The Machines · Runtime stack

seedmatrix

A reckoner seed: matrix, converting at the bridge — machines/seeds/seedmatrix.shoddy

Summary

seedmatrix is a seed: a small file that plugs one machine's words — its named commands — into the reckoner calculator. It bridges matrix: MAT IDENT TRANSP MMUL MATADD MGET DOT. There is no Array cell at the keyboard. Every vector-taking word here accepts a LIST and converts internally, and every vector-returning word answers a LIST back — one collection type at the keyboard. MMUL and MATADD reuse cuttle's own CutMatMul and CutMatAdd, which already pre-flight the same dimension checks matrix.shoddy Errors on. That is the same guard the engine core's polymorphic * and + (one symbol, working on many types) apply to a matrix mismatch reached through them.

Named MATADD, not MADD. A dictionary cannot hold two entries under one name, and matrix.shoddy's own error text already reads "MATADD: DIMENSION MISMATCH". That settles the name here in matrix's favour, and leaves seedmoney's MADD as the one un-renamed.

Why It's Useful

Bounds checking that would otherwise be a matrix-indexing Error is done once, at the bridge. MGET checks both the row and the column against the matrix's own shape before either reaches the flat array underneath. DOT checks that the two lists are the same length before either becomes an array Dot could run past the end of.

User's Guide

Let st0 = RckSeedMatrix(RckNew())
RckEval(st0, "2 2 { 1 2 3 4 } MAT")     ' x: 2x2 { { 1 2 } { 3 4 } }
RckEval(st0, "TRANSP")                  ' x: 2x2 { { 1 3 } { 2 4 } }
RckEval(st0, "3 IDENT")                 ' x: 3x3 identity
RckEval(st0, "{ 1 2 3 } { 4 5 6 } DOT") ' x: 32

Word Reference

Word	Description
MAT ( r c list -- matrix )	An r by c matrix from a list of r*c numbers, row by row; refuses r or c below one, or a list of the wrong length.
IDENT ( n -- matrix )	The n by n identity matrix; refuses n below one.
TRANSP ( matrix -- matrix )	The matrix flipped across its diagonal.
MMUL ( a b -- ab )	Matrix product; the columns of a must match the rows of b.
MATADD ( a b -- a+b )	Two matrices of one shape, added cell by cell.
MGET ( matrix r c -- x )	The cell at row r, column c, both 1-based; refuses either index out of the matrix's shape.
DOT ( xs ys -- d )	The dot product of two lists of numbers of the same length; refuses mismatched lengths.

Who Uses It

	User	How
	halifax	Matrices as cells, multiplied with the same * that multiplies two numbers.
	sparky	Sparky folds it too, so a model calling eval reaches the same words halifax puts at a prompt.

A mill — a complete Shoddy program — claims this seed by folding RckSeedMatrix over its reckoner state. That is all halifax does.

The Machines It Uses

	Machine	Why
	cuttle	The CutMat case, and CutMatAdd/CutMatMul for the pre-flighted dimension checks MATADD and MMUL reuse.
	matrix	The domain this seed bridges: Mat, Ident, Transp, MatGet, Rows and Cols.
	reckoner	RckReg, RckSeeding and the argument readers every registered word is built from.
	seq	List plumbing under the LIST-of-NUMBER reader MAT and DOT share.