parse←{⎕IO ⎕ML←0 1                              ⍝ Bunda-Gerth parsing.

    opt defs(⍵≡'')({⍺ ⍵}⍣(~0≡⊃0⍴⍺))⍺           ⍝ trace/format option and defns.

    defn←{                                      ⍝ binding table definition.
        words←' 'segs¨⊃¨'⍝'segs¨⍵               ⍝ blank-delimited words.
        pop←{(⊃⍵)(1↓⍵)}                         ⍝ head & tail of list.
        sects(⊂0⍴⊂'')segs words                ⍝ sections.
        csect defspop sects                    ⍝ separation of sections.
        bindx(⊃¨csect)⍳⊂'()'                   ⍝ index of bracket defn.
        bsegsbindxcsect,⊂,⊂'()'               ⍝ bracket pairs: () [] <> ...
        bkts blabs←↓⍉↑{(⌽2↑⍵)(2↓⍵)}¨¯1⌽¨bsegs   ⍝ brackets and their cat labels.
        cats reps←↓⍉↑pop¨csect~⊂bsegs           ⍝ categories & representatives.
        bonds(defs)-⍳⍴defs                    ⍝ binding strengths
        bmatcats∘.{0}cats                      ⍝ initialised binding table
        defn←{cats∘⍳¨'.'segs¨':→'segs ⍵}        ⍝ split a.b:c.d→z defn
        dist←{(,↑∘.,/2↑⍵),¨⊃⌽⍵}                 ⍝ distribution of productions
        lmatdistdefn¨¨¨defs                   ⍝ loading matrix
        bftz←⊃,/bonds,¨¨⊃∘(,/)⍣2¨lmat           ⍝ bond-from-to-rslt tuples
        cats reps bkts blabs,⊂[⍳2]↑⊃{           ⍝ binding structure.
            bond fm to rslt←⍺                   ⍝ binding and resulting cats.
            (bond rslt)@(fm to)⊢⍵             ⍝ populate cell
        }/bftz,⊂bmat                            ⍝ loaded binding matrix.
    }∘{                                         ⍝ pre-process alias=... lines.
        lines←↓' ',⎕FMT↑⍵                       ⍝ lines from char array.
        wds←⊃¨' 'segs¨lines                     ⍝ first word from each line.
        msk nsk←1 0=⊂'='∊¨wds                   ⍝ mask of alias lines.
        dict←'='segs¨msk/wds                    ⍝ (fm to) substitution pairs.
        {↑subs/dict,⊂⍵}¨nsk/lines               ⍝ lines with expanded aliases.
    }⍣(2≠⊃⍴⍴⊃⌽defs)                             ⍝ compile unless compiled.

    table←{                                     ⍝ formatted Bunda-Gerth table.
        (cats bmat zmat)←⍵                      ⍝ categories and binding matrix.
        fmt←{(×⍺)/(⍕⍺),' ',⍵⊃cats,'?'}          ⍝ bond and category.
        ttl←{↑' '⍺,.⍪⍺ ⍵}                       ⍝ row and column headers.
        cats ttl bmat fmt¨(1+⍴cats)|zmat        ⍝ formatted bonds & categories.
    }

    (cats reps bkts blabs bmat zmat)←defn defs  ⍝ definition structure.

    ⍵≡'':{                                      ⍝ null expr: binding matrix.
        ⍵=0:cats reps bkts blabs bmat zmat      ⍝ raw binding struct.
        trim←{                                  ⍝ without empty rows and cols.
            r c←1,¨1 0{∨/[⍺]⍵}¨⊂1 1↓~⍵∊⊂''      ⍝ occupied rows and cols.
            rc/⍵                               ⍝ masked out empties.
        }                                       ⍝ :: ∇ cells → cells
        snip←{                                  ⍝ snip out top corner.
            t(,⍵)⍳'┬'                          ⍝ uppermost, leftmost ┬
            cnr←↑1(t-1)1∘/¨'  ┌' '  │' '┌─┼'    ⍝ empty corner.
            cnr@((⍳3)∘.,⍳t+1)⊢⍵                 ⍝ snipped formatted matrix.
        }                                       ⍝ cmat ← ∇ cmat
        bfmtsnipdisp(⍕¨)trimtable          ⍝ binding matrix formatting.
        bfmt cats bmat zmat                     ⍝ formatted table.
    }opt                                        ⍝ opt-ional formatting.

    reduce←{                                    ⍝ 2-by-2 parsing.
        (∆_ L)Aa Bb Cc(R _∆)←⍵                  ⍝ 3-token window on stream.
        Aa Cc∧.≡eos:Bb                          ⍝ single node: done.
        Aa Bb∧.≡eos:⍵                           ⍝ error: partial parse.
        (A a)(B b)(C c)←Aa Bb Cc                ⍝ cats and toks.
        (b c)∊1↓bkts:∇ rgt(∆_ L)Aa(ebk b)R _∆  ⍝ empty brackets [].
        (a c)bkts:∇ rgt ∆_ L(a bkt Bb)R _∆    ⍝ bracketed single value Bb.
        (a)rbs:∇ lft lft ⍵                    ⍝ right bracket: skip left.
        ≥/xmat[(A B)(B C)+1]:∇ lft ⍵            ⍝ A:B ≥ B:C → skip left.
        BbCczmat[B;C],⊂b c                     ⍝ B bound with C.
        ∇ show(∆_ L)Aa BbCc R _∆                ⍝ binds with token to the right?
    }                                           ⍝ :: ∇ stream → stream

    show←⊣∘{⎕←sfmt lft⍣{eos≡⊃⍺}⍵}⍣opt⍨          ⍝ optional tracing, en passant.

    bkt←{                                       ⍝ bind of bracketed node [ ⍵ ].
        cat expr←⍵                              ⍝ category of bracketed expr.
        zcat(cat,1↓bcats)[lbs⍳⍺]               ⍝ resulting category.
        zcat(expr)                            ⍝ ⍺-bracketed node.
    }                                           ⍝ :: left_bkt ∇ node → node

    ebk←{bcats[lbs⍳⍵]⍵}                         ⍝ empty brackets. [] {} ...

    tfmt←{                                      ⍝ tree-formatted.
        0=≡⍵:1 1⍴⍵                              ⍝ atom: char matrix single.
        subs←⍉↑↑{⍺,' ',⍵}/↓[0]∘∇¨⍵              ⍝ formatted sub-expressions.
        mask←~(⊃↓subs)∊'┌─┐ '                   ⍝ sub-exprs connection points.
        mid(⍳⍴mask)=⌊(+/⍸mask)÷2               ⍝ mid-point for '┴' char.
        inxmask+2×+\mask                       ⍝ indices for box-draw chars.
        top←' ?─┌ ┐┴'[inx+4×mid]                ⍝ '  ┌─┴─┐  '
        topsubs                                ⍝ formatted expression.
    }

    atopcats{                                  ⍝ category atop tree.
        ⍺=¯1:⍵                                  ⍝ ignore bad cat.
        dent←+/∧\(⊃↓⍵)∊'┌─┐ '                   ⍝ indent for category.
        top(dent/' '),⍺⊃⍺⍺⊣0                   ⍝ indented category.
        ↑(top),↓⍵                              ⍝ categorised tree.
    }

    vect←{⍺←⍬                                   ⍝ vector from cons list
        ∆_ Aa Bb Cc _∆←⍵                        ⍝ 3-item window.
        ~Aaeos:(⍺,⊂Aa)rgt ⍵                  ⍝ accumlate next item.
        ~⍺≡⍬:⍺                                  ⍝ trailing eos: done.
        ⍺ ∇ rgt ⍵                               ⍝ skip leading eos.
    }

    class←{                                     ⍝ classification of expr tokens.
        pairs←↑,/⍺,¨¨⍳⍴⍺                        ⍝ token-category pairs.
        toks cats←↓⍉↑pairs                      ⍝ category of each token.
        (toks⍳⍵)⊃¨⊂cats,¯1                      ⍝ token categories.
    }

    pfmtatoptfmt⌿                             ⍝ format of (token cat) pair.
    sfmtdisppfmt∘⍉∘↑∘vect                     ⍝ format of parse stream.

    lft←{(∆_ L)A B C _∆←⍵ ⋄ ∆_ L A B(C _∆)}     ⍝ skip left.
    rgt←{∆_ A B C(R _∆)←⍵ ⋄ (∆_ A)B C R _∆}     ⍝ skip right.

    lbs rbs←↓⍉↑bkts                             ⍝ left and right brackets.
    bcatscatsblabs                            ⍝ bracket categories.
    xmat←0,0⍪bmat                               ⍝ extended bmat.
    pairs←{↓⍉↑(reps class)⍵}⍵~' '             ⍝ cat-token pairs.
    eos←¯1                                      ⍝ end of stream marker.

    ∆_←↑{⍺ ⍵}⍨/⌽eos,¯2↓pairs                    ⍝ left list.
    Aa Bb Cc←¯3↑eos eos,pairs,eos               ⍝ 3-token window

    treereduce show ∆_ Aa Bb Cc eos            ⍝ reduced expression.
    eos≡⊃tree:sfmt tree                         ⍝ bad parse: show stream.
    ⊃pfmt tree                                  ⍝ good parse: show tree.
}
code_colours

test script

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