get(0) == Some("{") { 601 + cur := String.trim(String.sliceToEnd(cur.contents, ~start=1)) 562 602 563 - try { 564 - switch subparser(cur.contents, ~scope, ~gen) { 565 - | Error(e) => raise(InternalParseError(e)) 566 - | Ok((subgoal, rest2)) => { 567 - cur := String.trim(rest2) 603 + try { 604 + switch subparser(cur.contents, ~scope, ~gen) { 605 + | Error(e) => raise(InternalParseError(e)) 606 + | Ok((subgoal, rest2)) => { 607 + cur := String.trim(rest2) 568 608 569 - if cur.contents->String.get(0) == Some("}") { 570 - cur := String.trim(String.sliceToEnd(cur.contents, ~start=1)) 571 - Ok(({equalityName, subgoal}, cur.contents)) 572 - } else { 573 - Error("Expected } after subgoal") 609 + if cur.contents->String.get(0) == Some("}") { 610 + cur := String.trim(String.sliceToEnd(cur.contents, ~start=1)) 611 + Ok(({equalityName, instantiation, subgoal}, cur.contents)) 612 + } else { 613 + Error("Expected } after subgoal") 614 + } 615 + } 574 616 } 617 + } catch { 618 + | InternalParseError(e) => Error(e) 575 619 } 620 + } else { 621 + Error("Expected { after equality instantiation") 576 622 } 577 - } catch { 578 - | InternalParseError(e) => Error(e) 623 + } else { 624 + Error(") or term expected") 579 625 } 580 - } else { 581 - Error("Expected { after equality name") 582 626 } 583 627 } 628 + } else { 629 + Error("Expected (") 584 630 } 585 631 } 586 632 587 - let rewriteJudgmentTerms = (judgment: Judgment.t, from: HOTerm.t, to: HOTerm.t): Judgment.t => { 588 - Judgment.mapTerms(judgment, term => HOTerm.discharge([(from, to)], term, ~prune=false)) 633 + let rewriteJudgmentTerms = ( 634 + judgment: Judgment.t, 635 + from: HOTerm.t, 636 + to: HOTerm.t, 637 + ~gen: option<HOTerm.gen>, 638 + ): (HOTerm.subst, Judgment.t) => { 639 + let subst: ref<HOTerm.subst> = ref(HOTerm.makeSubst()) 640 + let j = Judgment.mapTerms(judgment, term => { 641 + let (subst', newTerm) = HOTerm.rewrite(term, from, to, ~subst=subst.contents, ~gen) 642 + subst := subst' 643 + newTerm 644 + }) 645 + (subst.contents, j) 589 646 } 590 647 591 - let apply = (ctx: Context.t, j: Judgment.t, _gen: HOTerm.gen, f: Rule.t => 'a) => { 592 - let ret = Dict.make() 593 - // For HOTermJ, Judgment.subst is the same as HOTerm.subst 594 - let emptySubst: Judgment.subst = Obj.magic(HOTerm.makeSubst()) 648 + let apply = (ctx: Context.t, j: Judgment.t, gen: HOTerm.gen, f: Rule.t => 'a) => { 649 + let ret: Dict.t<(t<'a>, Judgment.subst)> = Dict.make() 595 650 596 651 ctx.facts->Dict.forEachWithKey((eqRule, name) => { 597 652 if isEqualityRule(eqRule) { 598 - switch extractEqualityTerms(eqRule.conclusion) { 653 + let insts = eqRule->Rule.schematise(gen, ~scope=ctx.fixes) 654 + let instantiatedRule = eqRule->Rule.instantiate(insts) 655 + 656 + switch extractEqualityTermsFromBare(instantiatedRule) { 599 657 | Some((lhs, rhs)) => { 600 658 let (from, to) = if Config.reversed { 601 659 (rhs, lhs) ··· 603 661 (lhs, rhs) 604 662 } 605 663 606 - let rewrittenGoal = rewriteJudgmentTerms(j, from, to) 607 - if !Judgment.equivalent(j, rewrittenGoal) { 664 + let (subst, rewrittenGoal) = rewriteJudgmentTerms(j, from, to, ~gen=Some(gen)) 665 + 666 + // If the rewritten one is the same as the original, for example rewriting with reflexivity, skip it 667 + if ( 668 + !Judgment.equivalent( 669 + j->Judgment.substitute(subst)->Judgment.reduce, 670 + rewrittenGoal->Judgment.substitute(subst)->Judgment.reduce, 671 + ) 672 + ) { 673 + let rewrittenRule: Rule.t = { 674 + vars: [], 675 + premises: [], 676 + conclusion: rewrittenGoal, 677 + } 608 678 let method = { 609 679 equalityName: name, 610 - subgoal: f(eqRule), 680 + instantiation: insts, 681 + subgoal: f(rewrittenRule), 611 682 } 612 - ret->Dict.set(`${Config.keyword} ${name}`, (method, emptySubst)) 683 + ret->Dict.set(`${Config.keyword} ${name}`, (method, subst)) 613 684 } 614 685 } 615 686 | None => () ··· 624 695 switch ctx.facts->Dict.get(it.equalityName) { 625 696 | None => Error(`Cannot find equality '${it.equalityName}'`) 626 697 | Some(eqRule) if !isEqualityRule(eqRule) => 627 - Error(`'${it.equalityName}' is not a valid equality (has variables or premises)`) 628 - | Some(eqRule) => 629 - switch extractEqualityTerms(eqRule.conclusion) { 630 - | None => 631 - Error(`Cannot extract equality from '${it.equalityName}' - not in expected equality form`) 632 - | Some((lhs, rhs)) => { 633 - let (from, to) = if Config.reversed { 634 - (rhs, lhs) 635 - } else { 636 - (lhs, rhs) 637 - } 698 + Error(`'${it.equalityName}' is not a valid equality (has premises)`) 699 + | Some(eqRule) if Array.length(eqRule.vars) != Array.length(it.instantiation) => 700 + Error(`Incorrect number of instantiation arguments for '${it.equalityName}'`) 701 + | Some(eqRule) => { 702 + let instantiatedRule = Rule.instantiate(eqRule, it.instantiation) 703 + 704 + switch extractEqualityTermsFromBare(instantiatedRule) { 705 + | None => 706 + Error(`Cannot extract equality from '${it.equalityName}' - not in expected equality form`) 707 + | Some((lhs, rhs)) => { 708 + let (from, to) = if Config.reversed { 709 + (rhs, lhs) 710 + } else { 711 + (lhs, rhs) 712 + } 713 + 714 + // TODO: what gen to use? 715 + let (_, rewrittenGoal) = rewriteJudgmentTerms(goal, from, to, ~gen=None) 638 716 639 - let rewrittenGoal = rewriteJudgmentTerms(goal, from, to) 717 + let rewrittenRule: Rule.t = { 718 + vars: [], 719 + premises: [], 720 + conclusion: rewrittenGoal, 721 + } 640 722 641 - let rewrittenRule: Rule.t = { 642 - vars: [], 643 - premises: [], 644 - conclusion: rewrittenGoal, 723 + Ok({ 724 + equalityName: it.equalityName, 725 + instantiation: it.instantiation, 726 + subgoal: f(it.subgoal, rewrittenRule), 727 + }) 645 728 } 646 - 647 - Ok({ 648 - equalityName: it.equalityName, 649 - subgoal: f(it.subgoal, rewrittenRule), 650 - }) 651 729 } 652 730 } 653 731 } 654 732 } 655 733 } 656 734 657 - module Rewrite = (Judgment: JUDGMENT with module Term := HOTerm) => MakeRewriteHOTerm( 735 + module Rewrite = ( 736 + Judgment: JUDGMENT with module Term := HOTerm and type subst = HOTerm.subst and type t = HOTerm.t, 737 + ) => MakeRewriteHOTerm( 658 738 Judgment, 659 739 { 660 740 let keyword = "rewrite" ··· 662 742 }, 663 743 ) 664 744 665 - module RewriteReverse = (Judgment: JUDGMENT with module Term := HOTerm) => MakeRewriteHOTerm( 745 + module RewriteReverse = ( 746 + Judgment: JUDGMENT with module Term := HOTerm and type subst = HOTerm.subst and type t = HOTerm.t, 747 + ) => MakeRewriteHOTerm( 666 748 Judgment, 667 749 { 668 750 let keyword = "rewrite_reverse"
+6 -2
src/MethodView.res
··· 158 158 } 159 159 } 160 160 161 - module RewriteView = (Judgment: JUDGMENT with module Term := HOTerm) => { 161 + module RewriteView = ( 162 + Judgment: JUDGMENT with module Term := HOTerm and type subst = HOTerm.subst and type t = HOTerm.t, 163 + ) => { 162 164 module Method = Rewrite(Judgment) 163 165 type props<'a> = { 164 166 method: Method.t<'a>, ··· 197 199 } 198 200 } 199 201 200 - module RewriteReverseView = (Judgment: JUDGMENT with module Term := HOTerm) => { 202 + module RewriteReverseView = ( 203 + Judgment: JUDGMENT with module Term := HOTerm and type subst = HOTerm.subst and type t = HOTerm.t, 204 + ) => { 201 205 module Method = RewriteReverse(Judgment) 202 206 type props<'a> = { 203 207 method: Method.t<'a>,
+3 -1
src/TermAsJudgment.res
··· 1 1 open Signatures 2 2 3 - module Make = (Term: TERM): (JUDGMENT with module Term := Term and type t = Term.t) => { 3 + module Make = (Term: TERM): ( 4 + JUDGMENT with module Term := Term and type t = Term.t and type subst = Term.subst 5 + ) => { 4 6 include Term 5 7 type substCodom = Term.t 6 8 let prettyPrintSubstCodom = Term.prettyPrint